Angular momentum conservation of bursting shell during the Type I X-ray burst

Transcription

1 On the angular momentum conservation of bursting shell during the Type I X-ray bursts Vahid Rezania Theoretical Physics Institute Department of Physics University of Alberta Edmonton, Alberta Based on: Vahid Rezania, Large frequency drifts during Type I X-ray bursts, submitted to A&A, astro-ph/ th Canadian Conference on General Relativity & Relativistic Astrophysics, Guelph May 30, 2003 Vahid Rezania 1

2 Introduction Among the known Galactic LMXBs, the highly coherent burst oscillations with large modulation amplitudes and stable frequencies in range Hz are seen in ten LMXBs during Type I X-ray bursts. These oscillations are most commonly seen during tails of bursts, when the burning is thought to have spread over the whole surface and obviously asymmetry is no longer present, are not observed in all Type I X-ray bursts from the same source. An initial puzzle seen in observations, the oscillation frequency increases by a few Hz during the burst. This frequency shift is firstly explained by Strohmayer et al a that the burning shell decouples from the star, and undergoes spin changes due to the conservation of angular momentum of the shell as it expands and contracts during the Type I X-ray bursts. Further observations and studies suggested that purely radial hydrostatic expansion and angular momentum a ApJ, 486, 355 Vahid Rezania 2

3 conservation alone cannot explain rather large frequency drifts ( %) observed in some bursts. In this work, we addressed the latter problem by studying the evolution of angular momentum of the burning shell during the Type I X-ray bursts in LMXBs. Based on particle acceleration models near a pulsar polar cap region, we studied the change in the angular momentum of the burning shell during the Type I X-ray burst. We claimed that the angular momentum of the expanding shell is not remaining conserve during the burst. The net charged particles that accelerated by parallel electric field in star s polar caps, flow from the star surface to infinity through open magnetic field lines, would exert a net torque on the burning shell (called wind torque) and cause the angular momentum of the shell changes during the burst. We show that the resulting stellar wind torque on the burning shell may change the shell s angular momentum during the burst. We conclude that the net change in the angular momentum of the star s atmosphere can account for rather large frequency drifts observed during Type I X-ray burst. Vahid Rezania 3

4 LMXBs: General features It is believed that thermonuclear flashes in pure helium or mixed hydrogen/helium layers on the surface of weakly magnetic accreting neutron stars cause the observed Type X-ray bursts in low mass X-ray binaries (LMXBs): G The accumulated hydrogen and helium on the surface of the neutron star by accretion ignites and burns periodically. These systems are shown X-ray burst with: erg burst fluorescences recurrence time few hours burst duration seconds radius expansion is observed in some bursts Further, coherent oscillations observed by RXTE in these stars with: seen in burst tail Hz (related to star spin freq.) oscillation frequency increases by few Hertz Vahid Rezania 4

5 Theoretical models Cumming & Bildsten 2000 a, considered one-dimensional vertical hydrostatic expansion: thermonuclear flashes in hydrogen/helium layers spherically expanding shell by m) conservation of Ang. Mom. of both shell star which leads to: 1 Hz After the burst, as the layer cools down and contracts,! the rising oscillations drifts upward by ν ν s a ApJ, 559, 127 shell ν s #"#"#"#"#"#"#"#" #"#"#"#"#"#"#"# #"#"#"#"# #$#$#$#$#$#$#$#$ #$#$#$#$#$#$#$# #$#$#$#$## NS # #"#"#"#"#"#"# #$#$#$#$#$#$# #"#"#"# #$#$#$# # B Vahid Rezania 5

6 Large frequency drifts Recent observations suggested that purely radial hydrostatic expansion and Ang. Mom. conservation alone cannot account for explaining rather large frequency drifts observed in some bursts a : % The required expansion by these frequency drifts is 4-5 times larger than the one predicted by Cumming & Bildsten: m In order to achieve the rather large frequency shift, Cumming et al b improved the calculattions by including the include general relativity and find the predicted drift is still 2-3 times less than observed values c. a Galloway et al 2001, ApJ, 549, L85; Wijnands et al. 2001, ApJ, 549, L71 b ApJ, 564, 343 c Here and thereafter we assumed that and Hz. Vahid Rezania 6

