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

The hot plasma filling galaxy clusters emits copious X-ray radiation. The classic unheated and unperturbed cooling flow model predicts dramatic cooling rates and an isobaric X-ray spectrum with constant differential luminosity distribution. The observed cores of clusters (and groups) show instead a strong deficit of soft X-ray emission: dLx/dT ∝ (T/Thot)^{α = 2 ± 1}. Using 3D hydrodynamic simulations, we show that such deficit arises from the tight self-regulation between thermal instability condensation and AGN outflow injection: condensing clouds boost the AGN outflows, which quench cooling as they thermalize through the core. The resultant average distribution slope is α ≃ 2, oscillating within the observed 1 < α < 3. In the absence of thermal instability, the X-ray spectrum remains isothermal (α ≳ 8), while unopposed cooling drives a too shallow slope, α < 1. AGN outflows deposit their energy inside-out, releasing more heat in the inner cooler phase; radially distributed heating alone induces a declining spectrum, 1 < α < 2. Turbulence further steepens the spectrum and increases the scatter: the turbulent Mach number in the hot phase is subsonic, while it becomes transonic in the cooler phase, making perturbations to depart from the isobaric mode. Such increase in dln P/dln T leads to α ≈ 3. Self-regulated AGN outflow feedback can address the soft X-ray problem through the interplay of heating and turbulence.