Perturbation growth in accreting filaments
  We use smoothed particle hydrodynamic simulations to investigate the growth
of perturbations in infinitely long, initially sub-critical but accreting
filaments. The growth of these perturbations leads to filament fragmentation
and the formation of cores. Most previous work on this subject has been
confined to the growth and fragmentation of equilibrium filaments and has found
that there exists a preferential fragmentation length scale which is roughly 4
times the filament's diameter. Our results show a more complicated dispersion
relation with a series of peaks linking perturbation wavelength and growth
rate. These are due to gravo-acoustic oscillations along the longitudinal axis
during the sub-critical phase of growth. The positions of the peaks in growth
rate have a strong dependence on both the mass accretion rate onto the filament
and the temperature of the gas. When seeded with a multi-wavelength density
power spectrum there exists a clear preferred core separation equal to the
largest peak in the dispersion relation. Our results allow one to estimate a
minimum age for a filament which is breaking up into regularly spaced
fragments, as well as a maximum accretion rate. We apply the model to
observations of filaments in Taurus by Tafalla & Hacar (2015) and find
accretion rates consistent with those estimated by Palmeirim et al. (2013).
