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Timing of Accreting Millisecond Pulsars: a Review

Timing of Accreting Millisecond Pulsars: a Review. T. Di Salvo (1) L. Burderi (2) , A. Riggio (2) , A. Papitto (3) , M.T. Menna (3) (1) Dipartimento di Scienze Fisiche ed Astronomiche, Università di Palermo Via Archirafi 36- 90123 Palermo Italy

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Timing of Accreting Millisecond Pulsars: a Review

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  1. Timing of Accreting Millisecond Pulsars: a Review T. Di Salvo(1) L. Burderi(2), A. Riggio(2), A. Papitto(3), M.T. Menna(3) (1) Dipartimento di Scienze Fisiche ed Astronomiche, Università di Palermo Via Archirafi 36- 90123 Palermo Italy (2) Università degli Studi di CagliariDipartimento di Fisica SP Monserratu-Sestu KM 0.7, 09042 Monserrato Italy (3) I.N.A.F.- Osservatorio Astronomico di Roma via Frascati 33, 00040 Monteporzio Catone (Roma) Italy Funasdalen (Sweden) 25 – 30 March 2008

  2. Astronomer at work

  3. The “classical” recycling scenario Low mass X-ray Binaries B ~ 108 – 109 G Low mass companion (M ~ 1 Msun) Progenitors (Pspin >> 1ms) Accretion of mass from the companion causes spin-up Millisecond radio Pulsars B ~ 108 – 109 G Low mass companion (M ~ 0.1 Msun) End products (Pspin ~ 1ms)

  4. The Recycling Scenario FieldDecay Radio PSR off Accretion Radio PSR on

  5. Confirmedby 10 (transient) LMXBswhich show X-raymillisecondcoherentpulsations Known accreting millisecond pulsars (in order of increasing spin period): IGR J00291+5934: Ps=1.7ms, Porb=2.5hr(Galloway et al. 2005) Aql X-1 (*): Ps=1.8ms, Porb=19hr(Casella et al. 2007) SAX J1748.9-2021: Ps=2.3ms, Porb=8.8hr(Altamirano et al. 2007) XTE J1751-306:Ps=2.3ms, Porb=42m (Markwardtet al. 2002) SAX J1808.4-3658:Ps=2.5ms, Porb=2hr (Wijnands & van derKlis 1998) HETE J1900.1-2455: Ps=2.7ms, Porb=1.4hr(Kaaret et al. 2005) XTE J1814-338:Ps=3.2ms, Porb=4hr (Markwardt et al. 2003) XTE J1807-294:Ps=5.2ms, Porb=40m (Markwardt et al. 2003) XTE J0929-314:Ps=5.4ms, Porb=43.6m (Galloway et al. 2002) SWIFT J1756.9-2508:Ps=5.5ms, Porb=54m (Markwardt et al. 2007)

  6. Light Curves of 5 AMSPs X-ray Outburst of 2002 All the 10 known accreting MSPs are transients, showing X-ray outbursts lasting a few tens of days. Typical light curves are from Wijnands (2005)

  7. Whereare they?(reconstruction of AMSPs position in the Galaxy)‏

  8. Disc–Magnetic Field Interaction‏ Magnetic Pressure ~ B2 Disc Ram Pressure ~ Mdot Rm = 10 B84/7 Mdot-8-2/7 m1/7 km Rco = 15 P–32/3 m1/3 km RLC = 47.7 P–3 km

  9. . M Accretion conditions (Illarionov & Sunyaev 1975) Accretion regime R(m) < R(cor) < R(lc) Pulsar spin-up • accretion of matter onto NS (magnetic poles) • energy release L = dotM G M/R* • Accretion of angular momentum tacc= dL/dt = l dotM where l = (G M Rm)1/2 is the specific angular momentum at Rm

