Broad-band Spectral Modeling of Large-Scale X-ray Jets in High-Redshift Quasars: An MHD-Informed Approach

Abstract

We present a systematic spectral analysis of kiloparsec-scale jets in high-redshift quasars, modeling their radio-to-X-ray emission as synchrotron radiation and inverse-comptonization of CMB by relativistic electrons. In contrast to the homogeneous one-zone approximation commonly adopted in the literature, we describe the jet as a current-carrying, axially symmetric outflow with a purely toroidal magnetic field in magnetohydrostatic equilibrium and with radial velocity shear. In this framework, the pressure, magnetic-field, and bulk-velocity profiles are linked self-consistently, capturing the radial stratification of the emitting region without introducing additional free parameters. For any individual source, the model effectively retains only a small number of free parameters, including the total jet power, $L_{\rm j}$, and the on-axis bulk Lorentz factor, $\Gamma_0$. We consider two prescriptions for the radial distribution of the radiating electrons -- proportional either to the gas pressure or to the rest-frame magnetic energy density -- and two toroidal-field profiles, yielding four model variants. Applying the model to a sample of ten quasar jets at $z \geq 2.5$ with X-ray features resolved by \textit{Chandra}, we perform Bayesian parameter inference and model comparison. The Bayesian evidence systematically favors electron distributions that follow the gas pressure rather than the magnetic energy density, while the data discriminate only weakly between the assumed field profiles. The inferred jet powers, reaching $L_{\rm j} \sim 10^{49}\,\mathrm{erg\,s^{-1}}$, are systematically larger than those obtained from one-zone models, and the corresponding global jet magnetization parameters are low. None of the derived quantities, including $\Gamma_0 \sim \mathcal{O}(10)$, shows a significant monotonic trend with redshift.