Results of the Swift Monitoring Campaign of the X-ray Binary 4U 1957+11: Constraints on Binary Parameters

TL;DR

This study analyzes Swift/XRT observations of the X-ray binary 4U 1957+11, constraining key binary parameters such as inclination, distance, and black hole spin through spectral modeling and statistical methods.

Contribution

It provides the first joint spectral analysis of 26 observations using chi-squared and MCMC methods, offering new constraints on the system's inclination, distance, and black hole spin.

Findings

Inclination angle of approximately 77.6 degrees.

Distance likely greater than 10 kpc for a black hole mass over 10 solar masses.

Distance less than 5 kpc is ruled out by analysis and prior observations.

Abstract

We present new results of uniform spectral analysis of Swift/XRT observations of the X-ray binary system 4U 1957+11. This includes 26 observations of the source made between MJD 54282$-$55890 (2007 July 01 $-$ 2011 November 25). All 26 spectra are predominantly thermal, and can be modeled well with emission from an accretion disk around a black hole. We analyze all 26 spectra jointly using traditional chi-squared fitting as well as Markov Chain Monte Carlo simulations. The results from both methods agree, and constrains on model parameters like inclination, column density, and black hole spin. These results indicate that the X-ray emitting inner accretion disk is inclined to our line-of-sight by $77.6^{+1.5}_{-2.2}$ degrees. Additionally, the other constraints we obtain on parameters like the column density and black hole spin are consistent with previous X-ray observations. Distances less than 5 kpc are unlikely and not only ruled out based on our analysis but also from other independent observations. Based on model-derived bolometric luminosities, we require the source distance to be >10 kpc if the black hole's mass is >10 M$_{Sun}$. If the hole's mass is <10 M$_{Sun}$, then the distance could be in the range of 5$-$10 kpc.