2017A&A...608A..72M

Context. This paper continues a series in which we predict the main observable characteristics of exoplanets based on their formation. In Paper I we described our global planet formation and evolution model that is based on the core accretion paradigm. In Paper II we studied the planetary mass-radius relationship with population syntheses.
Aims. In this paper we present an extensive study of the statistics of planetary luminosities during both formation and evolution. Our results can be compared with individual directly imaged extrasolar (proto)planets and with statistical results from surveys.
Methods. We calculated three populations of synthetic planets assuming different efficiencies of the accretional heating by gas and planetesimals during formation. We describe the temporal evolution of the planetary mass-luminosity relation. We investigate the relative importance of the shock and internal luminosity during formation, and predict a statistical version of the post-formation mass vs. entropy "tuning fork" diagram. Because the calculations now include deuterium burning we also update the planetary mass-radius relationship in time.
Results. We find significant overlap between the high post-formation luminosities of planets forming with hot and cold gas accretion because of the core-mass effect. Variations in the individual formation histories of planets can still lead to a factor 5 to 20 spread in the post-formation luminosity at a given mass. However, if the gas accretional heating and planetesimal accretion rate during the runaway phase is unknown, the post-formation luminosity may exhibit a spread of as much as 2-3 orders of magnitude at a fixed mass. As a key result we predict a flat log-luminosity distribution for giant planets, and a steep increase towards lower luminosities due to the higher occurrence rate of low-mass (M ≤10-40M_⊕) planets. Future surveys may detect this upturn.
Conclusions. Our results indicate that during formation an estimation of the planetary mass may be possible for cold gas accretion if the planetary gas accretion rate can be estimated. If it is unknown whether the planet still accretes gas, the spread in total luminosity (internal + accretional) at a given mass may be as large as two orders of magnitude, therefore inhibiting the mass estimation. Due to the core-mass effect even planets which underwent cold accretion can have large post-formation entropies and luminosities, such that alternative formation scenarios such as gravitational instabilities do not need to be invoked. Once the number of self-luminous exoplanets with known ages and luminosities increases, the resulting luminosity distributions may be compared with our predictions.