The Effect of the Equation of State on the Properties of Disc-Instability Planets

Abstract

The discs around young stars may be massive enough to trigger gravitational instability and fragmentation. This process may form a number of bound objects that collapse to form protoplanets. In this thesis I run hydrodynamic simulations to investigate the effect of the thermodynamics of the disc on the properties of planets that form by gravitational instability.

I model the thermodynamics of a gravitationally unstable disc with the Smoothed Particle Hydrodynamics code PHANTOM, using a barotropic equation of state (EOS) combined with a locally isothermal EOS to provide a minimum temperature floor. In doing so, I mimic the effect of radiative feedback from the central star. I explore a parameter space wherein the critical density (i.e. the density at which the EOS switches from isothermal to adiabatic), the adiabatic index and the initial disc temperature are varied. I discuss the effect of these variations on the properties of protoplanets.

Most of the fragments, regardless of the equation of state used, form second cores (i.e. protoplanets) with masses below the planetary mass threshold (13 MJ) and initial radii of 2-8R⊙. The mass of the first core increases with steeper equations of state, with the most massive fragments (> 80MJ) forming with equations of state with γ = 1.8. Broadly speaking, the fragments that form in discs governed by steeper equations of state have wider first core accretion shocks and higher specific angular momentum. Equations of state with shallow adiabatic zones (γ = 1.2) form fragments that do not reach sufficiently high temperatures in their centres to trigger the dissociation of hydrogen and so do not form a second core. These fragments fall in to one of two morphological groups: those with very small first cores with radii of ∼ 0.005 − 0.01AU and those first cores with larger radii of ∼ 0.1AU. The latter group often exhibit evidence of spirals centred on the fragment.

A key finding of this work is that though the fragments that form by gravitational instability are approximately axisymmetric, they show evidence of being flattened and are oblate spheroids rather than spherical objects as has previously been assumed. I also find that fragments accrete gas from the disc from polar-aligned inflows (along with flows on the the disc mid-plane).

I have shown that the fragments that form in gravitationally unstable discs are sensitive to the specific equation of state, with their final mass having a strong dependence on the adiabatic index. I have also found that they are not spherically symmetric and their 3D structure must not be overlooked.