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.
