What sets temperature gradients in galaxy clusters? Implications for non-thermal pressure support and mass-observable scaling relations

We present a spherically symmetric model for the origin and evolution of the temperature profiles in the hot plasma filling galaxy groups and clusters. We find that the gas in clusters is generically not isothermal, and that the temperature declines with radius at large distances from the cluster centre (outside the core and scale radii). This temperature profile is determined by the accretion history of the halo, and is not quantitatively well described by a polytropic model. We explain quantitatively how the large-scale temperature gradient persists in spite of thermal conduction and convection. These results are a consequence of the cosmological assembly of clusters and cannot be reproduced with non-cosmological simulations of isolated haloes. We show that the variation in halo assembly histories produces a ~10 per cent scatter in temperature at fixed mass. On top of this scatter, conduction decreases the temperature of the gas near the scale radius in massive clusters, which may bias hydrostatic mass estimates inferred from X-ray and Sunyaev-Zel'dovich observations. As an example application of our model profiles, we use mixing-length theory to estimate the turbulent pressure support created by themagnetothermal instability (MTI): in agreement with our earliermagnetohydrodynamic MHD simulations, we find that the convection produced by the MTI can provide ~5 per cent non-thermal pressure support near r₅₀₀. The magnitude of this turbulent pressure support is likely to be non-monotonic in halo mass, peaking in ~10^14.5M⊙ haloes.