Hierarchical Gravitational Fragmentation. I. Collapsing Cores Within Collapsing Clouds

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.

Scale-free gravitational collapse as the origin of ρ ∼ r−2 density profile – a possible role of turbulence in regulating gravitational collapse

“…These conditions are satisfied at least approximately in many situations, and can explain the r −2 profile found in previous papers (e.g. Larson 1969;Penston 1969;Naranjo-Romero et al 2015) 3 . What is universal among these models is that after some relaxation processes, the infall time of the gas become linked to the free-fall time of the gas, and this leads to the ρ ∼ r −2 profile.…”

“…The other set of models involves infall. These include models that involve free-fall collapse (Larson 1969;Penston 1969;Vázquez-Semadeni et al 2009;Ballesteros-Paredes et al 2011;Girichidis et al 2014;Naranjo-Romero et al 2015;Donkov & Stefanov 2017), where the r −2 profile is found to be the analytical solution (such as the case of (Larson 1969;Naranjo-Romero et al 2015;Donkov & Stefanov 2017)), as well as models that involve gravity and turbulence, including the turbulenceregulated gravitational collapse model presented above.…”

Mid-JCO shock tracing observations of infrared dark clouds

“…Such narrow line widths could be also explained from the natural evolution of a dense core inside a globally infalling cloud (Naranjo-Romero et al 2015).…”

Filamentary Accretion Flows in the Infrared Dark Cloud G14.225–0.506 Revealed by ALMA

“…Nevertheless, an increasing support of magnetic fields that compensates the non-thermal pressure also cannot be ruled out . Numerical simulations of prestellar cores based on the hierarchical collapse scenario develop structures not in hydrostatic equilibrium but with smaller infall velocities in the inner part, giving a smaller σ nt /c s (Naranjo-Romero et al 2015). The largest velocities occur in the outer parts of the core, making the collapse outside-in.…”