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 \(0.67\dot Mc^2 \). 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 Ф2. Depending on Ф2, this solution can also be interpreted as a solution that describes the field of either two Kerr black holes or two Kerr disks.
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References
M. A. Alpar, A. F. Cheng, M. A. Ruderman, and J. Shaham, Nature 300, 728 (1982).
W. D. Arnett and R. L. Bowers, Astrophys. J., Suppl. Ser. 33, 415 (1977).
J. M. Bardeen, W. H. Press, and S. A. Teukolsky, Astrophys. J. 178, 347 (1972).
J. M. Bardeen and R. V. Wagoner, Astrophys. J. 167, 359 (1971).
G. Biehle and R. D. Blanford, Astrophys. J. 411, 302 (1993).
L. Bildsten, astro-ph/0001135.
G. S. Bisnovatyi-Kogan and S. I. Blinnikov, Astron. Astrophys. 31, 391 (1974).
G. S. Bisnovatyi-Kogan and B. V. Komberg, Astron. Zh. 51, 373 (1974) [Sov. Astron. 18, 217 (1974)].
S. Bonazzola, E. Gourgoulhon, M. Salgado, and J. A. Marck, Astron. Astrophys. 278, 421 (1993).
S. Bonazzola and J. Schneider, Astrophys. J. 191, 273 (1974).
L. Burderi, A. Possenti, M. Colpi, et al., astro-ph/9904331.
I. M. Butterworth and J. R. Ipser, Astrophys. J. 204, 200 (1976).
G. Calamai, Astrophys. Space Sci. 8, 53 (1970).
F. Camilo, D. R. Lorimer, P. Freire, et al., Astrophys. J. 535, 975 (2000); astro-ph/9911234.
D. Chakrabarty and E. H. Morgan, Nature 394, 346 (1998).
S. Chandrasekhar, Ellipsoidal Figures of Equilibrium (Dover, New-York, 1986).
D. Christodolou and R. Ruffini, Phys. Rev. 4, 3552 (1973).
G. B. Cook, S. L. Shapiro, and S. A. Teukolsky, Astrophys. J. 424, 823 (1994).
B. Datta, A. V. Thampan, and I. Bombaci, Astron. Astrophys. 334, 943 (1998); astro-ph/9801312.
N. A. Dmitriev and S. A. Kholin, Vopr. Kosmog. 9, 254 (1963).
K. Ebisawa, K. Mitsuda, and T. Hanawa, Astrophys. J. 367, 213 (1991).
Y. Eriguchi and E. Mueller, Astron. Asrophys. 146, 260 (1985).
Y. Eriguchi, I. Hachisu, and K. Nomoto, Mon. Not. R. Astron. Soc. 266, 179 (1994).
F. J. Ernst, Phys. Rev. D. 50, 4993 (1994).
L. S. Finn and S. Shapiro, Astrophys. J. 359, 444 (1990).
G. Fodor, C. Hoenselaers, and Z. Perjes, J. Math. Phys. 30, 2252 (1989).
B. Friedman and V. R. Pandharipande, Nucl. Phys. A 361, 502 (1981).
J. F. Friedman, J. R. Ipser, and L. Parker, Astrophys. J. 304, 115 (1986).
M. Gilfanov, M. Revnivtsev, R. Sunyaev, and E. Churazov, Astron. Astrophys. 339, 483 (1998).
I. Hachisu, Astrophys. J., Suppl. Ser. 61, 479 (1986).
I. Hachisu, Y. Eriguchi, and D. Sugimoto, Prog. Theor. Phys. 68, 191 (1982).
R. O. Hansen, J. Math. Phys. 15(1), 46 (1974).
J. B. Hartle, Phys. Rep. 46, 202 (1978).
J. B. Hartle and D. H. Sharp, Astrophys. J. 147, 317 (1967).
J. B. Hartle, Astrophys. J. 195, 203 (1975).
J. B. Hartle and K. S. Thorne, Astrophys. J. 158, 719 (1969).
C. Hoenselaers, Prog. Theor. Phys. 72, 761 (1984).
A. F. Illarionov and R. A. Sunyaev, Astron. Zh. 51, 1162 (1974) [Sov. Astron. 18, 691 (1974)].
N. A. Inogamov and R. A. Sunyaev, Pis’ma Astron. Zh. 25, 323 (1999) [Astron. Lett. 25, 269 (1999)].
W. Kley, Astron. Astrophys. 247, 95 (1991).
W. Kluzniak, Ph.D. Thesis (Stanford Univ., 1987).
W. Kluzniak and R. V. Wagoner, Astrophys. J. 297, 548 (1985).
H. Komatsu, Y. Eriguchi, and I. Hachisu, Mon. Not. R. Astron. Soc. 237, 355 (1989).
D. Kramer and G. Neugebauer, Phys. Lett. A75, 259 (1980).
W. Laarakkers and E. Poisson, gr-qc/9709033.
M. J. Lighthill, Mon. Not. R. Astron. Soc. 110, 339 (1950).
L. Lindblom, Phys. Rev. D 58, 024008 (1998); gr-qc/9802072.
V. M. Lipunov and K. A. Postnov, Astrophys. Space Sci. 106, 103 (1984).
C. P. Lorenz, D. G. Ravenhall, and C. J. Pethick, Phys. Rev. Lett. 70, 379 (1993).
V. S. Manko, E. W. Mielke, and J. D. Sanabria-Gómez, Phys. Rev. D 61, 081501 (2000); gr-qc/0001081.
V. S. Manko, J. Martín, E. Ruíz, et al., Phys. Rev. D 49, 5144 (1994).
V. S. Manko and E. Ruíz, Class. Quantum. Grav. 15, 2007 (1998).
D. Markovic and F. K. Lamb, Rossi2000: Astrophysics with the Rossi X-ray Timing Explorer (NASA’s Goddard Space Flight Center, Greenbelt, 2000), p. E61.
