The velocity dispersion of the giant molecular clouds: a viscous origin

Abstract

We propose the energy source and study the details of the acceleration mechanism for the random motion of the Giant Molecular Clouds (GMCs) in the Galaxy. Gravitational scattering of the massive clouds off each other in the differentially rotating galactic disk constitutes an effective" gravitational" viscosity, which causes an increase in the random kinetic energy of the GMCs at the expense of their ordered, rotational kinetic energy in the galactic disk. We calculate the rate of increase, due to this effect, of the random kinetic energy of a GMC with a nonzero initial random velocity. In order to do this, we treat an encounter between the test cloud and a field cloud in the sheared disk as a perturbed, coupled, two-dimensional harmonic oscillator problem, with the gravitational interaction between the two clouds being the time-dependent perturbation force. The equations are solved analytically to second (lowest significant) order in the small parameter. In a steady state, the rate of energy input from the viscosity due to gravitational and physical interactions among the GMCs in the differentially rotating galactic disk equals the rate of energy loss due to the inelastic physical collisions among the GMCs; this yields the value for the equilibrium cloud velocity dispersion. The resulting one-component velocity dispersion is determined by a fifth-order polynomial having approximate solution V_1-D = 0.69[(Gm/r)KH]^I/3 = 0.38V_esc(K/K_z)(V_z/V_l.O)^½; where m, r and V_esc are the cloud mass, radius and escape velocity, respectively, K is the epicyclic frequency K_z is the z oscillation frequency, and H is the total vertical scale height of the gas distribution. This result is independent of the cloud number density and depends only weakly (through K/K_z) on the galactocentric radial distance of a cloud. Note that the cloud velocity dispersion is an increasing function of m/r and V²_esc. The derived value is V_1-D = 5-7 km s ^-1 and is nearly independent of cloud mass, in good agreement with current observations. Gravitational viscosity, therefore, can provide the main energy input for the random motion of the GMCs in the Galaxy. Locally the fraction of the rotational kinetic energy lost in supporting inelastic cloud motions for ~10 billion years is small, ~0.1. Thus the rotational kinetic energy of the GMCs proves to be more than adequate for the long-term support of their random motion. As a result of the viscous interaction among the clouds, the clouds drift inward. The viscous evolution of the radial distribution of the GMCs, which will be treated in a future paper, will tend to evacuate clouds from within ~3 kpc. Thus, the dynamics as well as the radial distribution in the Galaxy of the GMCs is determined by their gravitational viscous interaction, which operates because of their location in the differentially rotating galactic disk.