A positive correlation between broad HI Ly$\alpha$ absorptions and local overdensities of galaxies

A large fraction of the baryon budget at $z<1$ resides in large-scale filaments in the form of diffuse intergalactic gas, and numerous studies have reported a significant correlation between the strength of the absorptions produced by this gas in the spectra of bright background sources, and impact parameter to cosmic filaments intersected by these sightlines. However, a similar relation is harder to determine for the warm-hot phase of the intergalactic gas, since its higher Doppler parameter and significantly lower neutral gas fraction makes this gas difficult to detect in absorption. We use a sample of 13 broad Ly$\alpha$ absorbers (BLAs) detected in the HST/COS spectrum of a single QSO ($z\sim0.27$), whose sightline intersects several inter-cluster axes, to study the relation between BLAs and the large-scale structure of the Universe. Given their Doppler parameters of $b>40$ km s$^{-1}$, BLAs are good tracers of warm-hot intergalactic gas. We use VLT/MUSE and VLT/VIMOS data to infer local overdensities of galaxies at the redshifts of the BLAs, and to assess the potential association of the BLAs with nearby galaxies. We find that out of the 13 BLAs in our sample, four are associated with a strong overdensity of galaxies, and four with tentative overdensities. The remaining five are located at redshifts where we do not identify any excess of galaxies. We find that these overdensities of galaxies at the redshift of BLAs are local, and they vanish when larger cosmic volumes are considered, in terms of a larger velocity offset to the BLA or larger impact parameter to the QSO sightline. Finally, we find a positive correlation between the total hydrogen column densities inferred from the BLAs, and the relative excess of galaxies at the same redshifts, consistent with the picture where warm-hot gas resides deep within the gravitational potential well of cosmic filaments.