A perturbation study of axisymmetric strongly magnetic degenerate stars: the case of super-Chandrasekhar white dwarfs

Abstract

In the presence of a strong magnetic field a stellar equilibrium configuration, aided by the Lorentz force, can support a larger mass than a non-magnetic one. This has been considered a possible explanation of the super-Chandrasekhar mass white dwarfs giving rise to over-luminous Type-Ia supernovae. We present here linear and non-linear perturbation studies of such strongly magetised configurations and show that axisymmetric configurations with poloidal or toroidal fields are unstable. The numerical evolution of the perturbations shows instability after about an Alfvén crossing time. This time scale is very short for the magnetically supported super-Chandrasekhar mass white dwarfs. Uniform rotation about the symmetry axis can reduce the growth rate but can not stabilize the super-massive configurations. It is concluded that long-lived super-Chandrasekhar mass white dwarfs supported by magnetic field are unlikely to occur in Nature.

Does elasticity stabilize a magnetic neutron star?

“…A barotropic star with axisymmetric mixed poloidal and toroidal field, obtained from self-consistent field studies, also exhibits Tayler instability as the configurations are mainly dominated with a poloidal fraction (Lander & Jones 2012;Bera & Bhattacharya 2017a). Hence, we expect a similar effect due to the shear modulus on magnetic field evolution in such field geometries.…”

“…The linear order time evolution shows exponential growth in the perturbed values as characteristic of the Tayler instability. The growth rate is related to the corresponding Alfvén-crossing time as reported in other papers (Lander & Jones 2011a,b;Bera & Bhattacharya 2017a). In this section, we assume a star with a uniform shear modulus throughout the interior.…”

“…It is known that the Tayler instability is intrinsic to the magnetic field geometry and the temporal characteristics of the instability depend on the effective Alfvén time scale or magnetic field strength (Lander & Jones 2011a;Bera & Bhattacharya 2017a). To compare different configurations, we use the total magnetic energy M for a specific magnetic field geometry 1 .…”

“…Instead, the selfconsistent field technique generates configurations having either pure toroidal field or a poloidal field with a subdominant (< 10%) toroidal component (Tomimura & Eriguchi 2005;Lander & Jones 2009). These axisymmetric configurations remain unstable against a small perturbation and the instability grows on the characteristic Alfvén time scale (Lander & Jones 2011a,b;Bera & Bhattacharya 2017a). The problem of an unstable magnetic field remains, but one should keep in mind that these studies are based on an ideal fluid model with no dissipation, e.g.…”

Modified virial theorem for highly magnetized white dwarfs

“…On the other hand, it has been well-known since 1973 (Tayler 1973;Markey & Tayler 1973) that purely poloidal (or poloidally dominated) or purely toroidal fields are unstable. Hence any stability analysis of a magnetized star based on purely poloidal and purely toroidal field, as attempted by Bera & Bhattacharya (2016), does not make any sense (Mukhopadhyay et al 2016). However, it was shown by Wickramasinghe et al (2013) that a white dwarf with toroidally dominated mixed field configuration (with a small poloidal component) remains stable for a long time.…”