We investigate the structure of self-gravitating discs, their fragmentation and the evolution of the fragments (the clumps) using both an analytic approach and three-dimensional radiation hydrodynamics simulations starting from molecular cores. The simulations show that nonlocal radiative transfer determines the disc temperature. We find the disc structure is well described by an analytical model of a quasi-steady self-gravitating disc with radial radiative transfer. Because the radiative process is not local and radiation from the interstellar medium cannot be ignored, the local radiative cooling is not balanced with the viscous heating in a massive disc around a low-mass star. In our simulations, there are cases in which the disc does not fragment even though it satisfies the fragmentation criterion based on disc cooling time (Q ~ 1 and Ωtcool ~ 1). This indicates that, at least, the criterion is not a sufficient condition for fragmentation. We determine the parameter range for the host cloud core in which disc fragmentation occurs. In addition, we show that the temperature evolution of the centre of the clump is close to that of typical first cores, and that the minimum initial mass of clumps is about a few Jupiter masses.
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