Particle Conversions Beyond the WKB Approximation and Solar-Induced Gravitational Waves from Dark Photon Dark Matter

TL;DR

This paper develops an analytic approach beyond the WKB approximation to calculate gravitational wave signals from dark photon dark matter converting in the Sun's magnetic field, revealing significantly different strain predictions.

Contribution

It introduces a unitary evolution-based analytic solution for particle conversion processes, applicable when the WKB approximation fails, and extends it to various dark sector conversions.

Findings

Derived an analytic solution valid beyond WKB approximation.

Calculated gravitational wave strain from dark photon conversion in the Sun.

Found the strain signal is below current detector sensitivities.

Abstract

We investigate the conversion of kinetic mixing dark photon dark matter into gravitational waves within the magnetic field of the Sun. Our study reveals that the WKB approximation is invalid in this scenario. We derive an analytic solution for the conversion probability with unitary evolution feature. This solution aligns in form with previous studies on photon-gravitational wave conversion. Interestingly, it is applicable in situations where the WKB approximation fails. We extend the unitary evolution solution to other conversion processes, such as axion-photon and dark photon-photon conversions. When the WKB approximation conditions are met, this solution reduces to the WKB result. We compute the characteristic strain of gravitational waves resulting from dark photon conversion in the solar magnetic field, spanning frequencies from $10^{-5}$ Hz to $10^6$ Hz. Our findings indicate that the characteristic strain derived from the unitary evolution solution differs significantly from that of the WKB solution. The resulting strain signal is far below the sensitivity of current gravitational wave interferometers. Nevertheless, we have proposed an exotic gravitational wave source, which could be useful in non-minimal dark sector models.