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Accretion-Powered Millisecond Pulsars Juri Poutanen (University of Oulu, Finland) Plan:

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

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Accretion-Powered Millisecond Pulsars Juri Poutanen (University of Oulu, Finland) Plan:

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  1. 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

  2. Pulsar zoo • Pulsars are born with short spin periods Pand 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. spin-down BIRTH spin-up LMXRB SAX J1808.4-3658

  3. Low-mass X-ray binaries

  4. Nuclear powered millisecond pulsars (X-ray bursts)

  5. Coherent Oscillations during X-ray Bursts 4U 1702-429 Superburst in 4U 1636-53 332 Frequency [Hz] 330 328 Time (s) 10 20 Time (s) from Strohmayer, Markwardt (1999,2002)

  6. X-ray bursters = Nuclear-powered millisecond pulsars (see Strohmayer & Bildsten 2004)

  7. Accretion-powered millisecond pulsars

  8. Power density spectrum. From Wijnands & van der Klis (1998). SAX J1808.4-3658: the First Accreting Millisecond Pulsar April 1998 outburst. From Gilfanov et al. (1998).

  9. GEOMETRY (artist impression)

  10. Accretion-powered millisecond pulsars a: Wijnands & van der Klis 98, Chakrabarty & Morgan 98 b: Markwardt et al. 02 c: Remillard et al. 02; Galloway et al. 02 d: Markwardt et al. 03 e: Markwardt et al. 03 f: Markwardt, Swank, Strohmayer, Dec 3, 2004

  11. Companion properties

  12. SAX J1808.4-3658:Spectral Energy Distribution kTbb = 0.7 keV kTe = 60 keV tT = 0.9 Comptonization black body EFE 10-9 erg cm-2 s-1 reflection Energy, keV Poutanen & Gierlinski (2003).

  13. Phase resolved spectra and pulse profiles EFE 10-9 erg cm-2 s-1 Pulse profiles of SAX J1808.4-3658. April 1998 outburst. Time lag, ms from Gierlinski et al. (2002). Energy, keV

  14. Variability of the black body and Comptonized tail normalizations with pulsar phase Gierlinski, Done, Barret (2002)

  15. SAX J1808.4-3658: 2002 outburst

  16. secondary spot? Ibragimov & Poutanen (2005)

  17. XTE J1751-305 t=7.2 d

  18. Broad-band spectrum ofXTE J1751-305 Comptonization spot kTdisc=0.6 keV kTbb = 1 keV kTe = 33 keV tT = 1.7 Note: product tT x Tesame as in SAX J1808 disc Gierlinski & Poutanen (2005)

  19. Second ms accreting pulsar XTE J1751-305 A=0.04 RMS Time lag, ms Pulse profiles during April 2002 outburst. Energy, keV Gierlinski & Poutanen (2005).

  20. Pulse Profiles of the Two Spectral Components Gierlinski & Poutanen (2005).

  21. or Spectral variability of the hard component ? Gierlinski & Poutanen (2005).

  22. XTE J1807-294: Feb-April, 2003 t=19d Kirsch et al. (2003).

  23. Broad-band spectrum ofXTE J1807-294 Feb 28-March 1, 2003 kTdisc=0.43 keV kTseed = 0.75 keV Aseed = 26 km2 kTe = 37 keV tT = 1.7 Comptonization spot disc Falanga, Bonnet-Bidaud, Poutanen, et al. (2005)

  24. Broad-band spectrum ofXTE J1807-294 March 20-22, 2003 kTseed = 0.8 keV Aseed = 86 km2 kTe = 18 keV tT = 2.7 Falanga, Bonnet-Bidaud, Poutanen, et al. (2005)

  25. Other ms pulsars XTE J0929-314. Galloway et al. (2002) XTE J1814-338. Solid – persistent emission; histogram - X-ray bursts. Strohmayer et al. (2003) X-ray bursts oscillations

  26. Angular distribution of radiation from a shock

  27. Geometry and model parameters Parameters: M , R , θ , inclinationi, t- black body Ibb(m) ~e-t / m a – scatteredIsc(m) ~ 1+a m pulsar frequencyn • 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.

  28. Light Curves from Millisecond Pulsars Fbb(fast) = Fbb(slow) x d5 slow pulsar (dashes) fast pulsar, n=401 Hz Fsc(fast) ~ Fsc(slow) x d4 Doppler boosting Iobs=d4x Iem Aberration cos aobs=dx cos aem d -Doppler factor Phase from Poutanen & Gierlinski (2003).

  29. 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, t=0.16, and a=-0.78 (corresponds to tT~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).

  30. When harmonic content is high? cos ψ cos a ~ cos ψ( 1- Rs/R) + Rs/RBeloborodov 02 cos ψ = cos i cosθ + sin i sin θcos ωt Observed fluxF~ I(a) d Ω~ I(a) cos a cos a

  31. Bolometric flux from a black body spot • Oscillation amplitude (black body) • Harmonic content (Poutanen 04) • Anisotropic emission • Rapid rotation • Harmonics are strong, when amplitude is large!

  32. Constraints on inclination from the absence of the secondary spot II II I I k=Rs/(R-Rs); R=3Rs

  33. 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).

  34. 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 tT~1-2, kTe~20-60 keV with tT x Te ~ const Future: analysis of the data of other accretion-powered and nuclear-powered millisecond pulsars Summary

  35. Minimum orbital period 81 min for hydrogen MS* ~ 40 min for a helium star Paczynski & Sienkiewicz 1981

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