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Dust in spiral galaxies produces emission in the far-infrared (FIR) andinternal absorption in visible wavelengths. However, the relation of the twoamounts is not trivial because optical absorption may saturate, but the FIRemission does not. Moreover, the volume concentration of dust plays a role inthe relation of absorption and emission, which depends on the size of thegalaxy. We explore the relation of these three quantities. In order tounderstand the geometrical problem, we developed a model of dust distribution.We also investigated the relation of the three variables with real data ofspiral galaxies at z<0.2 using the spectroscopic SDSS and FIR AKARI surveys.Internal absorptions were derived with two different methods: the ratio ofemission lines H$_\alpha $ and H$_\beta $, and a previously calibrated relationbased on the color variations as a function of absolute magnitude andconcentration index.  We find that in our low-z sample, the dependence of the average internalattenuation on galaxy size is negligible on average. It allows us to derive theinternal attenuation of the galaxy, $A_V$, even when we only know its FIR flux.This attenuation approximately depends on the inclination of the galaxy $i$ as$\overline {A_V}=\gamma_V \log _{10}\left(\frac{1}{\cos i}\right)$, where$\gamma_V$ is a constant. We found that $\gamma_V$ has a maximum value of$1.45\pm 0.27$ magnitudes.  When similar properties of dust are assumed, a general expression can be usedat any $z$. For cases of nonsaturation, this might be used as a cosmologicaltest. Although the present-day sensitivity of FIR or mm surveys does not allowus to carry out this cosmological test at z>2 within the standard model, it maybe used in the future. For much lower z or different cosmological models, atest might be feasible at present.

astronomy and astrophysics

Relation of internal attenuation, dust emission, and the size of spiral  galaxies. Calibration at low-z and how to use it as a cosmological test at  high-z