2.3. Interstellar dust models with cosmic abundances constraints
An important advance in the construction of interstellar dust models was made by Zubko, Dwek, & Arendt  (hereafter ZDA). The ZDA approach differs from previous dust modeling efforts in two important ways: first, it includes, in addition to the average interstellar extinction and diffuse IR emission, cosmic abundances as an explicit constraint on the models; and second, it solves the problem of simultaneously fitting these three observational constraints by an inversion method called the method of regularization. Uncertainties in the data are propagated into uncertainties in the derived grain size distribution.
Interstellar abundances were previously not used as explicit constraints in dust models because of the large discrepancies between abundances inferred from solar, F and G stars, and B stars measurements (see  for a recent review). In particular, B star carbon abundances were found to be significantly different from solar abundance measurements given by, for example, Holweger . This discrepancy precipitated an interstellar carbon "crisis" [59, 41], since standard interstellar dust models by Mathis, Rumpl, & Nordsieck  or Draine & Lee  required more carbon to be locked up in dust than available in the ISM. Mathis  attempted to solve the crisis by suggesting that most of the interstellar carbon dust is in the form of amorphous fluffy dust. However, Dwek  showed that the Mathis model failed to include the amount of carbon needed to produce the PAH features, and that the fluffy carbon particles produced an excess of far-IR emission over that detected by the COBE satellite from the diffuse ISM .
A very recent analysis of solar absorption lines by Asplund, Grevesse, & Sauval , which included the application of a time-dependent 3D hydrodynamical model for the solar atmosphere, has led to a dramatic revision of the abundance of carbon in the sun. The revised carbon and oxygen abundances are now in much better agreement with local ISM , and with the B star abundances, which are commonly believed to represent those of the present day ISM.
ZDA considered five different dust compositions as potential model ingredients: (1) PAHs; (2) graphite; (3) hydrogenated amorphous carbon of type ACH2; (4) silicates (MgSiFeO4); and (5) composite particles containing different proportions of silicates, organic refractory material (C8H8O4N), water ice (H2O), and voids. These different compositions were used to create five different classes of dust models:
To accommodate the uncertainties in the ISM abundances, ZDA considered three different ISM abundance determinations: solar, B-star, and F-G star abundances, as constraints for the dust models. The method of regularization proved to be a robust method for deriving the grain size distribution and abundances (the two unknowns) for the different classes of dust models. The results show that there are many classes of interstellar dust models that provide good simultaneous fits to the far-UV to near-IR extinction, thermal IR emission, and elemental abundances constraints. The models can be grouped into two major categories: BARE and COMP models. The latter are distinguished from the former by the fact that they contain a population of composite dust particles which generally have larger radii than bare particles.