Accretion-Powered Millisecond Pulsars

Juri Poutanen (University of Oulu, Finland)

Plan:● X-ray bursts oscillations ● Millisecond pulsars● SAX J1808.4-3658: pulse-resolved spectra,

energy-dependent pulse profiles (1998, 2002 outbursts)

● XTE J1751-305● XTE J1807-294● Model and results ● Conclusions

Pulsar zoo• Pulsars are born with short

spin periods P and high B. • Spin-down by emission of

relativistic wind, waves, photons, magnetic field interaction with the surrounding.

• Spin-up in LMXRB phase by accretion.

• Spin-up line represents the minimum period of recycled pulsars for a given field strength.

• Death-line is an empirical estimate of the maximum period at which pulsars have detectable radio emission for a given field strength.

SAX J1808.4-3658

BIRTH

LMXRB

spin-down

spin-up

Low-mass X-ray binaries

(X-ray bursts)

Nuclear powered millisecond pulsars

Coherent Oscillations during X-ray Bursts

Time (s)10 20

330

328

33

2

Frequ

ency

[H

z]

Time (s)

4U 1702-429 Superburst in 4U 1636-53

from Strohmayer, Markwardt (1999,2002)

Source Orbital period

[h]

spin [Hz] QPO[Hz]

4U 1728-34 ? 363 280-3634U 1636-53 3.8 581 250-320KS 1731-260 ? 524 260at Gal. center ? 589 ? Agl X-1 19.0 549 ?4U 1702-429 ? 330 315-344 MXB 1658-298 7.1 567 ?4U 1916-053 0.83 270 290-3484U 1608-52 ? 619 225-325SAX J1750.8-2980 ? 601 ?SAX J1748.9-2021 ? 410 ?SAX J1808.4-3658 2.0 401 195XTE J1814-338 4.275 314 ?

X-ray bursters = Nuclear-powered millisecond pulsars

(see Strohmayer & Bildsten 2004)

Accretion-powered millisecond pulsars

SAX J1808.4-3658: the First Accreting Millisecond Pulsar

Power density spectrum.From Wijnands & van der Klis

(1998).

April 1998 outburst. From Gilfanov et al. (1998).

GEOMETRY (artist impression)

Accretion-powered millisecond pulsars

Source Porb min spin Hz

fX / MSun Mc/ MSun

SAX J1808.4-3658a 120 401 3.7789 x 10-5 0.05XTE J1751-305b 42 435 1.278 x 10-6 0.013XTE J0929-314c 44 185 2.7 x 10-7 0.01XTE J1807-294d 40 190 1.6 x 10-7 0.007XTE J1814-338e 257 314 0.002 0.16IGR J00291+5934f 148 599 2.81 x 10-5 0.038a: Wijnands & van der Klis 98, Chakrabarty & Morgan 98 b: Markwardt et al. 02c: Remillard et al. 02; Galloway et al. 02d: Markwardt et al. 03e: Markwardt et al. 03f: Markwardt, Swank, Strohmayer, Dec 3, 2004

Companion properties

SAX J1808.4-3658: Spectral Energy Distribution

EF E

10

-9 e

rg c

m-2 s

-1

Energy, keV

black body

reflection

Comptonization

Poutanen & Gierlinski (2003).

kTbb = 0.7 keVkTe = 60 keVT = 0.9

Phase resolved spectra and pulse profiles

Pulse profiles of SAX J1808.4-3658. April 1998 outburst. T

ime lag

, s

EF E

10

-9 e

rg c

m-2 s

-1

Energy, keVfrom Gierlinski et al. (2002).

Variability of the black body and Comptonized tail normalizations with pulsar phase

Gierlinski, Done, Barret (2002)

SAX J1808.4-3658: 2002 outburst

secondary spot?

Ibragimov & Poutanen (2005)

XTE J1751-305

=7.2 d

Broad-band spectrum of XTE J1751-305

Gierlinski & Poutanen (2005)

disc

spotkTdisc=0.6 keVkTbb = 1 keV

kTe = 33 keVT = 1.7

Note: product T x Te same as in SAX J1808

Comptonization

Second ms accreting pulsar XTE J1751-305

Pulse profiles during April 2002 outburst.

Energy, keVGierlinski & Poutanen (2005).

Tim

e

lag,s

RM

S

A=0.04

Pulse Profiles of the Two Spectral Components

Gierlinski & Poutanen (2005).

or Spectral variability of the hard component ?

