The dynamical role of drag force in gravitational instability: a path to form planetary cores in young protostellar discs

Explaining the formation of planetesimals is challenging for current planet formation scenarios. Indeed, according to Core Accretion theory, the timescale of solid cores formation is up to 1Myr, too long to explain the plethora of protoplanets observed in class II protostellar discs. As for the Gravitational Instability scenario, the expected mass of fragments is about 1 to 10 Jupiter masses, too big to form a planetary core.

In addition, the wide diversity of substructures such as rings, gaps, spirals in ALMA protoplanetary systems is often explained by the interaction between massive embedded protoplanets and the accretion disc. This necessarily implies that planet formation is already underway in young systems, when the protostar is still embedded into the molecular cloud and the accretion disc is massive. In these environments, the role of self gravity and gravitational instability is decisive in determining the dynamical evolution of the system. For this reason, studying the role of dust in gravitational instability is crucial to obtain a comprehensive knowledge of planetesimal formation process.

In this work, we present an analytical framework to study gravitational instability of a gas and dust disc, including the effect of drag force, as a path to solve the conundrum of planetesimal formation in protoplanetary discs. We found that the instability is determined by three parameters, that are the dust to gas ratio, the relative temperature between the two components and the Stokes number, that measures the strength of the aerodynamical coupling. When we consider the dynamical and gravitational effect of dust, the instability threshold is always higher compared to the one fluid model. In addition, the presence of the second component can trigger gravitational instability at very short wavelengths, reducing of several order of magnitudes the Jeans length and mass. In this picture, considering typical protoplanetary discs parameters, the Jeans mass can be of the order of the Earth mass, much lower compared to the one fluid scenario. In this respect, this phenomenon is a possible path to form planetary cores in early protoplanetary stages.