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 NICER and NuSTAR observations. Using the traditional frequentist approach, we build our model combining reflection spectroscopy with continuum-fitting techniques and analyze the data. In the Bayesian framework, we jointly constrain the black hole’s spin, mass, and inclination within a unified framework. Employing nested sampling, we capture parameter degeneracies and rigorously propagate both statistical and systematic uncertainties. Our results yield robust evidence for a high spin, with the exact value still subject to model-dependent systematic uncertainties from both approaches. Our Bayesian analysis infers spin <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mi>a</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>*</mml:mo> </mml:mrow> </mml:msup> <mml:mo>=</mml:mo> <mml:mn>0.9</mml:mn> <mml:msubsup> <mml:mrow> <mml:mn>6</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.03</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.02</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> , mass <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">BH</mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>12.1</mml:mn> <mml:msubsup> <mml:mrow> <mml:mn>9</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1.46</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>1.22</mml:mn> </mml:mrow> </mml:msubsup> <mml:mspace width="0.25em"/> <mml:msub> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>⊙</mml:mo> </mml:mrow> </mml:msub> </mml:math> , and inclination angle <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>i</mml:mi> <mml:mo>=</mml:mo> <mml:mn>55.7</mml:mn> <mml:msubsup> <mml:mrow> <mml:mn>5</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1.37</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>1.60</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> degrees, obtained via the relxillNS version of our model. It also demonstrates the power of Bayesian inference in providing valuable insights into the complex physics of black hole accretion and enabling high-confidence measurements of fundamental parameters.

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