Early planet formation in embedded protostellar disks

Setting the stage for the first generation of planetesimals

¹ Max-Planck-Institut für Extraterrestrishe Physik, Gießenbachstrasse 1, 85748 Garching, Germany
e-mail: cridland@strw.leidenuniv.nl
² School of Physics and Astronomy, University of Leicester, Leicester LE1 7RH, UK
³ Leiden Observatory, Leiden University, 2300 RA Leiden, The Netherlands
⁴ European Southern Observatory, Karl-Schwarzschild-Str. 2, 85748 Garching, Germany

Received: 13 September 2021
Accepted: 2 December 2021

Abstract

Recent surveys of young star formation regions have shown that the dust mass of the average class II object is not high enough to make up the cores of giant planets. Younger class O/I objects have enough dust in their embedded disk, which raises the question whether the first steps of planet formation occur in these younger systems. The first step is building the first planetesimals, which are generally thought to be the product of the streaming instability. Hence the question can be restated to read whether the physical conditions of embedded disks are conducive to the growth of the streaming instability. The streaming instability requires moderately coupled dust grains and a dust-to-gas mass ratio near unity. We model the collapse of a dusty proto-stellar cloud to show that if there is sufficient drift between the falling gas and dust, regions of the embedded disk can become sufficiently enhanced in dust to drive the streaming instability. We include four models to test a variety of collapse theories: three models with different dust grain sizes, and one model with a different initial cloud angular momentum. We find a sweet spot for planetesimal formation for grain sizes of a few 10s of micron because they fall sufficiently fast relative to the gas to build a high dust-to-gas ratio in the disk midplane, but their radial drift speeds are slow enough in the embedded disk to maintain the high dust-to-gas ratio. Unlike the gas, which is held in hydrostatic equilibrium for a time as a result of gas pressure, the dust can begin to collapse from all radii at a much earlier time. The dust mass flux in class O/I systems can thus be higher than the gas flux. This builds an embedded dusty disk with a global dust-to-gas mass ratio that exceeds the inter-stellar mass ratio by at least an order of magnitude. The streaming instability can produce at least between 7 and 35 M_⊕ of planetesimals in the class O/I phase of our smooth embedded disks, depending on the size of the falling dust grains. This mass is sufficient to build the core of the first giant planet in the system, and could be further enhanced by dust traps and/or pebble growth. This first generation of planetesimals could represent the first step in planet formation. It occurs earlier in the lifetime of the young star than is traditionally thought.