Probing magnetic fields of compact objects with continuous gravitational waves

Abstract: Spinning, deformed compact objects such as neutron stars are canonical sources of continuous gravitational waves. These objects may be born with magnetic fields that can strongly influence their spin evolution and, consequently, their gravitational wave detectability. Employing a Bayesian framework, we use for the first time, the non detection of continuous gravitational waves in the LIGO Virgo KAGRA (LVK) third observing run (O3), using reported amplitude upper limits from various LVK and Einstein@Home searches, to place population level constraints on the birth magnetic field distribution of Galactic compact objects. To this end, we simulate compact object populations whose spin evolution is governed by gravitational wave emission and magnetic dipole radiation. We explore multiple ellipticity models and magnetic field decay timescales, and find that the lower limit on the birth magnetic field distribution hyperparameter $B_0$ is constrained to lie in the range $$10^{{9.6}\mathrm{G}} \lesssim B_0\,\lesssim 10<sup>{13.3}\mathrm{G}$$. Furthermore, we reinterpret the number constraints on the total population of Galactic compact objects, reported previously by \citet{Prabhu_2024}, as upper limits on the number of compact objects with a population averaged magnetic field, presented as a function of ellipticity and gravitational wave frequency for all searches considered here.