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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 the compositional mix are also changing. We have investigated the character of these changes using parameterized extinction curves from Cardelli, Clayton, \& Mathis. Two cases are presented: the diffuse interstellar medium ($R_ {V}$ = 3.1); and a denser region ($R_{V}$ = 5.3).
For this exploratory investigation we adopted spherical bare silicate and bare graphite particles as in the Mathis, Rumpl, \& 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; these constraints play an active role in limiting the numbers of large particles which tend to contain a significant fraction of the total dust mass.
With the available wavelength range of the extinction data, from 0.1 to 5 \microns, the range over which the size distributions are reliable is 0.01 to 1 \microns; note that there is no direct information from extinction on the distribution for very small grains. For the case of the diffuse interstellar medium, we confirm MRN's basic result that a smooth size distribution is roughly a power law of index -3.5 out their sharp cutoff at $a_+ = 0.25$ \microns. Our model shows a smooth decrease near that size, perhaps compatible with an exponential cutoff. However, in order to achieve a good fit to the data at U, B, and V where the extinction curve changes slope, the silicate size distribution departs significantly (and robustly) from a simple power law. For the case of the denser region, the size distributions are no longer power laws with index -3.5; rather they are much flatter, indicating a significant reduction in the numbers of small particles and some increase at larger sizes.
This helps quantify what has been known for some time: the mean size of particles increases in a denser environment. The implications for the origin of the grain size evolution, by accretion and/or by coagulation are discussed.
