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

The gist: This work investigates heating processes in simulations by tracking passive entropy scalars to systematically disentangle contributions from different heating channels caused by AGN jets in galaxy clusters.

Theoretical Framework for Heating Estimation

The net heating rate density is derived from the thermodynamic equations, specifically relating it to the change in the specific entropy (Eq. 6) which is expressed as a function of pressure and density The paper introduces two entropy-based passive scalars, K = Pρ−γ and S = log(K), to quantify turbulent and mixing-induced heating These tracers are used to estimate the heating rate by comparing the entropy computed directly from energy conservation with the entropy evolved under pure advection The change in these passive scalars over a time step is then used to estimate the heating rate density H = (ρavg)γ−1/γ−1 d(Pρ−γ)/dt.

Validation of Heating Estimators

The method's validity is tested through several idealized scenarios, including turbulent heating by numerical viscosity and Braginskii-viscosity The study found that both K-based and s-based methods perform well for smooth problems but diverge at contact discontinuities or sharp gradients Specifically, the difference between the two methods stems from advection effects and sharp gradients near contact discontinuities where low- and high-entropy material meet. The authors confirm that they only consider heating contributions where both methods yield a positive value to discard spurious numerical heating at contact discontinuities.

Testing Specific Heating Mechanisms

The paper validates the estimator against various physical processes, including turbulent heating by numerical viscosity and Braginskii-viscosity. For Braginskii viscosity heating in a standing fast magnetosonic wave test, the heating rates derived from both entropy tracers agree excellently with the analytical solution The CR heating component is also tested by examining Alfvén-wave-mediated CR heating, where the estimates show excellent agreement with the analytical formula at early times. Furthermore, shock detection and associated dissipative and adiabatic heating are validated using a shock finder, showing good agreement with theoretical expectations in 1D shock-tube tests.

Results from Single Jet Outburst Simulations

The core of the study involves 3D MHD simulations of a single AGN jet outburst in an idealized Perseus-like cluster environment The results show that light jets, due to their wider bubbles, are most effective at suppressing cooling in the inner core when compared to intermediate-density jets For a fixed high-power outburst, light jets can offset cooling losses far more efficiently than intermediate-density jets because they displace a larger volume of central gas. The heating distribution varies by jet density; intermediate-density jets deposit most energy through shocks, while very light jets primarily heat the gas through turbulence and/or mixing between the jet plasma and ambient gas.

Conclusions on Jet Feedback

The study concludes that pre-existing turbulence within the cluster’s core alone is insufficient to balance cooling losses, highlighting the crucial role of AGN feedback For a fixed high-power outburst, light jets can offset cooling losses far more efficiently than intermediate-density jets. The residual heating from the jets persists for several tens of Myr even after they are switched off. The mode of cumulative energy transfer differs by density; denser jets inject most of their energy through shocks, while lighter jets primarily do so through turbulent heating and entropy mixing. Inside the jet cocoon, heating is dominated by turbulent dissipation and potential mixing in all cases. Outside the cocoon, shocks remain strong in intermediate-density jets but weaken rapidly in light jets, with a significant heating arising from acoustic compressions for light jets. The analysis confirms that the jet’s internal energy composition plays a key role in determining which heating mechanisms dominate.

