Correlation between planet formation rate and gas surface density: an analog of Kennicutt Schmidt law for planet formation

Abstract

The efficiency of planet formation is a fundamental question in planetary science, gaining increasing significance as observational data from planet-forming disks accumulates. Here we derive from first principles a correlation between the planet formation rate (PFR) and the gas surface density, i.e. $\rm{PFR}\propto \Sigma_g^n$. This relation serves as an analog for the well-established Kennicutt-Schmidt law for star-forming galaxies. We study the different planet formation mechanisms and the density dependence in each one of them, to finally formulate a simple relation. We find that the powerlaw ranges between $n\approx 4/3-2$, depending on the type of the forming planet, when we carry out different analyses for the formation rates of terrestrial planets, gas giants, and also planets formed by gravitational instability. We then compare our results with the available observational data. The relation we derive here aims to shed more light on the interpretation of observational data as well as analytical models, and give a new perspective on the properties of planet formation and its connection to gas.