Patchy blazar heating: diversifying the thermal history of the intergalactic medium

TeV-blazars potentially heat the intergalactic medium (IGM) as their gamma rays interact with photons of the extragalactic background light to produce electron-positron pairs, which lose their kinetic energy to the surrounding medium through plasma instabilities. This results in a heating mechanism that is only weakly sensitive to the local density, and therefore approximately spatially uniform, naturally producing an inverted temperature-density relation in underdense regions. In this paper we go beyond the approximation of uniform heating and quantify the heating rate fluctuations due to the clustered distribution of blazars and how this impacts on the thermal history of the IGM. We analytically compute a filtering function that relates the heating rate fluctuations to the underlying dark matter density field. We implement it in the cosmological code GADGET-3 and perform large scale simulations to determine the impact of inhomogeneous heating. We show that, because of blazar clustering, blazar heating is inhomogeneous for z>= 2. At high redshift, the temperature-density relation shows an important scatter and presents a low temperature envelope of unheated regions, in particular at low densities and within voids. However, the median temperature of the IGM is close to that in the uniform case, albeit slightly lower at low redshift. We find that blazar heating is more complex than initially assumed and that the temperature-density relation is not unique. Our analytic model for the heating rate fluctuations couples well with large scale simulations and provides a cost-effective alternative to subgrid models.