  10. . M Propeller phase Propeller regime R(cor) < R(m) < R(lc) No spin-down can be observed while accreting onto the NS • centrifugal barrier closes (B-field drag stronger than gravity) • matter accumulates or is ejected from Rm • accretion onto Rm: lower gravitational energy released • energy release from the disc L = e GM(dM/dt)/R*, e = R*/2 Rm

  11. Threaded disc model Magnetospheric radius Total Torque on the NS Rappaport et al. 2004 Pos. Threading Torque Zone Neg. Threading Torque Zone Romanova et al. 2004 Corotation radius

  12. Timing Technique Photon Arrival Times reported to the Solar System barycenter. Photon Arrival Times corrected for the source orbital motion: t =tarr– x sin(2 p / PORB (tarr– T*))‏ wherex = a sini/c is the projected semi-major axis in lt-sec and T* is the ascending node time transit. Compute phase delays of the pulses ( -> folding pulse profiles) with respect to constant frequency. Sum in quadrature statistical errors on pulse arrival time delays to the errors due to errors on the orbital parameters used. Main trends in Pulse Arrival Time delays are due to: 1) Orbital parameters residuals (sinusoidal terms)‏ 2) spin frequency correction (linear term)‏ 3) spin frequency derivaties (quadratic and/or greater terms)‏ 4) Timing noise (e.g. fluctuations in the accretion flow)‏ Theuncertantiespos on the source positioncan not be taken into account on the same way because are a systematic effect and will be discussed later.

  13. Accretion Torque modelling Bolometric luminosity L is observed to vary with time during an outburst. Assume it to be a good tracer of dotM:L= (GM/R)dotMwith 1, G gravitational constant, M and R neutron star mass and radius Matter accretes through a Keplerian disk truncated at magnetospheric radiusRm dotM-. In standard disk accretion  =2/7 Matter transfers to the neutron star its specific angular momentum l = (GM Rm)1/2at Rm, causing a torque= l  dotM. Possible threading of the accretion disk by the pulsar magnetic field is modelled here as in Rappaport et al. (2004), which gives the total accretion torque: t = I dotW = dotM l– m2 / 9 Rco3

  14. Accretion Torque modelling where d(t)/dtmust be derived by the accretion theory (e.g. exponentially decresing with time with the same decaying time of the X-ray flux).

  15. IGR J00291: the fastest accreting MSP Porb = 2.5 h ns = 600 Hz 8 0 dotn = 8.5(1.1) x 10-13Hz/s (c2/dof = 106/77) (Burderi et al. 2007, ApJ; Falanga et al. 2005, A&A)

  16. Spin-up in IGR J00291 In a good approximation the X-ray flux is observed to linearly decrease with time during the outburst: dotM(t) = dotM0 [1-(t – T0)/TB], where TB = 8.4 days IGR J00291+5934 shows a strong spin-up:dotn0 = 1.2 x 10-12Hz/s (at the beginning of the outburst, assuming a linear decay of the X-ray flux and hence of the spin-up rate),which indicates a mass accretion rate ofdotM0 = 7  10-9 Myr-1. Comparing the bolometric luminosity of the source as derived from the X-ray spectrum with the mass accretion rate of the source as derived from the timing, we find an agreement if we place the source at a quite large distance between7 and 10 kpc.

  17. Timing of XTE J1751 The X-ray flux of XTE J1751 decreases exponentially with time (TB = 7.2 days). The best fit of the phase delays dotn0 = 6.3 10-13 Hz/s and dotM0 = (3.4 – 8.7) 10-9 Msun/yr. Comparing this with the X-ray flux from the source, we obtain a distance of 7-8.5 kpc (using the same arguments used for IGR J00291). (Papitto et al. 2007, MNRAS) Porb = 42 min ns = 435 Hz

  18. Spin down in the case of XTE J0929-314 Porb = 44 min ns = 185 Hz Spin down in XTE J0929, (almost) the slowest among accreting MSPs, during the only outburst of this source observed by RXTE. Measured spin-down rate: dotn= -5.5 10-14 Hz/s Estimated magnetic field: B = 5 x 108 Gauss (Galloway et al. 2002; Di Salvo et al. 2007, arXiv:0705.0464)

