Energy release on the surface of a rapidly rotating neutron star during disk accretion: A thermodynamic approach

Abstract

.Abstract. The total energy E of a star as a function of its angular momentum J and mass M in the Newtonian theory: E = E(J, M) [in general relativity, the gravitational mass M of a star as a function of its angular momentum J and rest mass m, M = M(J, m)], is used to determine the remaining parameters (angular velocity, equatorial radius, chemical potential, etc.) in the case of rigid rotation. Expressions are derived for the energy release during accretion onto a cool (with constant entropy), rapidly rotating neutron star (NS) in the Newtonian theory and in general relativity. A separate analysis is performed for the cases where the NS equatorial radius is larger and smaller than the radius of the marginally stable orbit in the disk plane. An approximate formula is proposed for the NS equatorial radius for an arbitrary equation of state, which matches the exact one at J = 0.

Nodal and periastron precession of inclined orbits in the field of a rotating black hole

“…When observations are accumulated, formulas (51) and (52) make it possible to determine the orbital inclination to the spin axis of a slowly rotating black hole or neutron star. When analyzing the energy release in the boundary layer and in an extended disk for a rapidly rotating neutron star, we should took into account the appearance of an intrinsic quadrupole moment that exceeds the Kerr one (see Sibgatullin and Sunyaev 1998, 2000a, 2000b. We emphasize that formulas (51) and (52) are not related to the weak-field approximation and are valid up to the marginally stable orbit.…”

“…For NSs with a stiff equation of state, this component can be several times larger than the Kerr quadrupole moment. The effect of a non-Kerr NS field induced by rapid NS rotation on the parameters of the marginally stable orbit and energy release in the equatorial boundary layer was analyzed by Sibgatullin and Sunyaev (1998, 2000a, 2000b) using an exact solution for a rotating configuration with a quadrupole moment (Manko et al 1994) [approximate approaches with multipole expansions of the metric coefficients at large radii were developed by Laarakkers and Poisson (1998) and Shibata and Sasaki (1998)]. Our results refer to nonequatorial, nearly circular orbits in the fields of black holes and NSs with a soft equation of state at a moderate rotation frequency.…”

Nodal and periastron precession of inclined orbits in the field of a rapidly rotating neutron star

“…For clarity, the exact quadrupole solution is also given asymptotically as a Kerr metric perturbation in Boyer-Lindquist coordinates. Sibgatullin and Sunyaev (1998, 2000a, 2000b) (below referred to as SS 98, SS 00a, and SS 00b) provided formulas for the luminosity and spindown rate for various NS equations of state. These authors proposed a method of analytically constructing the quadrupole moment b as a function of the Kerr parameter j and NS rest mass m, b = b(j, m), based on the main NS thermodynamic function -its gravitational mass M as a function of the Kerr parameter and rest mass M = M(j, m).…”

Accretion onto Black Holes and Neutron Stars: Differences and Similarities

“…Fortunately, there is an exact solution of the GR equations for the case when the mass distribution has a quadrupole component. Using this solution, Sibgatullin & Sunyaev (2000) plotted the dependence of the energy release due to the accretion onto a neutron star as a function of the rotation frequency of that star (Fig. 3).…”

“…As predicted by standard accretion theory, this is a multicolor disk spectrum (cf. Shakura & Sunyaev 1973) or a power-law hard X-ray spectrum with a Wien-type decay at high energies formed due to comptonization (Sunyaev & Trümper 1979, Sunyaev & Titarchuk 1980). Sometimes we do not even see the high frequency decay yet.…”