spectral study of stellar winds interacting with x-rays from...

Spectral Study of Stellar Winds Interacting with

X-rays from Accreting Neutron Stars

Shin Watanabe

Department of Physics

Graduate School of Science

University of Tokyo

December 19, 2003

Abstract

We have observed two archetype high mass X-ray binaries (HMXBs), Vela X-1 and

GX 301−2, with the Chandra grating spectrometer HETGS. By using the instrument

with high energy resolving power E/∆E ∼ 100–1000, we perform precise measurements

of various emission lines and spectral features in their X-ray spectra. In the case of Vela

X-1, emission lines from highly ionized ions driven by photoionization, in addition to

fluorescent lines from ions in various charge states, are clearly detected. The intensities

and the centroid energies of these lines are determined with the highest accuracy ever

achieved for this source. In the case of GX 301−2, fluorescent emission lines are observed

without any signature associated with highly ionized ions. Additionally, the Compton

scattered line profile (Compton shoulder) is discovered in the intense iron Kα line of

GX 301−2, for the first time from a celestial source. In order to deal with such new probes,

we have developed the simulator on the basis of Monte Carlo methods. By adopting this

simulator to Vela X-1, we can find the ionization structure and the matter distribution,

which reproduce the observed line intensities and continuum shapes. Additionally, from

the amount of the Doppler shift due to the stellar wind velocity, we show that the stellar

wind flow is affected by the photoionization by the neutron star radiation. For GX 301−2,

we have demonstrated that Compton shoulders could become a new probe to diagnose

the physical conditions of cold material. In fact, we have found that a cold (< 3 eV) and

dense (NH ∼ 1024 cm−2) cloud is surrounding the neutron star almost spherically from

the profile of observed Compton shoulders. We argue that such a cold dense cloud is the

origin of the differences in the X-ray spectrum when compared with the spectrum of Vela

X-1.

Contents

1 Introduction 1

2 High Mass X-ray Binaries and X-ray Spectroscopy 3

2.1 High Mass X-ray Binaries . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.2 X-ray Spectroscopic Observations of HMXBs . . . . . . . . . . . . . . . . 4

2.2.1 Iron emission line and absorption edge . . . . . . . . . . . . . . . 4

2.2.2 Emission lines from lighter elements . . . . . . . . . . . . . . . . . 4

2.3 Basic Physical Processes in High Mass X-ray Binaries . . . . . . . . . . . 10

2.3.1 Stellar winds of OB super-giant stars . . . . . . . . . . . . . . . . 10

2.3.2 Capture of the stellar wind by the neutron star . . . . . . . . . . 10

2.3.3 Photoionized plasmas . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.3.4 Interactions between X-ray photons and photoionized plasmas . . 13

2.3.5 X-ray emission lines from photoionized plasmas . . . . . . . . . . 18

3 Instrumentation 24

3.1 Chandra Observatory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.2 High Energy Transmission Grating Spectrometer(HETGS) . . . . . . . . 25

3.2.1 HETGS overview . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.2.2 HETGS performance . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.3 Data Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4 Observations and Results of Vela X-1 30

4.1 Vela X-1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4.2 Observation and Data Reduction . . . . . . . . . . . . . . . . . . . . . . 31

4.3 Continuum Emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.4 Emission Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.5 Pulse Phase Dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.6 Summary of the Observation and the Implication . . . . . . . . . . . . . 49

5 Observations and Results of GX 301−2 50

5.1 GX 301−2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

5.2 Observation and Data Reduction . . . . . . . . . . . . . . . . . . . . . . 50

5.3 Continuum Emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

ii

5.4 Emission Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

5.5 Pulse Phase Dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

6 Simulation of Photoionized Plasma in HMXB 61

6.1 Modeling of Photoionized Plasmas . . . . . . . . . . . . . . . . . . . . . . 61

6.2 Calculation of the Distribution of Ionization Degree . . . . . . . . . . . . 62

6.3 Monte Carlo Calculation of the X-ray Emission from Photoionization Equi-

librium State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

6.3.1 Physical processes . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

7 Discussion on Vela X-1 70

7.1 Ionization Structure of the Stellar Wind in Vela X-1 System . . . . . . . 70

7.2 The Ionization Structure . . . . . . . . . . . . . . . . . . . . . . . . . . 72

7.3 Estimate of the Mass Loss Rate of the Stellar Wind . . . . . . . . . . . . 75

7.4 Reproduction of the Entire Spectrum . . . . . . . . . . . . . . . . . . . . 77

7.5 Diagnostics by Iron Kα Lines . . . . . . . . . . . . . . . . . . . . . . . . 85

7.6 Doppler Effects of the Stellar Wind . . . . . . . . . . . . . . . . . . . . . 88

7.6.1 Difference between the observation and the simulation . . . . . . 88

7.6.2 Interaction between X-rays and the stellar wind . . . . . . . . . . 89

7.6.3 One dimensional calculation of the velocity structure . . . . . . . 90

8 Discussion on GX 301−2 93

8.1 Compton Shoulder in the PP Phase . . . . . . . . . . . . . . . . . . . . . 93

8.1.1 Time variability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

8.1.2 Modeling with Monte Carlo simulation . . . . . . . . . . . . . . . 95

8.1.3 Spectral analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

8.2 Matter Distribution in GX 301−2 . . . . . . . . . . . . . . . . . . . . . . 103

8.3 Unified Picture of HMXBs . . . . . . . . . . . . . . . . . . . . . . . . . . 108

9 Conclusion 111

iii

Chapter 1

Introduction

In high mass X-ray binary (HMXB) systems, the neutron star captures the surrounding

material of the stellar wind from the massive hot star, and converts it into X-ray radi-

ation. This emission interacts with the stellar wind, resulting in various emission lines

and characteristic features in the X-ray spectrum. Because these structures are directly

connected to the physical state of the material, the precise measurement brought by

the high precision X-ray spectroscopy can provide essential information on the physical

conditions and geometry of the matter in the vicinity of the neutron star.

Chandra and XMM-Newton X-ray satellites have opened up a new dimension for X-

ray spectroscopic observations, in the 21st century. The grating instruments on board

Chandra and XMM-Newton have 10–100 times more improved energy resolving powers

than that of past instruments. A number of forested emission lines, which were formerly

seen as one broad line, can be fully-resolved individually. Additionally, hidden structures

can be observed and clearly measured without any ambiguities.

HMXB observations using these grating instruments allow us to study the structure

of stellar winds by the individual emission line from various ions, and, for the first time,

provide a dynamical view of the ionized stellar wind surrounding the neutron star. At the

same time, such observations also provide numerous difficulties that cannot be explained

in the terms of simple models such as a spherically symmetric geometry or uniform

density. Therefore, for capitalizing on the observation results and further understanding

the information contained, new analytical methods and calculations are needed.

In this thesis, we deal with two different archetypes of high mass X-ray binaries, Vela

X-1 and GX 301−2. The former has highly ionized gases while the latter is characterized

by heavy absorption and absence of any features connected with highly ionized ions. We

have observed these two HMXBs with the grating spectrometers on Chandra, and, have

obtained X-ray spectra with high precision. In order to analyze these X-ray spectral

features and investigate the physical nature and geometry of the material, we have newly

constructed a simulator on the basis of Monte Carlo methods.

Chapter 2 gives a description of the current understanding on HMXBs and the basic

physical processes taking place in them. Chapter 3 includes the brief descriptions of the

1

Chandra X-ray Observatory and the grating instrument HETGS used for our observa-

tions. The following two chapters describe observational results. Chapter 4 describes

the results of Vela X-1 observations, and Chapter 5 is for that of GX 301−2 observa-

tions. Chapter 6 describes our newly constructed simulator to calculate physical states

in a HMXB situation and to estimate observed X-ray spectra. The calculation scheme

and our assumptions are given in this chapter. Chapter 7 and Chapter 8 are devoted

to the interpretation and the discussion on the observed spectra by comparison with the

simulation results of Vela X-1 and GX 301−2. For Vela X-1, we attempt to calculate the

photoionized plasma structure and generate the X-ray spectrum within the scheme. For

GX 301−2, by using the first discovered spectral feature of the “Compton shoulder”, we

investigate the physical state of the matter such as the density distribution and electron

temperature, together with the metal abundance. A brief summary is given in Chapter 9.

2

Chapter 2

High Mass X-ray Binaries and X-ray

Spectroscopy

2.1 High Mass X-ray Binaries

A high mass X-ray binary (HMXB) is a system consisting of a neutron star or a black

hole and a massive O- or B-type companion star. OB stars, which are young giant stars,

have powerful stellar winds and are spreading a fraction of their mass continuously. A

neutron star is a compact high-density object with a mass of ∼ 1.4 M¯ and a radius of

∼ 10 km. As it revolves around the companion star, it sweeps up the matter transfered

by the stellar wind. When the matter is accreted on the neutron star, a fraction of its

gravitational potential energy is converted into X-ray radiation. They are among the

brightest X-ray sources in our galaxy and have been observed since the early days of

X-ray astronomy.

X-ray emission from the neutron star in HMXBs have several interesting features;

pulsation sometimes detected with a period of one to several hundred seconds and cy-

clotron absorption structures in the hard X-ray spectra (Mihara, Makishima, & Nagase

1998; Makishima et al. 1999). These features are connected with the accretion and the

strong magnetic field of the neutron star.

The radiation from the neutron star interacts with the stellar wind, which results

in ionization and heating. X-ray photons from the neutron star are reprocessed by the

ionized material, resulting in various emission lines, which carry a wealth of information

about the physical state of the material in HMXBs. The neutron star can, therefore,

be used as a radiation source to probe the structure of the stellar wind and derive the

physical parameters that characterize its nature. Line intensities give us information on

amounts of matter, and, the line energies reflect ionization structures. Energy shifts and

line broadenings due to Doppler effects could become probes of the stellar wind dynamics.

These spectral features can be available only by X-ray observations with high spectral

resolutions.

3

2.2 X-ray Spectroscopic Observations of HMXBs

2.2.1 Iron emission line and absorption edge

Since the early days of X-ray astronomy, emission lines and absorption edges of iron

have played important roles for probing the matter distribution in HMXBs. The gas

scintillation proportional counter (GSPC) on board Tenma satellite demonstrated the

importance of the spectroscopic study of plasmas by using the most abundant material

ions. With Tenma observations of several HMXBs, the emissions lines at 6.4 keV and

the K-edge absorption features of iron ions in a low ionization degree have been shown

in their X-ray spectra (e.g. Vela X-1 Ohashi et al. 1984; Nagase et al. 1986; GX 301−2

Makino 1985; see Figure 2.1).

Figure 2.2 shows the iron line intensity plotted against the absorption-corrected con-

tinuum intensity above the iron K edge energy. The proportional relation between these

two values and the observed energy of the line center indicates that the iron line from

HMXBs is produced through fluorescence of continuum X-rays by cold material.

The matter distribution around X-ray sources were estimated from the relations be-

tween the line equivalent widths and the absorption column densities obtained from the

continuum shape (Koyama 1985; Inoue 1985; Makishima 1986). Figure 2.3 shows the

relation between these two values calculated by Monte Carlo method for some models of

matter distributions, together with observed values for HMXBs and other X-ray sources.

The pictures inferred with Tenma in the 1980s have been confirmed by ASCA in the

1990s. Additionally, the X-ray CCD on board ASCA is capable of investigating energy

shifts and broadenings of the iron Kα line (Endo et al. 2002). However, the energy

resolving power had not reached the level to recognize quantum effects, which is directly

connected to the physical state of the matter.

2.2.2 Emission lines from lighter elements

Emission lines from elements ligher than iron (S, Si, Mg, Ne, O, N, C, etc.) carry

information on the ionization structure of the emission medium. The solid state detector,

X-ray CCD, on board ASCA is the first instrument that is capable of detecting emission

lines from lighter elements and of resolving bright spectral features from H-like and He-

like ions. ASCA observations of several HMXBs have shown that their X-ray spectra

exhibit both soft X-ray emission from highly ionized ions and fluorescent lines from cold,

less ionized material (Vela X-1 Nagase et al. 1994; Cen X-3 Ebisawa et al. 1996; GX 301−2

Saraswat et al. 1996, see Figure 2.4 and Figure 2.5). Although the dominant excitation

mechanism (i.e., collisional or photoionization-driven) that is resposible for producing

the soft X-ray lines cannot be discriminated unambiguously from these observations,

cascades following recombination processes seemed to be the most natural candidate for

the emission mechanism because of the intense X-ray continuum radiation observed at the

4

Figure 2.1: Energy spectrum of Vela X-1 (left) and that of GX 301−2 (right)

obtained with Tenma. ((left) From Nagase et al. 1986, (right) From Leahy et

al. 1989)

Figure 2.2: Correlation between the observed iron-line photon flux and the

observed continuum X-ray flux above the neutral iron K-edge energy (7.1 keV).

(left) Vela X-1 (Ohashi et al. 1984); (right) GX 301−2 (Makino 1985). These

results indicate that the iron line originates in the flourescence of continuum

X-rays. (from Makishima 1986)

5

Figure 2.3: Relation between the matter thickness NH and the iron line equiv-

alent width calculated by Monte Carlo method for the representative Models

I–III illustrated on the left. On the same diagram, the observed equivalent

width and the observed “line of sight” absorption column density are plotted.

(from Makishima 1986)

6

same time from the source. Subsequently, Liedahl & Paerels (1996) and Kawashima &

Kitamoto (1996), for the first time, detected a narrow radiative recombination continuum

(RRC) of S XVI in ASCA spectrum of Cyg X-3, which provided evidence that the plasma

in Cyg X-3 is ionized through photoionization, and the highly ionized gas in the plasma

makes emission lines in the X-ray spectrum.

The spectral resolutions (E/∆E ∼ 100–1000) of diffraction grating spectrometers on

board Chandra and XMM-Newton have a pottential to provide an unambiguous infor-

mation of narrow RRCs in HMXBs. Paerels et al. (2000) resolved narrow RRCs of Si

XIV and S XVI in the spectrum of Cyg X-3 with Chandra HETGS, and measured the

electron temperature, kTe ∼ 50 eV. Schulz et al. (2002) detected a narrow RRC from Ne

X with an electron temperature of ∼ 10 eV in the Chandra HETGS spectrum of Vela

X-1. These observations have revealed that the photoionization-driven plasma indeed

exists in HMXBs.

The first attempt to model the X-ray spectrum as a whole was presented by Sako

et al. (1999) by calculating the ionization structure of the HMXB. They used the X-ray

spectrum of Vela X-1 obtained with ASCA originally published by Nagase et al. (1994).

Sako et al. (1999) characterized the standard wind velocity profile of OB stars proposed

by Castor, Abbott & Klein (1975). Once the velocity profile is characterized and a mass

loss rate of stellar wind is given, the number density of particles is uniquely assigned

everywhere in the wind. And, hence, the ionization structure is determined for a given

X-ray luminosity. By adjusting the mass loss rate, they found a statistically acceptable

fit for the ASCA spectrum (Figure 2.6). However, since the energy resolution of ASCA is

not enough to resolve independent emission lines predicted from the ionization model, the

intensity measurement of each line is very limited. Additionally, the X-ray line shifts and

widths that carry the information of dynamics of the X-ray emitting gas are inaccessible.

7

Figure 2.4: Energy spectra of Vela X-1 obtained with ASCA SIS at (top)

posteclipse, (middle) pre-eclipse, and (bottom) eclipse phases during the or-

bital phase intervals of 0.11 to 0.15, −0.14 to −0.11, and −0.10 to 0.10,

respectively. (From Nagase et al. 1994)

Figure 2.5: Energy spectrum of GX 301−2 obtained with ASCA SIS. (From

Saraswat et al. 1996)

8

Figure 2.6: The energy spectrum of Vela X-1 at the eclipse phase obtained

with ASCA SIS and the model generated by Sako et al. (1999).

Stellar WindStellar Wind

Companion Star（O,B super-giant）

Neutron Star

Scattering

AbsorptionPhoto Ionization

Recombination

X-ray

Figure 2.7: Current understanding picture of HMXBs.

9

2.3 Basic Physical Processes in High Mass X-ray Bi-

naries

2.3.1 Stellar winds of OB super-giant stars

Winds ejected from hot stars such as O-stars and B-supergiants, are characterized by

two global parameters, the terminal velocity v∞ and the mass loss rate M∗. These

winds are initiated and then continuously accelerated by the radiation pressure on ions

with resonance lines in the ultraviolet region. The velocity of the wind reaches to the

maximum, v∞ at very large distances from the star, where the radiative acceleration

approaches zero.

Castor, Abbott & Klein (1975) and Pauldrach, Puls & Kudritzki (1986) showed that

the velocity of the stellar winds obey the approximate formula (CAK-model):

v(r) = v∞

(1− R∗

r

)β

(2.1)

for a given distance r from the center of the star, where R∗ is the stellar radius. Pauldrach,

Puls & Kudritzki (1986) show that the value of β ∼ 0.8 is a better representation of the

wind kinematics for isolated OB stars. From the observational point of view, v∞ and β

can be determined from the analysis of the “P Cygni” profile which appears in the UV

resonance line spectrum, and are actually obtained from many OB-stars. (e.g. Howarth

& Prinja 1989; Prinja et al. 1990; Blomme 1990)

Given the velocity profile, the wind density can be calculated by applying the equation

of mass continuity, assuming spherical symmetry:

n(r) =M∗

4πµmpv(r)r2, (2.2)

where µ is the gas mass per hydrogen atom. (µ = 1.3 for the cosmic chemical abundance.)

2.3.2 Capture of the stellar wind by the neutron star

In the case of high mass X-ray binary systems consisting of a neutron star and an OB

star, mass accretion onto the neutron star takes place through direct capture of the

stellar wind material. Material within a radius Racc will be accreted by the gravitation

of the neutron star, whereas material outside this cylinder will escape (Figure 2.8). This

radius is calculated by a simple assumption that material will be accreted only if it has

a kinetic energy less than the potential energy in the vicinity of the neutron star. When

the neutron star mass is quoted as Mns, it is set by

1

2mv2

rel =GMnsm

Racc

, (2.3)

10

Racc

Neutron Star

D

OB Star

Stellar wind

Mns

Figure 2.8: Geometry of accretion onto a neutron star.

for a particle of mass m. This relation gives

Racc =2GMns

v2rel

, (2.4)

where vrel is the relative velocity of the neutron star and the stellar wind. Therefore, the

mass accreting rate onto the neutron star Macc is given by

Macc =M∗R2

acc

4D2=

(GMns)2 M∗

v4relD

2, (2.5)

where D is the distance of the neutron star from the center of the OB star.

