Hierarchical gravitational fragmentation. I. Collapsing cores within collapsing clouds

TL;DR

This paper uses numerical simulations to explore hierarchical gravitational fragmentation, revealing that collapsing cores within unstable clouds evolve outside-in, challenging classical inside-out collapse models and explaining observed infall velocities.

Contribution

It demonstrates that cores form and collapse dynamically within unstable backgrounds, deviating from hydrostatic initial conditions and providing a new perspective on prestellar core evolution.

Findings

Cores develop Bonnor-Ebert-like density profiles during collapse.

Collapse proceeds from outside-in, not inside-out.

Cores can be stable or unstable while collapsing, influenced by the background.

Abstract

We investigate the Hierarchical Gravitational Fragmentation scenario through numerical simulations of the prestellar stages of the collapse of a marginally gravitationally unstable isothermal sphere immersed in a strongly gravitationally unstable, uniform background medium. The core developes a Bonnor-Ebert (BE)-like density profile, while at the time of singularity (the protostar) formation the envelope approaches a singular-isothermal-sphere (SIS)-like $r^-2$ density profile. However, these structures are never hydrostatic. In this case, the central flat region is characterized by an infall speed, while the envelope is characterized by a uniform speed. This implies that the hydrostatic SIS initial condition leading to Shu's classical inside-out solution is not expected to occur, and therefore neither should the inside-out solution. Instead, the solution collapses from the outside-in, naturally explaining the observation of extended infall velocities. The core, defined by the radius at which it merges with the background, has a time-variable mass, and evolves along the locus of the ensemble of observed prestellar cores in a plot of $M/M_{BE}$ vs. $M$, where $M$ is the core's mass and $M_{BE}$ is the critical Bonnor-Ebert mass, spanning the range from the "stable" to the "unstable" regimes, even though it is collapsing at all times. We conclude that the presence of an unstable background allows a core to evolve dynamically from the time when it first appears, even when it resembles a pressure-confined, stable BE-sphere. The core can be thought of as a ram-pressure confined BE-sphere, with an increasing mass due to the accretion from the unstable background.