Joint Radiative and Kinematic Modelling of X-ray Binary Ejecta: Energy Estimate and Reverse Shock Detection

Black hole X-ray binaries in outburst launch discrete, large-scale jet ejections which can propagate to parsec scales. The kinematics of these ejecta appear to be well described by relativistic blast wave models original devised for gamma-ray burst afterglows. In previous kinematic-only modelling, a crucial degeneracy prevented the initial ejecta energy and the interstellar medium density from being accurately determined. In this work, we present the first joint Bayesian modelling of the radiation and kinematics of a large-scale jet ejection from the X-ray binary MAXI J1535-571. We demonstrate that a reverse shock powers the bright, early ejecta emission. The joint model breaks the energetic degeneracy, and we find the ejecta has an initial energy of $E_{0} \sim 3 \times 10^{43} \, {\rm erg}$, and propagates into a low density interstellar medium of $n_{\rm ism} \sim 4 \times 10^{-5} \, {\rm cm^{-3}}$. The ejecta is consistent with being launched perpendicular to the disc and could be powered by an efficient conversion of available accretion power alone. This work lays the foundation for future parameter estimation studies using all available data of X-ray binary jet ejecta.