Probing the thermal history of the intergalactic medium with Lyα absorption lines

The Doppler parameter distribution of Ly alpha absorption lines-is calculated for a set of numerical simulations with different re-ionization histories. The differences in temperature between different re-ionization histories are as large as a factor of 3-4 depending on the spectrum of the ionizing sources and the redshift of helium re-ionization. These temperature differences result in observable differences in the Doppler parameter distribution. The best agreement with the observed Doppler parameter distribution between redshifts of 2 and 4 is found if hydrogen and helium are re-ionized simultaneously at or before a redshift of 5 with a quasar-like spectrum.