Anisotropic hydrodynamics, bulk viscosities, and r -modes of strange quark stars with strong magnetic fields
Year: 2010
Type: article
Abstract: In strong magnetic fields the transport coefficients of strange quark matter become anisotropic. We determine the general form of the complete set of transport coefficients in the presence of a strong magnetic field. By using a local linear response method, we calculate explicitly the bulk viscosities ${\ensuremath{\zeta}}_{\ensuremath{\perp}}$ and ${\ensuremath{\zeta}}_{\ensuremath{\parallel}}$ transverse and parallel to the $B$ field, respectively, which arise due to the nonleptonic weak processes $u+s\ensuremath{\leftrightarrow}u+d$. We find that for magnetic fields $B<{10}^{17}\text{ }\text{ }\mathrm{G}$, the dependence of ${\ensuremath{\zeta}}_{\ensuremath{\perp}}$ and ${\ensuremath{\zeta}}_{\ensuremath{\parallel}}$ on the field is weak, and they can be approximated by the bulk viscosity for the zero magnetic field. For fields $B>{10}^{18}\text{ }\text{ }\mathrm{G}$, the dependence of both ${\ensuremath{\zeta}}_{\ensuremath{\perp}}$ and ${\ensuremath{\zeta}}_{\ensuremath{\parallel}}$ on the field is strong, and they exhibit de Haas--van Alphen--type oscillations. With increasing magnetic field, the amplitude of these oscillations increases, which eventually leads to negative ${\ensuremath{\zeta}}_{\ensuremath{\perp}}$ in some regions of parameter space. We show that the change of sign of ${\ensuremath{\zeta}}_{\ensuremath{\perp}}$ signals a hydrodynamic instability. As an application, we discuss the effects of the new bulk viscosities on the $r$-mode instability in rotating strange quark stars. We find that the instability region in strange quark stars is affected when the magnetic fields exceed the value $B={10}^{17}\text{ }\text{ }\mathrm{G}$. For fields which are larger by an order of magnitude, the instability region is significantly enlarged, making magnetized strange stars more susceptible to $r$-mode instability than their unmagnetized counterparts.
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2000970644