Surface pressures and virial terms of molecular clouds

The virial theorem tracks expansive versus compressive energies in a molecular cloud. Star formation theory has long assumed that molecular clouds are in virial equilibrium, meaning expansive energies balance compressive energies, and that sur- face virial terms are negligible. Analytically, virial equilibrium is proven for isolated, spherical clouds. Real molecular clouds form in a turbulent medium and are ir- regularly shaped. Observationally, virial equilibrium is assumed when virial mass calculated from velocity dispersion, size, and column density matches total mass. These two quantities do not always agree (Heyer et al. 2009). In addition, many who cite the virial theorem mistakenly treat the second derivative of moment of inertia as the first derivative (Ballesteros-Paredes 2006). We consider whether numerical simulations in a supernova-driven turbulent medium produce clouds that are in virial equilibrium, whether virial surface terms are negligible, and what the signs and com- parative values of virial terms really imply. We calculate all Eulerian virial theorem surface and volume terms for one high-resolution, simulated molecular cloud in an environment with other clouds. The FLASH magnetohydrodynamics code in which we form our clouds includes physics of motion, gas heating and cooling, magnetic fields, and self-gravity. We define the clouds based on a number density threshold of 100 particles per cm3. We calculate the high-resolution cloud's virial terms according to the scalar Eulerian virial theorem, as defined in McKee & Zweibel (1992), except for the gravitational terms, which we calculate following Ballesteros-Paredes et al. (2009). We find that all four of the traditionally neglected terms surface pressure, surface magnetic pressure and tension, external gravitational torque, and change in moment of inertia flux are comparable in magnitude to the traditionally inspected terms kinetic energy, magnetic energy, and internal gravitational potential, and they amount to the often neglected second derivative of moment of inertia. Surface terms are comparable to their corresponding volume terms, all hovering around 1047 to 1048 ergs. The change in moment of inertia flux and second derivative of moment of iner- tia dominate the other virial terms by about one to three orders of magnitude. The first derivative of the moment of the moment of inertia is positive, while the second derivative of the moment of inertia is negative, implying the cloud is accreting mass and contracting. The cloud is not in virial equilibrium. If our model is correct, we propose observed clouds' virial mass and directly observed mass match because of equipartition between gravitational energy and kinetic energy as the cloud collapses, not because of virial equilibrium.