THE SIZE DISTRIBUTION OF INTERSTELLAR DUST PARTICLES AS DETERMINED FROM EXTINCTION

Variations in the shape of the interstellar extinction curve from place to place in the Galaxy indicate that the size distribution of interstellar dust particles and/or the compositional mix are also changing. Cardelli, Clayton, and Mathis have shown that the extinction changes can be parameterized using the ratio of total to selective extinction, R(v). We have investigated the character of the underlying changes in the size distribution, and illustrate this with two contrasting cases: the diffuse interstellar medium (R(v) = 3.1), and a dense cloud region (R(v) = 5.3). For this exploratory investigation we adopted spherical bare silicate and bare graphite particles as in the Mathis, Rumpl, and Nordsieck (MRN) modeling. To extract the size distributions of the two components as objectively as possible we used the Maximum Entropy Method which gives the smoothest solution compatible with the chi(2) confidence level on the goodness of fit to the extinction data. Abundance constraints were implemented directly in the method in order that the elements incorporated in the grains did not exceed their cosmically available abundances or contradict depletion data. With the available wavelength range of the extinction data, from 0.1 to 5 mu m, the range over which the derived size distributions are reliable is 0.02 to 1 mu m in radius a. Note that there is no direct information from extinction on the shape of the distribution for smaller grains (<0.02 mu m), but their total mass is reasonably well determined. For the largest sizes (>1 mu m), the distribution is also unknown, but the abundance constraints can play an active role in limiting their numbers since large particles tend to contribute a significant fraction of the total interstellar dust mass. The size distribution found by MRN for the diffuse interstellar medium was a smooth power law out to a sharp cutoff at a(+) = 0.25 mu m. We confirm the qualitative features of this distribution. However, in order to achieve a good fit to the data at U, B, and V where the extinction curve changes slope and in the ultraviolet, the silicate and graphite size distributions depart significantly (and robustly) from a simple power law. We also show how the size distribution falls off smoothly beyond a,, perhaps compatible with an exponential cutoff. It has been known for some time that the mean size of particles appears to increase in a denser environment, and our new results for the case R(v) = 5.3 now quantify this effect. Compared to the case of diffuse interstellar medium, this size distribution has a significant reduction in the number of intermediate and smaller particles (<0.1 mu m) and a more modest increase at larger sizes. The implications for the origin and evolution of the grain size distribution are discussed.