  19. Spin down in the case of XTE J1814 Papitto et al. 2007, MNRAS Phase Delays of The Fundamental Phase Delays of The First Harmonic Porb = 4 hr ns = 310 Hz Spin-down: dotn= -6.7 10-14 Hz/s

  20. Phase residuals anticorrelated to flux changes in XTE J1814-338 Modulations of the phase residuals, anticorrelated with the X-ray flux, and possibly caused by movements of the footpoints of the magnetic field lines in response to flux changes Post fit residuals of the Fundamental Post fit residuals of the harmonic Estimated magnetic field: B = 8 x 108 Gauss

  21. The Strange case of XTE J1807-294 The outburst of February 2003 (Riggio et al. 2007 MNRAS, Riggio et al. 2008 ApJ)

  22. But… There is order beyond the chaos! The key idea: Harmonic decomposition of the pulse profile The source shows a weak spin-up at a rate of: dotn = 2.1 10-14 Hz/s. In this case using dotM(t) decreasing exponentially with time gives an improvement of the fit with respect to a simple parabola (dotM = const).

  23. Back to the fundamental From the spin frequency derivative we can calculate the mass accretion rate to the NS, that is: 4 x 10-10 Msun/yr Corresponding to a luminosity of 4.7 x 1036 ergs/cm2/s. Comparing this to the observed X-ray flux of the source, we infer a distance to the source of about 4 kpc.

  24. Positional Uncertainties of XTE J1807 (0.6’’) Major source of error on the frequency derivative given by the uncertainty in the source position. From a scan of the chandra error box we find that the frequency derivative must be in the range: (1–3.5) 10-14 Hz/s

  25. SAX J1808: the outburst of 2002 (Burderi et al. 2006, ApJ Letters) Phase Delays of The First Harmonic Phase Delays of The Fundamental Spin-up: dotn= 4.4 10-13 Hz/s Porb = 2 h n = 401 Hz Spin-down at the end of the outburst: dotn= -7.6 10-14 Hz/s

  26. SAX J1808.4-3658: Pulse Profiles Folded light curves obtained from the 2002 outburst, on Oct 20 (before the phase shift of the fundamental) and on Nov 1-2 (after the phase shift), respectively

  27. SAX J1808.4-3658: phase shift and X-ray flux Phase shifts of the fundamental probably caused by a variation of the pulse shape in response to flux variations.

  28. Discussion of the results for SAX J1808 Spin up: dotn0 = 4.4 10-13 Hz/s corresponding to a mass accretion rate of dotM0 = 1.8 10-9 Msun/yr Spin-down: dotn0 = -7.6 10-14 Hz/s (see Hartman et al. 2007 for a different interpretation) In the case of SAX J1808 the distance of 3.5 kpc (Galloway & Cumming 2006) is known with good accuracy; in this case the mass accretion rate inferred from timing is barely consistent with the measured X-ray luminosity (the discrepancy is only about a factor 2), Using the formula of Rappaport et al. (2004) for the spin-down at the end of the outburst, interpreted as a threading of the accretion disc, we find: m2 / 9 Rc3 = 2 p dotnsd from where we evaluate the NS magnetic field: B = (3.5 +/- 0.5) 108 Gauss:(in agrement with previous results, B = 1-5 108 Gauss, Di Salvo & Burderi 2003)

  29. Orbital Solutions and Variation of the Periastron Time Passage dot Porb = (3.42 +/- 0.05) 10–12 s/s (Di Salvo et al. 2007; Hartman et al. 2007 See next talk by Luciano Burderi) Orbital cicles

