A simple analytical model is used to calculate the X-ray heating of the IGM for a range of black hole masses .
This process is efficient enough to decouple the spin temperature of the intergalactic medium from the cosmic microwave background ( CMB ) temperature and produce a differential brightness temperature of the order of \sim 5 - 20 ~ { } \mathrm { mK } out to distances as large as a few co-moving Mpc , depending on the redshift , black hole mass and lifetime .
We explore the influence of two types of black holes , those with and without ionising UV radiation .
The results of the simple analytical model are compared to those of a full spherically symmetric radiative transfer code .
Two simple scenarios are proposed for the formation and evolution of black hole mass density in the Universe .
The first considers an intermediate mass black hole that form as an end-product of Population III stars , whereas the second considers super-massive black holes that form directly through the collapse of massive halos with low spin parameter .
These scenarios are shown not to violate any of the observational constraints , yet produce enough X-ray photons to decouple the spin-temperature from that of the CMB .
This is an important issue for future high redshift 21 cm observations .