We present a novel procedure to estimate the Equation of State of the intergalactic medium in the quasi-linear regime of structure formation based on Lyα forest tomography and apply it to 21 high quality quasar spectra from the UVES_SQUAD survey at redshift z = 2.5. Our estimation is based on a full tomographic inversion of the line of sight. We invert the data with two different inversion algorithms, the iterative Gauss-Newton method and the regularized probability conservation approach, which depend on different priors and compare the inversion results in flux space and in density space. In this way our method combines fitting of absorption profiles in flux space with an analysis of the recovered density distributions featuring prior knowledge of the matter distribution. Our estimates are more precise than existing estimates, in particular on small redshift bins. In particular, we model the temperature-density relation with a power law and observe for the temperature at mean density $T_0 = 13400^{+1700}_{-1300}\, \mathrm{K}$ and for the slope of the power-law (polytropic index) γ = 1.42 ± 0.11 for the power-law parameters describing the temperature-density relation. Moreover, we measure an photoionization rate $\Gamma _{-12} = 1.1^{+0.16}_{-0.17}$. An implementation of the inversion techniques used will be made publicly available.

No abstract

We present a same-level comparison of the most prominent inversion methods for the reconstruction of the matter density field in the quasi-linear regime from the Lyα forest flux. Moreover, we present a pathway for refining the reconstruction in the framework of numerical optimization. We apply this approach to construct a novel hybrid method. The methods which are used so far for matter reconstructions are the Richardson-Lucy algorithm, an iterative Gauss-Newton method and a statistical approach assuming a one-to-one correspondence between matter and flux. We study these methods for high spectral resolutions such that thermal broadening becomes relevant. The inversion methods are compared on synthetic data (generated with the lognormal approach) with respect to their performance, accuracy, their stability against noise, and their robustness against systematic uncertainties. We conclude that the iterative Gauss-Newton method offers the most accurate reconstruction, in particular at small S/N, but has also the largest numerical complexity and requires the strongest assumptions. The other two algorithms are faster, comparably precise at small noise-levels, and, in the case of the statistical approach, more robust against inaccurate assumptions on the thermal history of the intergalactic medium (IGM). We use these results to refine the statistical approach using regularization. Our new approach has low numerical complexity and makes few assumptions about the history of the IGM, and is shown to be the most accurate reconstruction at small S/N, even if the thermal history of the IGM is not known. Our code will be made publicly available.