# Superradiance in rotating stars and pulsar-timing constraints on dark photons

## TL;DR

This paper explores how rotating stars can amplify electromagnetic waves through superradiance, leading to constraints on dark photon properties based on pulsar timing data, similar to black hole superradiance effects.

## Contribution

It demonstrates the existence of superradiant instabilities in conducting stars and derives pulsar-timing constraints on the mass of dark photons, extending superradiance concepts beyond black holes.

## Key findings

- Dark photons of mass ~10^{-12} eV are excluded by pulsar timing.
- Superradiant instabilities can cause pulsar spindown, constraining dark sector models.
- The effect depends on star properties like rotation, compactness, and conductivity.

## Abstract

In the presence of massive bosonic degrees of freedom, rotational superradiance can trigger an instability that spins down black holes. This leads to peculiar gravitational-wave signatures and distribution in the spin-mass plane, which in turn can impose stringent constraints on ultralight fields. Here, we demonstrate that there is an analogous spindown effect for conducting stars. We show that rotating stars amplify low frequency electromagnetic waves, and that this effect is largest when the time scale for conduction within the star is of the order of a light crossing time. This has interesting consequences for dark photons, as massive dark photons would cause stars to spin down due to superradiant instabilities. The time scale of the spindown depends on the mass of the dark photon, and on the rotation rate, compactness, and conductivity of the star. Existing measurements of the spindown rate of pulsars place direct constraints on models of dark sectors. Our analysis suggests that dark photons of mass $m_V \sim 10^{-12}$ eV are excluded by pulsar-timing observations. These constraints also exclude superradiant instabilities triggered by dark photons as an explanation for the spin limit of observed pulsars.