X-Ray Time Lags with Thermal and Bulk Comptonization Modeling

Juan C Luna

George Mason University

Introduction X-Ray Astronomy Models Spectral States Time Lags Our Model

Variable Sources

AGN (Active Galactic Nucleus) Neutron Star / White Dwarf Black Hole Candidate

Compact Objects

Neutron StarAfter a supernova explosion, the central region of the star collapses combining protons and electrons and forcing them to produce neutrons. A pulsar is a rotating neutron star.

Telescopes

Rossi XTEXMM NewtonChandra

Software: FTOOLS CIAO 3.1 XSPEC Sherpa Xronos

Xspec Output:Spectrum and Light Curve

Accretion Disc

Accretion Models Standard Disk

(Shakura & Sunyaev 1973)optically thick, geometrically thin, energy produced by viscous heating emitted locally as blackbody radiation (“cool disk”)

Two temperature Disks (Shapiro, Lightman & Eardley 1976)

The inner region of the disk is hot geometrically thicker than the cool disk, but optically thin to absorption (gas pressure is dominant “hot disk”)

Advection Dominated Accretion FlowAccretion flow in which as the gas spirals in and gets very hot, it does not radiate its heat energy efficiently. Instead of radiating and cooling down, the gas remains

hot and spirals in to the center. “The heat energy released by viscous dissipation is not radiated immediately, as in a thin disk, but is stored in the gas as thermal energy and advected with the flow” Narayan ‘’06

Main spectral states of accreting black holes

unabsorbed spectra

predicted detection by

Z. & Gierliński 2004

black hole

cold accretion disk

active region soft seedphotons

reflectedphotons

scatteredhard

photons

Spectral States:

A. Zdziarski ‘05

cold outer disk

direct softphotons

scatteredhard photons

reflectedphotons

hot inner disk

variable inner radius

gravity + Coulomb

black hole

outflow/jet emitting radio/IR/...

Soft State

Hard State

Power Spectra (Powspec & FFT)

QPO: quasiperidodical oscillationsFFT & PSD Statistics Terms:Power Spectral Density (PSD) FFT of the auto-correlation functionCross Spectral Density (CSD) FFT of the Cross-correlation function

Phase Info (autocorrelation FFT):

Time Lag

Time Lag: Time or Phase Shifts between X-ray Pulses at different energies.

Difference in Photon Arrival times gives us information about source size and propagation speed

Time Lags

Intrinsic signature of the interaction of the comptonized radiation with the NS and accretion disk plasma.

Energy dependent time lags are a result of downscattering and upscattering in a comptonized medium.

Justification

Comptonization spectra models cannot provide by themselves information about the size of the scattering plasma neither the dynamics of the accretion of the hot gas onto the compact object

Magnitude of the time lags provides an estimate of the size of the scattering medium. Time Lags in contrast with PSD are not affected by variations in the accretion rate, as a result they probe properties inherent to the scattering cloud. Hua,Kazanas,Cui 1999

Constraints

a) IGR J00291+5934.b) XTE J1751-305 c) SAX J1808.4-3658,Falanga, Titarchuk 2007

The data corresponds to MSP (millisecond pulsars), while our model had good fits in regular Pulsars (pulse period ~ seconds)

The RXTE-ASM light curve of LMC X-4, in 2–12 keV energy range, folded at the long term period of 30.276 ± 0.009 days. Naik,Paul 2003

Advection model references

Blandford & Begelman (1999) non-relativistic advection dominated inflow-outflow solution

Becker, Subramanian & Kazanas (2001)pseudo-newtonian process in the event horizon RADIOS (self-similar relativistic advection dominated inflow-outflow solution)

Truong V. Le & Becker (2005)relativistic outflows in advection dominated accretion disks with shocks

Becker & Wolff (2006)Thermal and Bulk Comptonization in accretion powered X-ray pulsars

Transport Equation

2 2 0 0 0 02 2 2 2

0 0

( ) ( ) ( )1 1v v

3 4

N r r t tf f d f fr r

t r r dr r r r r

First order Fermi energization Diffusion term

42 2

1e Te

e

n cf ff kT

t m c

Kompaneets Equation

Recoillosses

Stochastic energization by thermal electrons

2 2 0 0 0 02 2 2 2

0 0

( ) ( ) ( )1 1v v

3 4

N r r t tf f d f fr r

t r dr r rr r r

0

9 31/ 21/ 4 2

0 00

3 30 00 0

3 2, , exp

1 18 2 1

x

t

xx x xN eF x w I

xxr xx

0( ) 21( , )

2iw t t

eF t dt observed fluxe

22

2

164 81 9ln

4 2 1

AB

AB

v

v

5 10 15 20

-2.25

-2

-1.75

-1.5

-1.25

-1

-0.75

-0.5

M. Van Der Klis et Al. 1987

Future Work

42 2

1e TB e

e

n c ff k T

m c

2 2 40 0 0 02 2 2 2 2 2

0 0

( ) ( ) ( )1 1 1v v

3 4e T

B ee

N r r t t n cf f d f f fr r f k T

t r dr r rr r r m c

•Add stochastic energization by thermal electrons, and the effect of the electrons recoil (Kompaneets equation)•The transport equation has to be solved considering a disc geometry.

Kompaneets equation term

References Energy Dependent Time Lags as Observational Evidence of Comptonization Effects in The Neutron Star

Plasma Environment. Falanga, Titarchuk-2007 Thermal And Bulk Comptonization In Accretion-Powered X-RayPulsars. Becker,Wolff-2007 Timing and Spectral Studies of LMC X-4 in High and Low States with BeppoSAX: Detection of

pulsations in the soft spectral Component. Naik, Paul-2004 Probing The Structure of Accreting Compact Sources Through X-ray Time Lags and Spectra. Hua,

Kazanas,Cui-1999 Time Lags In Compact Objects: Constraints in the Emission Models.J.Poutanen-2000 X-Ray Spectral Formation In a Converging FluidFlow:Spherical Accretion Into Black Holes.

Titarchuk,Mstichiadis,Kylafis-1997 The Why & How of X-Ray timing

Z. Arzoumanian. 2003 X-Ray Summer School X-Ray Timing Analysis

Michael Novak- Chandra X-Ray Science Center / MIT Chandra X-ray Observatory

http://chandra.harvard.edu/ Dr. Peter Becker- Class Notes, Verbal Communication Dr. Lev Titarchuk- Class Notes, Seminars Dr. Rita M. Sambruna – Class Notes [1] A Catalog of Candidate Intermediate-luminosity X-ray Objects V2. ApJS 2002. E.J.M

Colbert, and A.F. Ptak. Gravity’s Fatal Attraction

Mitchell Begelman