Fates of the dense cores formed by fragmentation of filaments: Do they fragment again or not?

Fragmentation of filaments into dense cores is thought to be an important step in forming stars. The bar-mode instability of spherically collapsing cores found in previous linear analysis invokes a possibility of refragmentation of the cores due to their ellipsoidal (prolate or oblate) deformation. To investigate this possibility, here we perform three-dimensional selfgravitational hydrodynamics simulations that follow all the way from filament fragmentation to subsequent core collapse. We assume that the gas is polytropic with index ? , which determines the stability of the bar mode. For the case that the fragmentation of isolated hydrostatic filaments is triggered by the most unstable fragmentation mode, we find that the bar mode grows as collapse proceeds if < 1.1, in agreement with the linear analysis. However, it takes more than 10 orders-of-magnitude increase in the central density for the distortion to become non-linear. In addition to this fiducial case, we also study non-fiducial ones such as the fragmentation is triggered by a fragmentation mode with a longer wavelength and it occurs during radial collapse of filaments and find that the distortion rapidly grows. In most of astrophysical applications, the effective polytropic index of collapsing gas exceeds 1.1 before 10 orders-of-magnitude increase in the central density. Thus, supposing the fiducial case of filament fragmentation, refragmentation of dense cores would not be likely and their final mass would be determined when the filaments fragment.