Dust growth timescale and mass function of molecular clouds in the Galaxy

We examine the characteristic growth time of dust grains in the Galaxy, whe re the grain growth in molecular clouds is the dominant factor for dust-mas s increase. Since the timescale of grain growth depends on the gas density of molecular clouds, we reconsider the typical molecular-cloud density by u sing the "density function" of clouds [denoted as N(n) dn]. Here, the densi ty function expresses the probability that a cloud has a volume-averaged ga s density between n and n + dn, and it can be calculated by combining the o bserved mass function and the scaling law of molecular clouds. Through the formulation that combines N(n) with the characteristic dust growth timescal e, we find that the typical dust growth timescale is in the range of 10(7)- 10(8) yr. This range is equivalent to the timescale of the dust growth in m olecular clouds whose molecular number density is 3 x 10(2)-3 x 10(3) cm(-3 ). Thus, the dense molecular clouds (n > 10(4) 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.