**Authors**: Nathan K. Johnson-McDaniel, Benjamin J. Owen

**Date**: 26 Aug 2012

**Abstract**: We present a method for calculating the maximum elastic quadrupolar deformations of relativistic stars, generalizing the previous Newtonian, Cowling approximation integral given by [G. Ushomirsky et al., Mon. Not. R. Astron. Soc. 319, 902 (2000)]. (We also present a method for Newtonian gravity with no Cowling approximation.) We apply these methods to the m = 2 quadrupoles most relevant for gravitational radiation in three cases: crustal deformations, deformations of crystalline cores of hadron-quark hybrid stars, and deformations of entirely crystalline color superconducting quark stars. In all cases, we find suppressions of the quadrupole due to relativity compared to the Newtonian Cowling approximation, particularly for compact stars. For the crust these suppressions are up to a factor ~6, for hybrid stars they are up to ~4, and for solid quark stars they are at most ~2, with slight enhancements instead for low mass stars. We also explore ranges of masses and equations of state more than in previous work, and find that for some parameters the maximum quadrupoles can still be very large. Even with the relativistic suppressions, we find that 1.4 solar mass stars can sustain crustal quadrupoles of a few times 10ˆ39 g cmˆ2 for the SLy equation of state or close to 10ˆ40 g cmˆ2 for equations of state that produce less compact stars. Solid quark stars of 1.4 solar masses can sustain quadrupoles of around 10ˆ44 g cmˆ2. Hybrid stars typically do not have solid cores at 1.4 solar masses, but the most massive ones (~2 solar masses) can sustain quadrupoles of a few times 10ˆ41 g cmˆ2 for typical microphysical parameters and a few times 10ˆ42 g cmˆ2 for extreme ones. All of these quadrupoles assume a breaking strain of 0.1 and can be divided by 10ˆ45 g cmˆ2 to yield the fiducial "ellipticities" quoted elsewhere.

1208.5227
(/preprints)

2012-09-17, 13:45
**[edit]**

© M. Vallisneri 2012 — last modified on 2010/01/29

*Tantum in modicis, quantum in maximis*