The Reaction of Self-Gravitating Protostellar Discs to Moderate Lessening In Cooling Time-Scale: the Fragmentation Boundary Revisited |
Anumber of previous studies of the fragmentation of self-gravitatingprotostellar discs have involved suites of simulations in which radiativecooling is modelled in terms of a cooling time-scale (tcool) which is parametrized as a simple multiple (βcool) of the localdynamical time-scale. Such studies have delineated the ‘fragmentation boundary’in terms of a critical value of βcool(βcrit) such that the discfragments if βcool < βcrit. Such anapproach however begs the question of how in reality a disc could ever beassembled in a state with βcool< βcrit. Here weadopt the more realistic approach of effecting a gradual reduction in βcool, as might correspondto changes in thermal regime due to secular changes in the disc densityprofile.We find that the effect of graduallyreducing βcool(on a time-scale longer than tcool)is to stabilize the disc against fragmentation, compared with models in which βcool is reduced rapidly(over less than tcool).We therefore conclude that the ability of a disc to remain in a self-regulated,self-gravitating state (without fragmentation) is partly dependent on thedisc’s thermal history, as well as its current cooling rate. Nevertheless, theeffect of a slow reduction in tcoolappears only to lower the fragmentation boundary by about a factor of 2 in tcool and thus onlypermits maximum ‘α’ values(which parametrize the efficiency of angular momentum transfer in the disc)that are about a factor of 2 higher than determined hitherto. Our resultstherefore do not undermine the notion that there is a fundamental upper limitto the heating rate that can be delivered by gravitational instabilities beforethe disc is subject to fragmentation. An important implication of this work,therefore, is that self-gravitating discs can enter into the regime offragmentation via secular evolutionand it is not necessary to invoke rapid (impulsive) events to triggerfragmentation. Inthis paper, we use high-resolution smoothed particle hydrodynamics (SPH)simulations to investigate the response of a marginally stable self-gravitatingprotostellar disc to a close parabolic encounter with a companion disclessstar. Our main aim is to test whether close brown dwarfs or massive planets canform out of the fragmentation of such discs.We followthe thermal evolution ofthe disc by including the effects of heating due to compression and shocks anda simple prescription for cooling and find results that contrast with previousisothermal simulations. In the present case we find that fragmentation isinhibited by the interaction, due to the strong effect of tidal heating, whichresults in a strong stabilization of the disc. Asimilar behaviour was also previously observed in other simulations involvingdiscs in binary systems. As in the case of isolated discs, it appears that thecondition for fragmentation ultimately depends on the cooling rate.