Far-ultraviolet (FUV) and far-infrared (FIR) luminosity functions (LFs) of galaxies show a strong evolution from $z = 0$ to $z = 1$, but the FIR LF evolves much stronger than the FUV one. The FUV is dominantly radiated from newly formed short-lived O
B stars, while the FIR is emitted by dust grains heated by the FUV radiation field. It is known that dust is always associated with star formation activity. Thus, both FUV and FIR are tightly related to the star formation in galaxies, but in a very complicated manner. In order to disentangle the relation between FUV and FIR emissions, we estimate the UV-IR bivariate LF (BLF) of galaxies with {sl GALEX} and {sl AKARI} All-Sky Survey datasets. Recently we invented a new mathematical method to construct the BLF with given marginals and prescribed correlation coefficient. This method makes use of a tool from mathematical statistics, so called copula. The copula enables us to construct a bivariate distribution function from given marginal distributions with prescribed correlation and/or dependence structure. With this new formulation and FUV and FIR univariate LFs, we analyze various FUV and FIR data with {sl GALEX}, {sl Spitzer}, and {sl AKARI} to estimate the UV-IR BLF. The obtained BLFs naturally explain the nonlinear complicated relation between FUV and FIR emission from star-forming galaxies. Though the faint-end of the BLF was not well constrained for high-$z$ samples, the estimated linear correlation coefficient $rho$ was found to be very high, and is remarkably stable with redshifts (from 0.95 at $z = 0$ to 0.85 at $z = 1.0$). This implies the evolution of the UV-IR BLF is mainly due to the different evolution of the univariate LFs, and may not be controlled by the dependence structure.
The relation between the ratio of infrared (IR) and ultraviolet (UV) flux densities (the infrared excess: IRX) and the slope of the UV spectrum (beta) of galaxies plays a fundamental role in the evaluation of the dust attenuation of star forming gala
xies especially at high redshifts. Many authors, however, pointed out that there is a significant dispersion and/or deviation from the originally proposed IRX-beta relation depending on sample selection. We reexamined the IRX-beta relation by measuring the far- and near-UV flux densities of the original sample galaxies with GALEX and AKARI imaging data, and constructed a revised formula. We found that the newly obtained IRX values were lower than the original relation because of the significant underestimation of the UV flux densities of the galaxies, caused by the small aperture of IUE, Further, since the original relation was based on IRAS data which covered a wavelength range of lambda = 42--122mum, using the data from AKARI which has wider wavelength coverage toward longer wavelengths, we obtained an appropriate IRX-beta relation with total dust emission (TIR): log(L_{rm TIR}/L_{rm FUV}) = log [10^{0.4(3.06+1.58beta)}-1] +0.22. This new relation is consistent with most of the preceding results for samples selected at optical and UV, though there is a significant scatter around it. We also found that even the quiescent class of IR galaxies follows this new relation, though luminous and ultraluminous IR galaxies distribute completely differently as well known before.
The AKARI All-Sky Survey provided the first bright point source catalog detected at 90um. Starting from this catalog, we selected galaxies by matching AKARI sources with those in the IRAS PSCz. Next, we have measured total GALEX FUV and NUV flux dens
ities. Then, we have matched this sample with SDSS and 2MASS galaxies. By this procedure, we obtained the final sample which consists of 607 galaxies. If we sort the sample with respect to 90um, their average SED shows a coherent trend: the more luminous at 90um, the redder the global SED becomes. The M_r--NUV-r color-magnitude relation of our sample does not show bimodality, and the distribution is centered on the green valley between the blue cloud and red sequence seen in optical surveys. We have established formulae to convert FIR luminosity from AKARI bands to the total infrared (IR) luminosity L_TIR. With these formulae, we calculated the star formation directly visible with FUV and hidden by dust. The luminosity related to star formation activity (L_SF) is dominated by L_TIR even if we take into account the far-infrared (FIR) emission from dust heated by old stars. At high star formation rate (SFR) (> 20 Msun yr^-1), the fraction of directly visible SFR, SFR_FUV, decreases. We also estimated the FUV attenuation A_FUV from FUV-to-total IR (TIR) luminosity ratio. We also examined the L_TIR/L_FUV-UV slope (FUV- NUV) relation. The majority of the sample has L_TIR/L_FUV ratios 5 to 10 times lower than expected from the local starburst relation, while some LIRGs and all the ULIRGs of this sample have higher L_TIR/L_FUV ratios. We found that the attenuation indicator L_TIR/L_FUV is correlated to the stellar mass of galaxies, M*, but there is no correlation with specific SFR (SSFR), SFR/M*, and dust attenuation L_TIR/L_FUV. (abridged)
