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This thesis investigates the thermal state of the intergalactic medium in the redshift range \(z\simeq 1.5-3.8\). This phase of the IGM evolution is particularly interesting because it is characterized by the second reionization event, the He ii reionization, that may have left detectable imprints in the evolution of the temperature at the mean gas density (\(T_{0}\)) and in the steepness of the power-law that defines the relation between the IGM temperature and density (\(\gamma\)). The picture drawn by previous observations of the thermal state of the IGM is still confusing, with some indication of the imprints of the He ii reionization but still much room for more definitive evidence. The findings presented in the previous Chapters can help to improve the understanding of the evolution of the IGM in this complex phase of its thermal history. While detailed descriptions of our measurements can be found in the Conclusions of Chapters 3, 4 and 5, in this final Chapter we summarise the main results, discuss them in the context of the status of the field, and describe new prospects for future follow-up work.

Summary of the main results

The analyses presented in the previous Chapters aimed mainly to provide new constraints and methods to study the evolution of \(T_{0}\) and \(\gamma\) as a function of redshift. In particular, in Chapters 2 and 3 we provided new measurements of the IGM temperature at the characteristic gas overdensities probed by the H i Ly-\(\alpha\) forest, \(T(\bar{\Delta})\) (see Figure \ref{fig:TD}). With a sample of 60 high quality UVES spectra, for the first time we extended the curvature measurements (previously obtained for \(2\lesssim z\lesssim 4\) by (citation not found: Becker11)) to the lowest optically-accessible redshifts, down to \(z\sim 1.5\). We found that the values of \(T(\bar{\Delta})\) increase for increasing overdensities probed by the forest towards lower redshifts, from \(T(\bar{\Delta})\sim 22670\) K to 33740 K in the redshift range \(z\sim 2.8-1.6\). These results are broadly consistent with the trend found by others at higher redshifts. Moreover, in the overlapping redshift range \(2.1\lesssim z\lesssim 2.9\), our results (from a completely independent dataset) are in excellent agreement with the measurements of (citation not found: Becker11), demonstrating the self-consistency of the curvature method.

Using the temperature–density relation (Equation \ref{eq:TDrelation}) we translated the \(T(\bar{\Delta})\) values to temperatures at the gas mean density \(T_{0}\) to investigate the heating trend observed previously by others at redshifts \(2.8\lesssim z\lesssim 4\). While, later in Chapter 4 we attempted to constrain the parameter \(\gamma\), in Chapter 3 we assumed two reasonable values of \(\gamma\) to obtain the measurements in \(T_{0}\) (see Figure \ref{fig:slopes}). For both the choices of \(\gamma\) we observed some evidence for a change in the tendency of the temperature evolution for \(z\lesssim 2.8\), with indications of at least a flattening of the increasing temperature towards lower redshifts. In particular, for the case of a broadly constant \(\gamma\sim 1.5\), the extension towards lower redshifts provided by our work shows the evidence for a decrease in the IGM temperature from redshifts \(z\sim 2.8\) down to the lowest redshift \(z\sim 1.5\). This supports tentative evidence for the same from (citation not found: Becker11). Such a reversal of the heating trend can be interpreted as the end of the IGM reheating process driven by He ii reionization, with a subsequent tendency of a cooling of a rate depending on the UV background.

In Chapters 4 and 5 we proposed two new possible applications of the curvature method to constrain the parameter \(\gamma\). In particular, in Chapter 4 we presented and tested with hydrodynamical simulations the possibility of using the ratio of curvatures, \(\langle R_{\kappa}\rangle\), in the Ly-\(\alpha\) and \(\beta\) forests to trace simultaneously two different gas density regimes and obtain measurements of the slope of the \(T\)\(\rho\) relation. We applied this technique to a subsample of 27 UVES spectra selected for their high S/N (\(>24\) per pixel) in both the Ly-\(\alpha\) and \(\beta\) regions and we analysed the strengths and weakness of this method. The technique, relatively fast and simple to compute, appears robust against observational uncertainties in the noise level, metal contamination and effective optical depth. The evolution of \(\langle R_{\kappa}\rangle\), measured from our observational spectra in 3 redshift bins covering \(z=2.0-3.8\), matches that derived from our nominal simulations with \(\gamma\sim 1.5\). The statistical errors obtained from the 27 spectra are promising: in the absence of any systematic errors, the \(\approx\)6 per cent statistical uncertainties in our \(\langle R_{\kappa}\rangle\) measurements would translate to a \(\lesssim\)10  per cent uncertainty in \(\gamma\) in \(\Delta z\sim 0.6\) bins. This would be competitive with the most precise results available in the literature derived using line decomposition ((citation not found: Rudie13); (citation not found: Bolton13)). However, we did not present \(\gamma\) measurements with formal uncertainties because the nominal \(\gamma\)–log\(\langle R_{\kappa}\rangle\) relation, used to translate \(\langle R_{\kappa}\rangle\) measurements to \(\gamma\) values, may also be sensitive to assumptions in the simulations about the evolution of the IGM thermal state that need to be addressed in detail.

Finally, in Chapter 5 we also proposed the possibility of using a double curvature constraint, from coeval H i and He ii Ly-\(\alpha\) forests, to obtain measurements of the IGM temperature at the two different density regimes probed by these transitions and constrain \(\gamma\), independently of \(T_{0}\), in the redshift range \(2\lesssim z\lesssim 3\). Currently, it is clear that any curvature analysis of the He ii forest is prevented by the low quality of the observed spectra; however, future instruments and space telescopes may improve dramatically the availability of high resolution and S/N spectra. We then analysed the available hydrodynamical simulations to understand if the specific parameters (i.e. box size and mass resolution), previously adopted to reproduce the H i Ly-\(\alpha\) absorption features, could also be used to study the helium counterpart. Our convergence tests show that the underdense regions probed by the He ii Ly-\(\alpha\) forest would require future refinements of the current suite of simulations.

Starting from the general question that opened the Introduction of this thesis, in the following Section we will explain the contribution of our results in addressing some more specific queries that have represented the key investigation subjects in this field for more than a decade.

What is the thermal state of the IGM at low redshift?

The thermal state of the intergalactic medium is defined by its temperature–density relation that, in the simplest scenario, is represented by a power-law (Equation \ref{eq:TDrelation}). Understanding the evolution of the IGM thermal state therefore relies on measuring the evolution of the parameters \(T_{0}\) and \(\gamma\) of Equation \ref{eq:TDrelation}. For more than a decade, significant efforts have been invested in developing methods that would allow the two parameters to be determined independently of each other using quasar absorption lines. However, the necessity of using complex simulations and large statistical samples of high quality observational spectra, makes it particularly difficult. Nowadays, the main challenge is represented by the requirement to reduce the systematic and statistical uncertainties in the measurements to a level that would allow to clarify the confusing picture, drawn so far by previous estimations.

Including the constraints obtained in this work, Figure \ref{fig:finals} provides a summary of the state of the field to date. Panel (a) presents the observed evolution of \(T_{0}\) with redshift while panel (b) shows the constraints on the evolution of \(\gamma\) (reproduction of Figure \ref{fig:gamma}). Note that for clarity, in both the panels we could not include all the measurements available in the literature; rather, the comparison presented here is intended to provide a representative idea of the size of the error bars, obtained using different approaches, and of the dispersion of the values of temperature and \(\gamma\) measured in the broad redshift range \(z\simeq 1.5-5\).