Are X-ray Atmospheres Heated by Turbulent Dissipation? XRISM Constraints

Abstract

We evaluate whether dissipation of turbulence injected into hot cluster atmospheres by jets and bubbles can offset radiative cooling flows. No trends are found between atmospheric velocity dispersion, $\sigma_v$, and either the ratio of kinetic to thermal energy or jet power over nearly four decades of jet power. Apparently, jets disperse their energy gently at roughly constant energy per gram of gas. Assuming the velocity dispersions at the centers of Perseus, Virgo, and Hydra A reflect jetted turbulence, up to roughly half the bubble enthalpy could be dissipated by turbulent motion. A model is presented that balances radiation losses and turbulent power injected by radio bubbles rising at their terminal speeds. The model is anchored by XRISM measurements of $\sigma_v$ and is governed by the ratio of the bubble's terminal speed to the atmospheric sound speed. Bubbles must rise close to the sound speed and impart energy with a broad range of injection scales to heat the entire cooling volume. The level of turbulence in the powerful Hydra A system may offset cooling over some of the cooling volume. However, turbulent dissipation would struggle and probably fail to balance cooling in Perseus and Virgo, except perhaps in their inner regions. Several factors including, low velocity dispersions, small injection scales, short duty cycles, anisotropic turbulence injection, and long turbulent diffusion timescales present severe challenges for jetted turbulence heating models. A larger sample of spatially resolved cluster atmospheres is needed to reach a definitive conclusion.