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7.2.2 Internal Extinction Corrections

The corrections for internal extinction are based on models, but these have proven difficult to test due to a shortage of accurate surface photometry. The approach usually taken assumes that spiral and irregular galaxies are not optically thick, although the suggestion that galaxies are opaque has been expressed by Disney et al. (1989) and Valentijn (1990). There are three general forms for the optically thin models: (i) the light is assumed to be mixed evenly with the dust, (ii) the dust is assumed to lie in an infinitely thin obscuring layer, and (iii) a combination of the two, where the dust lies in a layer of finite thickness with a portion of the light being unobscured. While the second model is relatively simple and has some observational basis, the assumption of an infinitely thin absorbing layer results in a rapid variation of extinction between i = 45°, and i = 90°. Available data suggest that this is too severe (i.e., Tully and Fouqué 1985).

Tully and Fouqué (1985) discuss some of the problems with the first two formulations given above and offer a compromise between these extremes (the third model). This model is certainly the most physically sound, and it appears to provide the best fit to the available data. Under the assumptions of the third model the extinction correction becomes:

Equation 12 (12)

where as before, i is the inclination and tau is the optical depth. The additional parameter f is the fraction of the light that is unobscured by the dust layer. Thus, f = 0.5 leads to the infinitely thin layer model, while f = 0 leads to the model proposed by Holmberg. Tully and Fouqué (1985) adopted tau ~ 0.55 for the B band, f ~ 0.25, and suggested that the data are better fit if the extinction for i > 80° is held at the value for 80°. At present, this simplistic two-component model appears to be the most reasonable formulation for the internal extinction within galaxies, provided that they are optically thin. Surface photometry data over a broad wavelength range would greatly help to clarify the values of f and tau, particularly any dependence on morphological type for these parameters.