Investigating the global collapse of filaments using smoothed particle hydrodynamics

Abstract

We use smoothed particle hydrodynamic simulations of cold, uniform density, self-gravitating filaments, to investigate their longitudinal collapse time-scales; these time-scales are important because they determine the time available for a filament to fragment into cores. A filament is initially characterized by its line-mass, μO, its radius, RO (or equivalently its density ρO = μO/πRO2 ), and its aspect ratio, AO (=ZO/RO, where ZO is its half-length). The gas is only allowed to contract longitudinally, i.e. parallel to the symmetry axis of the filament (the z-axis). Pon et al. (2012) have considered the global dynamics of such filaments analytically. They conclude that short filaments (AO ≲ 5) collapse along the z-axis more-or-less homologously, on a time-scale tHOM ~ 0.44 AO (GρO)-1/2; in contrast, longer filaments (AO ≳ 5) undergo end-dominated collapse, i.e. two dense clumps form at the ends of the filament and converge on the centre sweeping up mass as they go, on a time-scale tEND ~ 0.98 AO1/2 (GρO)-1/2. Our simulations do not corroborate these predictions. First, for all AO ≳ 2, the collapse time satisfies a single equation tCOL ~ (0.49 + 0.26AO)(GρO)-1/2, which for large AO is much longer than the Pon et al. prediction. Secondly, for all AO ≳ 2, the collapse is end-dominated. Thirdly, before being swept up, the gas immediately ahead of an end-clump is actually accelerated outwards by the gravitational attraction of the approaching clump, resulting in a significant ram pressure. For high aspect ratio filaments, the end-clumps approach an asymptotic inward speed, due to the fact that they are doingwork both accelerating and compressing the gas they sweep up. Pon et al. appear to have neglected the outward acceleration and its consequences.