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

TL;DR

This paper investigates how strong magnetic fields induce anisotropic transport coefficients in strange quark matter, affecting bulk viscosities and the r-mode instability in strange quark stars, especially at fields above 10^{17} G.

Contribution

It provides a comprehensive calculation of anisotropic bulk viscosities in magnetized strange quark matter and explores their impact on stellar stability.

Findings

Bulk viscosities are weakly dependent on magnetic fields below 10^{17} G.

Strong magnetic fields above 10^{18} G cause oscillations and negative values in bulk viscosities.

Magnetic fields larger than 10^{17} G significantly enlarge the r-mode instability region.

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 $\zperp$ 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.