Star Formation Rate Function at z 4.5: An Analysis from Rest UV to Optical

We present a star formation rate function (SFRF) at z similar to 4.5 based on photometric data from the rest UV to optical of galaxies in the CANDELS GOODS-South field using spectral energy distribution (SED) fitting. We evaluate the incompleteness of our sample and correct for it to properly compare the SFRF in this study with those estimated based on other probes. The SFRF is obtained down to similar to 10 M (circle dot) yr(-1), and it shows a significant excess compared to that estimated from the UV luminosity function and dust correction based on the UV spectral slope. As compared with the UV-based SFRF, the number density is larger by similar to 1 dex at a fixed SFR, or the best-fit Schechter parameter of the characteristic SFR, SFR*, is larger by similar to 1 dex. We extensively examine several assumptions on SED fitting to see the robustness of our result and find that the excess still exists even if the assumptions change such as star formation histories, dust extinction laws, and a one- or two-component model. By integrating our SFRF to 0.22 M (circle dot) yr(-1), the cosmic star formation rate density (CSFRD) at this epoch is calculated to be 4.53(-0.87)(+0.94)x10(-2)M(circle dot)yr(-1)Mpc(-3) , which is similar to 0.25 dex larger than the previous measurement based on UV observations. We also find that galaxies with intensive star formation (>10 M (circle dot) yr(-1)) occupy most of the CSFRD (similar to 80%), suggesting that star formation activity at this epoch is dominated by intensively star-forming galaxies.