The gravitational energy of the accreting material is converted into X-rays. The X-

ray luminosity resulting from this accretion will simply be the rate at which gravitational

energy is released:

Lx =GMnsMacc

Rns

=(GMns)

3 M∗Rnsv4

relD2

(2.6)

where it is assumed that most of this energy is liberated near the neutron star surface (of

radius Rns). By applying typical parameters (Mns = 1.4M¯, M∗ = 1×10−6M¯ yr−1, Rns =

10 km, vrel = 500 km s−1, D = 50R¯), we obtain a typical X-ray luminosity of HMXB,

Lx ∼ 5× 1036 erg s−1.

A number of models have been proposed to explain the X-ray spectra from the neutron

star of HMXB, including the conventional power-law model with a high-energy exponen-

tial cutoff (White, Swank, & Holt 1983) and those that account for Comptonization in

11

the postshock accretion region (Lamb & Sanford 1979; Sunyaev & Titarchuk 1980; Becker

& Begelman 1986). Kretschmar et al. (1997) applied these models to the spectrum of

Vela X-1 obtained by HEXE on the RXTE satellite and TTM on MirKvant space station.

They concluded that the power-law with an exponential cutoff model generally provides

the best representation to the observed spectra. As the extension of the Comptonization

models, on the other hand, Mihara, Makishima, & Nagase (1998) proposed a new model

with a electron cyclotron resonance absorption feature, and claimed that the model pro-

vides a better representation for the spectra of HMXBs obtained with Ginga. These

analysis of cyclotron resonance absorptions results in the surface magnetic field of the

neutron stars of a few times 1012 G.

2.3.3 Photoionized plasmas

Strong X-ray radiation from the neutron star affect on the ionization and thermal struc-

ture of the surrounding gas. The plasma surrounding the X-ray source is ionized and

heated through photoionization and loses energy mainly through cascades following radia-

tive recombination. Both the equilibrium temperature and the charge state distribution

in this photoionized plasma are determined locally by the X-ray flux, the X-ray spectral

shape and the gas density, and are often characterized by the ionization parameter,

ξ =LX

ner2, (2.7)

where LX is the luminosity of the X-ray source, ne is the electron density of the region,

and r is the distance to the X-ray source (Tarter, Tucker & Salpeter 1969).

Theoretical efforts to determine the response of a gas to X-rays were also investi-

gated. These models are called X-ray nebular models. By Tarter, Tucker & Salpeter

(1969), Halpern & Grindlay (1980), Kallman & McCray (1982) and so on, models of

static gas clouds irradiated by hard X-rays have been developed to address the basic

issues of heating, cooling, ionization, recombination, and the global structure of X-ray

photoionized gases. Such a model begins with a cloud of specified size or column density,

shape, and elemental abundance placed in the vicinity of a point source of continuum X-

rays. Either the particle density or the gas pressure is fixed. Local heating is dominated

by the thermalization of photoelectrons and Auger electrons produced through photoion-

ization by the continuum X-rays. Photoelectrons and Auger electrons are assumed to

deposit their energy at the site of photoionization. Energy flow throughout the gas is in

the form of radiation. The charge state distribution is determined by a balance between

photoionization and recombination. In calculating the charge state distribution, the elec-

tron temperature, which determines the magnitude of the recombination rate coefficients,

must be known. However, since the local heating and cooling rates depend on the charge

state distribution, the energy equation is coupled to the equations of ionization balance.

Among the aims of nebular model calculations is to determine a self-consistent solution.

Several instructive examples are provided by Kallman & McCray (1982) (e.g. Figure 2.9).

12

The principal distinction between collisionally ionized and photoionized plasmas is the

very different electron temperatures that accompany a given charge state distribution.

For collisional ionization, the electron temperature must be comparable to the ionization

potential, whereas for photoionization, the X-ray radiation does most of the work, so

the electron temperature can be much lower. The most useful spectral diagnostic for

observationally distinguishing between the two cases is the radiative recombination con-

tinua. Descriptions of the radiative recombination continua are given in the following

subsections.

2.3.4 Interactions between X-ray photons and photoionized plas-

mas

The physical processes in photoionized plasmas can be summarized.

Photoionization and Radiative Recombination

In the energy region of X-rays, the dominant process by which photons lose energy is

photoionization. This process can be written as

Xi + γ −→ X(∗)i+1 + e−,

where Xi represents an ion in charge state i (i.e. of ion X i+), and an asterisk denotes

an ion in an excited state, while a parenthesized asterisk refers to an ion in either an

excited state or the ground state. If the energy of the incident photon is E, it can eject

electrons, which have binding energies Ebinding ≤ E from atoms, ions and molecules, the

remaining energy (E−Ebinding) being removed as the kinetic energy of the ejected electron.

The energy levels within the atom for which E = Ebinding are called “absorption edges”

because ejection of electrons from these energy levels is impossible if the photons have

lower energy. For photons with higher energies, the cross section for photoionization from

this level decrease roughly as E−3. There is an analytic solution for the photoionization

cross section for photons with energies E À Ebinding and E ¿ mec2 due to the ejection

of electrons from the K-shells of H-like ions,

σK = 2√

2σTα4Z5

(mec

2

E

) 72

(2.8)

In this cross section, α is the fine structure constant and σT is the Thomson cross section.

There is the strong dependence of the cross section on the atomic number Z. Therefore,

although heavy elements are very much less abundant than hydrogen, rare large-Z ele-

ments make important contributions to the photoionization cross section.

Photoionization is balanced by its inverse process, radiative recombination,

Xi + e−1 −→ X(∗)i−1 + γ.

13

Figure 2.9: The charge state distribution and temperature of optically thin

photoionized plasmas. From model 1 of Kallman & McCray (1982). Tem-

perature and relative abundances of the ions of each element are shown as a

function of log ξ for −3 < log ξ < 5.

14

The photons generated in recombination are distributed into a continuum, the radiative

recombination continuum (RRC), which is found above the recombination edge with

a width ∆E ≈ kTe. In photoionized plasmas with a low electron temperature, the

RRC feature is narrow, and appears “line-like”. The emission coefficient for radiative

recombination is given by

ji(E)dE = nevσPIi (v)f(v)dv (2.9)

where ne is the electron density, v is the velocity of the free electron, and f(v) is the

Maxwellian velocity distribution,

f(v) =4√π

(me

2kTe

)3/2

v2 exp

(−mv2

2kTe

). (2.10)

σPIi (v) is the photoionization cross section, and

E =1

2mev

2 + Ei, (2.11)

where Ei is the ionization potential energy of level i of the ion. To date, in X-ray regions,

the only identified RRC features have been associated with recombination to the ground

level of H-like and He-like ions, but more often recombination leaves an ion in an excited

state.

Subsequent to recombination into an excited level, the ion will decay in a series of

spontaneous radiative transitions, until it reaches the ground level.

X∗i −→ Xi + γ

These radiative transitions generate photons whose energies are identified with the source

ions, and form the emission line.

Fluorescence

Fluorescence line emission is also important process in photoionized plasmas, especially

for ions in a low charge state. A photon ionizes an inner-shell electron of an ion in the

ground state and leaves the ion in an excited state. One of the two following processes

can occur at this point. The ion can stabilize itself through either, ejection of one or

more Auger electrons, or emission of a photon. These processes can be described by the

following,

Xi + γ −→ X∗i+1 + e− −→

Xi+1 + e− + e′− (Auger)

Xi+1 + e− + γ′ (fluorescence)

The probability of producing a fluorescent line instead of emitting Auger electrons is

called the fluorescent yield, which increases as the atomic number. Fluorescent yields of

neutral atoms for K and L shells are shown in Figure 2.10. For example, the fluorescent

yield YK of the Kα line of iron at 6.4 keV is 0.30. For the Si Kα line at 1.74 keV, YK is

0.049.

15

Figure 2.10: Fluorescent yields for K and L shells for 5 ≤ Z ≤ 110. (From

X-RAY DATA BOOKLET(http://xdb.lbl.gov/))

Photoexcitation

Photoexcitation occurs when a photon excites a bound state of an ion, and is followed

by a radiative decay resulting in an emission of a photon.

Xi + γ −→ X∗i −→ Xi + γ′

In the X-ray region, photoexcitations due to H-like and He-like ions of C, N, O, Ne, Mg,

Si and so on play important roles on both emission and absorption line formations.

The cross section of photoexcitations from level i to level j (j > i) depends directly

on the oscillator strength of the transition between level i and j (fij), and is given by,

σPEij (E) =

√πe2

mec2

fij

∆νD

H(a, x),

where H(a, x) is a Voigt function,

H(a, x) =a

π

∫ ∞

−∞

e−t2dt

(x− t)2 + a2. (2.12)

In these equations, a = Ar/(4π∆νD), Ar is the radiative decay rate, and x = (ν−νij)/∆νD

is the frequency shift from the line center expressed in units of the Doppler width,

∆νD = νij

√2kT

mzc2. (2.13)

16

Radiative recombination

Photoexcitation

Fluorescence

Photoionization

Figure 2.11: Schematic diagram of physical processes in photoionized plasmas.

17

Compton Scattering

Compton scattering is a fundamental physical process that is responsible for transferring

energy between photons and electrons in a wide variety of astrophysical environments.

Since the Compton scattering opacity relative to that of photoionization is larger for

higher energy photons, it plays an important role in the hard X-ray region. When a pho-

ton propagating through a material undergoes Compton scattering with the constituent

electrons, the energy of photon is modified in a way that depends on the scattering an-

gle, the electron velocity and the electron state, whether it is bound or free. In the limit

where the electrons are free and at rest, a fraction of the photon energy is transferred to

the electron according to the Compton formula,

E1 =E0

1 + (E0/mec2) (1− cos θ), (2.14)

or,

cos θ = 1−mec2

(1

E1

− 1

E0

)(2.15)

where E0 is the energy of the incoming photon, E1 is the energy of the outgoing photon,

θ is the angle between the incoming and outgoing photons, and mec2 is the electron rest-

mass energy (=511 keV). The differential cross section for unpolarized photons is shown

in quantum electrodynamics to be given by the Klein-Nishina formula

dσ

dΩ=

r20

2

E21

E20

(E0

E1

+E1

E0

− sin2 θ

). (2.16)

The total cross section can be shown to be

σ = σT · 3

4

[1 + x

x3

2x (1 + x)

1 + 2x− ln (1 + 2x)

+

1

2xln (1 + 2x)− 1 + 3x

(1 + 2x)2

](2.17)

where x = E0/mec2 and σT is Thomson cross section.

2.3.5 X-ray emission lines from photoionized plasmas

From hydrogen like ions

The most prominent emission lines from H-like ions are the Lyman series transitions:

Lymanα1,2 : 2p 2P3/2,1/2 −→ 1s 2S1/2

Lymanβ1,2 : 3p 2P3/2,1/2 −→ 1s 2S1/2

Lymanγ1,2 : 4p 2P3/2,1/2 −→ 1s 2S1/2

... .

18

Figure 2.12: A model of emission lines from H-like Si.

In photoionized plasmas, Lyman series lines are formed by radiative decays following

either photoexcitation or radiative recombination. The energies of these lines can be

calculated precisely from theory. Therefore, observed profiles of the lines such as widths

and energy shifts enable us to investigate the dynamics of the emission site.

The RRC feature becomes narrow, and appears the line-like profile due to the low

electron temperature of the photoionized plasma. Additionally, the width of the RRC

corresponds to directly electron temperature of the recombination site. A model of X-ray

emission lines from H-like Si is shown in Figure 2.12.

From helium like ions

The most important K-shell He-like transitions are as follows:

w : 1s2p 1P1 −→ 1s2 1S0

x : 1s2p 3P2 −→ 1s2 1S0

y : 1s2p 3P1 −→ 1s2 1S0

z : 1s2s 3S1 −→ 1s2 1S0

19

The line w is an electric dipole transition, also called the resonance transition, and is

sometimes designated with the symbol r. Lines x and y are the so-called intercombination

lines. These are usually blended and are collectively designated with the symbol i. Lastly,

z is the forbidden line, often designated by the symbol f . Emissions from He-like ions

are characterized with the triplet lines of r, i and f .

In photoionization plasmas, as in the H-like case, the excited levels for He-like ions

are fed directly by photoexcitation and radiative recombination. The three He-like lines

ratios can be affected by the electron density and the presence of a significant ultraviolet

radiation field. The density sensitivity comes from the fact that the 3S1 level can be

collisionally excited to the 3P levels. At high-enough electron density, this process suc-

cessfully competes with radiative decay of the forbidden line. In the UV radiation field,3S1 level can be also excited to 3P levels by photoexcitation. These lead to suppression

of the forbidden line and enhancement of the intercombination lines. Additionally, inner-

shell ionization of Li-like ions can lead to the production of the forbidden line in He-like

ions. Despite its use as density, temperature and UV radiation diagnostics, the behavior

of the triplet lines ratios from He-like ions is very complex.

The transition energies of He-like ions can also be determined accurately from the-

oretical calculations. The energy shift of the observed line from the calculated value is

available for study of dynamics. The RRC feature also appears in the same way as that

of H-like ions. A model of emission lines from He-like Si is shown in Figure 2.13.

From ions in a low charge state

Fluorescent line emission from ions in a low charge state is another important line for-

mation process in photoionized plasmas. An intensity of a fluorescent emission is propor-

tional to the fluorescent yield (§ 2.3.4), which increases as the atomic number. Therefore,

an emission line from a fluorescence of a high-Z element like iron becomes appreciable.

The energy of the fluorescent emission is affected by the charge state of the ion, and

behaves intricately. Therefore, in comparison to emission lines from H-like and He-like

ions, it is complex for study of dynamics to utilize fluorescent lines.

Compton shoulder

As described in § 2.3.4, when an X-ray photon propagating through a low-temperature

(< 105 K) medium undergoes Compton scattering with the constituent electrons, a frac-

tion of the photon energy is is transferred to the electron according to the Compton

formula (eq. 2.14, 2.15). The maximum energy shift per scattering due to the electron

recoil is, therefore,

∆Emax =2E2

0

mec2 + 2E0

, (2.18)

for photons that are back-scattered (θ = 180). An X-ray emission line with the en-

ergy of E0 propagating through a medium with substantial Compton optical depth

20

Figure 2.13: A model of emission lines from He-like Si.

21

(τCompton > 0.1) has a non-negligible probability of interacting with an electron, resulting

in down-scattering of photons and, hence, producing a discernible ”Compton shoulder”

between E0 and E0−∆Emax. Alternatively, this Compton energy shift can be written in

wavelength form:

∆λmax =hc

E0 −∆Emax

− hc

E0

=2h

mec= 2λC, (2.19)

where λC = h/mec ∼ 0.024 A is Compton wavelength. Therefore, the maximum wave-

length shift due to Compton scattering is constant independent of the incident energy.

X-ray emission lines at higher energies are ideal for studying the properties of the

Compton shoulders, since the Compton scattering opacity relative to that of photoion-

ization is larger for higher energy photons. The iron Kα fluorescent line complex at

E0 = 6.40 keV, therefore, is particularly promising, and can be produced over an ex-

tremely wide range in column density, which makes it ideal for diagnosing the physical

properties of a cold medium irradiated by X-rays. The energy shift of an iron line photon

due to a single Compton scattering is 156 eV from eq. (2.18).

The 6.4 keV line profile after single Compton scattering by at rest electrons is shown

in Figure 2.14. The shape and flux of the Compton shoulder is sensitive to the electron

column density and electron temperature of the scattering medium, and is also affected

by geometrical conditions. Compton scattering by electrons in bound systems produces

spectral signatures that are distinct from those produced by free electrons (Sunyaev &

Churazov 1996; Vainshtein et al. 1998; Sunyaev, Uskov & Churazov 1999).

22

Figure 2.14: Line profile after single Compton scattering by at rest electrons.

Initial energy is 6.4 keV, comparable to an iron Kα. The differential cross

section is given by the the Klein-Nishina formula (eq. 2.16).

23

Chapter 3

Instrumentation

In this thesis, we utilize observational data obtained with the grating spectrometer on

board the Chandra X-Ray Observatory. In this chapter, we summarize the basic proper-

ties and performance of the satellite and the instruments.

3.1 Chandra Observatory

The Chandra X-Ray Observatory was launched by NASA’s Space Shuttle Columbia on

July 23, 1999. The schematic view of the satellite is shown in Figure 3.1. The Chandra

satellite carries a high resolution X-ray mirror, two imaging detectors, and two sets of

transmission gratings. The important features are: an order of magnitude improvement

in spatial resolution, and the capability for high spectral resolution with the gratings.

The X-ray mirror, High Resolution Mirror Assembly (HRMA), consists of a nested

set of four paraboloid-hyperboloid (Wolter-1) grazing-incidence X-ray mirror pairs. It

achieves an excellent angular resolution of 0.5′′. There are two focal plane instruments.

One is the microchannel plate, High Resolution Camera (HRC). It is used for high an-

gular resolution imaging, fast timing measurements, and for observations requiring a

combination of both. The second instrument, the Advanced CCD Imaging Spectrometer

(ACIS), is an array of charged coupled devices. A two-dimensional array of these small

detectors performs imaging and spectroscopy simultaneously. Pictures of extended ob-

jects can be obtained along with spectral information from each element of the picture.

There are two transmission grating spectrometers, formed by sets of gold gratings placed

just behind the mirrors. One set is optimized for low energies (LETG) and the other

for high energies (HETG). Spectral resolving powers (E/∆E) in the range 100–2000 can

be achieved with good efficiency. These gratings produce spectra dispersed in space at

the focal plane. Either the ACIS array or the HRC can be used to record data. The

thesis utilizes the observation data with the High Energy Transmission Grating Spec-

trometer(HETGS), consisting of HRMA, HETG and ACIS. In the subsequent section,

the properties of HETGS are briefly summarized.

