The Critical Line Mass of Filament Gas: Thermal Support, Turbulent Support and Fragmentation Scales

An isothermal self-gravitating cylinder has a maximum mass per unit length it can hold against its own gravity: the Ostriker critical line mass, two times the square of the support speed divided by Newton's constant. This paper evaluates that limit for warm-hot filament gas. Pure thermal support at 1e5 kelvin holds 6.51e+11 solar masses per megaparsec; at 1e6 kelvin, 6.51e+12; at 1e7 kelvin, 6.51e+13. Adding a stated turbulent support of 100 kilometres per second raises the 1e6 kelvin limit to 1.12e+13 solar masses per megaparsec. A representative filament gas line mass of 1.77e+11 solar masses per megaparsec is only 0.0272 of the thermal critical value at a million kelvin: the gas in filaments is far from self-gravitating as a cylinder in its own right, and its structure is imposed by the dark matter potential and the accretion flow, not by its own gravity. The fastest-growing fragmentation wavelength for a two-megaparsec-diameter filament, about 8 megaparsecs, exceeds typical filament lengths between nodes, which further suppresses bead-like fragmentation of the gas.