The Self-Limiting Nature of Jet-Modulated Thermal Conduction in Cool Core Clusters

Abstract

Conduction as a mechanism for explaining the disrupted cooling-flow in galaxy clusters has been mostly discounted, as the process is inefficient at transporting heat all the way from the cluster into the core. However, thermal conduction can be strongly enhanced when materials of significantly different temperature are brought into proximity, and thus into close thermal contact. Jets of active galactic nuclei may act as heat pumps by bringing low-entropy gas from the cluster core into thermal contact with the hot outer atmosphere of the cluster, significantly increasing the feedback efficiency of active galactic nuclei. We test this hypothesis by running a suite of 3D magnetohydrodynamic simulations of active galactic nuclei jets in a Perseus-like cluster, including anisotropic conduction. We find that the heat pump efficiency $η$ can reach up to 50\% of the maximum possible efficiency $η_{\rm max}$ if conduction operates near the Spitzer-Braginskii limit, while $η\approx f_{\rm sp}η_{\rm max}$ if conduction along the field lines is substantially suppressed below the Spitzer-Braginskii value by a factor $f_{\rm sp}$ by kinetic effects, as recently suggested. We further find that jet-induced thermal conduction is self-limiting: Magnetic draping during the uplift results in a magnetic field orientation close to perpendicular to the induced temperature gradients, significantly reducing conduction along the ideal conductive pathways. Thus, for conservative assumptions about thermal conduction suppression by $f_{\rm sp} \lesssim 0.1$, the heat pump effect leads to only marginal heat transfer and, correspondingly, to immaterial changes in the overall thermal evolution of cool core clusters beyond the isolated effects of conduction and jet-induced heating alone.

Figures (18)

• Figure 1: Magnetic field overlay on temperature slices for the 0, 256, 512, and 1024 Myr slices in Fig. \ref{['fig:tempslices']}. Panel 1 shows the initial magnetic field setup. Panels 2, 3, and 4 demonstrate how the field lines drape around the uplifted gas, turning off anisotropic conduction by turning the field perpendicular to the temperature gradient between the cooler uplifted gas and the hotter cluster gas.
• Figure 2: List of simulations and parameters for the suite of simulations referenced in this paper. The gray highlighted row shows the parameters from the initial Chen_2019 paper, prior to the addition of conduction and magnetic fields. The top section lists the jet model runs and the bottom section lists the no jet control models.
• Figure 3: Temperature slices for the JHC run at the indicated times ranging from 8 Myrs to 1024 Myrs showing the evolution and uplift of cool core gas. The temperature color bar is scaled to highlight fluctuations in the thermal gas rather than the hot, non-thermal cocoon/cavity inflated by the jets.
• Figure 4: Temperature slices for the NJC run cluster core at 0 and 1024 Myrs. The small irregularities in the structure are due to magnetic field induced low level motions driving weak turbulence and conductive heat transport in random, non-radial directions, leading to small temperature anisotropies.
• Figure 5: Phase plots (2D histograms) of net conductive heat $H$ as functions of radius and entropy for time steps at 64, 128, 256, 512, 768, and 1024 Myrs for the JHC simulation. The time sequence shows the cycling of lower entropy gas as it rises and falls throughout the simulation. Red colors indicated net conductive heating while blue colors indicate net cooling. The bright quasi-hyperbolic line corresponds to the mean cluster profile and can also be observed in Fig. \ref{['fig:heatphase_nj']} for the control simulation. Gas above this line (in the upper left corner of the plot) corresponds to uplifted gas that has lower entropy than the average hydrostatic gas at the same radius. Gas below the line (lower right corner) corresponds to gas with excess entropy, either due to down-draft in the inward-moving part of the buoyancy cycle at 512 Myrs and 1024 Myrs, or shock heating (early frames). We are interested in how uplifted gas is heated by conduction, which we can quantify by summing over the (generally heated) gas above the equilibrium line, using the masks shown in Fig.\ref{['fig:heatphase_nj']}.