Modification to the Jeans criterion by external tides: anisotropic fragmentation and formation of filaments

Abstract

ABSTRACT The Jeans criterion sets the foundation of our understanding of gravitational collapse. Jog studied the fragmentation of gas under external tides and derived a dispersion relation $l^{\prime } = l_{\rm Jeans} \frac{1}{(1 + \lambda _0^{\prime } / 4 \pi G \rho _0)^{1/2}} \,\,.$ She further concludes that the Jeans mass is $m_{\rm incorrect}^{\prime }=m_{\rm Jeans} [1/(1 + \lambda _0^{\prime } / 4 \pi G \rho _0)^{3/2}]$. We clarify that due to the inhomogeneous nature of tides, this characteristic mass is incorrect. Under weak tides, the mass is $m \approx \rho \, l_1 l_2 l_3$, where the modifications to Jeans lengths along all three dimensions need to be considered; when the tide is strong enough, collapse can only occur once 1 or 2 dimensions. In the latter case, tides can stretch the gas, leading to the formation of filaments.