accretion-powered millisecond pulsars juri poutanen (university of oulu, finland) plan:
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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
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