Modeling the kinematics of the decelerating jets from the black hole X-ray binary MAXI J1348$-$630

Abstract

Black hole low mass X-ray binaries (BH LMXBs) can launch powerful outflows in the form of discrete ejecta. Observing the entire trajectory of these ejecta allows us to model their motion with great accuracy, and this is essential for measuring their physical properties. In particular, observing the final deceleration phase, often poorly sampled, is fundamental to obtain a reliable estimate of the jet's energy. During its 2019/2020 outburst, the BH LMXB MAXI J1348$-$630 launched a single-sided radio-emitting jet that was detected at large scales after a strong deceleration due to the interaction with the interstellar medium (ISM). We successfully modelled the jet motion with a dynamical external shock model, which allowed us to constrain the jet initial Lorentz factor $\Gamma_0 = 1.85^{+0.15}_{-0.12}$, inclination angle $\theta = 29.3_{-3.2}^{+2.7}$ deg and ejection date $t_{\rm ej} = 21.5_{-3.0}^{+1.8}$ (MJD $-$ $58500$). Under simple assumptions on the jet opening angle and on the external ISM density, we find that the jet has a large initial kinetic energy $E_0 = 4.6^{+20.0}_{-3.4} \times 10^{46}$ erg, far greater than what commonly measured for LMXBs from the jet's synchrotron emission. This implies that discrete ejecta radiate away only a small fraction of their total energy, which is instead transferred to the environment. The jet power estimate is larger than the simultaneous available accretion power, and we present several options to mitigate this discrepancy. We infer that MAXI J1348$-$630 is likely embedded in an ISM cavity with internal density $n = 0.0010^{+0.0005}_{-0.0003}$ cm$^{-3}$ and radius $R_{\rm c} = 0.61^{+0.11}_{-0.09}$ pc, which could have been produced by the system's previous activity, as proposed for other BH LMXBs.