Formation, orbital and thermal evolution, and survival of planetary-mass clumps in the early phase of circumstellar disc evolution

Abstract

We report the results of our three-dimensional radiation hydrodynamics simulation of collapsing unmagnetized molecular cloud cores. We investigate the formation and evolution of the circumstellar disc and the clumps formed by disc fragmentation. Our simulation shows that disc fragmentation occurs in the early phase of circumstellar disc evolution and many clumps form. The clump can be represented by a polytrope sphere of index n ∼ 3 and n ≳ 4 at central temperature Tc ≲ 100 K and Tc ≳ 100 K, respectively. We demonstrate, numerically and theoretically, that the maximum mass of the clump, beyond which it inevitably collapses, is ∼0.03 M⊙. The entropy of the clump increases during its evolution, implying that evolution is chiefly determined by mass accretion from the disc rather than by radiative cooling. Although most of the clumps rapidly migrate inward and finally fall on to the protostar, a few clumps remain in the disc. The central density and temperature of the surviving clump rapidly increase and the clump undergoes a second collapse within 1000–2000 years after its formation. In our simulation, three second cores of masses 0.2 M⊙, 0.15 M⊙ and 0.06 M⊙ formed. These are protostars or brown dwarfs rather than protoplanets. For the clumps to survive as planetary-mass objects, the rapid mass accretion should be prevented by some mechanisms.