Anisotropic Hydrodynamics, Bulk Viscosities and R-Modes of Strange Quark Stars with Strong Magnetic Fields

Xu-Guang Huang, Mei Huang, Dirk H. Rischke, Armen Sedrakian

Published 2009-10-19, updated 2010-02-26Version 3

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 $\zperp$ and $\zpara$ transverse and parallel to the $B$-field respectively, which arise due to the non-leptonic weak processes $u+s\leftrightarrow u+d$. We find that for magnetic fields $B<10^{17}$ G, the dependence of $\zperp$ and $\zpara$ on the field is weak, and they can be approximated by the bulk viscosity for zero magnetic field. For fields $B>10^{18}$ G, the dependence of both $\zperp$ and $\zpara$ 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 $\zperp$ in some regions of parameter space. We show that the change of sign of $\zperp$ 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 exceeds the value $B= 10^{17}$ 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.