Improving IGM temperature constraints using wavelet analysis on high-redshift quasars

The thermal state of the intergalactic medium (IGM) contains vital information about epoch reionization, one most transformative yet poorly understood periods in young universe. This is encoded small-scale structure Lyman-$\alpha$ (Ly$\alpha$) absorption quasar spectra. 1D flux power spectrum measures average along sightlines. At high redshifts, where opacity large, averaging mixes signal-to-noise ratio transmission spikes with noisy troughs. Wavelet amplitudes are an alternate statistic that maintains spatial while quantifying fluctuations at same frequencies as spectrum, giving them potential to more sensitively measure structure. Previous Ly$\alpha$ forest studies using wavelet amplitude probability density functions (PDFs) used limited and neglected strong correlations between PDF bins across wavelets scales, resulting sub-optimal unreliable parameter inference. Here we present a novel method for performing statistical inference PDFs spans full range probed by fully accounts these correlations. We applied this procedure realistic mock data drawn from simple model parameterized temperature mean density, $T_0$, find deliver 1$\sigma$ constraints on $T_0$ 7% sensitive $z=5$ (12% $z=6$) than those spectrum. consider possibility combing power, but does not lead improved sensitivity.