Thermal Deformations in Super-Eddington Magnetized Neutron Stars: Implications for Continuous Gravitational-Wave Detectability

Rapidly rotating neutron stars (NSs) are promising targets for continuous gravitational-wave (CGW) searches with current and next-generation ground-based GW detectors. In this work, we present the first study of thermal deformations in super-Eddington magnetized NSs with column accretion, where magnetic fields induce anisotropic heat conduction that leads to crustal temperature asymmetries. We compute the resulting mass quadrupole moments and estimate the associated CGW strain amplitudes. Our results show that Galactic magnetized NSs undergoing super-Eddington column accretion can emit detectable CGWs in upcoming observatories. Assuming a 2-yr coherent integration, the Einstein Telescope and Cosmic Explorer could detect such CGW signals from rapidly spinning NSs with spin periods $P \lesssim 20\,\rm ms$, while the LIGO O5 run may detect systems with $P \lesssim 6 \,{\rm ms}$. These findings suggest that super-Eddington magnetized NSs could represent a new class of CGW sources, providing a unique opportunity to probe the NS crust and bridge accretion physics with GW astronomy.