# Radial oscillations of boson stars made of ultralight repulsive dark matter

## TL;DR

This paper analyzes the radial oscillation modes of boson stars composed of ultralight repulsive dark matter, revealing how their oscillation frequencies relate to star mass and particle physics parameters.

## Contribution

It provides the first detailed calculation of radial oscillation modes for boson stars with repulsive self-interactions, linking oscillation properties to fundamental particle parameters.

## Key findings

- Oscillation frequencies depend on star mass and particle physics scales.
- The frequency separation scales with the square root of star mass and cube of the scale Λ.
- The study offers insights into the stability and structure of boson stars made of ultralight dark matter.

## Abstract

We compute the lowest frequency radial oscillation modes of boson stars. It is assumed that the object is made of pseudo-Goldstone bosons subjected to a scalar potential that leads to a repulsive self-interaction force, and which is characterized by two unknown mass scales $m$ (mass of the particle) and $F$ (decay constant). First we integrate the Tolman-Oppenheimer-Volkoff equations for the hydrostatic equilibrium of the star, and then we solve the Sturm-Liouville boundary value problem for the perturbations using the shooting method. The effective potential that enters into the Schr{\"o}dinger-like equation as well as several associated eigenfunctions are shown as well. Moreover, we found that the large frequency separation, i.e. the difference between consecutive modes, is proportional to the square root of the mass of the star and the cube of the mass scale defined by $\Lambda \equiv \sqrt{m F}$.