We present the detection of excited fine-structure energy levels of singly-ionized silicon and neutral carbon associated with the proximate damped Lyman-$alpha$ system at $z_{rm abs}=2.811$ towards qso. This absorber has an apparent relative velocity that is inconsistent with the Hubble flow indicating motion along the line-of-sight towards the quasar, i.e., $z_{rm abs}>z_{rm em}$. We measure the metallicity of the system to be ${rm [Zn/H]}=-0.68pm 0.02$. Using the relative populations of the fine-structure levels of SiII and CI, as well as the populations of H$_2$ rotational levels, we constrain the physical conditions of the gas. We derive hydrogen number densities of $n_{rm H}=190^{+70}_{-50}$ cm$^{-3}$ and $260^{+30}_{-20}$ cm$^{-3}$ in two velocity components where both CI and H$_2$ are detected. Taking into account the kinetic temperature in each component, $sim 150$K, we infer high values of thermal pressure in the cold neutral medium probed by the observations. The strengths of the UV field in Draines unit are $I_{rm UV} = 10^{+5}_{-3}$ and $14^{+3}_{-3}$ in each of these two components, respectively. Such enhanced UV fluxes and thermal pressure compared to intervening DLAs are likely due to the proximity of the quasar. The typical size of the absorber is $sim 10^4$ a.u. Assuming the UV flux is dominated by the quasar, we constrain the distance between the quasar and the absorber to be $sim 150-200$ kpc. This favours a scenario where the absorption occurs in a companion galaxy located in the group where the quasar-host galaxy resides. This is in line with studies in emission that revealed the presence of several galaxies around the quasar.
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