An improved equation of state for protoplanetary simulations

Physics

Scientific paper

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Scientific paper

In the theory of planetary formation via gravitational instabilities in discs, people have been using effective equations of state, which mimic the effects of the phenomena supposed to take place at these densities and pressures, without a real description of them. As these phenomena are strongly non linear, this approach leads to large discrepancies with respect to reality. The aim our work is to develop a correct equation of state, starting from physical principles, able to give a real representation of the physics involved, with particular attention to the dissociation of hydrogen. Indeed this phenomena strongly affects the collapsing phase due to the gravitational instabilities which leads to the formation of gas giant planets; therefore a correct representation of this phase is needed in order to describe the structure and proprieties of protoplanets. In our work we derived the equation of state for a gas composed of a mixture of atomic and diatomic hydrogen in chemical equilibrium, including details of rotational and vibrational modes. We implemented this equation in the Gasoline code and ran simulations of protoplanetary clumps starting from physical initial conditions (given by previous works). From our results it is clear that the structure of the protoplanets which form after the collapse is strongly dependent on the equation of state involved, in particular for the timescales, the mass involved and the highest temperatures reached. The former result is especially important, as a correct estimate of this timescale will give strong constrains to the theory of planets formation. The next step of this project is to increase the complexity of our equation of state, adding more and more chemical components, in order to give a more thorough description of the physics of the gas.

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