3. The model and results for optical extinction
A brief description of the model for the internal extinction in galaxy disks is given in the following. More details can be found in Paper I and Paper II. The so called 'frequency converter' model is based on the following energy conservation consideration: the extinguished stellar light (from UV to NIR) by dust absorption must be re-emitted in the FIR. Therefore, the dust radiation integrated over the entire FIR band (10 - 1000 ) tells how much stellar radiation, integrated over the entire UV to NIR range (500 - 10000 Å), has been extinguished. If the internal extinction in galaxies were gray (i.e. constant with wavelength), then the B-band extinction could be easily calculated:
where is the bolometric luminosity, namely the sum of the stellar and dust radiations in all bands. However in reality the extinction is of course not gray. Thus, in order to determine from the comparison between the stellar radiation (UV to NIR) and the dust radiation (FIR), a constraint on the frequency dependence of the extinction must be imposed in addition to the energy conservation consideration. This constraint is provided by a radiative transfer model which assumes a dust grain model (specified by the extinction curve, albedo and phase function) similar to that observed in the Solar Neighborhood (SN), and a sandwich configuration for the star and dust distribution in galaxy disks. Detailed discussions on the implications of these assumptions on the results as well as the uncertainties and limitations of this model can be found in Paper II. In particular it should be noticed that although in our radiative transfer model we assumed uniform dust and star distributions (Paper I), our results on are basically constrained by the FIR to UV-plus-optical flux ratios and are therefore not sensitive to this assumption (Paper II). In fact, the most significant uncertainty for our model is related to the partition of the dust-heating sources, namely the estimate of the relative contributions from the UV radiation and from the optical radiation to the FIR emission.
Results on the B-band extinction , not corrected for face-on, are obtained for individual galaxies in the sample including 13 upper limits due to nondetections in FIR. In order to exploit the information contained in the upper limits, the Kaplan-Meier estimator (Schmitt 1993; Feigelson & Nelson 1985) has been used in the statistical analyses in this paper.
The distribution of is presented in the histogram of Fig. 1. A mean with a dispersion of 0.20 is found for the entire sample (79 galaxies). This means that on average about 15 percent of the blue radiation is extinguished by dust within galaxy disks. The field galaxies (25) and the galaxies in Virgo, Coma and A1367 clusters (54) have similar extinction: the former have a mean of and the later of (Fig. 1). However, it should be pointed out that our sample is very inhomogeneous. For example the sample is much deeper for the field and Virgo galaxies which are nearby, than for the Coma and A1367 cluster galaxies which are far away. Any possible intrinsic difference between field and cluster galaxies may well be missed due to this inhomogeneity.
These results are in good agreement with Paper I where we showed the face-on optical depth instead of extinction . Both demonstrate that for blue radiation galaxy disks are optically thin, at least when the radiation from an entire galaxy is concerned. Some galaxies in our sample do show a rather high extinction ( mag), they are likely to be active star-forming galaxies (like M82) with a large part of the blue radiation coming from the heavily extinguished star-formation regions (local extinction can be as high as ). On the other end of the distribution (Fig. 1), 17 galaxies which are seen face-on have negative extinctions ('brightening') because of the effect of scattering (Bruzual et al. 1988; Witt et al. 1992). Excluding these galaxies the remaining 62 galaxies in our sample have a mean .
© European Southern Observatory (ESO) 1997
Online publication: May 26, 1998