Dust Growth Timescale and Mass Function of Molecular Clouds in the Galaxy

We examine the characteristic growth time of dust grains in the Galaxy, where the grain growth in molecular clouds is the dominant factor for dust-mass increase. Since the timescale of grain growth depends on the gas density of molecular clouds, we reconsider the typical molecular-cloud density by using the ``density function'' of clouds [denoted as N(n) dn]. Here, the density function expresses the probability that a cloud has a volume-averaged gas density between n and n+dn, and it can be calculated by combining the observed mass function and the scaling law of molecular clouds. Through the formulation that combines N(n) with the characteristic dust growth timescale, we find that the typical dust growth timescale is in the range of 10⁷-10⁸ yr. This range is equivalent to the timescale of the dust growth in molecular clouds whose molecular number density is 3 x 10²-3 x 10³ cm^-3. Thus, the dense molecular clouds (n>10⁴ cm^-3) contribute little to dust growth. The timescale supports the value constrained in our previous model and provides an upper limit for the lifetimes of molecular clouds.