Probing the thermal history of the Intergalactic Medium with Lyman-alpha absorption lines

The Doppler parameter distribution of Lyman-alpha absorption is calculated for a set of different reionization histories. The differences in temperature between different reionization histories are as large as a factor three to four depending on the spectrum of the ionizing sources and the redshift of helium reionization. These temperature differences result in observable differences in the Doppler parameter distribution. Best agreement with the observed Doppler parameter distribution between redshift two and four is found if hydrogen and helium are reionized simultaneously at or before redshift five with a quasar-like spectrum.