Thermal history of the low-density neutral inter galactic medium (IGM) due to heating by accreting stellar black holes in high mass X-ray binaries (BH-HMXBs). This figure shows the gas temperature of the IGM as a function of redshift z for three possible values of fX as defined in Eq. (6): fX = 0.1 (blue dashed line), fX = 1.0 (black dotted line), fX = 10.0 (red solid line)). As discussed in the text, most likely fX > 1.
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