Energy release during disk accretion onto a rapidly rotating neutron star

Abstract

.Abstract The energy release L s on the surface of a neutron star (NS) with a weak magnetic field and the energy release L d in the surrounding accretion disk depend on two independent parameters that determine its state (for example, mass M and cyclic rotation frequency f ) and is proportional to the accretion rate. We derive simple approximation formulas illustrating the dependence of the efficiency of energy release in an extended disk and in a boundary layer near the NS surface on the frequency and sense of rotation for various NS equations of state. Such formulas are obtained for the quadrupole moment of a NS, for a gap between its surface and a marginally stable orbit, for the rotation frequency in an equatorial Keplerian orbit and in the marginally stable circular orbit, and for the rate of NS spinup via disk accretion. In the case of NS and disk counterrotation, the energy release during accretion can reach 0.67Ṁc2 . The sense of NS rotation is a factor that strongly affects the observed ratio of nuclear energy release during bursts to gravitational energy release between bursts in X-ray bursters. The possible existence of binary systems with NS and disk counterrotation in the Galaxy is discussed. Based on the static criterion for stability, we present a method of constructing the dependence of gravitational mass M on Kerr rotation parameter j and on total baryon mass (rest mass) m for a rigidly rotating neutron star. We show that all global NS characteristics can be expressed in terms of the function M(j, m) and its derivatives. We determine parameters of the equatorial circular orbit and the marginally stable orbit by using M(j, m) and an exact solution of the Einstein equations in a vacuum, which includes the following three parameters: gravitational mass M, angular momentum J, and quadrupole moment Φ 2 . Depending on Φ 2 , this solution can also be interpreted as a solution that describes the field of either two Kerr black holes or two Kerr disks.

Realistic exact solution for the exterior field of a rotating neutron star

“…In 2004 by Berti & Stergioulas [1] and Yoshida & Eriguchi [18]. In previous years by Stute & Camenzind in 2003 [19], Manko, Mielke & Sanabria-Gómez in 2000 [20], Sibgatullin & Sunyaev [21] in 1998, Bocquet Bonazzola, Gourgoulhon & Novak [22], in 1995, and by Cook, Shapiro & Teukolsky in 1994 [10] and 1992 [23]. and references therein).…”

“…Nevertheless, Kerr solution does not present an accurate fit with the expected values of some of the physical properties of realistic stars in the regime of rapid rotation rates (like the radii of ISCOs, see [1,10,19] and the mass-quadrupole moment [29]). Sibgatullin & Sunyaev [21] adjusted the free parameters of the exact solution by Manko, Martin, Ruíz, Sibgatullin & Zaripov in [30] with the numerical data for the ISCO and the gravitational redshift of Cook, Shapiro & Teukolsky [10]. They analyzed the effects of the mass-quadrupole moment of a rapidly rotating NS on the energy release in the equatorial layer on the surface of the accreting star and in the accretion disk, using the normal sequences of Equations of State (EOS) A [31], AU [32] and FPS [33].…”

“…), (ii) it could be useful for studying the dynamical properties of the space-time, like gravitational wave emission and chaotic trajectories of particles around it. Furthermore, having an analytic solution could simplify the calculation of properties of accretion disks, epicyclic frequencies [21] and so on.…”

“…Then, Stute & Camenzind [19] decided to study that solution to describe the gravitational field of a rapidly rotating NS. They matched the solution by Manko et al with the numerical interior solutions from Cook et al [10] by a similar procedure to the one used in [21], concluding that the accuracy of that solution is high in the case of the redshift, but poor describing the radius of the marginally stable orbit (the matching was made using non invariants local properties of the solution, as it was pointed out in [1] Recently, the full Einstein equations were solved in a numerical approach by Berti & Stergioulas (B&S) [1], to determine the NS space-time along of sequences of constant rest mass for selected EOS (denoted as EOS A [31], EOS AU [32], EOS FPS [33], EOS L [35] and EOS APRb [36]). They matched the Manko et.…”

Thin accretion discs around neutron and quark stars

“…Sibgatullin & Sunyaev (1998) analyzed the effect of the quadrupole component in the mass distribution of a rapidly rotating neutron star, on the energy release in the equatorial (or boundary) layer on the surface of the accreting star and in the accretion disc in the cases where the stellar radius is smaller (or larger) than the radius of the last stable circular orbit. The temperature profiles of (thin) accretion discs around rapidly rotating neutron stars (with low surface magnetic fields), taking into account the full effects of general relativity were obtained in Bhattacharyya et al (2000).…”