Mass-radius relationship and gravitational wave emission from magnetized spheroidal quark stars

Abstract

In this work, we investigate the structure and gravitational wave (GW) signatures of strongly magnetized, oblate spheroidal quark stars by employing an anisotropic equation of state (EoS) derived from the MIT Bag model, extended to include the effects of density-dependent strong magnetic fields and the resulting pressure anisotropy arising from the breaking of spatial symmetry. Both magnetized strange quark matter (MSQM) and magnetized color-flavor locked (MCFL) phases are examined within the framework of the $\gamma$-metric formalism, which captures the deviation from spherical symmetry. We compute the mass-radius relation, ellipticity, gravitational redshift, mass quadrupole moment and tidal deformability for representative bag constants of $\rm{65\,MeV/fm^3}$ and $\rm{75\,MeV/fm^3}$. Using the obtained quadrupole moments, we further estimate the continuous gravitational wave strain amplitude ($h_{0}$) for isolated deformed rotating quark stars. Our results indicate that density-dependent strong magnetic fields and color superconductivity can significantly alter stellar compactness and yield gravitational wave signals, potentially detectable by next generation observatories like the Einstein Telescope and Cosmic Explorer.