  The magma ocean (MO) is a crucial stage in the build-up of terrestrial
planets. Its solidification and the accompanying outgassing of volatiles set
the conditions for important processes occurring later or even simultaneously,
such as solid-state mantle convection and atmospheric escape. To constrain the
duration of a global-scale Earth MO we have built and applied a 1D interior
model coupled alternatively with a grey H2O/CO2 atmosphere or with a pure H2O
atmosphere treated with a line-by-line model described in a companion paper by
Katyal et al. (2019). We study in detail the effects of several factors
affecting the MO lifetime, such as the initial abundance of H2O and CO2, the
convection regime, the viscosity, the mantle melting temperature, and the
longwave radiation absorption from the atmosphere. In this specifically
multi-variable system we assess the impact of each factor with respect to a
reference setting commonly assumed in the literature. We find that the MO stage
can last from a few thousand to several million years. By coupling the interior
model with the line-by-line atmosphere model, we identify the conditions that
determine whether the planet experiences a transient magma ocean or it ceases
to cool and maintains a continuous magma ocean. We find a dependence of this
distinction simultaneously on the mass of the outgassed H2O atmosphere and on
the MO surface melting temperature. We discuss their combined impact on the
MO's lifetime in addition to the known dependence on albedo, orbital distance
and stellar luminosity and we note observational degeneracies that arise
thereby for target exoplanets.
