Erratum: “A two-dimensional hydrostatically equilibrium atmosphere of a neutron star with given differential rotation” [Pis’ma Astron. Zh. 26, 917 (2000); Astronomy Letters 26, 788 (2000)]

A hydrodynamic model for asymmetric explosions of rapidly rotating collapsing supernovae with a toroidal atmosphere

“…Recall that the rotational mechanism implies a crucial role of the rotation effects in explaining the explosions of collapsing supernovae (Imshennik 1992). As was roughly estimated by Aksenov et al (1997), for high-mass (M > 10M ⊙ ) main-sequence stars, the equatorial rotational velocities of their iron cores at the final stages of their existence could be close in magnitude to the parabolic velocity.…”

“…To completely determine the parameters of the binary, it remains only to specify the pulsar's velocity and the relationship between the masses of the pulsar and its lighter companion. A similar problem of the explosion of a low-mass neutron star was studied by Aksenov et al (1997) and Imshennik and Zabrodina (1999). Nevertheless, these studies had a number of fundamental differences from the problem considered here.…”

“…This property of the atmosphere (∇S ≃ 0) and the distribution of specific angular momentum in it (which satisfies the condition ∂j 2 /∂r > 0, wherer is the cylindrical radius) derived previously (Imshennik et al 2003) are necessary and sufficient conditions for the Viertoft-Lebowitz dynamical stability criterion to be fulfilled (Tassoul 1982). All of this allows the toroidal atmosphere obtained previously (Imshennik et al 2003) to be deemed to be a long-lived structure with a total lifetime that is comparable, at least, to the evolution time of a neutron-star binary ( 1 h) considered in the context of a rotational explosion mechanism for collapsing supernovae (Imshennik and Popov 1994;Imshennik and Ryazhskaya 2004).…”

“…The filling of a Roche lobe with known characteristics (Paczynski 1971) leads to intense mass transfer from the less massive component to the more massive component of a neutron-star binary that ends with explosive destruction of the light component when it reaches the minimum possible neutron-star mass, ≃ 0.1M ⊙ (Blinnikov et al 1984(Blinnikov et al , 1990; Colpi et al 1989Colpi et al , 1991Colpi et al , 1993. It should be emphasized that the process of mass transfer in a neutron-star binary, which was considered in detail by Imshennik and Popov (1998), was simplified by using the so-called conservative approximation in which the possible formation of an accretion disk around the high-mass component was disregarded . The existence of such an accretion disk during the mass transfer between the components of the binary under consideration has recently been analyzed by Colpi and Wasserman (2004).…”

“…In the presence of such fast rotation, the iron core collapses to form a rapidly rotating protoneutron star that is generally unstable against the quadrupole dynamical rotational mode m = 2 (Aksenov et al 1995) or, in other words, against its fragmentation. The neutron-star binary formed through such fragmentation (in the simplest case) evolves due to the losses of energy and angular momentum via the emission of gravitational waves, and the orbit of the binary becomes circular by the time the low-mass companion fills its Roche lobe almost independently of the initial eccentricity of the binary (Imshennik and Popov 1994). The filling of a Roche lobe with known characteristics (Paczynski 1971) leads to intense mass transfer from the less massive component to the more massive component of a neutron-star binary that ends with explosive destruction of the light component when it reaches the minimum possible neutron-star mass, ≃ 0.1M ⊙ (Blinnikov et al 1984(Blinnikov et al , 1990; Colpi et al 1989Colpi et al , 1991Colpi et al , 1993.…”