Characterising the contribution of dust-obscured star formation at z ≳ 5 using 18 serendipitously identified [ C ii ] emitters

We present a new method to determine the star formation rate density (SFRD) of the Universe at $z \gtrsim 5$ that includes the contribution of dust-obscured star formation. For this purpose, we use a [C ii] (158 $\mu$m) selected sample of galaxies serendipitously identified in the fields of known $z\gtrsim 4.5$ objects to characterise the fraction of obscured star formation rate (SFR). The advantage of a [C ii] selection is that our sample is SFR-selected, in contrast to an ultraviolet (UV)-selection that would be biased towards unobscured star formation. We obtain a sample of 23 [C ii] emitters near star-forming (SF) galaxies and quasi-stellar objects (QSOs) – three of which we identify for the first time – using previous literature and archival Atacama Large Millimeter/submillimeter Array data. 18 of these serendipitously identified galaxies have sufficiently deep rest-UV data and are used to characterise the obscured fraction of the star formation in galaxies with SFRs $\gtrsim 30\ \text{M}_{\odot } \ \text{yr}^{-1}$. We find that [C ii] emitters identified around SF galaxies have $\approx$63 per cent of their SFR obscured, while [C ii] emitters around QSOs have $\approx$93 per cent of their SFR obscured. By forward modelling existing wide-area UV luminosity function (LF) determinations, we derive the intrinsic UV LF using our characterisation of the obscured SFR. Integrating the intrinsic LF to $M_{\mathrm{ UV}}$ = $-$20, we find that the obscured SFRD contributes to $\gt 3~{{\ \rm per\ cent}}$ and $\gt 10~{{\ \rm per\ cent}}$ of the total SFRD at $z \sim 5$ and $z \sim 6$ based on our sample of companions galaxies near SF galaxies and QSOs, respectively. Our results suggest that dust obscuration is not negligible at $z\gtrsim 5$, further underlining the importance of far-infrared observations of the $z\gtrsim 5$ Universe.