  Short-period and low-mass water-rich planets are subject to strong
irradiation from their host star, resulting in hydrospheres in supercritical
state. In this context, we explore the role of irradiation on small terrestrial
planets that are moderately wet in the low-mass regime (0.2--1$M_{\oplus}$). We
investigate their bulk properties for water contents in the 0.01--5\% range by
making use of an internal structure model that is coupled to an atmosphere
model. This coupling allows us to take into account both the compression of the
interior due to the weight of the hydrosphere and the possibility of
atmospheric instability in the low-mass regime. We show that even for low
masses and low water contents, these planets display inflated atmospheres. For
extremely low planetary masses and high irradiation temperatures, we find that
steam atmospheres become gravitationally unstable when the ratio $\eta$ of
their scale height to planetary radius exceeds a critical value of $\sim 0.1$.
This result is supported by observational data, as all currently detected
exoplanets exhibit values of $\eta$ smaller than 0.013. Depending on their
water content, our results show that highly irradiated and low-mass planets up
to $0.9M_{\oplus}$ with significative hydrospheres are not in stable form and
should loose their volatile envelope.
