The hydrodynamical response of cold circumgalactic clouds to quasar radiation

Recent simulations increasingly resolve the small-scale structure of the circumgalactic medium (CGM), but the dynamical impact of ionising radiation on its cold $10^4$ K component remains poorly understood. We investigate the evolution of cold gas structures exposed to quasars' EUV radiation. We develop an analytical framework to describe the evolution of such clouds, introducing a new threshold that defines when a cloud becomes radiation-shielded. The framework is validated using radiation-hydrodynamic simulations of single static clouds. It predicts three evolutionary paths: (i) an optically thin regime, in which radiation uniformly ionises the cloud; (ii) a radiation-shielded regime, where the cloud remains largely unaffected; and (iii) a rocket-effect regime, in which the propagation of the ionisation front ionises the illuminated side while compressing the opposite side, later accelerating the surviving cold clump. In the latter regime, the cloud's Ly$\alpha$ luminosity can be up to one order of magnitude higher than the optically thin case. Such luminosities are as high as $70\%$ of the values obtained from a fluorescent regime without considering hydrodynamical response. Unless the cloud is shielded, at least $\sim 50$-$60\,\%$ of Ly$\alpha$ emission arises from recombination. Applying this framework to both a ray crossing a population of clouds, and a ray propagating inside a cold stream, we find that the cold CGM around bright quasars ($L_{\mathrm{\nu,LL}} \sim 10^{31.6} \, \mathrm{erg\, s^{-1}\, Hz^{-1}}$) is likely fully ionised, whereas the one around faint quasars ($L_{\mathrm{\nu,LL}} \sim 10^{28.6} \, \mathrm{erg\, s^{-1}\, Hz^{-1}}$) predominantly experiences a rocket-effect regime. These results imply that the hydrodynamical response of cold CGM structures to quasar radiation must be considered when deriving their physical properties, particularly for faint quasars.