7 5 Particle acceleration mechanism In this work we study the change in the angular momentum of the burning shell during the Type I X-ray burst. This study is based on polar cap particle acceleration models in the pulsar polar cap regions. Due to the star s rotation and magnetic field, an electric field must be induced in magnetosphere a : with number charge density simple estimate for gives: "! # $ )+* &(' % +,.- 0/ that can easily accelerate upward free iones and electrons from the surface. The beam of accelerated particles produce a current: :9<;>=, outgoing from star to infinity 7? is dimensionless factor such that 7 is the actuall number density of the accelerated particles the induced current exert a wind torque to the 6 C D E GF:7 H I KJML N a Goldreich & Julian 1969, ApJ, 157, 869; Arons 1981,ApJ, 248, 1099 Vahid Rezania 7

8 Particle acceleration mechanism noting that A > we find a ν ν s beam of charged particles Polar cap region E = 0 ν s B E = 0 Polar cap region beam of charged particles in next section we study the effect of this torque on the expanding shell during the X-ray burst. a where is the moment inertia of the shell. Vahid Rezania 8

9 Application to the Type I X-ray burst before the X-ray burst the parallel electric field inside the ocean is nearly zero due to the charge redistribution the accretion flow shuts down the polar cap acclerartion mechanism the expected number of particles that may leave the star is more or less, so 7 further the shell nearly coupled to the star surface, so the torque will transfer more or less to the whole star A! C C C F 7 H as a result we would expect that the spin-down torque has no significant effect in this period. a where is the mass of the star. Vahid Rezania 9

10 7 Application to the Type I X-ray burst during the X-ray burst abruptly thermonuclear ignition of the accumulated materials H/He during the recurrence time the erupting materials from the surface overcome the accretion flow number of particle will increase significantly due to the thermal activities: 7 due to the decoupling of the star and shell, the torque more or less exerts on the shell only! A H for 7 and G we get therefore, we may expect that a frequency drift about Vahid Rezania 10

11 Application to the Type I X-ray burst after the X-ray burst the expansion will be ceased by the gravity and lack of thermal energy, so the shell starts to contract as the cool down the accretion flow shuts down the polar cap acclerartion mechanism due to the lack of outward electrostatic force, the particles are mostly accelrated downward so the expected number of particles that may leave the star is more or less, so 7 as a result the spin-down torque may relax The magnetic recoupling of the shell forces the shell to spin up until it achieves the star s spin frequency. The shell gains its angular momentum deficit from the star, and then it reduces the angular velocity of the star by!. As a result, one would expect that the oscillations frequency will increase as the shell spins up by. Vahid Rezania 11

12 Summary Before the burst burst After the burst Ω s Ω (Cumming et al 2001) Ω (Particle wind model) Here we schematically compare the change in angular velocity of the expanding shell and then oscillations frequency during the type I X-ray burst suggsted by Cumming et al (dotted line) and the one proposed here (solid line). Due to the exerted torque on the shell by the particle wind from the magnetic polar cap regions during the burst, we expect a larger depth in rather than the model discussed by Cumming et al As a result, the larger drift would be expected in the burst tail. The solid and dotted curve after the burst are drawn schematically to show star-shell recoupling in this period. Vahid Rezania 12

13 Summary * %- (Hz) ( / ) (m) ( G) Object, 4U U U Aql X U MXB In this table we obtain the lowest radius expansion (based on hydrostatic expansion models) and the scaled magnetic field (based on the polar cap particle acceleration models) for some X-ray bursts in LMXBs. We calculate these quantities for a chosen values of the star spin frequency, Hz. is the oscillation frequency and its corresponding shift seen during the burst. The value of is based on the assumed value of m. Different data for one source is related to the observations done at different date. Vahid Rezania 13