Investigating the Global Collapse of Filaments Using Smoothed Particle Hydrodynamics

We use Smoothed Particle Hydrodynamic simulations of cold, uniform density, self-gravitating filaments, to investigate their longitudinal collapse timescales; these timescales are important because they determine the time available for a filament to fragment into cores. A filament is initially characterised by its line-mass, $\mu$, its radius, $R$ (or equivalently its density $\rho\!=\!\mu/\pi R^2$), and its aspect ratio, $A\;\,(\equiv Z/R$, where $Z$ 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 ($A\! < \!5$) collapse along the $z$-axis more-or-less homologously, on a time-scale $t_{_{\rm HOM}} \sim 0.44\,A\,(G\rho)^{-1/2}$; in contrast, longer filaments ($A\! > \!5$) 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 $t_{_{\rm END}} \sim 0.98\,A^{1/2}\,(G\rho)^{-1/2}$. Our simulations do not corroborate these predictions. First, for all $A\! > \!2$, the collapse time satisfies a single equation \[t_{_{\rm COL}}\;\sim\;(0.49+0.26A)(G\rho)^{-1/2}\,,\] which for large $A$ is much longer than the Pon et al. prediction. Second, for all $A\! > \!2$, the collapse is end-dominated. Third, 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 doing work both accelerating and compressing the gas they sweep up. Pon et al. appear to have neglected the outward acceleration and its consequences.