  30. Results for 6 of the 8 known LMXBs which show X-ray millisecond coherent pulsations Results for accreting millisecond pulsars (in order of increasing spin period. See Di Salvo et al. 2007 for a review): IGR J00291+5934: Ps=1.7ms, Porb=2.5hrSPIN UP (Burderi et al. 2007) XTE J1751-306:Ps=2.3ms, Porb=42m SPIN UP (Papitto et al. 2007) SAX J1748.9-2021: Ps=2.3ms, Porb=8.8hr???(Altamirano et al. 2007) SAX J1808.4-3658:Ps=2.5ms, Porb=2hr SPIN UP (& SPIN DOWN,Burderi et al. 2006, but see also Hartman et al. 2007) XTE J1814-338:Ps=3.2ms, Porb=4hr SPIN DOWN (Papitto et al. 2007) XTE J1807-294:Ps=5.2ms, Porb=40m SPIN UP (Riggio et al. 2007) XTE J0929-314:Ps=5.4ms, Porb=43.6m SPIN DOWN (Galloway et al. 2002)

  31. We conclude that spin-up dominates in sources with relatively high mass accretion rate (producing fast pulsars) and spin down dominates in sources with relatively strong magnetic field (producing slow pulsars). See a review of these results in Di Salvo et al. 2007 (arXiv:0705.0464) Thank you very much!

  32. Timing Technique • Correct time for orbital motion delays:t tarr – xsin 2/PORB (tarr –T*)wherex = a sini/c is the projected semimajor axis in light-s and T* is the time of ascending node passage. • Compute phase delays of the pulses ( -> folding pulse profiles) with respect to constant frequency • If a good orbital solution is available: small delays caused by orbital uncertainties, that average to zero over Porb << Tobs, propagated as further uncertainties on the phase delays. • Main overall delays caused by spin period correction (linear term) and spin period derivative (quadratic term) • Uncertainties on the source coordinates (producing a modulation of the phase delays over 1 yr) can be considered as systematic uncertainties on the linear and quadratic term

  33. Accretion Torque modelling Bolometric luminosity L is observed to vary with time during an outburst. Assume it to be a good tracer of dotM:L= (GM/R)dotMwith 1, G gravitational constant, M and R neutron star mass and radius Matter accretes through a Keplerian disk truncated at magnetospheric radiusRm dotM-. In standard disk accretion  =2/7 Matter transfers to the neutron star its specific angular momentum l = (GM Rm)1/2at Rm, causing a torque= l  dotM. Possible threading of the accretion disk by the pulsar magnetic field is modelled here as in Rappaport et al. (2004, but see next talk by Burderi): t = dotM l– m2 / 9 Rc3

  34. Results for IGR J00291+5934 In a good approximation the X-ray flux is observed to linearly decrease with time during the outburst: dotM(t) = dotM0 [1-(t – T0)/TB], where TB = 8.4 days AssumingRm dotM-. ( = 2/7 for standard accretion disks; a = 0 for a constant accretion radius equal to Rc; a= 2 for a simple parabolic function), we calculate the expected phase delays vs. time: f = - f0 – Dn0 (t-T0) – ½ dotn0 (t – T0)2 [1 – (2-a) (t-T0)/6TB] We have calculated a lower limit to the mass accretion rate (obtained for the case a = 0 and no negative threading (m = 1.4, I45 = 1.29) dotM = 5.9 10-10 dotn–13 I45 m-2/3Msun/yr Maesured dotn–13= 11.7, gives a lower limit of dotM = (7+/-1) 10-9 Msun/yr, corresponding to Lbol = 7 x 1037 ergs/s

  35. Distance to IGR J00291+5934 The timing-based calculation of the bolometric luminosity is one order of magnitude higher than the X-ray luminosity determined by the X-ray flux and assuming a distanceof 5 kpc ! The X-ray luminosity is not a good tracer of dotM, or the distance to the source is quite large (15 kpc, beyond the Galaxy edge in the direction of IGR J00291 !) We argue that, since the pulse profile is very sinusoidal, probaly we just see only one of the two polar caps, and possibly we are missing part of the X-ray flux.. In this way we can reduce the discrepancy between the timing-determined mass accretion rate and observed X-ray flux by about a factor of 2, and we can put the source at a more reliable distance of7.4 – 10.7 kpc