24

Figure 3.1: A schematic view of Chandra satellite. The satellite is more than

10 m long and weights about 5 tons. The satellite is thrown into an elliptical

high-Earth orbit with the perigee altitude of 10,000 km, the apogee altitude

of 140,000 km, with the orbital period of about 64 hours.

3.2 High Energy Transmission Grating Spectrome-

ter(HETGS)

3.2.1 HETGS overview

The HETGS provides high resolution spectra (with E/∆E up to 1000) between 0.4 keV

and 10.0 keV for point and slightly extended (few arc seconds) sources. The HETGS

consists of two sets of gratings, each with different period. One set, the Medium Energy

Grating (MEG), is optimized for medium energies. The second set, the High Energy

Grating (HEG), is optimized for high energies. The HETG is designed for use with the

spectroscopic array of the Chandra CCD Advanced Imaging Spectrometer (ACIS-S).

A schematic layout of the HRMA-HETG-detector system is shown in Figure 3.2. X-

rays from the HRMA strike the transmission gratings and are diffracted by an angle β

given according to the grating equation,

sin β = mλ/p, (3.1)

where m is the integer order number, λ is the photon wavelength, p is the spatial period

of the grating lines, and β is the dispersion angle. An undispersed image is formed by

the zeroth-order events, m = 0, and dispersed images are formed by the higher orders,

25

Figure 3.2: A schematic layout of the High Energy Transmission Grating

Spectrometer. (from The Chandra Proposers’ Observatory Guide)

Figure 3.3: A HETGS raw image.

primarily the first-order, |m| = 1. MEG has a period of 4001.41 A and HEG has a

period of 2000.81 A. The two sets of gratings are mounted with their rulings at different

angles so that the dispersed images from the HEG and MEG form a shallow “X” like

image centered on the undispersed (zeroth order) position: one leg of the “X” is from

the HEG, and the other from the MEG (Figure 3.3).

3.2.2 HETGS performance

The effective area of HETGS depends on the HETG efficiency coupled with the HRMA

effective area and the ACIS efficiency. Additional effects that could reduce the effective

area comes from the process of selecting events and the effect of gaps between chips.

Combining the HETG diffraction efficiencies with the HRMA effective area and the ACIS-

S detection efficiency produces the total effective area of the system as a function of

26

Figure 3.4: The HETGS effective area, integrated over the Point Spread Func-

tion (PSF), is shown with energy and wavelength scales. The two panels in

the left side show HEG effective areas, and the two panels in the right side

show MEG effective areas. The m = +1, +2, +3 orders are displayed in the

top panels and m = −1,−2,−3 orders are in the bottom panels. The thick

solid lines are first order, the thin solid lines are third order, and the dotted

lines are second order. (from The Chandra Proposers’ Observatory Guide)

energy, described as an “ancillary response file” or ARF. Effective area of HEG and

MEG extracted from nominal HETGS ARF ’s are shown in Figure 3.4. Based on the

results from the HETGS calibration observations, the systematic uncertainties of HETGS

spectral fluxes are estimated as follows,

• 10 % for 1.5 < E < 6 keV (both MEG and HEG)

• 20 % for 6 < E < 8 keV (HEG only)

• 20 % in the Si-K edge region (1.83–1.84 keV) (both MEG and HEG)

• 20 % for 0.8 < E < 1.5 keV (both MEG and HEG)

• 30 % for 0.5 < E < 0.8 keV (MEG only).

The HETGS covers an energy range between 0.5 keV and 10.0 keV. The short wave-

length is limited by the declining reflectivity of the mirrors and the efficiency of the

gratings at approximately 1.2 A (10 keV). The long wavelength end is determined by the

declining efficiency of the gratings (which are mounted on a thin plastic sheet for extra

support), and ultimately, the finite linear extent of the detectors. The MEG spectrum

goes out to ∼ 24 A (500 eV).

27

Figure 3.5: HEG and MEG Resolving Power (E/∆E = λ/∆λ) as a function of

energy for the nominal HETGS configuration. The ”optimistic” dashed curve

is calculated from pre-flight models and parameter values. The ”conservative”

dotted curve is the same except for using plausibly degraded values of aspect,

focus, and grating period uniformity. The cut-off at low-energy is determined

by the length of the ACIS-S array. Measurements from the HEG and MEG

m = −1 spectra, are typical of flight performance and are shown here by

the diamond symbols. The values plotted are the as-measured values and

therefore include any natural line width in the lines; for example, the ”line”

around 12.2 A is a blend of Fe and Ne lines. (from The Chandra Proposers’

Observatory Guide)

The wavelength resolution ∆λ is written as

∆λ =p

mcos β∆β, (3.2)

according to eq.(3.1). For small β, the resolution is independent of λ for a fixed telescope

angular resolution ∆β. The resolving power, E/∆E = λ/∆λ, of HETGS are shown with

respect to the energy of incident photons in Figure 3.5. The ∆λs (FWHM) are 0.012 A

and 0.024 A for HEG and MEG, respectively. Therefore, the energy resolutions of HEG

are 4 eV at 2 keV and 40 eV at 6.4 keV.

The absolute energy scale is measured to be less than 100 km/s in doppler velocities.

It is limited by the knowledge of the ACIS-S chip locations, which is of order 0.5 pixels:

0.0028 A for the HEG and 0.0055 A for the MEG in the wavelength. In addition, the

location of the zeroth order image can be in error by ∼ 0.5 pixels, which translates to

slight and opposite sign-shifts of the wavelengths derived from the plus and minus orders.

28

Figure 3.6: A HEG event distribution in dispersion angle/energy obtained

from CCD pulse height space. Each order events can be seen.

3.3 Data Process

When we observe an X-ray source with HETGS, we obtain a dispersed image such as

raw data (Figure 3.3). By using the image, we can select dispersed events of MEG and

HEG on the basis of spatial positions. And then, we use an order sorting mask by using

the energy information obtained with ACIS. Figure 3.6 shows a distribution of events

in the dispersion angle/CCD pulse height space. Dispersion angles are converted from

the distance from the center point of the zeroth order image. As shown in Figure 3.6,

events of each order are clearly separated. In the data analysis, we first select events of

the intended order, and then, extract a spectrum by projecting the events on dispersion

angle axis. Finally, by converting the dispersion angle into wavelength or energy on the

basis of eq.(3.1), we obtain a wavelength spectrum or an energy spectrum.

Thanks to the order sorting mask, background events of HETGS can be removed

and can be kept to a low level. The background events are usually estimated from the

adjacent region to the dispersed events region.

29

Chapter 4

Observations and Results of

Vela X-1

4.1 Vela X-1

Vela X-1 is an eclipsing high mass X-ray binary pulsar with a pulse period of 283 s

(McClintock et al. 1976) and an orbital period of 8.964 days (Forman et al. 1973). The

optical companion star, HD 77581, is a B05 Ib supergiant (Brucato & Kristian 1972;

Hiltner, Werner & Osmer 1972), which drives a stellar wind with a mass-loss rate of (1–

7) × 10−6M¯ yr−1 (Hutchings 1976; Dupree et al. 1980; Kallman & White 1982; Sadakane

et al. 1985; Sato et al. 1986a). The 1100 km s−1 terminal velocity of the stellar wind was

measured by Prinja et al. (1990) from the P-Cygni profile of the UV resonance line. Its

intrinsic X-ray luminosity is ∼ 1036 erg s−1, consistent with accretion of a stellar wind

captured by the neutron star gravitation for the mass-loss rate and the velocity structure

(see Chapter 2).

Neutron Star

EarthEclipse

Phase 0.25

Phase 0.50

HD 77581

Figure 4.1: The location between the neutron star and the companion star in

Vela X-1. The bold lines show the observed orbital phases.

30

streak

Zeroth order

HEG

MEG

Figure 4.2: The grating image of Vela X-1 in the phase 0.50.

4.2 Observation and Data Reduction

Chandra observed Vela X-1 three times. In order to observe from different places and

to compare the results, we have planned to observe Vela X-1 at different orbital phases

in the same orbit. The actually observed orbital phases are (1) φ = 0.237–0.278, (2)

φ = 0.481–0.522, and (3) φ = 0.980–0.093, hereafter referred to as phase 0.25, phase 0.50,

and eclipse, respectively. The observation dates and exposure times are summarized in

Table 4.1.

All of the data are processed using CIAO v2.3, and spectral analyses are performed

using XSPEC 1. Since the zeroth order image was severely piled-up (Figure 4.2) during

phase 0.25 and phase 0.50, the locations of the zeroth order image were determined by

finding the intersection of the streak events and the dispersed events. We apply spatial

filters for both the MEG and the HEG, and then use an order sorting mask by using the

energy information obtained with ACIS. In our analysis, only the first order events are

used to extract spectra. The background events are estimated from the adjacent region

to the dispersed event region. According to this estimation, the background levels are at

most 5% for the eclipse data and 3% for phase 0.25 and phase 0.50 data.

The light curves in the three orbital phases extracted from the HEG in the energy

interval between 1 and 10 keV (Figure 4.3). Pulsations with periods of 283.2 s and

283.5 s are found from the light curves of phase 0.25 and phase 0.50, respectively, by the

epoch holding method. The HEG integrated spectra for each orbital phase are shown in

Figure 4.4.

1http://heasarc.gsfc.nasa.gov/docs/xanadu/xspec/

31

Table 4.1. Summary of Vela X-1 Observations

Label OBSID Start Date Orbital Phase Exposure (sec)

0.25 1928 2001-02-05 05:29:55 0.237 – 0.278 29570

0.50 1927 2001-02-07 09:57:17 0.481 – 0.522 29430

eclipse 1926 2001-02-11 21:20:17 0.980 – 0.093 83150

Figure 4.3: The light curves of Vela X-1 in phase 0.25 (top), phase 0.50

(middle) and the eclipse (bottom). The bin sizes are 10 sec for phase 0.25 and

phase 0.50, and 500 sec for the eclipse.

32

Table 4.2. Properties of continuum spectra derived from spectral fits.

Orbital NHa Photon Index Observed Flux Luminosityb χ2/ d.o.f.

Phase (1022 cm−2) (erg cm−2 s−1) (erg s−1)

0.25 1.45 ± 0.03 1.01 ± 0.01 3.0 × 10−9 1.6 × 1036 2872./ 3318

0.50 18.5 ± 0.3 1.01 (fixed) 1.5 × 10−9 1.6 × 1036 1000./ 1051

Note. — Fitting regions are 1.0–10.0 keV and 3.0–10.0 keV from HEG for 0.25 and

0.50 orbital phases, respectively. The iron K-line region (6.3–6.5 keV) is excluded.

Errors correspond to 90 % confidence levels.

aThe metal abundance is assumed to be 0.75 cosmic.

b0.5–10.0 keV luminosity corrected for absorption.

4.3 Continuum Emission

X-rays emitted from the neutron star are clearly observed from the spectra taken in

phase 0.25 and phase 0.50, as featureless continuum spectra. As expected from the

geometry, the spectrum taken in the eclipse phase is dominated by line emission and

scattered components. In order to parameterize the properties of the continuum part of

the spectra, we fit it with a photo-absorbed power-law function. Since the spectrum of

phase 0.25 is less affected by absorption, we leave both the hydrogen column density and

the photon index as free parameters in the fit. On the other hand, for phase 0.5, we fix

the photon index to the value obtained from phase 0.25 and calculate the absorption. As

for a metal abundance of the photo-absorption material, we use 0.75 times the cosmic

chemical abundance (Feldman 1992), which is known to be representative for typical

OB-stars (Bord et al. 1976). The derived parameters from the spectral fits are listed

in Table 4.2. The best-fit models are superimposed on the spectra in Figure 4.4. The

absorption-corrected luminosity is determined to be identical for observations in phase

0.25 and in phase 0.50 and corresponds to 1.6 × 1036 erg s−1 in the 0.5–10 keV range,

assuming a distance of 1.9 kpc (Sadakane et al. 1985).

4.4 Emission Lines

A number of emission lines are clearly seen in the spectra of phase 0.50 and eclipse. The

observed spectra in the entire energy range are shown in Figure 4.5 and Figure 4.6. It is

apparent that the data obtained with an extremely high energy resolution leads to the

33

Figure 4.4: The spectrum of Vela X-1 obtained with HEG. The green, the blue

and the red show the spectra of the phase 0.25, the phase 0.50 and the eclipse,

respectively. The black lines are spectral fits results listed in Table 4.2.

34

detection and the identification of K-shell Si fluorescent lines from a wide range of charge

state, for the first time from Vela X-1. The emission lines from highly ionized S, Si, Mg

and Ne can be seen, in addition to fluorescent lines from Fe, Ca, S, and Si ions in lower

charge states. Additionally, in the both spectra of phase 0.50 and eclipse, emission lines

from the same ions are detected.

Blown-up spectra of the Si K lines region are shown in Figure 4.7. Intense Lyα line

from H-like ions and fully-resolved He-like triplet lines are clearly seen in phase 0.50 and

eclipse. At the lower energy end below 1.74 keV, fluorescent lines from near-neutral Si is

also detected in both phases. Additionally, between the He-like lines and nearly neutral

line, Si VII–Si XI Kα lines can be resolved. The forest of Si K lines is a clear evidence

that plasma in various ionization states exist in the Vela X-1 system.

The centroid of energies, the widths and the intensities of each line are determined by

fitting the data with a single gaussian model. In the spectral fittings, we use the Poisson

likelihood statistics, in stead of the χ2 statisitics, because numbers of photons in some

of the bins in the spectra are very small. As an example of the fittings, the Lyα line

profiles from H-like ions of Si are shown in Figure 4.8, together with the best-fit models.

The derived parameters for phase 0.50 and eclipse are listed in Table 4.3 and Table 4.4,

respectively. The line intensity ratios of phase 0.50 to eclipse are listed on Table 4.5 for

lines from H- and He-like ions which were detected with statistical significance of more

than 5 σ. These ratios are 8–10 for the H-like lines and are 4–7 for the He-like lines.

One of the striking results seen from Figure 4.8 is the Doppler shift of lines. Thanks

to the resolving power of the HEG, Doppler shifts can be measured with an accuracy of

∼ 100 km s−1. Figure 4.9 compares the line profiles of Si Lyα and Mg Lyα between the

phase 0.50 and the eclipse data. The differences in the line center energies are clearly

seen in each line.

In Figure 4.10, the velocity shifts are plotted for both of the phases for all emission

lines from H- and He-like ions. Though some fluctuations are seen, there is a trend that

blue shifts are detected in phase 0.50 and red shifts are observed in eclipse. The shifts

between phase 0.50 and eclipse (∆v) range in ∼ 300–600 km s−1 (Table 4.5). Additionally,

the emission lines from highly ionized ions have widths of σ . 300 km s−1.

The radiative recombination continuum (RRC) is detected clearly from H-like Ne.

The blow-up spectra of phase 0.50 and that of eclipse are shown in Figure 4.11. We

fitted the RRC spectra using the “redge” model in XSPEC. The electron temperatures

are derived to be kTe = 7.4+1.6−1.3 eV and kTe = 6.6+2.5

−1.8 eV during phase 0.50 and eclipse,

respectively.

Iron Kα fluorescent lines are detected in all three orbital phases. The profiles of these

lines are shown in Figure 4.12. The parameters derived from the spectral fittings with a

single gaussian model are listed in Table 4.4. The equivalent width of the iron Kα line is

measured to be 116 eV and 51 eV for phase 0.50 and for phase 0.25, respectively. At the

eclipse phase, a high equivalent width of 844 eV is observed. As shown in Figure 4.12,

35

there is a sign of a Compton shoulder in the iron Kα spectrum of phase 0.50.

36

Figure 4.5: The spectrum of Vela X-1 in the orbital phase of 0.50. The red

shows MEG data and the blue shows HEG data. The green lines mark the

energies of the emission lines listed in Table 4.3.

37

Figure 4.6: The spectrum of Vela X-1 in the eclipse phase. The red shows

MEG data and the blue shows HEG data. The green lines mark the emission

lines listed in Table 4.4.

38

Si XIV Lyα

Si XIII

rf

i

Si II-VI

Si X

IS

i XS

i IX

Si V

III

Si V

II

phase 0.25

phase 0.50

eclipse

due to the detector

response (Si-Kedge)

Figure 4.7: The spectrum of the Si K lines regions in each orbital phase.

39

Figure 4.8: The Lyα lines from H-like Si in phase 0.50 (left) and in eclipse

(right). The bold lines show the best-fit models. Fitting model is the single

gaussian.

40

Table 4.3. Derived Parameters of emission lines in the 0.5 orbital phase spectrum

Center Energy Sigma Intensitya Candidate Line Shift

(keV) (eV) (photon cm−2 s−1) (energy keV) (km s−1)

3.69053 0.35 8.82e−5 Ca Kα

(3.68963–3.69273) (0.00–3.84) (5.73–11.87)

2.62213 4.04 1.77e−4 S XVI Lyα

(2.62094–2.62327) (2.81–5.53) (1.44–2.09)

2.46197 0.64 6.84e−5 S XV r

(2.46110–2.46273) (0.00–1.71) (5.18–8.66)

2.31112 0.20 1.03e−4 S Kα

(2.31070–2.31184) (0.00–2.12) (8.32–12.5)

2.00634 1.16 2.38e−4 Si XIV Lyα +127

(2.00618–2.00650) (0.89–1.42) (2.23–2.52) (2.00549) (+103–+151)

1.86614 1.38 1.36e−4 Si XIII r +183

(1.86592–1.86636) (1.09–1.67) (1.25–1.48) (1.86500) (+148–+219)

1.85537 0.82 3.05e−5 Si XIII i +257

(1.85483–1.85592) (0.00–1.77) (2.39–3.77) (1.85378) (+170–+346)

1.84136 2.15 1.41e−4 Si XIII f +311

(1.84109–1.84162) (1.86–2.47) (1.29–1.53) (1.83945) (+267–+353)

1.74447 2.35 1.46e−4 Si Kα

(1.74421–1.74473) (2.07–2.67) (1.36–1.58)

1.72998 0.44 3.36e−5 Al XIII Lyα?

(1.72962–1.73033) (0.00–1.10) (2.78–3.99)

1.59900 0.66 1.31e−5 Al XII r ?

(1.59832–1.59967) (0.00–1.68) (0.86–1.87)

1.57976 2.01 3.90e−5 Mg XI

(1.57920–1.58032) (1.38–2.64) (3.18–4.64)

1.55231 0.58 1.78e−5 Fe XXIV ?

