Exploring the conditions for forming planetesimals by the streaming instability and planetary systems by pebble accretion

TL;DR

This paper investigates the specific disc conditions under which streaming instability and pebble accretion can lead to various planetary formations, identifying optimal parameters and potential enhancements.

Contribution

It provides a detailed analysis of protoplanetary disc parameters necessary for forming different planetary types via streaming instability and pebble accretion, including new analytical insights.

Findings

Optimal Stokes number range for planetesimal and planetary formation is 0.01 to 0.03.

Cold gas giants require very low turbulence and large initial disc sizes.

High Stokes numbers hinder cold gas giant formation due to short pebble flux.

Abstract

The streaming instability and pebble accretion are two physical mechanisms with demonstrated potentials to drive, respectively, the formation of planetesimals and the growth of planetary systems containing a diverse range of planetary types. Here we explore the protoplanetary disc conditions in terms of turbulence strength, Stokes number and initial disc size that are needed to (i) form planetesimals by the streaming instability, (ii) form gas giant planets in cold orbits, (iii) form super-Earths and sub-Neptunes close to the star and (iv) form rocky planet embryos in temperate orbits. We identify an optimum Stokes number range between St= 0.01 and St= 0.03 where all three planetary classes form and where the streaming instability is triggered for a slightly elevated pebble metallicity. Cold gas giants require a turbulence strength of at most $\delta=10^{-4}$ and furthermore need large initial disc sizes to benefit from a prolonged pebble flux; super-Earths and rocky planet embryos tolerate higher turbulence strengths similar to those measured for the vertical shear instability. A higher Stokes number of St=0.1 is detrimental to the formation of cold gas giants due to the short-lived pebble flux. For Stokes numbers below St= 0.003, extremely low values of turbulence ($\delta<10^{-5}$) are required to form cold gas giants. We highlight how loss of gas to disc winds, reduction in the migration speed by thermal or dynamical torques or the presence of pressure bumps in the outer disc could increase the parameter space for the formation of cold gas giants. We derive analytically that the mass of the largest planetesimals formed by the streaming instability is of similar magnitude to the threshold mass beyond which pebble accretion becomes efficient, if planetesimals form in the earliest phases of protoplanetary disc evolution.