Shaping the X-ray spectrum of galaxy clusters with AGN feedback and turbulence

M. Gaspari, S. Peng Oh, M. Ruszkowski

Published 2014-10-28Version 1

The hot plasma filling galaxy clusters emits copious radiation in the X-ray band. The classic unheated and unperturbed cooling flow model predicts dramatic cooling rates and an isobaric X-ray spectrum with constant differential luminosity distribution, $dL_{\rm x}/dT \propto (T/T_{\rm hot})^0$. Combining past observations, it is however clear that the cores of clusters (and groups) show a strong deficit of emission increasing toward the soft X-ray band: $dL_{\rm x}/dT \propto (T/T_{\rm hot})^{\alpha=2\pm1}$. Using 3D hydrodynamic simulations, we show that the deficit arises from the competition of thermal instability condensation and AGN outflow injection. During tight self-regulated feedback, the average luminosity distribution slope is $\alpha\approx2$, oscillating within the observed $1<\alpha<3$. In the absence of thermal instability (i.e. breaking self-regulation), the spectrum remains nearly isothermal ($\alpha>8$), while pure cooling drives a too shallow slope, $\alpha<1$. We disentangle the role of heating and turbulence via controlled experiments. Distributed heating alone induces a declining X-ray spectrum with $1<\alpha<2$. Since AGN heating is tied to inside-out energy deposition, relatively more heat is released in the inner, cooler phase. Turbulence plays an important role. The turbulent Mach number in the hot phase is subsonic, while it becomes transonic in the cooler phase, shifting the perturbation mode from isobaric toward adiabatic. Such increase in the $d\ln P/d\ln T$ index leads to the further suppression of the soft X-ray spectrum up to $\alpha\approx3$, with scatter widening to 1 dex. The non-isobaric scenario is also valid in unheated cooling flows, as thermal instability condensation excites turbulent motions. Self-regulated mechanical AGN feedback is able to solve both the mass sink and soft X-ray problem through the interplay of heating and turbulence.