  It is conceivable that a few thousand confirmed exoplanets initially
harboured satellites similar to the moons of the Solar system or larger. Could
some of them have survived over the aeons of dynamical evolution to the present
day? The dynamical conditions are harsh for exomoons in such systems because of
the greater influence of the host star and of the tidal torque it exerts on the
planet. We investigate the stability niches of exomoons around hundreds
innermost exoplanets for which the needed parameters are known today, and
determine the conditions of these moons' long-term survival. General lower and
upper bounds on the exomoon survival niches are derived for orbital
separations, periods, and masses. The fate of an exomoon residing in a
stability niche depends on the initial relative rate of the planet's rotation
and on the ability of the moon to synchronise the planet by overpowering the
tidal action from the star. State of the art models of tidal dissipation and
secular orbital evolution are applied to a large sample of known exoplanet
systems with their estimated physical parameters. We show that in some
plausible scenarios, exomoons can prevent close exoplanets from spiraling into
their host stars, thus extending these planets' lifetimes. This is achieved
when exomoons synchronise the rotation of their parent planets, overpowering
the tidal action from the stars. Massive moons are more likely to survive and
to maintain a high rotation rate of their host planets (higher than these
planets' mean motion).