(1.55175–1.55284) (0.00–1.42) (1.27–2.35)

1.47282 1.18 2.35e−4 Mg XII Lyα +102

(1.47268–1.47296) (1.02–1.35) (2.17–2.53) (1.47232) (+73–+130)

1.35279 1.00 1.47e−4 Mg XI r +120

(1.35263–1.35296) (0.81–1.20) (1.32–1.62) (1.35225) (+84–+157)

1.34346 0.69 7.34e−5 Mg XI i +80

(1.34324–1.34367) (0.36–1.02) (6.25–8.53) (1.34310) (+31–+127)

41

Table 4.3—Continued



1.33213 0.95 9.13e−5 Mg XI f +230

(1.33190–1.33236) (0.65–1.25) (7.89–10.5) (1.33111) (+178–281)

1.30808 1.06 4.99e−5 Fe XXI ?

(1.30766–1.30843) (0.61–1.49) (3.96–6.12)

1.27783 1.10 8.44e−5 Ne X Lyγ

(1.27756–1.27811) (0.78–1.38) (7.18–9.84)

1.21160 0.94 1.33e−4 Ne X Lyβ

(1.21139–1.21181) (0.72–1.17) (1.15–1.52)

1.12732 1.54 7.41e−5 Ne IX

(1.12683–1.12780) (1.13–2.03) (5.71–9.27)

1.07432 0.12 5.76e−5 Ne IX

(1.07397–1.07450) (0.00–0.73) (4.07–7.74)

1.02242 0.64 4.42e−4 Ne X Lyα +182

(1.02230–1.02253) (0.52–0.76) (3.91–4.97) (1.02180) (+147–+214)

0.922458 0.80 2.89e−4 Ne IX r +149

(0.922186–0.922725) (0.52–1.11) (2.24–3.64) (0.922001) (+60–+235)

0.916254 1.44 4.91e−4 Ne IX i +475

(0.915937–0.916584) (1.21–1.73) (4.03–5.89) (0.914803) (+371–+583)

0.905561 1.78 3.71e−4 Ne IX f +165

(0.905013–0.906071) (1.38–2.27) (2.88–4.65) (0.905062) (−16–+334)

aInter stellar gas absorption is corrected. The hydrogen column density of

6 × 1021 cm−2 is assumed, corresponding to the density of 1 H cm−3 and the distance

of 1.9 kpc.

Note. — Errors correspond to 90 % confidence level.

42

Table 4.4. Derived Parameters of emission lines in the 0.0 orbital phase spectrum



3.69431 8.59 9.27e−6 Ca Kα

(3.69006–3.69836) (5.35–12.9) (6.57–12.3)

2.95657 0.00 4.92e−6 Ar Kα

(2.95507–2.95849) (0.00–3.35) (2.97–7.27)

2.61857 0.57 1.38e−5 S XVI Lyα

(2.61781–2.61947) (0.04–2.62) (1.08–1.73)

2.31035 2.19 1.76e−5 S Kα

(2.30935–2.31138) (0.87–3.50) (1.35–2.23)

2.00339 1.70 2.32e−5 Si XIV Lyα −314

(2.00305–2.00373) (1.28–2.14) (2.07–2.59) (2.00549) (−365–−263)

1.86299 1.58 2.34e−5 Si XIII r −323

(1.86267–1.86330) (1.25–1.94) (2.08–2.62) (1.86500) (−375–−273)

1.85271 0.00 2.76e−6 Si XIII i −173

(1.85254–1.85357) (0.00–1.12) (1.67–4.05) (1.85378) (−201–−34)

1.83924 2.92 2.11e−5 Si XIII f −34

(1.83878–1.83969) (2.48–3.43) (1.88–2.36) (1.83945) (−109–+39)

1.74247 1.67 1.96e−5 Si Kα

(1.74217–1.74276) (1.39–1.99) (1.74–2.20)

1.65752 0.12 2.84e−6 Mg XI or

(1.65697–1.65855) (0.00–1.53) (1.86–4.00) Fe XXIII

1.57719 1.34 6.02e−6 Mg XI

(1.57659–1.57776) (0.68–2.05) (4.59–7.64)

1.47068 1.23 2.63e−5 Mg XII Lyα −334

(1.47044–1.47093) (0.99–1.50) (2.29–2.99) (1.47232) (−383–−283)

1.35057 1.54 2.58e−5 Mg XI r −373

(1.35026–1.35088) (1.21–1.90) (2.23–2.97) (1.35225) (−442–−304)

1.34238 1.18 6.33e−6 Mg XI i −161

(1.34170–1.34307) (0.39–2.04) (4.33–8.65) (1.34310) (−313–−7)

1.33122 2.27 2.03e−5 Mg XI f +25

(1.33072–1.33171) (1.87–2.77) (1.70–2.40) (1.33111) (−89–+135)

1.30640 1.26 6.61e−6 Fe XXI ?

(1.30574–1.30701) (0.71–1.97) (4.56–9.05)

43




1.27592 0.89 8.70e−6 Ne X Lyγ

(1.27547–1.27636) (0.00–1.44) (5.62–11.4)

1.23618 1.57 5.94e−6 Fe XX ?

(1.23507–1.23727) (0.71–2.79) (3.13–8.95)

1.20980 1.34 1.43e−5 Ne X Lyβ

(1.20930–1.21033) (0.96–1.82) (1.07–1.84)

1.07241 0.78 1.91e−5 Ne IX

(1.07205–1.07276) (0.44–1.19) (1.38–2.54)

1.02075 0.99 8.54e−5 Ne X Lyα −308

(1.02056–1.02095) (0.81–1.18) (7.25–9.98) (1.02180) (−364–−249)

0.920773 0.92 5.48e−5 Ne IX r −400

(0.920390–0.921159) (0.60–1.30) (3.86–7.43) (0.922001) (−524–−274)

0.914926 1.05 4.68e−5 Ne IX i +40

(0.914407–0.915448) (0.75–1.53) (3.03–6.70) (0.914803) (−130–+211)

0.904058 0.75 8.98e−5 Ne IX f −333

(0.903784–0.904342) (0.48–1.10) (6.75–11.6) (0.905062) (−424–−239)

aInter stellar gas absorption is corrected. The hydrogen column density of

6 × 1021 cm−2 is assumed, corresponding to the density of 1 H cm−3 and the distance

of 1.9 kpc.


4.5 Pulse Phase Dependence

Figure 4.13 shows the pulse profiles at the orbital phase 0.25 and phase 0.50 obtained by

folding the light curve of the 1–10 keV events from HEG ± 1 order. The pulse periods

are 283.2 s and 283.5 s for phase 0.25 and phase 0.50, respectively. The pulse phase of

0.0 employed the barycentric start time of each observation. The observed pulse profiles

are consistent with those reported in past observations; e.g. McClintock et al. (1976);

Sato et al. (1986a); Kreykenbohm et al. (1999).

In order to examine the pulse phase dependence of the X-ray spectra, we extract two

spectra by dividing each dataset into two pulse phases (“peak” and “bottom”). These two

pulse phases are defined in Figure 4.13. Figure 4.14 shows the spectra of peak and bottom

44

Figure 4.9: The line profiles of Si H-like Lyα (left) and Mg H-like Lyα. The

blue lines show the observed data in phase 0.5, and the red lines show the

data in eclipse. The HEG data is used for the Si Lyα lines, and the MEG

data is used for the Mg Lyα lines.

Figure 4.10: The plot of velocity shift for emission lines from highly ionized

ions. Closed circles show the data from phase 0.50, and open circles show the

data from eclipse.

45

Table 4.5. Comparison between lines of the phase 0.50 and of the eclipse.

line Intensity(0.50)/Intensity(eclipse) ∆v (km s−1)

Si XIV Lyα 10.3 ± 1.3 441 ± 56

Si XIII resonance 5.81 ± 0.83 506 ± 62

Si XIII forbidden 6.68 ± 0.95 345 ± 86

Mg XII Lyα 8.94 ± 1.37 436 ± 58

Mg XI resonance 5.70 ± 1.00 493 ± 78

Mg XI forbidden 4.50 ± 1.01 205 ± 123

Ne X Lyα 5.18 ± 1.04 490 ± 60

Ne IX resonance 5.27 ± 2.14 549 ± 153

Ne IX forbidden 4.13 ± 1.49 498 ± 198

Figure 4.11: The spectra of radiative recombination continua from H-like Ne

in phase 0.50 (left) and in eclipse (right). The best-fit models based on the

“redge” model in XSPEC are shown in lines. The electron temperature is

derived to be 7.4 eV and 6.6 eV, respectively.

46

Table 4.6. Derived Parameters of the Fe Kα line.

Orbital Phase Center Energy Sigma Intensity EW

(keV) (eV) (photon cm−2 s−1) (eV)

0.00 6.3958 (6.3936–6.3980) 7.2 (1.9–11.1) 1.70e−4 (1.50–1.90) 844

0.25 6.3992 (6.3987–6.4010) 0.0 (0.0–7.4) 1.92e−3 (1.78–2.07) 51

0.50 6.3965 (6.3953–6.3976) 11.0 (9.1–12.8) 3.40e−3 (3.21–3.58) 116

Note. — Only HEG data is used. The fitting model is single gaussian.


Figure 4.12: The blow-up spectra of the iron Kα lines in eclipse (left), in phase

0.25 (middle), and in phase 0.50 (right).

47

Figure 4.13: Pulse profiles of Vela X-1 at orbital phase 0.25 (top panel) and

0.50 (bottom panel), obtained by folding the light curves at the barycentric

periods of 283.2 s and 283.5 s, respectively. Two phase cycles are shown for

clarity. The HEG ± 1 order events are used, and the energy band is 1–10 keV.

The pulse phase of 0.0 corresponds to the start time of each observation.

for each orbital phase, and Table 4.7 lists the observed fluxes and the corresponding iron

Kα intensities.

Although the observed overall flux changes between the peak and the bottom by a

factor of 1.3, the iron Kα line flux does not change within statistical uncertainty. Addi-

tionally, the 1.0–2.1 keV count rate in orbital phase 0.50, dominated by Ne, Mg and Si

emission lines, is constant between the peak and the bottom; specifically, 0.15 ± 0.01 c s−1

and 0.14 ± 0.01 c s−1 for the peak and the bottom, respectively.

Table 4.7. Total and iron Kα fluxes of the pulse phase divided spectra

orbital Flux (1.0–10.0 keV)(erg s−1) Fe Kα flux (photon cm−2 s−1)

phase peak bottom peak bottom

phase 0.25 (3.3 ± 0.1) × 10−9 (2.5 ± 0.1) × 10−9 (1.8 ± 0.2) × 10−3 (2.1 ± 0.2) × 10−3

phase 0.50 (2.0 ± 0.1) × 10−9 (1.5 ± 0.1) × 10−9 (3.3 ± 0.3) × 10−3 (3.5 ± 0.4) × 10−3

48

Figure 4.14: X-ray spectra divided by the pulse phase. The left panel shows

spectra at orbital phase 0.25, and the right panel at orbital phase 0.50. Ma-

genta and cyan spectra refer to the pulse peak and pulse bottom, respectively,

as defined in Figure 4.13.

4.6 Summary of the Observation and the Implication

From the continuum spectral shapes, the direct radiation from the neutron star are the

same between phase 0.50 and phase 0.25 after correction for absorption. Considering the

geometric relationship, this absorber is located behind the neutron star as viewed from

the companion star. Due to this absorption, the emission lines in the low energy range

can be observed in phase 0.50.

The intensity ratios of emission lines in phase 0.50 to that in eclipse are 8–10 for lines

from H-like ions and 4–7 for lines from He-like ions. These ratios indicate that the region

emitting these line X-rays is mostly located between the neutron star and the companion

star, which is occulted during eclipse.

The information of the Doppler effects also confine the line emission region. The

energy shifted emission lines are detected and the shift direction in the eclipse is opposite

to that in phase 0.5. The Doppler broadenings of emission lines from highly ionized ions

are less than 300 km s−1. These observational results shows that the emission site of

lines from highly ionized ions is distributed on a plane between the neutron star and the

companion star.

Narrow radiative recombination continua from H-like ions of Ne are detected in phase

0.5 and in eclipse. Electron temperatures of 6–8 eV are derived from the spectral fits. It

is a direct evidence that the emission lines from highly ionized gas in Vela X-1 are driven

through photoionization, not collisional origin.

49

Chapter 5

Observations and Results of

GX 301−2

5.1 GX 301−2

GX 301−2 is a high mass X-ray binary consisting of a neutron star and a B2 Iae Com-

panion star, WRA 977. The neutron star moves in a highly eccentric orbit (e = 0.46;

Sato et al. 1986b; Koh et al. 1997) with an orbital period of ∼ 41 days. The X-ray light

curve is known to lack a signature of eclipse. X-ray pulsations with a period of ∼ 700 s

were discovered by White et al. (1976).

The mass loss rate of WRA 977 is estimated to be in the range (3–10) × 10−6 M¯ yr−1

from optical spectroscopic observations (Parkes et al. 1980). The stellar wind velocity

of WRA 977 measured by Parkes et al. (1980) is ∼ 300 km s−1 at a distance of 3 Rc,

where Rc is the radius of the companion star. This result suggests a terminal velocity

400 km s−1.

The X-ray luminosity varies in the range (2–200) × 1035 erg s−1. It is known that an

X-ray flare always appears at an orbital phase ∼ 1.4 days before the periastron passage

of the neutron star (Sato et al. 1986b). In the flare, the X-ray luminosity, absorbing

column density, and the iron line equivalent width reach the highest level among in the

entire orbit (Endo et al. 2002). In addition, BATSE observations reported the presence

of secondary X-ray flares near the apastron passage (Pravdo et al. 1995; Koh et al. 1997).

5.2 Observation and Data Reduction

Chandra observed GX 301−2 at three different orbital phases: (1) φ = 0.167–0.179, (2)

φ = 0.480–0.497, and (3) φ = 0.970–0.982, hereafter referred to as intermediate (IM), near-

apastron (NA), and pre-periastron (PP) phases, respectively. NA and PP correspond to

the X-ray flare phases mentioned previously. The observation dates and exposure times

are summarized in Table 5.1.

50

IM

NA

PP

Neutron Star

WRA 977

Figure 5.1: The location between the neutron star and the companion star in

GX 301−2. The bold lines show the observed orbital phases.

Table 5.1. Summary of GX 301−2 Observations

Label OBSID Start Date Orbital Phase Exposure (sec)

IM 103 2000-06-19 13:57:26 0.167 – 0.179 39516

NA 3433 2002-02-03 12:34:10 0.480 – 0.497 59033

PP 2733 2002-01-13 09:00:24 0.970 – 0.982 39233

All of the data are processed using CIAO v2.2.1, and spectral fittings were performed

using XSPEC. As in the case of Vela X-1, the zeroth order images are severely piled-up,

especially during the NA and PP. Therefore, the locations of the zeroth order image are

determined by finding the intersection of the streak events and the dispersed events. We

apply a spatial filter for both the MEG and the HEG, and then use an order sorting mask

by using the photon energy information obtained with ACIS. In our analysis, only the

first order events are used for extracting spectra. The background events are estimated

from the adjacent region events to the dispersed event region. The background level is

less than 5% for all three phase observations.

The light curves in the three orbital phases extracted from the HEG 1–10 keV events

are shown in Figure 5.2. By applying the epoch holding method, we confirmed the

presence of pulsations with periods of 683.2 s, 680.8 s and 681.2 s in the light curves of

IM, NA and PP phase, respectively.

51

Figure 5.2: The light curves of GX 301−2 in IM (top), in NA (middle) and

in PP (bottom). Pulsations are found with the epoch holding method. The

periods are determined to be 683.2 s, 680.8 s and 681.2 s for IM, NA and PP,

respectively.

52

Figure 5.3: The spectra of GX 301−2 obtained with HEG. The red, the blue

and the green plots show the spectra in PP phase, NA phase and IM phase,

respectively.

5.3 Continuum Emission

In order to constrain the continuum emission, we extract energy spectra from 4 keV to

10 keV for three orbital phases. The HEG spectra above 4 keV are shown in Figure 5.3.

We fit the spectra by a photo-absorbed power-law model, in which the metal abundance

of the absorption material is assumed to be 0.75 times the cosmic chemical abundance

(Feldman 1992), as we do in the case of Vela X-1. The energy region, 6.3–6.5 keV,

is excluded in the fit because of the strong iron Kα emission. First, we fit the NA

spectrum. In this fit, both the hydrogen column density and the photon index are left

as free parameters. From this analysis, we obtain the photon index of 0.98–1.12 for

the NA spectrum. In the following analysis, the photon index is fixed to 1.0 assuming

that there is no change in it. By fitting all three spectra with the fixed photo index

of 1.0, the hydrogen column densities are derived. The derived parameters are listed

on Table 5.2, and the best-fit models for each phase data are also shown in Figure 5.3.

Heavy absorptions (2–10 × 1023 cm−2) are observed in all three phases. Assuming a

distance of 1.8 kpc (Parkes et al. 1980), the absorption-corrected X-ray luminosities in

the 0.5–10 keV band are 3.8 × 1035 erg s−1, 1.4 × 1036 erg s−1 and 2.7 × 1036 erg s−1 for

the IM, NA and PP phases, respectively.

53

Table 5.2. Derived Parameters from spectral fits of the GX 301−2 continuum

Orbital NHa Photon Index Observed Flux Luminosityb χ2/ d.o.f.

Phase (1023 cm−2) (erg cm−2 s−1) (erg s−1)

NA 3.05 ± 0.11 1.05 ± 0.07 1.1 × 10−9 1.3 × 1036 655./ 743

IM 6.51 ± 0.24 1.0 (fixed) 2.4 × 10−10 3.8 × 1035 220./ 302

NA 2.97 ± 0.05 1.0 (fixed) 1.2 × 10−9 1.4 × 1036 657./ 744

PP 10.3 ± 0.2 1.0 (fixed) 1.0 × 10−9 2.7 × 1036 903./ 515

Note. — Fitting regions are 4.0–10.0 keV. Only HEG data is used. The iron

K-line region (6.3–6.5 keV) is excluded. Errors are corresponding 90 % confidence

levels.aThe metal abundance is 0.75 cosmic.

b0.5–10.0 keV luminosity. The absorption is corrected.

