Spin up/down processes of X-ray pulsars

1. Spin up/down processes of X-ray pulsars arXiv:1106.5497v1; 1103.4996v2; 1109.0536v1; 1106.6264 reporter: Shaoyong 2011.11.14

3. THE WHITE DWARF COMPANION OF A2Msun NEUTRON STAR PSRJ1614–2230 (Demorest et al. 2010) 2.2Gyr old He–CO white dwarfWDcooling models(Chabrier et al. 2000)

5. where n is the “braking index” for the pulsar, with n = 3appropriate for a dipole radiating into vacuum

6. Case A RLO 1) forced mass loss from theRoche-lobe filling donor star results in a lower core massas the donor now evolves less massive, and 2) the formationof an outgoing hydrogen shell source during the finalphase (phase AB, see below) of the mass transfer causes the core mass to grow with the helium ashes left behind.Therefore, to obtain the final mass of the white dwarf requires detailed numerical stellar models.

8. Mdonor = 4.5 Msun MNS = 1.8 Msun Porb,i = 3 days

9. GRAVITATIONAL WAVES AND THE MAXIMUM SPIN FREQUENCY OF NEUTRON STARS The ten accreting NS used by White & Zhang (1997) showed a spreadin luminosities over two orders ofmagnitude whereas thespin periods clustered between 2.8 and 3.8 ms (263-362Hz). the small range of spin periods over a large span in luminosity can be explained within the spin equilibrium scenario only if B ∝ Lx^1/2(under the reasonable assumption that Lx ∝ Mdot ).

10. The distribution ofmillisecond radio pulsars also appears to have a cutoffat around 700 Hz (Hessels et al. 2006).

11. The inner parts of thedisk become radiation-pressure dominated, and the spin equilibrium condition translates then into the relation: (Andersson et al. 2005) The spin-down torque comes from the interaction between the disk and field outside co-rotation. (D’Angelo & Spruit 2010) GWemission ?

12. XTE J1814-338 &SAX J1808.4-3658 XTE J1814-338 No significant spinup/down episodes are detected during these outbursts, with upper limits of the order of (Hartman et al. 2008, 2009). The measured longterm spindown is , which has been interpreted as due to magneto-dipole torquesinduced by a NS magnetic field of ~ 1.5×10^8G. SAX J1808.4-3658 spin frequency of 314.4Hz and orbits in 4.3 hr around a ~ 0.1Msun companion (Markwardt & Swank 2003). The results indicate upper limits on the spin frequencyderivative of the order of at the95% confidence level.

13. Standard accretion theory predicts a spin-up of theform Bildstenet al. (1997): ξ parametrises the uncertainties in evaluatingthe torque at the edge of the accretion disc and is thoughtto be in the range ξ ≈ 0.3 − 1 (Psaltis & Chakrabarty1999). The average accretion rate for the outburst is≃5 × 10^-10Msun/yr and 2 × 10^-10Msun/yrfor SAXJ1808 and XTE J1814, respectively, when consideringthe bolometric flux (using the data reported by Heinke et al. 2009; Wijnands & Reynolds 2003). Thus, for SAX J1808 for XTE J1814

14. Gravitational wave torques Gravitational wave emission was first suggested as thecause for the cutoff in the spin distribution of the LMXBsmore than thirty years ago (Papaloizou & Pringle 1978).The main emission mechanisms that could be at workin these systems are crustal “mountains” (Bildsten 1998; Ushomirsky, Cutler & Bildsten 2000), magnetic deformations (Cutler 2002; Melatos & Payne 2005) or unstablemodes (Andersson 1998). All these processes can produce a substantial quadrupole Q22 and thus a spindowntorque due to GW emission. Crustal mountains The crust consists of several layers of different nuclearcomposition and as accreted matter gets pushed furtherinto the star it undergoes a series of nuclear reactions,including electron captures, neutron emission and pyc- nonuclear reactions (Sato 1979; Haensel & Zdunik 1990).

15. These reactions willheat the region by an amount (Ushomirsky & Rutledge2001): If the energy deposition is (partly) asymmetric this would perturb theequilibrium stellar structure and give rise to amass quadrupole(Ushomirsky, Cutler & Bildsten 2000): The quadrupole required for spin equilibrium during an outburst is Q ≈ 10^37 gcm^2 for both systems. It is clearthat even under the most optimisticassumptions it is very unlikely to build a “mountain”large enough to balance spin-up during accretion.

16. Magnetic mountains It is well known that a magnetic star will not be spherical and, if the rotation axis and the magnetic axis are notaligned, one could have a “magnetic mountain” leadingto GWemission. However suchdeformations are unlikely to be large enough to balance the accretion torques inweakly magnetised systems such as the LMXBs (Haskellet al. 2008). Large internal fields could also cause a deformation (Cutler 2002), but this would persist in quiescence, leading to a rapid spin-down, of the order ofthe spin-up in (1), which is not observed in SAX J1808(Hartman et al. 2009). Another possibility is that the magnetic field lines arestretched by the accretedmaterial itself as it spreadson the star, giving rise to a large magnetically confinedmountain. The results of Melatos & Payne (2005) suggest that the quadrupole built this way could balance theaccretion torque only if the surface field is significantlystronger than the external dipole component. Furtherore such a mountain would persist on an ohmic dissipation timescale τohm ≈ 10^2 yrs (Melatos & Payne 2005)and thus should also give rise to a strong additional spin-down in quiescence.

17. Unstable modes An oscillationmode of the NS being driven unstable by GW emission, the main candidate for this mechanism being thel = m = 2 r-mode(Andersson 1998). An r-mode is atoroidal mode of oscillation for which the restoring forceis the Coriolis force. It can be driven unstable by theemission of GWs, as long as viscosity does not damp iton a faster timescale. This will only happen in a narrowwindow in frequency and temperature which depends onthe microphysical details of the damping mechanisms (fora review see Andersson, Kokkotas & Ferrari (2001)). The temperatures we obtain for the stars are 1.5×10^7 K for SAX J1808, 1.6×10^7 k for XTE J1814. Compare with observational constraints: A core temperature ofT < 8.6 × 10^6 K for SAX J1808 and T < 3.4 × 10^7 K for XTE J1814.

18. Accretion torques The results of (Andersson et al. 2005) indicate that thetorque will vanish when the ratio betweenthe propellerflux (fprop) and the average flux (favg) is such that (fprop/favg)^2/7 ≈ 0.8. We find that ((fprop/favg)^2/7 ≈0.75 for XTE J1814 and 0.75-0.84 for SAX J1808 in the2002, 2005 and 2008 outbursts.

19. For SAX J1808 it is reasonably safe to say thatGW torques can beexcluded. For XTE J1814 a definiteconclusion is harder to draw, as only one outburst hasbeen observed and thus we do not have a measurementof the spin-down in quiescence. GW emission may stillbe marginally consistent withobservations.

20. Thanks