Spin Constraints on 4U 1630-47 via combined Continuum Fitting and Reflection methods: a comparative study using Frequentist and Bayesian statistics

Abstract: We present a comprehensive Bayesian spectral analysis of the black hole X-ray binary 4U 1630-47 during its 2022 outburst, using simultaneous \textit{NICER} and \textit{NuSTAR} observations. Using the traditional frequentist approach, we build our model combining reflection spectroscopy with continuum fitting techniques and analyse the data. In the Bayesian framework, we jointly constrain the black hole's spin, mass, inclination, and distance within a unified framework. Employing nested sampling, we capture parameter degeneracies and rigorously propagate both statistical and systematic uncertainties. Our results yield robust and precise spin measurements from both approaches. Our Bayesian analysis fetches spin $a_*= 0.93_{-0.04}^{+0.05}$, mass $M_{\rm BH} = 9.0_{-2.0}^{+2.0} \, M_\odot$, distance $d_{\rm BH} = 10.5_{-1.2}^{+1.3}$~kpc, and inclination angle $i=53.8_{-1.3}^{+1.3}$~deg. It also demonstrates the power of Bayesian inference in fetching valuable insights into the complex physics of black hole accretion and enabling high-confidence measurements of fundamental parameters.