Finding Halos in the Lyman-$\alpha$ forest

It has been demonstrated that one can track down galaxies in absorption 'hidden' in the Lyman-$\alpha$ forest through the use of 'strong, blended Lyman-$\alpha$' (or SBLA) absorption. Specifically a series of publications studied SBLA absorption systems with Lyman-$\alpha$ flux transmission, $F_{Ly \alpha} < 0.25$ on scales of 138 km s$^{-1}$ in the Sloan Digital Sky Survey (SDSS). In order to better understand the connection between halos and these SBLAs, we make use of several million synthetic absorption spectra from the TNG50 cosmological simulation, at z=2 and z=3. We explore spectra with SDSS-like resolution in order to understand the nature of SBLAs as defined thus far, as well as with high resolution (or 'resolved') spectra to generalise and optimise SBLAs as halo finders. For the SDSS SBLAs, we find that up to 78% of these absorption systems reside in hlaos, where the stronger the absorption and the lower the redshift, the higher the probability. We also manage to recover a mean halo mass of $10^{12.25} M_{\odot}$, in line with what is measured in observations. For the resolved SBLAs, we expand on the previous definition and allow the SBLA spectra size to vary between 54 km s$^{-1}$ and 483 km s$^{-1}$. We find that the largest absorbers have the highest probability of finding halos. When applying a hierarchical framework, where we allow the largest SBLAs to consume the smaller ones, we find that the halo mass distributions for each SBLA spectral size becomes narrower with respect to the non-hierarchical case. We are also able to probe halo masses from $M_h \approx 10^{9.5} M_{\odot}$ (for 100 km s$^{-1}$ SBLAs) to $M_h \approx 10^{11.5} M_{\odot}$ (for 450 km s$^{-1}$ SBLAs). With these results, we show that we are able to transform the Lyman-$\alpha$ forest into a powerful halo finding machine for not only identifying CGM regions, but also estimating their host halo masses.