The Critical Core Mass Of Core Accretion Model For Planet Formation

Core accretion model is a widely accepted mechanism of planet formation.The critical core mass is the mass of protoplanetary core,above which runaway accretion ensues to form gas giants.When core mass is less than critical mass,the atmosphere can be considered satisfying hydrostatic equilibrium.Once the core exceed the criti-cal mass,the atmosphere follows hydrodynamic evolution and there are no solutions of equilibrium.We use static model to calculate the structure of planet,and the largest planet core mass from the solutions of hydrostatic equilibrium is the critical core mass.In the standard calculation of planet envelope structure,the convection is usu-ally assumed to be very efficient and the convective region is completely adiabatic.But this is not necessarily the case.Super-adiabatic regions would be formed in the convective region under certain circumstances and mixing length theory(MLT)is always adapted.How do they affect the critical core mass during the planet for-mation process still remains an open question.We investigate the effect of MLT on the structure of envelopes accumulated around protoplanetary cores for different planetesimal accretion rates.The outer boundaries of the envelopes are determined by the physical conditions within the protoplanetary disks(PPDs).We study the structure of the envelope for different locations within the PPDs as well.We show that the critical core mass can be enhanced compared with the case that the MLT is not included.The super-adiabatic region would push the radiative-convective boundary of the envelope outwards,leading to the increase of critical core mass.We also focus on the mixing length parameter,which suggests the efficiency of convection.The parameter always chosen as 1.0 in previous work,can significantly affect the extent of the increase of critical mass and the structure of the envelope.The exact value of the mixing length parameter used in planetary model may need to be determined by future observations.