A SPectroscopic survey of biased halos In the Reionization Era (ASPIRE): Spectroscopically Complete Census of Obscured Cosmic Star Formation Rate Density at $z=4-6$

Abstract: We present a stringent measurement of the dust-obscured star-formation rate density (SFRD) at $z=4-6$ from the ASPIRE JWST Cycle-1 medium and ALMA Cycle-9 large program. We obtained JWST/NIRCam grism spectroscopy and ALMA 1.2-mm continuum map along 25 independent quasar sightlines, covering a total survey area of $\sim$35 arcmin$^2$ where we search for dusty star-forming galaxies (DSFGs) at $z = 0 - 7$. We identify eight DSFGs in seven fields at $z=4-6$ through the detection of H$\alpha$ or [O III] $\lambda$5008 lines, including fainter lines such as H$\beta$, [O III] $\lambda$4960, [N II] $\lambda$6585, [S II] $\lambda\lambda$6718,6733 for six sources. With this spectroscopically complete DSFG sample at $z=4-6$ and negligible impact from cosmic variance (shot noise), we measure the infrared luminosity function (IRLF) down to $L_\mathrm{IR} \sim 2\times10^{11}$ $L_\odot$. We find flattening of IRLF at $z=4-6$ towards the faint end (power-law slope $\alpha = 0.59_{-0.45}^{+0.39}$). We determine the dust-obscured cosmic SFRD at this epoch as $\log[\rho_\mathrm{SFR,IR} / (\mathrm{M}\odot\,\mathrm{yr}^{-1}\,\mathrm{Mpc}^{-3})] = -1.52{-0.13}^{+0.14}$. This is significantly higher than previous determination using ALMA data in the Hubble Ultra Deep Field, which is void of DSFGs at $z=4-6$ because of strong cosmic variance (shot noise). We conclude that the majority ($66\pm7$%) of cosmic star formation at $z \sim 5$ is still obscured by dust. We also discuss the uncertainty of SFRD propagated from far-IR spectral energy distribution and IRLF at the bright end, which will need to be resolved with future ALMA and JWST observations.