Constraining the physical properties of large-scale jets from black hole X-ray binaries and their impact on the local environment with blast-wave dynamical models

Relativistic discrete ejecta launched by black hole X-ray binaries (BH XRBs) can be observed to propagate up to parsec-scales from the central object. Observing the final deceleration phase of these jets is crucial to estimate their physical parameters and to reconstruct their full trajectory, with implications for the jet powering mechanism, composition and formation. In this paper we present the results of the modelling of the motion of the ejecta from three BH XRBs: MAXI J1820+070, MAXI J1535$-$571 and XTE J1752$-$223, for which high-resolution radio and X-ray observations of jets propagating up to $\sim$15 arcsec ($\sim$0.6 pc at 3 kpc) from the core have been published in the recent years. For each jet, we modeled its entire motion with a dynamical blast-wave model, inferring robust values for the jet Lorentz factor, inclination angle and ejection time. Under several assumptions associated to the ejection duration, the jet opening angle and the available accretion power, we are able to derive stringent constraints on the maximum jet kinetic energy for each source (between $10^{43}$ and $10^{44}$ erg, including also H1743$-$322), as well as placing interesting upper limits on the density of the ISM through which the jets are propagating (from $n_{\rm ISM} \lesssim 0.4$ cm$^{-3}$ down to $n_{\rm ISM} \lesssim 10^{-4}$ cm$^{-3}$). Overall, our results highlight the potential of applying models derived from gamma-ray bursts to the physics of jets from BH XRBs and support the emerging picture of these sources as preferentially embedded in low-density environments.