# Radial modes of levitating atmospheres around Eddington-luminosity neutron stars

## TL;DR

This paper analyzes the oscillation modes of a thin, radiation-supported atmosphere around a neutron star near the Eddington luminosity, deriving eigenfrequencies based on the atmosphere's properties.

## Contribution

It provides a theoretical calculation of the eigenmodes and frequencies of levitating atmospheres in a Newtonian framework, highlighting the dependence on the adiabatic index.

## Key findings

- Eigenfrequency ratio depends only on the adiabatic index, b3+1.
- The atmosphere's oscillation frequencies are derived analytically.
- The study enhances understanding of neutron star atmospheres near Eddington luminosity.

## Abstract

We consider an optically thin radiation-supported levitating atmosphere suspended well above the stellar surface, as discussed recently in the Schwarzschild metric for a star of luminosity close to the Eddington value. Assuming the atmosphere to be geometrically thin and polytropic, we investigate the eigenmodes and calculate the frequencies of the oscillations of the atmosphere in Newtonian formalism. The ratio of the two lowest eigenfrequencies is $\sqrt{\gamma+1}$, i.e., it only depends on the adiabatic index.