Software and Acknowledgements

The Arepo data were processed using Paicos, which relies on Astropy (Astropy Collaboration et al. 2013) for unit handling and incorporates parallelized routines implemented in Cython (Behnel et al. 2011). The authors acknowledge support by the European Research Council under ERC-AdG grant PICOGAL-101019746, and support by the DFG Research Unit FOR-5195. The calculations for this research were conducted with computing resources under the project JARDS ID 26548, and using the in-house computing facility ‘Newton’ at AIP. The references list includes Astropy Collaboration et al. 2013, Bauer & Springel 2012, Behnel et al. 2011, Berlok et al. 2020, Blanton et al. 2011, Churazov et al. 2003, David et al. 2009, Ehlert & Weinberger & Pfrommer & Pakmor & Springel 2018, English et al. 2019, Fabian 1994, Fabian 2012, Hillel & Soker 2016, Hudson et al. 2010, Hunter 2007, Kunz et al. 2011, Kulsrud & Pearce 1969, Lemmerz et al. 2025, Li & Yang K. and Reynolds C. S., Martizzi et al. 2019, Mathews et al. 2006, Navarro et al. 1996, Omoruyi et al. 2025, O’Sullivan et al. 2011, Pakmor & Springel 2013, Perrone & Latter 2022a/b, Perucho et al. 2014/2018/23, Peterson et al. 2003, Rafferty et al. 2006, Ressler et al. 2015, Ruszkowski & Pfrommer 2017/23, Sanders et al. 2008, Schaal & Springel 2015, Shalaby et al. 2021/23, Springel 2010, Stewart et al. 2025, Tang & Churazov 2017, Thomas & Pfrommer 2019/Pfrommer et al. 206, Weinberger et al. 2017/Ehlert et al. 23/Weinberger et al. 518, English & Hardcastle & Krause G., Hunter J., Werner N., Urban O., Simionescu A., Allen S. W., Yang H.-Y K. and Reynolds C. S. 2016a/b, Zhuravleva et al. 2016/2014, Zweibel et al. 2018; Werner et al. 2013, Springel 590, A33, Springel 454, A37.

How it works

The net heating rate density is derived from the thermodynamic equations, specifically relating it to the change in the specific entropy (Eq. 6) which is expressed as a function of pressure and density The paper introduces two entropy-based passive scalars, K = Pρ−γ and S = log(K), to quantify turbulent and mixing-induced heating These tracers are used to estimate the heating rate by comparing the entropy computed directly from energy conservation with the entropy evolved under pure advection The change in these passive scalars over a time step is then used to estimate the heating rate density H = (ρavg)γ−1/γ−1 d(Pρ−γ)/dt.

Testing Specific Heating Mechanisms

The paper validates the estimator against various physical processes, including turbulent heating by numerical viscosity and Braginskii-viscosity.

1. Bold header: Enhanced Heating Mechanism Discrimination

This system can systematically disentangle contributions from different heating channels by tracking passive entropy scalars in magnetohydrodynamic (MHD) simulations, enabling researchers to systematically disentangle the contributions from different heating channels.

2. Bold header: Robust Shock and Dissipative Heating Quantification

The AI can accurately estimate shock-induced energy deposition by utilizing the in-situ shock-detection methods and analyzing the corresponding heating estimates described by equations (13) and (14), which are validated against analytical solutions.

3. Bold header: Spurious Numerical Heating Filtering

The improved system can identify and discard nonphysical heat additions by implementing a filtering criterion: we only consider the heating contribution in regions where both (formally equivalent) heating estimators indicate a positive value, thus avoiding spurious numerical heating arising from discretization errors.

4. Bold header: Jet-Dependent Heating Regime Prediction

The AI can predict the dominant physical mechanism based on jet density, as it can identify that for intermediate-density jets, most of the heating arises from shocks driven into the surroundings, whereas the very light jets primarily heat the gas through turbulence and/or mixing.

5. Bold header: Post-Jet Outburst Thermal Evolution Modeling

The system can model long-term cluster evolution by assessing residual heating, noting that the residual heating from the jets persists for several tens of Myr, even after the jets are switched off, providing a more complete picture than models neglecting post-outburst effects.

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 of the ICM prevails irrespective of jet density. At later times, light jets primarily heat the ICM through turbulently induced heating (which includes dissipation of vortices emerging from a turbulent cascade and mixing gas of different temperatures) and compressible dissipation of sound waves and very weak shocks, while denser jets continue to dissipate most of their energy via shocks. Particularly, turbulently induced heating by solenoidal-shear motions prevails inside the cocoon, whereas shocks and acoustic compressions dominate outside. In light jets, the forward shock weakens rapidly, whereas dense jets can sustain strong bow shocks to large distances.