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

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' = l ₉₄₀₍ₒ 1 (1 + ₀' / 4 G ₀) ^{1/2} \;. She further concludes that the Jeans mass is m ₈₍₂₎ₑₑ₄₂ₓ'=m ₉₄₀₍ₒ (1/ (1 + ₀' / 4 G 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 \, l₁ l₂ l₃, 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.