  The intrinsic luminosity of young Jupiters is of high interest for planet
formation theory. It is an observable quantity that is determined by important
physical mechanisms during formation, namely the accretion shock structure, and
even more fundamentally, the basic formation mechanism (core accretion or
gravitational instability). We study the impact of the core mass on the
post-formation entropy and luminosity of young giant planets forming via core
accretion with a supercritical shock (cold accretion). For this, we conduct
self-consistently coupled formation and evolution calculations of giant planets
with masses between 1 and 12 Jovian masses and core masses between 20 and 120
Earth masses. We find that the post-formation luminosity of massive giant
planets is very sensitive to the core mass. An increase of the core mass by a
factor 6 results in an increase of the post-formation luminosity of a 10 Jovian
mass planet by a factor 120. Due to this dependency, there is no single well
defined post-formation luminosity for core accretion, but a wide range. For
massive cores (~100 Earth masses), the post-formation luminosities of core
accretion planets become so high that they approach those in the hot start
scenario that is often associated with gravitational instability. For the
mechanism to work, it is necessary that the solids are accreted before or
during gas runaway accretion, and that they sink deep into the planet. We make
no claims whether or not such massive cores can actually form in giant planets.
But if yes, it becomes difficult to rule out core accretion as formation
mechanism based solely on luminosity for directly imaged planets that are more
luminous than predicted for low core masses. Instead of invoking gravitational
instability as the consequently necessary formation mode, the high luminosity
could also be caused simply by a more massive core.
