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Observational evidence suggests that gas disk instability may be responsiblefor the formation of at least some gas giant exoplanets, particularly massiveor distant gas giants. With regard to close-in gas giants, Boss (2017) used the$\beta$ cooling approximation to calculate hydrodynamical models of inner gasdisk instability, finding that provided disks with low values of the initialminimum Toomre stability parameter (i.e., $Q_i < 2$ inside 20 au) form,fragmentation into self-gravitating clumps could occur even for $\beta$ as highas 100 (i.e., extremely slow cooling). Those results implied that the evolutionof disks toward low $Q_i$ must be taken into account. This paper presents suchmodels: initial disk masses of 0.091 $M_\odot$ extending from 4 to 20 au arounda 1 $M_\odot$ protostar, with a range (1 to 100) of $\beta$ cooling parameters,the same as in Boss (2017), but with all the disks starting with $Q_i = 2.7$,i.e., gravitationally stable, and allowed to cool from their initial outer disktemperature of 180 K to as low as 40 K. All the disks eventually fragment intoat least one dense clump. The clumps were again replaced by virtualprotoplanets (VPs) and the masses and orbits of the resulting ensemble of VPscompare favorably with those of Boss (2017), supporting the claim that diskinstability can form gas giants rapidly inside 20 au, provided thatsufficiently massive protoplanetary disks exist.

The Effect of the Approach to Gas Disk Gravitational Instability on the Rapid Formation of Gas Giant Planets