2025MNRAS.538.2008K

Radial gradients of the brightness temperatures along the parsec-scale jets of active galactic nuclei (AGNs) can be used to infer the energy balance and to estimate the parameter range of physical conditions in these regions. In this paper, we present a detailed study of the brightness temperature gradients and geometry profiles of the relativistic jets of 447 AGNs based on 15-GHz Very Long Baseline Array observations performed between 1994 and 2019. We used models of the jet structure using two-dimensional Gaussian components and analysed variations in their brightness temperatures and sizes along the jets. The size of the jet components, R, increases with projected distance from the jet base, r, as $R\propto r^{1.02\pm 0.03}$; that is, typically following a conically expanding streamline and therefore indicating that the size of the jet components is a good tracer of jet geometry. The brightness temperature gradients along the jets typically follow a power law, $T_\mathrm{b} \propto r^{-2.82\pm 0.07}$. Half of the sample sources show non-monotonic $R(r)$ or $T_\mathrm{b}(r)$ profiles, and their distributions are characterized by a double-power-law model. We found at least six scenarios to explain the enhancement of the brightness temperature by the presence of inhomogeneities (shocks, jet recollimation) or curvature effects (helical structures, helical magnetic field, non-radial motion, bent jets). Our results are consistent with the scenario that the jet features can be simplified as optically thin moving blobs. In the sources demonstrating a transition from a conical to a parabolic jet shape, the gradient of $T_{\rm b}(R)$ changes at the position of the break, consistent with the model of magnetohydrodynamic acceleration.