5.4 Emission Lines

Figure 5.4 shows the low energy regions of the spectra of the three orbital phases. Flu-

orescence emission lines from Si, S, Ar, Ca ions in low charge states are detected in all

orbital phases. As shown in Figure 5.3, intense iron Kα and Kβ lines are observed in

each spectrum. In the PP phase data, fluorescent lines from Cr and Ni are also seen. We

fit these lines with a single gaussian model. For lines from Si, S, Ar, Ca and Cr, both

the HEG and the MEG data are used. For other lines above 6.0 keV, only HEG data

are applied to spectral fits because MEG does not have sufficient efficiency. The derived

parameters are listed in Table 5.3. In contrast to the detection of these fluorescent lines,

emission lines from highly ionized ions are entirely absent in the spectra of the three

phases.

The blown-up spectra of the iron Kα region in the three orbital phases are shown

in Figure 5.5. A “shoulder” component in low energy side of the iron Kα line is clearly

detected and fully resolved. The shoulder extends down to ∼ 6.24 keV and its width

is ∼ 160 eV. This value precisely matches what is predicted in § 2.3.5, which strongly

indicates that the feature is formed primarily through single Compton scattering of the

iron Kα photons.

54

Figure 5.4: The low energy part of spectra in NA (top), in IM (middle) and

in PP (bottom). The red lines show MEG data and the blue lines show HEG

data. The fluorescence lines from Si, S, Ar and Ca are observed.

55

Table 5.3. Derived Parameters of emission lines in the GX 301−2 spectra of the three

phases.

Orbital phase line Energy Sigma Intensityb

(keV) (eV) (photon cm−2 s−1)

IM Si Kα 1.74136 0.01 5.74e−6

(1.74104–1.74197) (0.00–1.05) (4.18–7.62)

IM S Kα 2.30917 3.14 2.03e−5

(2.30773–2.31057) (0.64–4.90) (1.47–2.71)

IM Ar Kα 2.95837 4.56 8.75e−6

(2.95438–2.96157) (4.56–8.88) (5.02–13.1)

IM Ca Kα 3.69217 0.00 1.58e−5

(3.69012–3.69239) (0.00–4.62) (1.10–2.13)

IM Fe Kαa 6.39483 11.8 8.91e−4

(6.39325–6.39641) (9.39–14.2) (8.33–9.52)

IM Fe Kβ 7.05415 28.2 2.68e−4

(7.02218–7.06881) (12.7–69.2) (1.53–3.72)

NA Si Kα 1.74242 1.35 1.34e−5

(1.74207–1.74277) (0.95–1.76) (1.13–1.56)

NA S Kα 2.31014 4.49 3.33e−5

(2.30873–2.31158) (3.12–6.11) (2.64–4.10)

NA Ar Kα 2.95907 6.01 3.39e−5

(2.95582–2.96223) (3.42–10.2) (2.38–4.53)

NA Ca Kα 3.69164 1.86 3.88e−5

(3.68809–3.69434) (0.00–7.57) (2.52–5.34)

NA Fe Kαa 6.39574 13.2 3.43e−3

(6.39500–6.39649) (12.2–14.2) (3.33–3.54)

NA Fe Kβ 7.06731 15.9 4.77e−4

(7.06032–7.07438) (6.04–24.9) (3.63–6.01)

PP Si Kα 1.74350 0.42 6.64e−6

(1.74298–1.74396) (0.00–1.31) (4.96–8.65)

PP S Kα 2.31211 2.59 2.77e−5

(2.31106–2.31315) (1.68–3.77) (2.11–3.56)

PP Ar Kα 2.95942 4.60 2.49e−5

(2.95765–2.96115) (2.83–6.48) (1.95–3.11)

PP Ca Kα 3.69166 2.93 5.92e−5

(3.69051–3.69283) (1.67–4.94) (5.06–6.87)

56


Orbital phase line Energy Sigma Intensityb

(keV) (eV) (photon cm−2 s−1)

PP Cr Kα 5.41140 0.00 7.53e−5

(5.40826–5.41166) (0.00–5.98) (4.99–10.2)

PP Fe Kαa 6.39469 13.2 8.12e−3

(6.39421–6.39516) (12.5–13.9) (7.94–8.31)

PP Fe Kβ 7.05755 13.8 1.54e−3

(7.05476–7.06035) (9.85–17.5) (1.37–1.69)

PP Ni Kα 7.45984 0.00 5.07e−4

(7.45682–7.46916) (0.00–15.5) (3.73–6.40)

aThe Compton shoulder region (6.24–6.34 keV) is excluded.

bInter stellar gas absorption is corrected. The hydrogen column density of

6 × 1021 cm−2 is assumed, corresponding to the density of 1 H cm−3 and a

distance of 1.8 kpc.

Note. — Errors correspond to 90 % confidence levels.

5.5 Pulse Phase Dependence

Figure 5.6 shows the pulse profiles obtained by folding the light curve of the 1–10 keV

events from HEG ± 1 order. The barycentric pulse periods are 683.2 s, 680.8 s and 681.2 s

for IM, NA and PP, respectively, which are obtained from the epoch holding method.

The pulse phase of 0.0 corresponds to the start time of each orbital phase observation.

As seen from Figure 5.6, the pulse profiles of GX 301−2 have a double-peak structure,

as has already been reported previously (e.g. Orlandini et al. 2000; Endo et al. 2002).

In order to examine the pulse phase dependence, we extract two spectra by dividing

into two pulse phases. One is the pulse phase with the larger peak (“peak(1)”), and the

other is the pulse phase with the smaller peak (“peak(2)”). The peak(1) and the peak(2)

of each orbital phase are defined in Figure 5.6. Figure 5.7 shows the spectra of peak(1)

and peak(2) for each orbital phase, and Table 5.4 lists the observed fluxes and the iron

Kα intensities. Although the observed flux changes between peak(1) and peak(2), there

is no significant change of the intensity of the iron Kα line within statistical uncertainty.

57

Figure 5.5: The blown-up spectra of the iron Kα lines in the PP (bottom),

the IM (middle) and the NA (top). A shoulder component extending toward

the low-energy side of the line is clearly seen and fully resolved. The width of

the shoulder (∆E ∼ 160 eV: 6.24–6.40 keV) matches the energy distribution

of iron Kα photons that suffer single Compton scattering. The line shows the

best-fit model in the spectral fits of the continuum.

58

Figure 5.6: Pulse profiles of GX 301−2 in IM (top panel), NA (middle) and

PP (bottom) by folding the light curves at the periods of 683.2 s, 680.8 s and

681.2 s, respectively. Two phase cycles are shown for clarity. The HEG ± 1

order events are used, and the energy band is 1–10 keV. The pulse phase of

0.0 corresponds to the start time of each observation.

Table 5.4. Total and iron Kα fluxes of pulse phase divided spectra

orbital Flux (2.0–10.0 keV)(erg s−1) Fe Kα flux (photon cm−2 s−1)

phase peak(1) peak(2) peak(1) peak(2)

IM (2.5 ± 0.1) × 10−10 (1.8 ± 0.1) × 10−10 (8.8 ± 1.1) × 10−4 (6.9 ± 0.8) × 10−4

NA (1.5 ± 0.2) × 10−9 (1.1 ± 0.1) × 10−9 (3.3 ± 0.2) × 10−3 (3.2 ± 0.2) × 10−3

PP (1.2 ± 0.1) × 10−9 (8.9 ± 0.2) × 10−10 (7.8 ± 0.4) × 10−3 (7.7 ± 0.4) × 10−3

59

Figure 5.7: X-ray spectra divided by pulse phase. The magenta spectra are

obtained from the events in peak(1), whose count rates are relatively high (see

Figure 5.6). The cyan spectra are extracted from the events in peak(2).

60

Chapter 6

Simulation of Photoionized Plasma

in HMXB

6.1 Modeling of Photoionized Plasmas

The unprecedented spectral resolution of the grating system onboard the Chandra satel-

lite gives us a wealth of information about X-ray emission lines from HMXBs, Vela X-1

and GX 301−2. As already shown in previous chapters, we have succeeded in detecting

lines from highly ionized ions, such as H-like and He-like Si, S, Mg, from photoionized

plasma, together with clear signals from radiative recombination continua in Vela X-1.

As expected from the dynamical motion of the gas in the stellar wind, opposite shifts of

the central energy appear to exist in phase 0.50 and eclipse for Vela X-1. On the other

hand, GX 301−2 shows only fluorescent lines from low charge states. From the detail

analysis of the line profiles of the iron fluorescence line, we discovered a shoulder-like

structure which could be accounted by the effect of Compton scattering.

The emission lines we detected from Vela X-1 and GX 301−2 can be interpreted

as due to emission from a gas photoionized by the X-ray radiation from the neutron

star. In this case, the spectrum emerged from the binary system is the result of the

propagation of X-rays through the gas. Line emission, presumably due to processes,

such as photoionization, recombination and fluorescence, are controlled by the ionization

structure and the density distribution of the gas in the stellar wind. Therefore, by

investigating characteristics of lines, we will be able to obtain an important clue to

addressing the questions about how the photoionized plasma is distributed spatially in

the stellar wind and how the distributions can affect the nature of the X-ray emission

observed in HMXBs.

In previous studies of photoionization plasmas, modeling were performed based on

very simple assumptions. Kallman & McCray (1982) presented theoretical models to

calculate the ion abundances and the temperature for the given X-ray spectrum and the

wind density. Since the introduction of their model as a computer code (called XSTAR

61

1), it has been frequently used to characterize X-ray spectra from HMXBs. However,

most of the analysis are based on very simple assumptions such as symmetric geometry

and constant density distribution in the volume.

In order to find the ionization structure from the HETGS results, it is necessary to

model the emission from more realistic environments in the stellar wind. Therefore, we

have developed a new code to simulate X-ray interactions in the stellar wind. Most

important ingredients in the code is that fully three dimensional treatment is adopted for

both the ionization structure and the photon transportation in the plasma. For the case

that the optically thin approximations are allowed, the condition of photoionized plasma

can be characterized only by the ionization parameter ξ. However, the Chandra results

indeed imply that the emission lines with high ionization degree actually come from a

dense region (particle density n > 109 cm−3). In this situation, we have to consider not

only the ξs, but also the effect of absorption by the matter between the neutron star and

the emission site, because, the incident flux is absorbed by the material and changes the

shape and the flux.

Another important issue to be stressed is that we now see the effect of the Doppler

shift due to the emission from the material moving with fast velocity. The information

on the Doppler shift could also constrain the velocity field of the X-ray emitting region

in the stellar wind. The model to be used for the re-construction of physical environment

in the stellar wind has to deal with these kinematical effects.

Our simulation code consists of two parts:

(1) Calculation of the ionization structure,

(2) Monte Carlo simulation for tracking X-ray photon transportation.

In part (1), we construct the map of the ion abundance in the stellar wind. In part (2), we

have implemented the physical process which are related to highly ionized gas, together

with the Lorentz transformation for the calculation of Doppler effects. The simulation is

held in three dimensional space divided into grids such that we can handle more complex

geometries. Our procedure of each of these parts is described in the following sections.

6.2 Calculation of the Distribution of Ionization De-

gree

An ionization balance and an electron temperature are dictated by the flux and spectral

shape of injected X-rays and the density of the region. Figure 6.1 shows a schematic of

the calculation of the ionization structure. The intrinsic luminosity and spectrum shape

of the X-ray source are deduced from the observation. The density structure around the

1http://heasarc.gsfc.nasa.gov/docs/software/xstar/xstar.html

62

Region1 Region2 Region3 RegionN

Neutron Star

abund[0]1

abund[1]1

:

abund[139]1

abund[0]2

abund[1]2

:

abund[139]2

abund[0]3

abund[1]3

:

abund[139]3

abund[0]N

abund[1]N

:

abund[139]N

ni : particle density of region i

abund[0]-abund[139] : ion abundance of

H I, He I-II, C I-VI, N I-VII, O I-VIII,

Ne I-X, Mg I-XII, Si I-XIV, S I-XVI,

Ar I-XVIII, Ca I-XX, Fe I-XXVI

n1 n2 n3 nN

Calculation Sequence

X-ray spectrum

E

Ph

oto

n

E

Ph

oto

n

E

Ph

oto

n

E

Ph

oto

n

Figure 6.1: The schematic of the software for calculations of ionization structures

companion star is given from the velocity profile determined from the UV obserservation

as mentioned in § 2.3.1. Since an X-ray flux and spectrum shape injected into the

region are derived from the distance and the ions’ column densities in between the X-ray

source, the central neutron star, and the region, we can obtain the ionization structure

by calculating the ionization balance starting from the grid closest to the neutron star to

the most distant grid, sequentially. In order to calculate the ionization abundance and

the electron temperatures for the given X-ray spectrum (and the flux) and the density

as inputs, we use the XSTAR program.

6.3 Monte Carlo Calculation of the X-ray Emission

from Photoionization Equilibrium State

The map of the ionization abundance (ionization structure) calculated by following the

prescription given in the previous section assures equilibrium between photoionization

63

Geometrydivided into small cubes

Parameters:

Density

Wind Velocity and Direction

Metal Abundance (Z>2)

Electron Temperature

Ion Abundance

(H,He,C,N,O,Ne,Mg,Si,S,Ar,Ca,Fe)

Physical ProcessesPhotoionization(nelectron > 2) -> Fluorescence

Photoionization(H-,He-like) -> Recombination

Photoexcitation(H-,He-like) -> Radiative Transition

Compton Scattering

(with Doppler effect due to Stellar Wind)

Data Pick-up and Savefor escaped photons

energy, momentum direction,

generating postion, incident energy

Incident Generatorenergy distribution

(e.g. power-law)

Monte Carlo

Managers

Monte Carlo Simulator

Simulated Spectrum

calculation ofstellar windconditions

assumption ofphotoionizationequilibrium

observationresults

data

data

data

data

Figure 6.2: The schematic of our Monte Carlo simulation.

and recombination. Therefore, an X-ray spectrum emitted from the given ionization

structure can be obtained through the transportation of X-ray photons by Monte Carlo

methods.

We start the Monte Carlo simulation with a photon at the position of the central neu-

tron star (X-ray source). The incident photons to the region are generated in accordance

with the energy distribution like a power-law, which is provided from the observation

results. The X-ray photon interacts with the stellar wind that includes highly ionized gas

and generates secondary photons through radiative recombination, radiative transitions,

fluorescent emission, and so on. In the simulation code, the incident and all other photons

produced by interactions are tracked until they either completely escape the simulation

space or are destroyed by some physical processes. The emergent photons are then se-

lected under some conditions which depend on the analysis, and the energy distribution

of the selected photons are histogrammed to produce a spectrum.

64

6.3.1 Physical processes

As for physical processes for X-ray photons, we account for photoionization, photoexcita-

tion and Compton scattering. In the newly developed code, we have implemented these

processes. We only deal with photons in the code. Although processes mentioned above

generate electrons with some amount of energies, we do not trace these secondary elec-

trons, because we are interested in only X-ray photons, and the probability of secondary

electrons further emitting X-ray photons by bremsstrahlung is small.

As mentioned earlier, our code to deal with physical processes are constructed on

the premise that photoionization equilibrium is established locally everywhere in the

plasma. Therefore, if photoionization takes place in the Monte Carlo simulation, radiative

recombination and radiative transitions to the ground level always follow, or, fluorescent

emissions are induced at the same place, and then, X-ray photons with appropriate

energies are generated. In this way, the recombination rate equals the photoionization

rate locally. In the case of photoexcitation, the ion in an excited state produces an X-

ray photon by one or more transitions that eventually lead to the ground level. Various

emission lines arise as results of such photoionization and photoexcitation.

For the physical processes related to H-like and He-like ions, photoionization followed

by radiative recombination and radiative transitions, and photoexcitation are taken into

account. The cross sections of photoionization and emission line probabilities from recom-

bination cascades are needed for photoionization codes. Additionally, transition energies,

oscillator strength, radiative decay rate and line emission probabilities for each excited

level to the ground level are required for the Monte Carlo codes of photoexcitation. We

look up a table generated with the Flexible Atomic Code (FAC) 2. The table is used

in our code to handle physical proceses. Collisional transfers and UV photoexcitations

in the He-like ions are not included in the current version of the code. Results from

simple Monte Carlo simulations for H-like and He-like Si ions are shown in Figure 6.3

and Figure 6.4.

In our Monte Carlo codes, photoionization by ions with three or more electrons de-

excites by fluorescent emission or ejection of Auger electrons. The K-shell cross sections

of this type photoionization are applied to the fitting formulae provided by Band et al.

(1990), which include changes of K-edge energy and cross section for ions in each charge

state. Subsequent K fluorescent emissions are induced according to the K fluorescent

yields. However, in K fluorescent emission processes, the effects of ion charge states are

not included, and, X-ray energies (Larkins 1977) and fluorescent yields (Salem, Panossian

& Krause 1974; Krause 1979) for neutral atoms are applied to ions in all charge state.

Therefore, we do not take into account K-shell ionization of Li-like ions, which can lead

to the production of the forbidden line in He-like ions. For the L-shell cross sections,

we utilized EPDL97 3, which is also for neutral atoms. The L1, L2 and L3-shell cross

2http://kipac-tree.stanford.edu/fac/3http://www.llnl.gov/cullen1/photon.htm, and distributed with Geant4 low energy electromagnetic

65

Figure 6.3: A result of a Monte Carlo simulation. Emission lines from a cloud

made of only H-like ions of Si are shown. The column density of H-like Si

is 1016 cm−2. The electron temperatures are 2 eV, 5 eV, 10 eV and 20 eV

from the top to the bottom. The widths of RRCs change as a function of the

electron temperatures.

66

Figure 6.4: A result of a Monte Carlo simulation. Emission lines from a cloud

made of only He-like ions of Si are shown. The electron temperature is 5 eV.

The column densities of He-like Si are 1014 cm−2, 1015 cm−2, 1016 cm−2 and

1017 cm−2 from the top to the bottom. The amount of emission is increased

as a function of the column densities. The ratios of He-like triplet lines also

change with to the column density.

67

sections are taken into account for the ions with three, five, and six electrons, respectively.

