Intergalactic medium temperature is a powerful probe of the epoch of reionisation , as information is retained long after reionisation itself .
However , mean temperatures are highly degenerate with the timing of reionisation , with the amount heat injected during the epoch , and with the subsequent cooling rates .
We post-process a suite of semi-analytic galaxy formation models to characterise how different thermal statistics of the intergalactic medium can be used to constrain reionisation .
Temperature is highly correlated with redshift of reionisation for a period of time after the gas is heated .
However as the gas cools , thermal memory of reionisation is lost , and a power-law temperature-density relation is formed , T = T _ { 0 } ( 1 + \delta ) ^ { 1 - \gamma } with \gamma \approx 1.5 .
Constraining our model against observations of electron optical depth and temperature at mean density , we find that reionisation likely finished at z _ { reion } = 6.8 ^ { +0.5 } _ { -0.8 } with a soft spectral slope of \alpha = 2.8 ^ { +1.2 } _ { -1.0 } .
By restricting spectral slope to the range [ 0.5 , 2.5 ] motivated by population II synthesis models , reionisation timing is further constrained to z _ { reion } = 6.9 ^ { +0.4 } _ { -0.5 } .
We find that , in the future , the degeneracies between reionisation timing and background spectrum can be broken using the scatter in temperatures and integrated thermal history .