  36. The Strange case of XTE J1807 The outburst of February 2003 (Riggio et al. 2007, submitted)

  37. The Strange case of XTE J1807 The outburst of February 2003 (Riggio et al. 2007, submitted)

  38. Discussion of the results for SAX J1808 In a good approximation the X-ray flux is observed to decrease exponentially with time during the outburst: dotM(t) = dotM0 exp[(t – T0)/TB], where TB = 9.3 days derived from a fit of the first 14 days of the light curve. AssumingRm dotM-. (with  = 0 for a constant accretion radius equal to Rc), we calculate the expected phase delays vs. time: f = - f0 – B (t-T0) – C exp[(t-T0)/TB] + ½ dotn0 (t – T0)2 where B = Dn0 + C/TB and C = 1.067 10-4 I45-1 P-31/3 m2/3 TB2 dotM-10 (the last term takes into account a possible spin-down term at the end of the outburst). We find that the best fit is constituted by a spin up at the beginning of the outburst plus a (barely significant) spin down term at the end of the outburst.

  39. XTE J0929-314: the most puzzling AMSP The mass accretion rate is varying with time, while instead the phase delays clearly indicate a constant (or at most decreasing) spin-down rate of the source. We therefore assume nspin-up << -nspin-down = 5.5 x 10-14 Hz /s Assuming that the spin-up is at least a factor of 5 less than the spin-down, we find a mass accretion rate at the beginning of the outburst of dotM < 6 x 10-11 Msun/yr, which would correspond to the quite low X-ray luminosity of Lbol < 6 x 1035 ergs/s. Comparing this with the X-ray flux of the source we find an upper limit to the source distance of about 1.2 kpc (too small !!)

  40. Conclusions: Spin-up IGR J00291+5934 shows a strong spin-up: ndot = 1.2 10-12 Hz/s, which indicates a mass accretion rate of dotM = 7  10-9 Myr-1. Comparing the bolometric luminosity of the source as derived from the X-ray spectrum with the mass accretion rate of the source as derived from the timing, we find a good agreement if we place the source at a quite large distance between7 and 10 kpc. SAX J1808.4-3658 shows a noisy fundamental and a clear spin-up in the second harmonic: ndot = 4.4 10-13 Hz/s. The spin up switches off at the end of the outburst, as expected for a substantial decrease of the accretion rate. XTE J1807-294 shows a noisy fundamental and a clear spin-up in the second harmonic: ndot = 2.1 10-14 Hz/s.

  41. Conclusions: Spin-down XTE J1814-338 shows noisy fundamental and harmonic phase delays, and a strong spin-down: ndot = -6.7 10-14 Hz/s, which indicates a quite large magnetic field of B = 8  108 Gauss. XTE J0929-314 shows a clear spin-down of ndot = -5.5 10-14 Hz/s, which indicates a magnetic field of B = 4-5  108 Gauss. Imposing that the spin-up contribution due to the mass accretion is negligible, we find however that the source is at the very close distance of about 1 kpc. Independent measures of the distance to this source will give important information on the torque acting on the NS and its response.

  42. Another Strange case: XTE J1807 The outburst of February 2003 (Riggio et al. 2007, in preparation)

  43. Spin Frequencies of AMSPs From Wijnands (2005)

  44. But… There is order beyond the chaos! The key idea: Harmonic decomposition of the pulse profile

  45. The accreting matter transfers its specific angular momentum (the Keplerian AM at the accretion radius) to the neutron star: L=(GMRacc)1/2 The process goes on until the pulsar reaches the keplerian velocity at Racc (equilibrium period); Pmin when Racc = Rns The conservation of AM tells us how much mass is necessary to reach Pmin starting from a non-rotating NS. Simulations give ~0.3Msun (e.g. Lavagetto et al. 2004) Pulsars spin up

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