Relation of internal attenuation, dust emission, and the size of spiral galaxies

Aims. Dust in spiral galaxies produces emission in the far-infrared (FIR) and internal absorption in visible wavelengths. However, the relation of the two amounts is not trivial because optical absorption may saturate, but the FIR emission does not. Moreover, the volume concentration of dust plays a role in the relation of absorption and emission, which depends on the size of the galaxy. We explore the relation of these three quantities. Methods. In order to understand the geometrical problem, we developed a model of dust distribution. We also investigated the relation of the three variables with real data of spiral galaxies at z < 0.2 using the spectroscopic Sloan Digital Sky Survey (SDSS) and FIR AKARI survey. Internal absorptions were derived with two different methods: the ratio of emission lines Hα and Hβ, and a previously calibrated relation based on the color variations as a function of absolute magnitude and concentration index. Results. We find that in our low-z sample, the dependence of the average internal attenuation on galaxy size is negligible on average because of the relation of dust mass with size. It allows us to derive the internal attenuation of the galaxy, AV , even when we only know its FIR flux. This attenuation approximately depends on the inclination of the galaxy i as AV = γV log10 ( 1 cos i ) , where γV is a constant. We found that γV has a maximum value for galaxies of 1.45 ± 0.27 magnitudes. When similar properties of dust are assumed, a general expression can be used at any z: γV = (1.45 ± 0.27) f exp [−(1.0±0.6) fM ] M and fM = 7.6×10−6α−1.75 hR × ( FFIR 700 Jy )1.87 × fcosmol.(z); the dependence on the cosmological model is embedded in fcosmol.(z) = dL(z)(Mpc)(1+ z)(1.75η−1.87), where η = 2 for cosmologies following Etherington’s relation, dL is the luminosity distance, αhR is the angular size of the scalelength, and FFIR the flux at wavelength 100(1 + z) μm. Conclusions. For cases of nonsaturation ( f . 3.6), this might be used as a cosmological test because the factor fcosmol. at high z varies strongly in different cosmologies. Although the present-day sensitivity of FIR or millimeter surveys does not allow us to carry out this cosmological test within the standard model, it may be used in the future, when we can observe galaxies at z = 3− 5 with a sensitivity at ∼500 μm better than ∼ 10 μJy, for instance. For much lower z or different cosmological models, a test might be feasible at present.