Bonnor-Ebert sphere collapse in filamentary structures

TL;DR

The paper tackles why some star-forming cores in filaments appear at separations smaller than the linear theory's minimum wavelength. It uses 3D hydrodynamical simulations with RAMSES to evolve perturbations in isothermal filaments and compares growth rates to linear predictions. A key finding is that nonlinear evolution begins when the Bonnor-Ebert sphere's gravity dominates over the cylindrical filament potential, causing collapse to proceed via Bonnor-Ebert stability and establishing a line-mass–dependent threshold (around $f_\text{cyl}\approx 0.66$). For large line-mass perturbations, cores can collapse directly at separations as small as $2.61$ times closer than the dominant wavelength, providing a mechanism to reconcile theoretical predictions with observed close core spacings and suggesting a pathway for hierarchical fragmentation in massive filaments.

Abstract

Star formation within filaments may arise due to the growth of cores according to linear perturbation theory. This implies a minimum core separation, as shorter modes would not be able to grow. While many observations agree with core separations by theoretical predictions, some observations also show star forming cores which lie closer together than the minimum wavelength given by perturbation theory. We explore whether non-linear effects during the late stages of core growth can explain the discrepancy between theory and observations. We perform three-dimensional hydrodynamical simulations with the Ramses code to follow the evolution of initial perturbations within filaments and compare the measured growth rates to expectations from theoretical models. Non-linear evolution sets in as soon as the core mass reaches a value where the gravitational potential is not any longer dominated by the cylindrical potential of the filament but by the spherical potential of the Bonnor-Ebert sphere. Consequently, core collapse is not triggered by the loss of hydrostatic stability of the filament but by the loss of hydrostatic stability of the Bonnor-Ebert sphere. As the core is embedded in the filament, the maximum core mass is given by the pressure within the filament which results in a constant line-mass threshold for core collapse. As core collapse is triggered as soon as overdensities reach a certain line-mass, cores which form as large line-mass perturbations during filament formation can go into direct collapse even if their separation is closer than predicted by linear perturbation theory. Therefore, our result can explain the discrepancy between theory and observations.

Figures (10)

• Figure 1: Maximum perturbation strength in dependence of the line-mass in order to keep the relative line-mass error below different thresholds. The thresholds plotted are 1, 2 and 3% given by the solid, dashed and dashed-dotted lines, respectively.
• Figure 2: Time evolution of the perturbation strength of different variables, shown as solid lines, compared to the theoretical prediction, given by the dashed line. The blue, cyan and orange lines show the evolution of the maximum in density, x-acceleration and x-velocity, respectively, for a filament of a line-mass of $f_\text{cyl}=0.25$.
• Figure 3: Time evolution of the absolute relative error of the growth time scale $\omega$ measured in the simulation for a line-mass of $f_\text{cyl}=0.25$. The solid blue, cyan and orange line shows the error of the density, x-acceleration and x-velocity, respectively. We define the begin of the non-linear evolution by determining the point in time when the error exceeds a value of 5% when measuring back from the end of the simulation. The thresholds are indicated by the vertical dashed-dotted lines, for which we also determine the line-masses at the position of the core which are given in the legend.
• Figure 4: Evolution of the radial density profile of the core from the linear growth phase until the start of the collapse for a line-mass of $f_\text{cyl}=0.25$. Shown are snapshots before the first threshold in light blue, between the first and second threshold in blue and just after the second threshold in dark blue. The density as well as the radius are normalised to a dimensionless form in order to compare profiles with different concentrations. The filament profile as defined in Eq. \ref{['eq:rho']} is given as dotted line and the Bonnor-Ebert sphere profile as dashed line.
• Figure 5: Threshold line-masses at the position of the core in dependence of the filament line-mass $f_\text{cyl}$. The begin of the non-linear evolution in acceleration is given by the cyan points for the velocity by the orange points. The solid line indicates where the Bonnor-Ebert sphere potential dominates over the filament potential. The vertical dashes-dotted line shows the lower mass limit for a collapsing Bonnor-Ebert sphere and the horizontal dashed line shows the result of calculating the maximum supported Bonnor-Ebert mass assuming a external pressure given by the density within the filament.