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: dL(X)/dT proportional to (T/T-hot)(alpha) (= 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 alpha similar or equal to 2, oscillating within the observed 1 < alpha < 3. In the absence of thermal instability, the X-ray spectrum remains isothermal (alpha greater than or similar to 8), while unopposed cooling drives a too shallow slope, alpha < 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 < alpha < 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 alpha approximate to 3. Self-regulated AGN outflow feedback can address the soft X-ray problem through the interplay of heating and turbulence.