How Fast Can Gas-Phase Metals Grow a Grain? Accretion Timescales from Diffuse Clouds to Dense Cores

Grain growth by accretion of gas-phase metals is often invoked and seldom timed. This paper computes the accretion growth rate of a spherical grain for a stated condensible reservoir, sticking probability, and thermal speeds across five environments from diffuse clouds to dense cores. The time to add 0.09 microns of radius is 2111.43 million years in diffuse gas at 30 particles per cubic centimetre, 298.6 million years in translucent gas, and 2.0 million years in a dense core at one hundred thousand per cubic centimetre, where the growth rate reaches 0.04493 microns per million years; the diffuse-to-dense ratio of times is 1055.7. Accretion is therefore negligible over a diffuse cloud lifetime and rapid inside dense cores, which locates grain growth, in space and in time, inside the molecular phase rather than the diffuse phase. The rates are optimistic lower bounds on the time, because the reservoir depletes as growth proceeds. All values are computed, not measured.