# On the compactness of the isolated neutron star RX J0720.4-3125

## TL;DR

This study reanalyzed extensive X-ray data of neutron star RX J0720.4-3125 using Bayesian methods, revealing complex, energy-dependent light curves, a revised spin period, and estimates of gravitational redshift and compactness.

## Contribution

It introduces a Bayesian approach to analyze neutron star light curves and determines a revised spin period, gravitational redshift, and compactness of RX J0720.4-3125.

## Key findings

- The spin period is likely 16.78 seconds, twice the previously reported value.
- Light curves are complex and energy-dependent, best modeled with a double-peaked profile.
- Estimated gravitational redshift is approximately 0.205, indicating high compactness.

## Abstract

The data from all observations of RX J0720.4-3125 conducted by XMM-Newton EPIC-pn with the same instrumental setup in 2000-2012 were reprocessed to form a homogenous data set of solar barycenter corrected photon arrival times registered from RX J0720.4-3125. A Bayesian method for the search, detection, and estimation of the parameters of an unknown-shaped periodic signal was employed as developed by Gregory & Loredo (1992). A number of complex models (single and double peaked) of light curves from pulsating neutron stars were statistically analyzed. The distribution of phases for the registered photons was calculated by folding the arrival times with the derived spin-period and the resulting distribution of phases approximated with a mixed von Mises distribution, and its parameters were estimated by using the Expected Maximization method. Spin phase-resolved spectra were extracted, and a number of highly magnetized atmosphere models of an INS were used to fit simultaneously, the results were verified via an MCMC approach. The phase-folded light curves in different energy bands with high S/N ratio show a high complexity and variations depending on time and energy. They can be parameterized with a mixed von Mises distribution, i.e. with double-peaked light curve profile showing a dependence of the estimated parameters (mean directions, concentrations, and proportion) upon the energy band, indicating that radiation emerges from at least two emitting areas. The genuine spin-period of the isolated neutron star RX J0720-3125 derived as more likely is twice of that reported in the literature (16.78s instead of 8.39s). The gravitational redshift of RX J0720.4-3125 was determined to $z=0.205_{-0.003}^{+0.006}$ and the compactness was estimated to $(M/M_{Sun})/R(km)=0.105 \pm 0.002 $.