Identifying heating processes in simulations with an entropy-based scheme: A single jet episode in a galaxy cluster

Abstract

Understanding heating processes in galaxy clusters is essential for predicting the regulation of radiative cooling and star formation, and for clarifying the mechanisms underlying active galactic nucleus (AGN) feedback in cool-core clusters. We investigate the processes through which AGN jets deposit heat into the intracluster medium (ICM) by tracking passive entropy scalars in magneto-hydrodynamic (MHD) simulations. This enables us to systematically disentangle the contributions from different heating channels. We successfully validate this method with several idealized tests, including turbulent heating, heating by anisotropic Braginskii viscosity, dissipative and adiabatic heating by shocks using in-situ shock-detection methods, and cosmic ray (CR) heating through the excitations and damping of Alfvén waves. Using this methodology, we simulate single-epoch outbursts of high-power jets with varying densities in a cluster environment. Light jets produce wider bubbles, displacing a larger fraction of the gas in the cluster's core, whereas comparatively denser jets propagate more efficiently to larger distances without significantly disturbing the central region. During early evolution, shock heating dominates for the jets irrespective of their densities. At later times, light jets primarily heat the ICM through turbulent dissipation, while the denser jets continue to dissipate most of their energy via shocks. Turbulent and/or mixing-driven heating prevails inside the cocoon, whereas shock and acoustic compressions dominate outside. In light jets, the forward shock weakens rapidly, whereas dense jets can sustain strong bow shocks to large distances. This heating estimator allows us to identify the dominant heating mechanism responsible for resolving the cooling flow problem in future self-regulated AGN jet simulations.

Figures (13)

• Figure 1: Dissipative (Eq. \ref{['eq:fdi']}) and adiabatic heating (Eq. \ref{['eq:fad']})) rates at shocks as functions of the Mach number. The rates are normalized by the upstream thermal energy density times the sound speed to make them dimensionless. The markers indicate the heating corresponding to the weak ($\mathcal{M}\approx 2$) and strong shocks ($\mathcal{M}\approx 10$) in our tests.
• Figure 2: Left: Volume-weighted projected vorticity ($|\bm{\nabla} \times \bm{\varv}|$), and turbulent heating rate due to numerical viscosity, both weighted by volume, for the entire box width. Right: Volume-integrated turbulent heating rates, $H_\mathrm{tu}(K)$ and $H_\mathrm{tu}(s)$, thermal energy gain rate, and the adiabatic term $H_\mathrm{ad}$ over the entire simulation box are shown in the top panel, while the bottom panel presents the relative error between the two heating-estimation methods, $\Delta H/H=H_\mathrm{tu}(K)-H_\mathrm{tu}(s)/H_\mathrm{tu}(K)$.
• Figure 3: Volume-integrated Braginskii viscosity heating as a function of time, $t$. The relative error between the two heating-estimation methods is shown in the bottom panel.
• Figure 4: Volume-integrated CR Alfvén-wave heating in a periodic 2D domain as a function of time, $t$. The relative error between the two heating-estimation methods is shown in the bottom panel.
• Figure 5: Left and center: Density (top), pressure (middle), and Mach number (bottom) profiles from a 1D shock test for weak and strong shocks. The black dashed curves show the analytical solution, while the red solid curves show the simulation results. Right: We compare the distribution of the dissipative (green) and adiabatic (blue) shock heating (obtained from the two shock surfaces) against the analytical solution (black dashed).