Description
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 a correlation between the planet formation rate (PFR) and the gas surface density, i.e. PFR ∝ Σ_g^n. We define the planet formation rate as the number of planets of a given type (and hence a typical mass), formed per unit surface per unit time, and examine the dependence of this quantity on the gas surface density of the protoplanetary disk in which they formed. This relation serves as an analog for the well-established Kennicutt-Schmidt law for star-forming galaxies, with proper modifications, as star formation differs significantly from planet formation. We study the
different planet formation mechanisms and the density dependence in each one of them, to finally formulate simple powerlaw relations. We find that the powerlaw ranges between 𝑛 ≈ 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.
