2013ApJ...770..120B

Using detailed numerical simulations, we study the formation of bodies near the deuterium-burning limit according to the core-nucleated giant planet accretion scenario. The objects, with heavy-element cores in the range 5-30 M _⊕, are assumed to accrete gas up to final masses of 10-15 Jupiter masses (M_Jup). After the formation process, which lasts 1-5 Myr and which ends with a "cold-start," low-entropy configuration, the bodies evolve at constant mass up to an age of several Gyr. Deuterium burning via proton capture is included in the calculation, and we determined the mass, M₅₀, above which more than 50% of the initial deuterium is burned. This often-quoted borderline between giant planets and brown dwarfs is found to depend only slightly on parameters, such as core mass, stellar mass, formation location, solid surface density in the protoplanetary disk, disk viscosity, and dust opacity. The values for M₅₀ fall in the range 11.6-13.6 M_Jup, in agreement with previous determinations that do not take the formation process into account. For a given opacity law during the formation process, objects with higher core masses form more quickly. The result is higher entropy in the envelope at the completion of accretion, yielding lower values of M₅₀. For masses above M₅₀, during the deuterium-burning phase, objects expand and increase in luminosity by one to three orders of magnitude. Evolutionary tracks in the luminosity versus time diagram are compared with the observed position of the companion to Beta Pictoris.