Accretion Shock Temperatures of Filament Gas: The Inflow Speeds That Manufacture the Warm-Hot Phase

The warm-hot intergalactic medium exists because gas falling onto filaments and nodes passes through shocks that convert its infall kinetic energy into heat. This paper evaluates the strong-shock temperature, T = (3/16) mu m_p v^2 / k_B with mean molecular weight 0.59, across the plausible range of inflow speeds. Gas arriving at 100 kilometres per second is heated to 1.34e+05 kelvin; at 200, to 5.36e+05; at 300, to 1.21e+06; at 400, to 2.14e+06; at 500, to 3.35e+06; and at 600 kilometres per second, to 4.82e+06 kelvin. Reaching one million kelvin requires 273 kilometres per second and ten million kelvin requires 864. Against photoionised pre-shock gas with a sound speed of 14.0 kilometres per second, these inflows are Mach 7.1 to Mach 43.0 — strong shocks throughout. The table ties the warm-hot phase's temperature range directly to the web's velocity field: filaments fed at a few hundred kilometres per second manufacture million-degree gas, and only node-scale potentials reach ten million.