A. J. Cooper, J. H. Matthews, F. Carotenuto, R. Fender, G. P. Lamb, T. D. Russell, N. Sarin, K. Savard

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 a conservative initial ejecta energy of $E_{0} \sim 4 \times 10^{43} \, {\rm erg}$, consistent with the disc luminosity integrated over a flare-informed launching timescale, and a low interstellar medium density of $n_{\rm ism} \sim 5 \times 10^{-5} \, {\rm cm^{-3}}$. This work lays the foundation for future parameter estimation studies using all available data of X-ray binary jet ejecta.