Additionally, we do not include L fluorescent emissions for any ions.

For Compton scattering, we considered only scattering by unbound electrons. The

differential cross section given by the the Klein-Nishina formula (eq. 2.16) and the total

cross section shown in eq. 2.17 are taken into account. The Compton Doppler effects due

to an electron velocity according to Maxwellian energy distribution with a temperature

are calculated in our code.

We took Doppler shifts due to stellar winds into account for all of the physical pro-

cesses. When a photon comes into a region, we calculate cross sections of all physical

processes from the photon energy in the co-moving frame with the stellar wind. Then,

if a physical process is selected and any secondary photons are generated, energies and

directions of the photons are converted to the rest frame. An example result of a simple

Monte Carlo simulation for the Doppler shift is shown in Figure 6.5.

package

68

500 km/s

Si Cloud(H-like 50%,

He-like 50% )

(1)

(2)

(3)

Figure 6.5: A example result of a Monte Carlo simulation for the Doppler

shift. Emission lines from a moving Si cloud consisting of 50% H-like ions and

50% He-like ions are shown. The velocity of the cloud is 500 km s−1. The

shift of line energy change as a faction of the direction to the line of sight.

69

Chapter 7

Discussion on Vela X-1

7.1 Ionization Structure of the Stellar Wind in Vela

X-1 System

One of most important features of the Vela X-1 observations with Chandra is the precise

measurement of line intensities with a high resolution instrument, HETGS. The intensities

of strong lines such as the H-like Lyαs and the He-like triplets from three different location

in the orbit provide us an important clue to study the physical condition and the spatial

structure of the stellar wind near the neutron star, because the intensities of the observed

lines are actually determined from the ionization structure, e.g. the distribution of ion

abundance and the ion density in the wind. First, we try to find the distributions that

could account for the observed line emissions, both the absolute intensities and the ratios

of the intensities at different phase.

As already discussed in Chapter 2, the wind density can be expressed as

n(r) =M∗

4πµmpv(r)r2, (7.1)

where µ is the gas mass per hydrogen atom, and µ = 1.3 for cosmic chemical abundances.

Once the mass loss rate and the velocity profile are provided, the map of the wind density

can be calculated. For the calculated density distribution and the X-ray luminosity from

the neutron star, we obtain the map of the ionization structure, which controls the line

emission. Here, we adopt a forward method to find the structure. Namely, we simulate the

HMXBs based on a set of parameters that describes the Vela X-1 system with different

mass loss rates. The simulation gives us line spectra from Vela X-1 corresponding to

the phase of the observation. By changing the mass loss rate, we try to find the most

appropriate number that reproduces the observational results.

The parameters used in the Vela X-1 calculations and Monte Carlo simulations are

listed in Table 7.1. The X-ray radiation from the neutron star is modeled based on the

parameter determined from the fits to the observed spectra in the phase 0.25 and in

the phase 0.5. Since no change in the average intrinsic luminosity is observed between

70

Table 7.1. Adopted parameters for the Vela X-1 simulation

Parameter Value Reference

Geometry · · ·Binary Separation D 53.4 R¯ van Kerkwijk et al. (1995)

Companion Star Radius R∗ 30.0 R¯ van Kerkwijk et al. (1995)

Stellar Wind · · ·Velocity Structure v(r) v∞(1−R∗/r)β Castor, Abbott & Klein (1975)

Terminal Velocity v∞ 1100 km s−1 Prinja et al. (1990)

β 0.80 Pauldrach, Puls & Kudritzki (1986)

Mass Loss Rate M [M¯ yr−1] (0.5, 1.0, 1.5, 2.0) × 10−6 (a variable parameter)

Metal Abundance (Z > 2) 0.75 comic for typical OB-stars

(Bord et al. 1976)

X-ray Radiation · · ·Luminosity(0.5–20 keV) 3.5 × 1036 erg s−1 This observation

(1.6 × 1036 erg s−1 (0.5–10 keV))

Spectrum Shape Power-Law (Γ = 1.0) This observation

Energy Range 13.6 eV – 20.0 keV

the phase 0.25 and the phase 0.5 observations, we assumed that the luminosity stays

unchanged in the three orbital phases. The power-law spectrum with a photon index

Γ = 1 is assumed to be extended up to 20 keV, which is the cut-off energy detected

by past hard X-ray observations such as Ginga (Makishima et al. 1999) and RXTE

(Kreykenbohm et al. 1999). The 0.5–20 keV X-ray luminosity of 3.5 × 1036 erg s−1 in

simulations is derived from the observed 0.5–10 keV luminosity of 1.6 × 1036 erg s−1.

We assume that the velocity structure of the stellar wind is followed by the formulation

of the CAK-model (eq.(2.1)). We use the 1100 km s−1 terminal velocity of the stellar

wind is given from the results of Prinja et al. (1990) and the fixed β of 0.80 as expected

from the assumption by Pauldrach, Puls & Kudritzki (1986). In the following simulation,

we simulate the cases for four mass loss rates; 5.0 × 10−7, 1.0 × 10−6, 1.5 × 10−6 and

2.0 × 10−6 M¯ yr−1.

In order to handle the three dimensional distributions of physical parameters in the

vicinity of the neutron star and the companion star, the calculations and the simulations

are performed under the geometry divided into the grid. The grids used in the calculation

of the ionization structure and in the Monte Carlo simulation are shown in Figure 7.1.

A smaller grid is used for regions closer to the neutron star so that we can minimize

the possible error caused by the rapid change of parameters. In the calculation of the

71

ionization structure, all elements in the region hatched by a shadow in the figure are

assumed to be neutral, because the X-rays from the neutron star are blocked by the

companion star.

7.2 The Ionization Structure

Based on the parameter listed in Table 7.1 and the code described in § 6.2, we calculate

how the photoionization by the neutron star radiation is related to the amount of the

material, which surrounds the neutron star. From the calculations, an electron temper-

ature map and relative ionic abundance maps for 140 ions (H, He, C, N, O, Ne, Mg, Si,

S, Ar, Ca, and Fe) are obtained for each mass loss rate. Figure 7.2–7.4 show parts of our

results for H-like Si.

In order to predict the intensities of the emission lines from the ionized ions, we

need to calculate the wind density and the ionization abundance at each grid point.

Figure 7.2 shows maps of relative abundances of H-like Si ion at different mass loss rates.

As clearly visualized in the figure, when the mass loss rate becomes higher the H-like

Si is more pronounced in the region closer to the neutron star. This can be explained

by the fact that the recombination rate is higher and the X-rays are more absorbed

when the density becomes higher. Figure 7.3 shows the distribution of the number

density of H-like Si (nSiH−like), which are given by multiplying the relative abundance of

H-like Si to the number density of Si ions in the region. Maps of nSiH−like/r2ns, where

rns is the distance from the neutron star, are shown in Figure 7.4. Since the cross

section of the photoionization of H-like Si is proportional to nSiH−like and the X-ray flux

injected into the grid is approximately proportional to 1/r2ns, nSiH−like/r

2ns corresponds

to the photoionization rate. Under the condition of the photoionization equilibrium, the

photoionization rate is balanced with the recombination rate. Since the rate is equal to

the emissivity of X-ray photons that produce emission lines, maps given in Figure 7.4

show the emission site of X-ray lines related to H-like Si.

According to the above calculations and calculations for other ions that are located

at different ionization degree, a large fraction of emission lines from highly ionized ions

such as H-like Si are produced in the region between the companion star and the neutron

star. This tendency is much more clear for the case of higher mass loss rate. Importantly,

this is the region where the companion star obscures during the eclipse phase. Therefore,

the mass loss rate is very sensitive to the ratio of line fluxes between phase 0.5 and the

eclipse, because the area of the region becomes larger when we increase the mass loss

rate.

If a different terminal velocity is used for the velocity profile, another mass loss rate

would come out for the same ionization structure. Since the density structure is propor-

tional to M∗/v∞, if we increase both the mass loss rate and the terminal velocity by a

factor of two, the ionization structure is identical to the original one.

72

Companion StarNeutron Star

Shadow Region 4 x 1011 cm

2.44 x 1013 cm

12.4

x 1

01

3 c

m

Companion Star Neutron Star

2.1 x 1013 cm

Figure 7.1: Vela X-1 geometries in the calculation of the ionization structure

(top) and in the Monte Carlo simulation (bottom).

73

-2 0 2 4 6 8 10

0

2

4

6

8

10

12

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

-2 0 2 4 6 8 10

0

2

4

6

8

10

12

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

-2 0 2 4 6 8 10

0

2

4

6

8

10

12

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Abundance for

all

Si

x [1012 cm] x [1012 cm] x [1012 cm]

y[1

01

2 c

m]

Companion

Star

Shadow

Neutron

Star

Figure 7.2: The map of Si H-like ion abundance for all charge state Si.

-2 0 2 4 6 8 10

0

2

4

6

8

10

12

0

1

2

3

4

5

6

7

8

9

10

-2 0 2 4 6 8 10

0

2

4

6

8

10

12

0

1

2

3

4

5

6

7

8

9

10

-2 0 2 4 6 8 10

0

2

4

6

8

10

12

0

1

2

3

4

5

6

7

8

9

10

x [1012 cm] x [1012 cm] x [1012 cm]

y[1

012 c

m]

Companion

Star

Shadow

Neutron

Star

Density [10

4 c

m-3

]Figure 7.3: The density map of Si H-like ion.

-2 0 2 4 6 8 10

0

2

4

6

8

10

12

0

1

2

3

4

5

-2 0 2 4 6 8 10

0

2

4

6

8

10

12

0

1

2

3

4

5

-2 0 2 4 6 8 10

0

2

4

6

8

10

12

0

1

2

3

4

5

x [1012 cm] x [1012 cm] x [1012 cm]

y[1

01

2 c

m]

Companion

Star

Shadow

Neutron

Star

De

nsity/r

ns2 [

10

-20 c

m-5

]

Figure 7.4: The map of nSiH−like/r2ns, where nSiH−like is the density of H-like

Si, and rns is the distance from the neutron star. This value corresponds to

the ionization rate and the recombination rate.

74

Table 7.2. Summary of Si Lyα line in the Vela X-1 spectra.

Intensity in the phase 0.50 Intensity in the eclipse Intensity ratio

(photon cm−2 s−1) (photon cm−2 s−1) (the phase 0.50/eclipse)

2.38 × 10−4 2.32 × 10−5 10.3 ± 1.3

(2.23–2.52) × 10−4 (2.07–2.59) × 10−5

7.3 Estimate of the Mass Loss Rate of the Stellar

Wind

In order to find an ionization structure of the stellar wind that can consistently explain

the spectrum of Vela X-1 taken at three different phases, we try to estimate the mass

loss rate by a forward method. In this method, photons from the central neutron star are

transported one by one in the space defined by the map of ionization structure describe

in the previous section. Then we compare results related to line emissions which are

collected from the simulated events with the results obtained from the actual observation.

In order to allow a comparison with high accuracy, we focus on the the Lyα lines from

H-like Si in phase 0.50 and eclipse. Both the absolute intensity at each phase and the

ratio between the two phases are used for the comparison. Observed Si Lyα parameters

derived in Chapter 4 are summarized in Table 7.2.

Monte Carlo simulations are performed for each mass loss rate. The ionization struc-

ture and the distribution of electron temperature are calculated by following the prescript

described in § 7.2. In order to select photons that come out from the region of stellar

wind and reach to the earth, we use the angle (θ) of the momentum vector of photons

with respect to the line defined by the center of companion star and the neutron star

(see Figure 7.5). If θ < 10, the photons are classified into the phase 0.50 photons, and

if 170 < θ < 180, then, the photons are categorized as the photons in the eclipse. In

this calculation, photons directly coming from the neutron star are neglected since only

the emission lines are of interest.

Figure 7.6 shows spectra obtained from the simulations in the energy range from 1.0

keV to 2.28 keV for a mass loss rate of 1.0 × 10−6 M¯ yr−1 at phase 0.5 and the eclipse.

All emission lines from highly ionized ions of Si, Mg, Ne and so on are clearly seen in the

spectra simulated for two phases.

Although many emission lines are resolved in the Chandra observations, we only use

the Lyα line from H-like Si for the estimation of the mass loss rate because the energy

of these line is sufficiently high and the possible errors caused by systematics of the

absorptions can be minimized in comparison with other low energy lines. If there exists a

75

θ

Companion Star

Neutron Star

Escaped Photon

Momentum Vector

Figure 7.5: The definition of θ.

Figure 7.6: Spectra obtained from the Monte Carlo simulations for the phase

0.50 (left) and the eclipse (right). The mass loss rate of the stellar wind is

1.0 × 10−6 M¯ yr−1. The number of Si Lymanα photons (2.005 keV) are 99

and 25 in the phase 0.50 and in the eclipse, respectively.

76

fluctuation of 1 × 1021 cm−2 in localized absorptions, the change of the Si Lyα intensity is

estimated to be smaller than 5%. Additionally, in our Monte Carlo simulation, emission

lines from He-like ions have uncertainties because we do not include the behaviors of

emission lines from He-like ions such as collisional transfers, UV photoexcitations in He-

like ions, and forbidden line productions by Li-like ions.

The intensity ratio of Si Lyα between phase 0.5 and eclipse is shown in Figure 7.7.

The points with errors are results of the simulation, and the horizontal lines show the

range of observed value. As expected from the discussion in § 7.2, the ratio becomes

larger as the mass loss rate is increased. The intensities of the Si Lyα in the phase 0.5

and in the eclipse are shown in Figure 7.8. The number of photons obtained with the

simulation is multiplied by a factor of:

LX

4πd2

/ (Esim

Ω

4π

)(7.2)

where LX is the luminosity derived from the observation, d is the distance to Vela X-1,

Esim is the total energy of incident photons in the Monte Carlo simulation and Ω is the

solid angle of objective momentum directions for escaped photons (= (2π (1− cos 10))),and then, is converted into an intensity. From these three plots in Figure 7.7 and Fig-

ure 7.8, the mass loss rate is estimated to be (1.5–2.0) ×10−6M¯yr−1.

The estimated mass loss rate of the stellar wind is consistent with the observed X-

ray continuum luminosity. If Mns = 1.7M¯ (van Paradijs et al. 1977; Barziv et al.

2001), Rns = 10 km, vrel = 640 km s−1 (vwind = 570 km s−1, vorbit = 300 km s−1),

D = 53.4R¯ and M∗ = 1.5 × 10−6M¯yr−1 are applied to eq.(2.6), an X-ray luminosity

of LX = 4.7 × 1036 erg s−1 is obtained, which agrees with the observed luminosity of

3.5 × 1036 erg s−1 within a factor of 2.

7.4 Reproduction of the Entire Spectrum

By using the estimated mass loss rate of 1.5 × 10−6 M¯ yr−1, we further perform Monte

Carlo simulations to generate a spectrum spanning the whole energy band covered by

HETGS for the three orbital phases. The criteria to make model spectra in three phases

from Monte Carlo events are as follows. Photons with the θ of 0–10, 85–95and 170–180, are selected and are classified into the photons of phase 0.50, phase 0.25 and eclipse,

respectively. Then, the energy distribution of photons in each phase is accumulated

to a histogram to produce the model spectrum. However, since the absorption of the

continuum component is observed in phase 0.50, we multiply the absorption factor for

photons directly coming from the neutron star in the case of phase 0.50. An NH of

1.7 × 1023 cm−2 is applied, which is subtracted the absorption of the stellar wind from

the observed NH (1.85× 1023 cm−2). Additionally, for the phase 0.25, the model spectrum

is scaled by a factor ((1− cos 10)/2 cos 85) in order to correct for the solid angle.

77

Figure 7.7: Intensity ratio of Si Lyα between the phase 0.5 and the eclipse. The

data is derived from the Monte Carlo simulations, and the error corresponds

to a 1σ Poisson error due to a limited number of trials. The horizontal lines

show the range of the observed value.

Figure 7.8: Simulation results of the Si Lyα intensity for the eclipse (left)

and for the phase 0.50 (right). The horizontal lines show the ranges of the

observational results.

78

Figure 7.9: Monte Carlo simulation spectrum for the mass loss rate of

1.5 × 10−6 M¯ yr−1. The three panels show the spectra in the phase 0.25, in

the phase 0.5 and in the eclipse, in order from the top.

Figure 7.9 shows the Monte Carlo simulation spectra in the three orbital phases. These

spectra are multiplied by the effects of inter-stellar absorption (NH = 6 × 1021 cm−2),

and are convolved with the response of the HETGS for comparison with the observed

spectra.

Figure 7.10 shows both the observed spectra and the simulated model spectra above

2 keV. The normalization of the simulation models are fixed between the three phases

assuming that the X-ray luminosity does not change. Since we assumed a continuum

spectral shape derived from the observation data, the line free of the spectra in the phase

0.25 and the phase 0.50 are well-fitted to the data. Not only in the direct component

observed in the non-eclipse phase well-fit, but the scattered-dominant spectrum in eclipse

is also well reprocessed.

The observed spectra of the emission line region are shown parallel with the simulation

spectra in Figure 7.11 and Figure 7.12 for phase 0.50 and eclipse, respectively. The

79

Figure 7.10: Comparison of the simulation spectra with observed data above

2 keV. The normalization of the simulation models are fixed among the three

phases models, assuming that the X-ray luminosity does not change. The

simulated models shown in Figure 7.9 are multiplied by the absorption effects

due to inter stellar gas (NH = 6 × 1021 cm−2), and then, convolved with the

response of the instruments.

80

simulation spectra match well the emission lines from H-like, He-like and neutral ions,

as well as the radiative recombination continuum emission. It is noted that the emission

lines from Li-like or lower charge state ions, which are seen in observed spectra, are not

reproduced in the simulation spectra, because such ions are not included in the simulation.

The ratios of simulated line intensities to observations are plotted for the 5 σ detected

lines from the highly ionized ions in Figure 7.13. All line intensities obtained with the

simulation are consistent with those of the observations to within a factor of 3.

81

Figure 7.11: The spectra in the phase 0.50. Upper two panels show observation

data obtained with MEG and the Monte Carlo data with the MEG response.

Lower two panels are for those for the HEG.

82

Figure 7.12: Comparison of spectra between the Monte Carlo simulation and

the observation in eclipse.