Gierlinski & Poutanen (2005).

XTE J1807-294: Feb-April, 2003

Kirsch et al. (2003).

=19d

Broad-band spectrum of XTE J1807-294

Falanga, Bonnet-Bidaud, Poutanen, et al. (2005)

disc

spot

Feb 28-March 1, 2003

kTdisc=0.43 keV

kTseed = 0.75 keVAseed = 26 km2

kTe = 37 keVT = 1.7

Comptonization

Broad-band spectrum of XTE J1807-294

Falanga, Bonnet-Bidaud, Poutanen, et al. (2005)

March 20-22, 2003

kTseed = 0.8 keVAseed = 86 km2

kTe = 18 keVT = 2.7

Other ms pulsars

X-ray bursts oscillations

XTE J0929-314.Galloway et al. (2002)

XTE J1814-338. Solid – persistent emission; histogram - X-ray bursts.Strohmayer et al. (2003)

Angular distribution of radiation from a shock

Geometry and model parametersParameters:

M , R , θ , inclination i,

- black body Ibb() ~e-

a – scattered Isc() ~ 1+a

pulsar frequency

• Take intrinsic spectrum Fbb (E) and Fsc( E) as obtained

from the fit to the phase-averaged spectrum • Assume angular distribution of Fbb and Fsc

• Lorentz transform to the non-rotating frame, account for relativistic aberration and Doppler boosting

• Gravitational light deflection• Obtain observed model spectrum as function of phase • Compare with data in 2 terms.

Light Curves from Millisecond Pulsars

D

op

ple

r fa

ctor

Phase

slow pulsar (dashes)

fast pulsar, =401 Hz

Fsc(fast) ~ Fsc(slow) x 4

Doppler boosting Iobs4 x Iem

Aberrationcos obs x cos em

Fbb(fast) = Fbb(slow) x 5

from Poutanen & Gierlinski (2003).

Fitting the Light Curves of SAX J1808.4-3658

• a) Pulse profiles.

Mass M=1.4MSun,

radius R=2rg =8.4 km, inclination i=80o. Fitted θ =11o, =0.16, and a=-0.78 (corresponds to T~0.7) with 2/dof=40.1/28.

• b) Angular distribution of fluxes.

• c) Phase lags at the pulsar frequency relative to 3-4 keV band

from Poutanen & Gierlinski (2003).

cos ~ cos ψ ( 1- Rs /R ) + Rs /R Beloborodov 02

cos ψ = cos i cos θ + sin i sin θ cos ω t

Observed flux F~ I() d Ω ~ I() cos

cos

ψcos

When harmonic content is high?

• Bolometric flux from

a black body spot

• Oscillation amplitude

(black body)

• Harmonic content

(Poutanen 04)

1. Anisotropic emission

2. Rapid rotation

• Harmonics are strong, when amplitude is large!

cos cos ) / -(1 /

sin sin )/ -1(

ss

s0

iRRRR

iRRA

sin sin )/ -1( s0

1iRRa

A

A

sin sin / -1c

2

5s

eq

0

1iRR

A

A v

]cos)/ -1(/ [ ~ ss5 RRRRF

Constraints on inclination from the absence of the secondary spot

I

III

II

Rs/(R-Rs); R=3Rs

Constraints on the Neutron Star Equation of State

Constraints on the radius of the compact star depending on the assumed mass.

BBB1 and BBB2 - Baldo,

Bombaci & Burgio (1997), BPAL12 - Prakash et al.

(1997), SBD - Sahu, Basu & Datta

(1993), SS1 and SS2 - MIT bag

model; DEY1 and DEY2 - Dey etal.

(1998).

Mass

Poutanen & Gierlinski (2003).

Summary● Accretion-powered ms pulsars: unique

laboratories for precise measurements of NS parameters

● Light bending in the strong field regime● Doppler effect distorts pulse profile ● For SAX1808.4-3658, radius R=8.5 km constrains

NS EOS● Spectrum: Comptonized (fan-like emission) &

black body (pencil)● Accretion shock of T~1-2, kTe~20-60 keV with

T x Te ~ const● Future: analysis of the data of other accretion-

powered and nuclear-powered millisecond pulsars

Minimum orbital period

Paczynski & Sienkiewicz 1981

81 min for hydrogen MS*

~ 40 min for a helium star