Searching for fluctuations in the IGM temperature using the Lyman alpha forest

We propose a statistical method to search for fluctuations in the temperature of the intergalactic medium (IGM) using the Lyman $\alpha$ forest. The power on small scales ($\sim 25 \km/\s$) 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 ten quasars are needed constrain factors of two fluctuations in small scale power power.