S. L. W. McMillan and P. Hut, Astrophys. J. 467, 348 (1996).
M. C. Miller and F. K. Lamb, Astrophys. J. 470, 1033 (1996).
M. C. Miller, F. K. Lamb, and G. B. Cook, Astrophys. J. 509, 793 (1998); astro-ph/9805007.
Ch. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (Freeman, New York, 1973).
G. Neugebauer, J. Phys. 13, L19 (1980).
I. D. Novikov and V. P. Frolov, Physics of Black Holes (Nauka, Moscow, 1986).
T. Nozawa, N. Stergioulas, E. Gourgoulhon, and Y. Eriguchi, Astron. Astrophys. 132, 431N (1998); gr-qc/9804048.
J. P. Ostriker and J. W.-K. Mark, Astrophys. J. 151, 1075 (1968).
V. R. Pandharipande, Nucl. Phys. A 174, 641 (1971).
R. Popham and R. Narayan, Astrophys. J. 442, 337 (1995).
P. Popham and R. Sunyaev, astro-ph/0004017.
J. E. Pringle and M. J. Rees, Astron. Astrophys. 21, 1 (1972).
W. H. Ramsey, Mon. Not. R. Astron. Soc. 110, 325 (1950).
D. G. Ravenhall and C. J. Pethick, Astrophys. J. 424, 846 (1994).
R. Ruffini and J. A. Wheeler, Bull. Am. Phys. Soc. 15(11), 76 (1970).
F. D. Ryan, Phys. Rev. D 52, 5707 (1995).
F. D. Ryan, Phys. Rev. D 55, 6081 (1997).
M. Salgado, S. Bonazzola, E. Gourgulhon, and P. Haensel, Astron. Astrophys. 291, 155 (1994).
Z. F. Seidov, Astron. Zh. 48, 443 (1971) [Sov. Astron. 15, 347 (1971)].
N. I. Shakura and R. A. Sunyaev, Adv. Space Res. 8(2–3), 135 (1988).
S. L. Shapiro and S. A. Teukolsky, Black Holes, White Dwarfs, and Neutron Stars: the Physics of Compact Objects (Wiley, New York, 1983; Mir, Moscow, 1985).
M. Shibata and M. Sasaki, Phys. Rev. D 58, 104011 (1998); gr-qc/9807046.
N. R. Sibgatullin, Oscillations and Waves in Strong Gravitational and Electromagnetic Fields (Nauka, Moscow, 1984; Springer-Verlag, Berlin, 1991).
N. R. Sibgatullin and R. A. Sunyaev, Pis’ma Astron. Zh. 24, 894 (1998) [Astron. Lett. 24, 774 (1998)]; astro-ph/9811028.
N. R. Sibgatullin and R. A. Sunyaev, Pis’ma Astron. Zh. 26 (2000) [Astron. Lett. (2000) (in press)].
H. C. Spruit and E. S. Phinney, Nature 393, 139 (1998).
N. Stergioulas, http://pauli.phys.uwm.edu/Code/rns; http://www.livingreviews.org/Articles/Volume1/1998-8stergio.
N. Stergioulas and J. L. Friedman, Astrophys. J. 444, 306 (1995).
T. Stromayer, W. Zhang, J. H. Swank, et al., Astrophys. J. Lett. 498, L135 (1998); astro-ph/03119.
R. A. Sunyaev and N. I. Shakura, Pis’ma Astron. Zh. 12, 286 (1986) [Sov. Astron. Lett. 12, 117 (1986)].
J. L. Tassoul, Theory of Rotating Stars (Princeton Univ. Press, Princeton, 1978).
A. Thampan and B. Datta, Mon. Not. R. Astron. Soc. 297, 570 (1998).
S. E. Thorsett and D. Chakrabarty, Astrophys. J. 512, 288 (1999); astro-ph/9803260.
L. Titarchuk and V. Osherovich, astro-ph/0005375.
M. van der Klis, astro-ph/0001167.
R. A. D. Wijnands and M. van der Klis, Astrophys. J. Lett. 482, L65 (1997).
R. B. Wiringa, V. Fiks, and A. Fabroccini, Phys. Rev. C 38, 1010 (1988).
M. N. Zaripov, N. R. Sibgatullin, and A. Chamorro, Prikl. Mat. Mekh. 59(5), 750 (1995).
M. N. Zaripov, N. R. Sibgatullin, and A. Chamorro, Vestn. Mosk. Univ., Ser. 1: Mat., Mekh., No. 6, 61 (1994).
Ya. B. Zel’dovich, Vopr. Kosmog. 9, 157 (1963).
Ya. B. Zel’dovich and I. D. Novikov, The Theory of Gravitation and Evolution of Stars (Nauka, Moscow, 1971).
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Translated from Pis’ma v Astronomicheski\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) Zhurnal, Vol. 26, No. 11, 2000, pp. 813–841.
Original Russian Text Copyright © 2000 by Sibgatullin, Sunyaev.
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Sibgatullin, N.R., Sunyaev, R.A. Energy release during disk accretion onto a rapidly rotating neutron star. Astron. Lett. 26, 699–724 (2000). https://doi.org/10.1134/1.1323277
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DOI: https://doi.org/10.1134/1.1323277