2021A&A...652A..83L

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 and FIR AKARI survey. Internal absorptions were derived with two different methods: the ratio of emission lines H_α and H_β, 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, A_V, even when we only know its FIR flux. This attenuation approximately depends on the inclination of the galaxy i as A_V^–=γV^–log₁₀₁^cosi, where γV^– is a constant. We found that γ_V 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_M^exp[-(1.0±0.6)f_M] and f_M=7.6x10^–6α_hR^–1.75x(F_FIR/700Jy)1.87xf_cosmol.(z); the dependence on the cosmological model is embedded in f_cosmol.(z)=d_L(z)(Mpc)²(1+z)^{(1.75η–1.87)}, where η=2 for cosmologies following Etherington's relation, d_L is the luminosity distance, α_hR is the angular size of the scalelength, and F_FIR 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 f_cosmol. 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 ∼500µm better than ∼10µJy, for instance. For much lower z or different cosmological models, a test might be feasible at present.