# Circumbinary discs with radiative cooling and embedded planets

## TL;DR

This study uses advanced simulations to explore how radiative cooling and disc parameters influence the final positions of planets in circumbinary systems, aligning theoretical models with observed planetary locations.

## Contribution

It introduces a more realistic thermal disc model and analyzes how disc viscosity and planet mass affect planet migration and final parking locations.

## Key findings

- Lower viscosity discs allow planets to migrate closer to the binary.
- Gap-opening planets tend to have more circular orbits.
- Final planet position depends on planet mass and disc viscosity.

## Abstract

As of today ten circumbinary planets orbiting solar type main sequence stars have been discovered. Nearly all of them orbit around the central binary very closely to the region of instability where it is difficult to form them in situ. It is assumed that they formed further out and migrated to their observed position. We extend previous studies to a more realistic thermal disc structure and determine what parameter influence the final parking location of a planet around a binary star. We perform two-dimensional numerical simulations of viscous accretion discs around a central binary that include viscous heating and radiative cooling from the disc surfaces. We vary the binary eccentricity as well as disc viscosity and mass. Concerning the disc evolution we find that it can take well over 100000 binary orbits until an equilibrium state is reached. As seen previously, we find that the central cavity opened by the binary becomes eccentric and precesses slowly in a prograde sense. Embedded planets migrate to the inner edge of the disc. In cases of lower disc viscosity they migrate further in maintaining a circular orbit, while for high viscosity they are parked further out on an eccentric orbit. The final location of an embedded planet is linked to its ability to open a gap in the disc. Gap opening planets separate inner from outer disc, preventing eccentricity excitation in the latter and making it more circular. This allows embedded planets to migrate closer to the binary, in agreement with the observations. The necessary condition for gap opening and the final planet position depend on the planet mass and disc viscosity.