equation. For an optically thin envelope the condition $\tau < 1$ must be satisfied, imposing an upper bound to the black hole mass, namely $$\frac{M}{M_\odot} < \frac{1.3\times 10^5}{n_{\infty}}$$ where $n_{\infty}$ is the gas particle density far from the influence radius of the black hole. Hence, if accreting spherically, SMBHs at high-z with masses around $10^8-10^9 ~ M_\odot$ will necessarily have an optically thick envelope and a different inflow regime. An optically thick envelope reduces the distance to the critical point and reduces also the accretion rate with respect to the optically thin case. In particular, when the radiation field is quite important, a second critical point may exist in the flow besides the hydrodynamical one, according to Nobili et al. (1991).

Accretion flows affected by radiation effects have been investigated by many authors in the past years (Maraschi et al. 1974; Flammang 1982; Milosavljevic et al. 2009). The radiation from the accreting envelope is essentially due to the free-free emission. For the optically thin case, the resulting luminosity is proportional to the square of the accretion rate and inversely proportional to the BH mass, i.e., $L \sim {\dot M^2}/M$. The flow becomes nearly self-regulated when the optical depth of the 