A preprint modeling lobed active galactic nuclei, or AGNs, reports a split between cluster cores and their outskirts. In its calculations, AGN heating offsets radiative cooling in seven of ten mock clusters for duty cycles above 0.08 and up to 1. Beyond 100 kiloparsecs, cooling exceeds AGN heating in seven of ten clusters even at a 100% duty cycle. The result is a modeled core balance alongside an outer cooling excess.
A model that follows energy by location
The study presents an analytic framework for radial and polar-angle feedback-energy distributions from lobed AGNs. It extends the RAiSE model to account for gravitational work, the internal energy of swept-up gas and bremsstrahlung cooling.
Ten mock clusters, referred to as Clusters A through K, form the main set of calculations. Their atmospheres assume hydrostatic equilibrium, spherically symmetric ambient-density profiles and isothermal temperature profiles. The improved RAiSE model remains consistent with the reference hydrodynamic simulation calibration. The numerical comparisons are made within those stated atmospheric conditions.
Using normalized active-age and jet-power weighting across outbursts, the time-averaged radial heating rate peaks at 1 to 3 kiloparsecs in all ten clusters. The strongest modeled average heating is therefore concentrated near the central few kiloparsecs.
The remnant changes the heating pattern
The modeled heating pattern changes with the remnant scenario. In a Cluster D example, total buoyant-bubble heating is 65% greater than remnant-implosion heating, while collapsing shocked-shell heating is 35% lower than implosion heating at lower radii.
When ablation is included, the modeled cases have 30% and 45% lower total heating than a perfectly adiabatic bubble at ablation rates of 0.2 and 0.5, respectively. A separate coasting scenario lasting 3 Myr leaves comparable total energy within the shocked-shell extent but spreads it over a larger radial range, producing a factor-of-two decrease in energy density.
Active age also changes the location of modeled heating. At low jet powers and active ages under 10 Myr, most gas heating is confined to the innermost 10 kiloparsecs, while increasing active age shifts the coupling peak outward. For sources with active ages of at least 100 Myr, less than 1% of input energy is deposited within 30 kiloparsecs. For sources with active ages of at least 20 Myr, less than 1% is deposited within 10 kiloparsecs.
The radius of most effective bubble heating varies with the assumed environment. It depends strongly on the core radius and on the slope of the density profile beyond the core, tending toward the core radius in steeper environments.
The result is tied to its setup
The model does not produce heating-cooling balance in every mock core. Clusters F, H and K do not offset cooling even at a 100% duty cycle, unlike the seven clusters that do reach balance across the reported duty-cycle range.
The study's main results use ten mock atmospheres with hydrostatic equilibrium, spherically symmetric density profiles and isothermal temperatures. The numerical findings therefore describe the stated modeled conditions.
Processed data products are stated to be available in a GitHub repository, and the online supplement tabulates gas-heating rates for the ten clusters. The document is labeled a preprint on arXiv as arXiv:2608.25571v1 and reports an acceptance date of 25 August 2026.
Paper data and sources
Original title: Energetics of AGN Feedback
Authors: Ross J. Turner, Andrew Sullivan, William R. Q. Gaffney
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
Original paper · Full text