A wavelet analysis of the spectra of quasi-stellar objects

The temperature of the intergalactic medium (IGM) is an important factor in determining the linewidths of the absorption lines in the Ly α forest. We present a method to characterize the linewidth distribution using a decomposition of an Ly α spectrum in terms of discrete wavelets. Such wavelets form an orthogonal basis, so the decomposition is unique. We demonstrate using hydrodynamic simulations that the mean and dispersion of the wavelet amplitudes are strongly correlated with both the temperature of the absorbing gas and its dependence on the gas density. Since wavelets are also localized in space, we are able to analyse the temperature distribution as a function of position along the spectrum. We illustrate how this method could be used to identify fluctuations in the IGM temperature that might result from late reionization or local effects.