Searching for Fluctuations in the Intergalactic Medium Temperature Using the Lyα Forest

We propose a statistical method to search for fluctuations in the temperature of the intergalactic medium using the Lyα forest. The power on small scales (~25 km s^-1) is used as a thermometer, and fluctuations of this power are constrained. The method is illustrated using Q1422+231. We see no evidence of temperature fluctuations. We show that in a model with two temperatures that occupy comparable fractions of the spectra, the ratio of small-scale powers is constrained to be smaller than 3.5 (corresponding to a factor of 2.5 in temperature). We show that approximately 10 quasars are needed to constrain temperature fluctuations of a factor of 1.7.