83

Figure 7.13: Plots of intensity ratios of the simulated lines to the observed

lines. Each filled circle shows the data in the phase 0.50, and each open circle

shows that in the eclipse. All data fall within the range of a factor of 3.

84

Figure 7.14: The blown-up spectra of the iron Kα region. The data show the

observation results obtained with the HEG. The lines show the Monte Carlo

models, which include iron fluorescent X-rays only from the stellar wind.

7.5 Diagnostics by Iron Kα Lines

Iron fluorescence Emission lines give information about the distribution of cold matter

around the X-ray source. Figure 7.14 shows the blown-up spectra of the iron Kα lines at

the three orbital phases, together with the models obtained with the simulations described

in the last section. In eclipse, the iron Kα line intensity calculated from the simulation is

consistent with the observed one. Therefore, we can attribute the iron Kα line observed

in the eclipse to the fluorescence by the stellar wind, which is distributed in the Vela X-1

system. On the other hand, the contributions from the stellar wind are not sufficient to

explain the observed intensity of Kα line in the other two phases. The equivalent widths

of the simulations are only 4 eV and 11 eV in phase 0.25 and in phase 0.50, whereas the

observed values are 51 eV and 116 eV, respectively.

As an obvious source of the additional line production, we firstly estimate the con-

tribution from the surface of the companion star by means of a simple Monte Carlo

simulation. By adopting the geometrical parameters listed in Table 7.1, we have ob-

tained iron Kα equivalent widths of 29 eV and 65 eV for phase 0.25 and phase 0.50,

respectively. In this simulation, we assume that the metal abundance of the companion

star is 0.75 cosmic. Thus, the stellar wind and the companion surface add up together to

explain the equivalent widths of 33 eV (phase 0.25) and 76 eV (phase 0.50). The observed

values are still in excess, by 18 eV and 40 eV at phase 0.25 and 0.5, respectively.

At phase 0.50, additional absorption of NH = 1.7 × 1023 cm−2, relative to phase 0.25,

is observed in the continuum spectrum. This suggests that a cold cloud partially covers

85

Solid Angle

Ω

NH = 1.7 x 1023 cm-2

Neutron Star

Cloud

Phase 0.50Phase 0.25

Figure 7.15: Geometry for Monte Carlo simulation to calculate the iron Kα

equivalent width from a local cloud.

the neutron star, and the effects of the cloud is enhanced at phase 0.50. We then expect

that the remaining Fe-K line photons are produced in this cloud, as already pointed out

by Inoue (1985) using the Tenma data.

In order to estimate the contribution of the cloud to the iron line production, we

performed a Monte Carlo simulation for the partially covered cloud. Figure 7.15 shows

the geometry of the simulation. The thickness of the cloud is taken to be NH = 1.7 ×1023 cm−2, and a uniform density is assumed. The cloud is assumed to be neutral, and

its metal abundance is set to 0.75 cosmic. Firstly, the energy of the escaped photons

from the cloud are accumulated to make spectra if the direction of photons satisfy the

condition for one of the three phases. Secondly, the equivalent width of the Fe Kα line

is calculated from the spectra for each phase.

Figure 7.16 shows the relation between the covered solid angle of the cloud and the iron

line equivalent width, calculated according to this method. Thus, the missing equivalent

widths in both orbital phases (18 eV at phase 0.25 and 40 eV at phase 0.50) can be

explained if the cloud covers 25–40 % of the solid angle viewed from the neutron star.

This configuration is consistent with the fact that the spectrum observed at phase 0.25

does not show such a heavy absorption and that we do observe emission lines of highly

ionized ions from the region between the neutron star and the companion star. Sato et

al. (1986a) have shown that the gradual increase of average absorption column density

were seen from NH ' 1 × 1022 cm−2 at orbital phase of 0.2 to NH ' 3 × 1022 cm−2 at

orbital phase of 0.9 in Tenma observations. This may indicate the existence of the cloud

following the orbiting neutron star (”tailing cloud”), which would be consistent with our

86

Figure 7.16: Relation between the covered solid angle and the equivalent width

of the iron Kα line, calculated with a Monte Carlo simulation. The thickness

of the cloud is NH = 1.7 × 1023 cm−2, with a uniform density. Open circles

show the case of phase 0.25, and filled circles phase 0.50.

results.

The enhanced absorption at orbital phase 0.50, and the local cloud responsible for the

iron line production, may be attributed to the “accretion wake”, which is produced when

the stellar wind flow influenced by a variety of competing effects, including gravitational,

rotational, and radiation pressure forces and X-ray heating. Sawada, Matsuda & Hachisu

(1986), Blondin et al. (1990), Blondin, Stevens & Kallman (1991) and Blondin (1994)

carried out numerical simulations of the stellar wind behavior near an accreting neutron

star, and suggested the presence of such density enhancements.

87

Figure 7.17: The line profiles of Si H-like Lyα with HEG (left) and Mg H-like

Lyα with MEG (right). The blue shows in the phase 0.50, and the red appears

in the eclipse. The observed data are shown in the histograms, and the Monte

Carlo simulation models are drawn in the smooth lines. The simulation models

are also convolved with the each HETGS responses.

7.6 Doppler Effects of the Stellar Wind

The energy shifts and broadening of emission lines due to Doppler effects are new in-

formation obtained only with the high energy resolving power by HETGS. The velocity

information derived from the shift of the central energy of lines gives strong constraints

on the location of the line emission, and can be used as a probe to investigate the stellar

wind dynamics.

7.6.1 Difference between the observation and the simulation

We firstly compare the observed line profiles with the spectra obtained from Monte Carlo

simulation of the stellar wind described in § 7.4. Figure 7.17 shows the line profile

obtained from the simulation together with the deta. The simulated line profiles are

convolved with the spectral responses. Despite the fact that the directions of the Doppler

shifts are same for the observations and simulations, the amount of the velocity shift in

the data are smaller than that estimated from the simulation. Figure 7.18 shows the

velocity shift for all emission lines from highly ionized ions in the spectrum. In the

observation, the shifts between the phase 0.50 and the eclipse (∆v) range in ∼ 300–

600 km s−1. However, the ∆v derived from the simulations are ∼ 1000 km s−1, which is

approximately twice as large when compared at the neutron star (∼ 570 km s−1).

88

Figure 7.18: The plot of velocity shift for emission lines from highly ionized

ions. The symbols of circles show the data from the observations, and, the

squares are data derived from the Monte Carlo simulations. Filled symbols

and open symbols show values in the phase 0.50 and in the eclipse, respectively.

7.6.2 Interaction between X-rays and the stellar wind

Since the velocity derived from the Doppler shifts of X-ray lines should reflect the actual

velocity of the material that emit X-rays, we investigate the possible reasons why the

velocity profile used in the simulation does not reproduce the observed Doppler shift.

To this end, we reexamine the acceleration mechanisms of plasmas in stellar winds of

OB-stars. The forces which material in the stellar wind are affected are the gravity, the

gas pressure, and the radiation force by the OB-star. In the CAK-model, the velocity

structure is calculated by taking these forces into account (Castor, Abbott & Klein 1975).

In the stellar wind of OB-stars, the most dominant force is the radiation force due to

the large number of resonance lines in UV range, a large fraction of which is attributed

to lines related to L-electrons in ions of C, N and O, because of their large chemical

abundances.

In HMXB, strong X-ray radiation from the central neutron star are expected to ionize

the material in the stellar wind and, therefore, weaken the acceleration around the neutron

star. If C, N and O are ionized to He-like or higher by photoionization process and lose

their L-electrons, the resonance absorptions producing the acceleration in the stellar

wind become ineffective. As a result, the stellar wind at the site of the X-ray emission

should have lower velocity than that predicted by the CAK-model. The velocity profile

suggested by the UV observation would depend on the environment of the UV emitting

region, while the observed X-ray lines comes from a much deeper region near the neutron

star. This could also explain the discrepancy. The effect of X-ray irradiation on such line-

89

Figure 7.19: The velocity plot of the CAK-model stellar wind (v∞ =

1100 km s−1, β = 0.8) as a function of the distance from the center of the

companion star (left). The right panel shows the relation between the force

for a particle in the stellar wind and the distance. The force is numerically

derived from the CAK-model velocity structure.

driven stellar wind in HMXB systems has been studied only theoretically by MacGregor

& Vitello (1982) and Masai (1984) or on the basis of UV spectral observations (Kaper

et al. 1993).

7.6.3 One dimensional calculation of the velocity structure

In order to study the modification of the stellar wind velocity due to X-ray ionization, we

performed a one dimensional calculation of the velocity structure on the axis connecting

the companion star center and the neutron star. In the calculation, we make two sim-

plifying assumptions. One assumption is that the only force to make the CAK-model

velocity structure is due to the UV resonance absorption. Figure 7.19 shows the velocity

structure of the CAK-model and the relation between the force and the distance, which

is numerically derived from the CAK-model velocity structure. The other assumption is

that the force is proportional to the number of C, N and O ions that have more than

one L-electrons. Therefore, the acceleration of the stellar wind becomes ineffective in the

region where the C, N, O ions exist as He-like, H-like, or fully ionized ions.

If a velocity structure is given, densities for all point is determined, and then, we

can calculate the ionization structure by using our software described in § 6.2. The

obtained ion distribution of C, N and O leads to the radiation force structure, and, on the

basis of the force, another velocity structure is calculated. In other words, the velocity

90

structure determines the ionization structure, and, the ionization structure affects the

velocity structure. Therefore, in order to obtain a self-consistent solution of the velocity

structure, we iterate the calculations as follows:

1. start from the velocity structure (v′1(r) = v0(r) (CAK-model)), and, calculate a

force structure (f1(r)), then, obtain v1(r).

2. start from v′2(r) = v1(r), and, calculate f2(r), then obtain v2(r).

3. start from v′3(r) = (v1(r) + v2(r))/2, and, calculate f3(r), then obtain v3(r).


5. start from v′5(r) = (v3(r) + v4(r))/2, and, calculate f5(r), then obtain v5(r).


The obtained velocity structures (v0(r), v1(r), v2(r), v3(r), v4(r), v5(r) and v6(r)) are

plotted in Figure 7.20. The stellar wind velocity at the point of the neutron star tends to

have a smaller value of∼ 180 km s−1 than the initial velocity∼ 570 km s−1 of CAK-model.

From the reduced velocity, a Doppler shift difference ∆v ∼ 360 km s−1 is expected, which

is almost equal to the observed values.

Further considerations will be needed to conclude the velocity of this mechanism.

For example, 3-dimensional gas flows including gas pressure forces not for only radial

directions but circumferential direction, and time evolution due to the orbital motion of

the neutron star can be important. However, it is evident from our simple calculations

that effects of photoionization by the X-ray radiation can make the stellar wind of the

X-ray line emission region slower by a factor of 2–3.

In addition to the X-ray photoionization effects, the gravitational force and the orbital

motion of the neutron star can be responsible for the small Doppler shifts in comparison

with the CAK-model prediction. This is because the two effects can disperse the flow of

the stellar wind, and make a density enhancement (Blondin et al. 1990; Blondin, Stevens

& Kallman 1991; Blondin 1994). This enhancement would lead to the heavy absorption

seen in the spectrum in phase 0.50. The velocity of the stellar wind in the affected region

should become smaller than that expected from CAK-model as discussed in Blondin et

al. (1990), Blondin, Stevens & Kallman (1991), and Blondin (1994). Therefore, if the

X-ray emission lines are generated in this region, it can explain the discrepancy.

91

Figure 7.20: The results of 1 dimensional calculations of the tellar wind veloc-

ity on the axis between the companion star and the neutron star. The mass

loss rate is assumed to be 1.5 × 10−6M¯yr−1. The flat velocity region in the

plot is corresponds to the highly ionized region.

92

Chapter 8

Discussion on GX 301−2

The X-ray spectra of GX 301−2 is characterized by heavily absorbed continua and fluo-

rescent lines from ions in low charge states. In contrast to the Vela X-1 cases, no emission

line from highly ionized ions is observed. Additionally, thanks to high energy resolving

power of HETGS, we have detected the remarkable Compton shoulder. In this chapter,

we will discuss physical states in the GX 301−2 system by using the observed spectral

features as probes. We will also consider an unified picture of the environment of HMXBs.

8.1 Compton Shoulder in the PP Phase

As shown in Figure 5.5, we have detected a fully-resolved Compton shoulder of the iron

Kα line during the PP phase observation. The Compton shoulder reflects the physical

conditions of the scattering medium. Therefore, we can use this profile as a probe for

diagnosing the matter around the X-ray source. In this section, we will investigate the

properties of the Compton shoulder and discuss what it can provide.

8.1.1 Time variability

We have observed not only the Compton shoulder feature, but also a time variability in

its profiles during the PP phase observation. The X-ray light curve of the PP phase in the

1.0–10.0 keV band extracted from the HEG events is shown in Figure 8.1. An X-ray out-

burst is seen in the first half of the observation. Hence, we chose to divide the data into the

first and second halves as indicated by the vertical dotted line, and extract spectra from

each data segment separately. The observed 2–10 keV flux is 13.2 × 10−10 erg cm−2 s−1

and 9.0 × 10−10 erg cm−2 s−1 during the first and second halves, respectively. The iron

Kα line spectra divided into two periods are shown in Figure 8.2. Changes in the shape

of the Compton shoulder, as well as in the shoulder flux relative to the un-scattered line

flux, is clearly visible. The equivalent widths of the iron Kα lines including the shoulders

are 643 ± 20 eV and 486 ± 18 eV for the first and second halves, respectively.

93

count

s–1

Time [ksec]

Light Curve

Figure 8.1: The light curve of GX 301−2 in the pre-periastron (PP) phase

observed with the Chandra HETGS in the band 1–10 keV (± 1 order of HEG).

Energy[keV] Energy[keV]

cou

nt

s–1 k

eV–1 (a)First

20 ksec

(b)Second

20 ksec

6.24 keV 6.24 keV

Figure 8.2: The spectra of the iron Kα region (6.0–6.6 keV) for the first and

the second halves of the observation as defined by the dotted vertical line

shown in Figure 8.1.

94

8.1.2 Modeling with Monte Carlo simulation

The Compton shoulder can be used to infer various physical parameters that characterize

the scattering medium. The flux ratio of the shoulder to the line is determined by the

metal abundance and the optical thickness of the scattering cloud. Its energy distribution,

on the other hand, is sensitive to the temperature and the geometrical distribution of

the scattering electrons. A discernible change in the profile shown in Figure 8.2 implies

that these physical parameters are variable between the first and second halves of the

observation.

In order to obtain some quantitative information from the spectra, we have con-

structed a Monte Carlo simulator to compute the emergent spectrum from an X-ray

source surrounded by a cloud. We assume a spherical distribution of material and a

constant density cloud. The cloud consists of H, He and astrophysically abundant met-

als (C, N, O, Ne, Na, Mg, Al, Si, S, Cl, Ar, Ca, Cr, Fe and Ni), and all of the metal

abundances (Z > 2) are allowed to vary together relative to the cosmic values of Feldman

(1992). We account for photoionization and subsequent fluorescent emission, as well as

Compton scattering by free electron. The angular-dependence of the Compton scattering

cross section is fully accounted for and the electrons are assumed to have a Maxwellian

energy distribution. The photons may suffer multiple interactions and are traced until

they completely escape from the cloud. The energy distribution of the emergent photons

are then histogrammed to produce a spectrum.

Figure 8.3 shows some of the results from the simulations for the iron line and its

Compton shoulder with varying hydrogen column density (NH) and electron temperature

(kTe). The original iron Kα1 and Kα2 photons are assumed to be distributed according

to the K-shell photoionization rate at each radius from the central continuum source.

This distribution is also calculated using the same simulator, in which a power-law X-ray

source with a photon index of 1.0 is assumed.

In the upper panels of Figure 8.3, one can see an increase in the scattered flux relative

to the narrow line flux as NH is increased. Photons between 6.24 keV and 6.40 keV are

due primarily to single-scattered photons, and the component below 6.24 keV results from

multiple-scattering, which are not negligible even at moderate optical depths. Figure 8.4

shows the intensity ratio of the shoulder to the narrow line as a function of NH. In the

figure, the dependence on the metal abundance is also presented. The intensity ratio of

the shoulder to the line increases as the metal abundance is decreased, because the larger

relative cross section of Compton scattering to absorption is attained at the smaller metal

abundance.

The lower panels of Figure 8.3 show the temperature dependence of the shape of the

Compton shoulder. Larger smearing effects are seen at higher kTe. Therefore, if a square-

shouldered profile is observed, it means that electrons of the scattering region have low

temperatures.

95

0 eV 1 eV 2 eV 5 eV

2x1023cm–2 5x1023cm–2 1x1024cm–2 2x1024cm–2

Figure 8.3: Dependence of the iron Kα line profile on the hydrogen column

density (NH) and the electron temperature (kTe). The upper panels show the

variation of the iron Kα line and its shoulder as a function NH for a fixed kTe

at 0 eV. The lower panels show the variation as a function of kTe between

0 eV and 5 eV for a fixed NH at 1 × 1024 cm−2. In these simulations, the

metal abundances were assumed to be 0.75 times of the cosmic value (Feldman

1992).

96

0.5 cosmic

0.7 cosmic

1.0 cosmic

Figure 8.4: The relations between the flux ratio of the Compton shoulder

to the un-scattered line and the hydrogen column density. As the hydrogen

column density is increased, the Compton shoulder becomes larger relative

to the narrow line component. The colors mean the difference in the metal

abundance. The blue, the green and the red plot show the cases of 0.5, 0.7

and 1.0 times of the cosmic metal abundance (Feldman 1992). As the metal

abundance decreases, the Compton shoulder becomes larger.

97

8.1.3 Spectral analysis

We perform spectral fittings based on the simulation for the iron line and the Compton

shoulder. A file of ”table models” is generated from the result of a set of the simulations

with different parameters, which is then incorporated into XSPEC v11.2. The parameters

of the model are NH, kTe, and the metal abundances. The radial dependence of the

intrinsic Kα line emissivity is fixed to what one expects from a photon index of Γ = 1.0.

We have confirmed that this assumption produces at most a 5 % error in the emergent

line profile for Γ between 0.0 and 2.0.

Metal Abundance

We first attempt to determine the metal abundances from the total PP-phase spectrum.

In doing this, we note that two independent constraints between the abundance and the

hydrogen column density are available, as described below. The first one arises from the

observed intensity ratio of the shoulder to the narrow line. For a given ratio, an increase

in column density must be accompanied by an increase in abundance (Figure 8.4), and

hence, the two parameters are correlated as shown in Figure 8.5. The other constraint

originates from the observed equivalent width of the line. In this case, the abundance

is anti-correlated with the column density. From these two constraints (see Figure 8.5),

the metal abundance is determined to be 0.65–0.82 times of the cosmic value (Feldman

1992), assuming Γ = 1.0. The slope of the seed power-law emission, however, is not

well-measured due to the limited bandpass of Chandra HETGS and its heavy absorbed

spectrum. If we allow a range in Γ of 1.0–1.5, which has been seen in previous hard

X-ray observations (Pravdo et al. 1995; Orlandini et al. 2000), the metal abundance is

determined to be 0.65–0.90 times of the cosmic value. Note that this is consistent with

that of typical OB-stars (Daflon et al. 2001).

Hydrogen Column Density and Electron Temperature

Adopting the metal abundance of 0.75 cosmic, we find the values for NH by spectral

fittings to the first and the second halves of the PP phase data, separately. The derived

values are listed in Table 8.1, and the models are shown by the lines superimposed on the

data in Figure 8.6. The difference in the observed Compton profile can be described by

a change in the column density, which results in a variation in the number-of-scatterings

distribution even at these moderate optical depths. We have also obtained upper-limits

(90 % confidence levels) to kTe of < 3.4 eV and < 0.6 eV for the first- and second-

half spectra, respectively. In other words, the observed tight and non-smeared Compton

shoulders become direct evidences for the presence of a cold and dense cloud.

The column density as inferred from the Compton profile, in fact, reproduces the

spectrum in the entire HEG bandpass for a power-law photon index of 1.0. Figure 8.7

shows the observed spectra overlaid with the simulated spectra. Reduced chi-squared

98

1.0

0.8

0.6

0.4

Meta

l A

bundance

5 10 20 5 10 20NH [1023 cm-2] NH [1023 cm-2]

First Second

Γ=1.0

Γ=1.0

Γ=1.5

Γ=1.5

Figure 8.5: Confidence contour for NH vs. the metal abundance during the

first half (left) and the second half (right). Each contour represents 68 %,

90 % and 99 % confidence level. The region between each pair of dashed lines

are the values allowed by the observed line equivalent widths of 643 ± 20 eV

(left) and 486 ± 18 eV (right) for two assumed values for the photon index

(Γ = 1.0 and Γ = 1.5). The metal abundance is determined to be 0.65–0.90

(90 % confidence range) times the cosmic value.

99

Figure 8.6: The spectra of the iron Kα region (6.0–6.6 keV) for the first and

the second halves of the observation.

values of 1.30 and 0.95 were obtained for the first and second halves spectra, respectively.

Though some residual flux still remain, the simulations, which are based on parameters

derived from the line and Compton shoulder, provide fairly good descriptions of the

broadband data.

100

Energy [keV]

count

s–1 k

eV–1

count

s–1 k

eV–1

First 20 ksec

Second 20 ksec

χχ

Figure 8.7: The spectra of GX 301−2 from 5 keV to 10 keV for the first and

second halves of the PP-phase observation. The solid lines show the Monte

Carlo models inferred from the data. In addition to the iron Kα emission

line profile, the continuum shape is also successfully reproduced with the pa-

rameters inferred from the Compton shoulder profile. The values for NH are

12.0 × 1023 cm−2 and 8.5 × 1023 cm−2 for the first and second halves, respec-

tively. A photon power-law index of 1.0 is assumed for the seed emission.

101

Table 8.1. Derived Parameters from Spectral fits of the Compton shoulder observed at

the PP phase.

NH (1023 cm−2) τCompton kTe (eV) (upper limit) χ2/ d.o.f.a

First 12.0+3.5−1.3 0.96+0.28

−0.10 0.5 (< 3.4) 65.6 / 71

Second 8.5+2.3−1.4 0.68+0.18

−0.11 0.0 (< 0.6) 82.4 / 71

Note. — Errors and upper limits designate 90 % confidence levels.

aOnly the 6.0 – 6.6 keV region has been used in the spectral fit.

102

8.2 Matter Distribution in GX 301−2

We attempt to consider the distribution of the matter, which creates heavily absorbed

continuum spectra, various fluorescent lines, and Compton shoulders. First, we inves-

tigate how the stellar wind of GX 301−2 contributes the absorption. The mass loss

rate is assumed to be 5 × 10−6 M¯ yr−1, and the velocity structure is followed by the

CAK-model with a terminal velocity of 400 km s−1 and β of 0.8. Figure 8.8 shows the

hydrogen column density (NH) integrated from the position of the neutron star to the

observer. Although the angle we are observing from (θ) is not determined exactly in the

case of GX 301−2, the observed absorptions in all three phases are too high. It cannot

be explained by assuming that the line of sight is passing close to the companion star

surface, because the three observations cover very different orbital phases. If θ = 90 is

assumed, NH of 9.0 × 1022 cm−2, 2.3 × 1022 cm−2 and 4.5 × 1022 cm−2 are derived for PP,

NA and IM, respectively, from the assumed mass loss rate. The amounts are about one

order of magnitude below the observed absorptions of 1.0 × 1024 cm−2, 3.0 × 1023 cm−2

and 6.5 × 1023 cm−2, respectively. In other words, material in addition to the flowing

stellar wind contribute 90% of the total observed absorption.

The leading candidate region where the remaining matters exist is near and around

the neutron star. Since the material is expected in all the three phases, a localized region

in the binary system can be rejected. The Compton shoulder and the whole spectrum

observed during the PP phase also indicates the presence of an almost spherically cloud

surrounding the neutron star. Therefore, we consider a situation where the neutron star

accompanied by a cold dense cloud is moving in the stellar wind of the companion star.

In order to estimate the observed spectra from this situation, we again perform the

Monte Carlo simulation. The GX 301−2 parameters used in the simulation are listed in

Table 8.2, and the grid to describe the stellar wind geometry of GX 301−2 is shown in

Figure 8.9. The concept of such a grid is the same as that in the case of Vela X-1. In

addition to the stellar wind, a cold dense cloud is located at the position of the neutron

star. The hydrogen column density of the cloud in each phase is set to the observed

NH value subtracted the estimated contribution of the stellar wind assuming θ = 90.Concerning the physical processes, photoionization by neutral elements and Compton

scattering by free electrons are taken into account. Since the emission lines from highly

ionized ions are not observed, which is different from the case of Vela X-1, physical

processes of H- and He-like ions and any ionization structures are not included in this

simulation. The simulations of photon transport are started from the neutron star, and

all photons are tracked until they either vanish or escape from the simulation region. We

accumulate the emergent photons with their momentum direction of 60 < θ < 120,and produce spectra to compare with the observed data.

Figure 8.10 shows the results of the Monte Carlo simulations for the three orbital

phases, together with the HEG observation data above 4 keV. The results in the energy

103

Neutron Star

Companion Star

Figure 8.8: The relation between the amount of the hydrogen column density

due to the stellar wind of GX 301−2 and the direction of line of sight. The

mass loss rate of the stellar wind is 5 × 10−6 M¯ yr−1. The velocity structure

is followed by the CAK-model with the terminal velocity of 400 km s−1 and

β of 0.8. The NH at θ = 90 are 9.0 × 1022 cm−2, 2.3 × 1022 cm−2 and

4.5 × 1022 cm−2 for PP, NA and IM, respectively.

104

Table 8.2. Adopted parameters for the GX 301−2 simulation

Parameter Value Reference

Geometry · · ·Binary Separation D ∼ 89 R¯ (PP)

∼ 230 R¯ (NA)

∼ 140 R¯ (IM)

Companion Star Radius R∗ 43.0 R¯ Parkes et al. (1980)

Stellar Wind · · ·Velocity Structure v(r) v∞(1−R∗/r)β Castor, Abbott & Klein (1975)

Terminal Velocity v∞ 400 km s−1 Parkes et al. (1980)

β 0.80 Pauldrach, Puls & Kudritzki (1986)

Mass Loss Rate M 5.0 × 10−6 M¯ yr−1 Parkes et al. (1980)

Metal Abundance (Z > 2) 0.75 comic from Compton shoulder

X-ray Radiation · · ·Spectrum Shape Power-Law (Γ = 1.0)

Energy Range 13.6 eV – 20.0 keV

Neutron Star

(PP)

Neutron Star

(IM)

Neutron Star

(NA)

Companion Star

8.66 x 1013 cm

Figure 8.9: GX 301−2 geometry in the Monte Carlo simulation

105

Figure 8.10: Observed data and results of the Monte Carlo simulation. The

red, the blue, and the green plots show the HEG observation data for the

PP, NA, and IM phases, respectively. The lines overlaid the data appear the

model built by the Monte Carlo simulations.

region of the fluorescent lines from Si, S, Ar and Ca are shown in Figure 8.11 with

the MEG observation data. Although the assumption is very simple, the simulations

reproduce the observed spectral features including the emission lines and continuum

shapes well.

The presence of the dense cloud around the neutron star is consistent with the absence

of emission lines from highly ionized ions in observed spectra. Outside the cloud, the ion-

ized metals cannot exist because the X-ray radiations for photoionization are heavily

absorbed. In the inner side of the cloud, there should be a highly ionized region. How-

ever, the emission lines from this region must be absorbed by the dense cloud material.

Therefore, we can never observe these emission lines.

106

Figure 8.11: Observed data and results of the Monte Carlo simulation. The

IM, NA and PP data are shown in the top, the middle and the bottom panels,

respectively. The red histograms is the MEG observation data, and the black

lines show the model made by the Monte Carlo simulations.

107

8.3 Unified Picture of HMXBs

We have investigated the matter distribution and their physical conditions for Vela X-1

and GX 301−2 using X-ray spectroscopy with high energy resolving power. In Fig-

ure 8.12, we present a conceptual picture of Vela X-1 and GX 301−2 on the basis of the

information obtained from our study. The cold and dense cloud is surrounding the neu-

tron star of GX 301−2, and prevent the stellar wind from photoionization. This situation

makes the heavily absorbed continuum, the fluorescent lines and the Compton shoulder

in their X-ray spectrum. On the other hand, the neutron star of Vela X-1 do not have

such a dense cloud obscuring over all of the directions, and its X-ray radiation ionize the

stellar wind directly. The highly ionized gases in the stellar wind produces the emission

lines by recombination and cascades. Additionally, X-ray photoionization by the neutron

star affects the flow of the stellar wind.

The two types of HMXBs can be distinguished by the presence or absence of the

cold cloud. The one is the “type I HXMB” like Vela X-1, which has highly photoionized

plasmas, and the other is the “type II HXMB” represented by GX 301−2, which has

heavy absorbers and only cold material.

A mechanism to produce such a cloud is possibly related to the efficiency of the X-ray

production. In the case of Vela X-1, the efficiency to capture matter and to convert them

into X-ray radiation is high. The luminosity calculated from eq.(2.6) is given as,

LX =(GMns)

3 M∗Rnsv4

relD2

= 4.7× 1036 erg s−1. (8.1)

Here, we assume a reasonable value for this system; Mns = 1.7M¯, Rns = 10 km,

vrel = 640 km s−1 (vwind = 570 km s−1, vorbit = 300 km s−1), D = 53.4R¯ and M∗ =

1.5 × 10−6M¯yr−1. Assuming that the X-ray spectrum extends up to ∼ 20 keV, the

observed absorption corrected X-ray luminosity is 3.5 × 1036 erg s−1, which is comparable

to the value calculated in eq.(8.1). In other words, almost all of the captured stellar wind

material is accreted onto the neutron star, producing strong X-ray radiation. On the

other hand, the observed luminosity of GX 301−2 does not reach the value calculated

from the stellar wind parameters. We can estimate the luminosity as

LX =(GMns)

3 M∗Rnsv4

relD2

= 8.3× 1036 erg s−1. (8.2)

Here, we assume a value for the IM phase as the most ordinary case; Mns = 1.4M¯,

Rns = 10 km, vrel ∼ 400 km s−1, D ∼ 140R¯ and M∗ = 5.0×10−6M¯yr−1. The observed

absorption corrected luminosity, ∼ 7.9 × 1035 erg s−1 in the energy range of 0.5–20 keV,

is about an order of magnitude lower the value in eq.(8.2).

Such accretions of matters onto a neutron star should be affected by the physical en-

vironment nearby the surface of the neutron star, such as the gravitational field, strength

of the magnetic field, and the spin of the neutron star. These physical states would show

108

their true figures in the hard X-ray spectrum. Therefore, hard X-ray observations with

high precision will become important measurements together with high energy resolution

X-ray observations.

109

Cloud(accretion wake?)

absorption

+fluorescent line

Neutron Star

Emission Region

of lines from highly

ionized ions

Stellar Wind affected

by photoionization of

the X-ray radiation

Companion Star

Stellar Wind

Stellar Wind

(low charge state)

Hard X-ray

(Heavily absorbed)

+ fluorescent X-ray

Neutron Star

+ Cloud

Companion Star

Neutron Star

Ionized gas

Cold Cloud

(fluorescent X-ray,

Compton shoulder)

Vela X-1

GX 301-2

Figure 8.12: Conceptual pictures of Vela X-1 and GX 301−2.

110

Chapter 9

Conclusion

We have observed two high mass X-ray binaries (Vela X-1 and GX 301−2) with the

Chandra HETGS. The observations have been performed at different three orbital phases

for each source. From their X-ray spectra with the high energy resolutions, the following

results have been newly obtained.

• Vela X-1

– A number of emission lines are detected and clearly resolved. The emission

lines from highly ionized S, Si, Mg, and Ne, in addition to fluorescent lines

from Fe, Ca, S, and Si ions in lower charge states are detected in the spectra

of the eclipse phase and the opposite orbital phase (phase 0.50). The narrow

radiative recombination continuum features from H-like ions of Ne are observed

in the both phases, and their widths correspond to the electron temperature of

6.6+2.5−1.8 eV and 7.4+1.6

−1.3 eV for the eclipse and the phase 0.50, respectively. These

results indicate that highly ionized plasmas driven through photoionization

exist in Vela X-1.

– Multiple Si K fluorescent lines from a wide range of charge states are detected

individually for the first time, which is evidence that there exist photoionized

plasmas in various ionization degrees in Vela X-1.

– The similar kinds of emission lines are detected in the both spectra of the

eclipse phase and the phase 0.50. The intensity ratios of emission lines in

phase 0.50 to those in the eclipse are 8–10 for lines from H-like ions and 4–7

for lines from He-like ions.

– From emission lines from highly ionized ions, Doppler shifts are observed.

The lines in the eclipse phase are red-shifted, and those in the phase 0.50 are

blue-shifted. The amount of shifts between these two orbital phases ranged in

∼ 300–600 km s−1.

• GX 301−2

111

– For all three orbital phases, heavily absorbed (NH ∼ (2–10) × 1023 cm−2)

continuum spectra are observed. The emission lines due to fluorescence of Si,

S, Ar, Ca ions in low charge states, in addition to an intense iron Kα line are

also detected in all phases. In contrast, emission lines from highly ionized ions

are entirely absent.

– In the pre-periastron phase observation, the Compton-scattered iron Kα line

profile (“Compton shoulder”) is clearly detected and fully resolved for the first

time from an astrophysical object.

In order to handle such high energy resolution spectra, we have newly constructed the

simulator on the basis of Monte Carlo method. With this simulator, we can deal with

situations, which include asymmetrical geometries and not-optically-thin media. In the

Monte Carlo part for calculations of photo transport, various physical physical processes

are considered, including processes related to highly ionized ions and Doppler effects. By

using this simulator, we have explained the observed spectra as follows.

• Vela X-1

– Assuming that the velocity structure of the stellar wind is followed by CAK-

model, we calculated the ionization structure of the stellar wind and X-ray

spectra of each phase. By using the intensity ratio of Si Lyα between phase

0.50 and eclipse, we found the ionization structure and the matter distribution,

which satisfy line intensities and continuum shapes in both phase 0.50 and

eclipse.

– However, the amount of observed Doppler shifts in the emission lines were

inconsistent with the CAK-model velocity structure, which is assumed in the

ionization structure calculations. As a main cause of this inconsistency, we

showed that photoionization effects by the X-rays slows the stellar wind veloc-

ity and changes the velocity structure. There should be a velocity structure,

which reproduces the observed Doppler shifts leaving the ionization structure

and the matter distribution. Further calculations are needed to search the

solution.

• GX 301−2

– We have demonstrated that Compton shoulders has become a new probe to

investigate the physical conditions of cold material. In fact, we derived from

the observed Compton shoulders that a cold and dense cloud is surrounding

the neutron star almost spherically.

– The geometry consisting of the CAK-model stellar wind and a cold dense cloud

surrounding the neutron star give a good explanation to the observed spectra

of GX 301−2 as the Monte Carlo simulation results.

112

Through the analysis and the consideration, we have established a new method to

investigate the physical state of the HMXBs on the basis of the high precision X-ray

spectrum. And for the different types of HMXBs, Vela X-1 and GX 301−2, we have

specified the physical conditions. GX 301−2 has a cold dense cloud surrounding the

neutron star, while Vela X-1 do not have such a cloud obscuring over all direction. This

difference is probably induced by the accreting mechanism onto the neutron star. In order

to reveal the mechanism, hard X-ray and gamma-ray observations with high precision

are needed together with X-ray spectroscopy.

113

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Acknowledgments

First of all, I would like to thank very much my supervisor Prof. T. Takahashi for his

continuous guidance throughout the five years of my graduate course. It is my pleasure

to thank Dr. M. Sako for his introducing me to HMXB analysis and his precise comment

on atomic physics and photoionized plasma physics. I gratefully thank Prof. F. Nagase

for his advice and comments on this thesis. I thank Prof. M. Ishida and Dr. Y. Ishisaki

for their contributions to discussion on HMXB’s physics. I would also express my thanks

to Prof. S. M. Kahn and Prof. F. Paerels for their suggestions. I thank Dr. K. Nakazawa

for his reading of this thesis.

Finally, I thank my family for their support and understanding.

118

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