The Atacama Large Millimeter/submillimeter Array (ALMA) Spectroscopic Survey in the Hubble Ultra Deep Field (ASPECS) Band 6 scan (212-272 GHz) covers potential [C ii] emission in galaxies at 6 ≤ z ≤ 8 throughout a 2.9 arcmin2 area. By selecting on known Lyα emitters (LAEs) and photometric dropout galaxies in the field, we perform targeted searches down to a 5σ [C ii] luminosity depth L [C II] ∼ 2.0 108 L o˙, corresponding roughly to star formation rates (SFRs) of 10-20 M o˙ yr-1 when applying a locally calibrated conversion for star-forming galaxies, yielding zero detections. While the majority of galaxies in this sample are characterized by lower SFRs, the resulting upper limits on [C ii] luminosity in these sources are consistent with the current literature sample of targeted ALMA observations of z = 6-7 LAEs and Lyman-break galaxies (LBGs), as well as the locally calibrated relations between L [C ii] and SFR - with the exception of a single [C ii]-deficient, UV-luminous LBG. We also perform a blind search for [C ii]-bright galaxies that may have been missed by optical selections, resulting in an upper limit on the cumulative number density of [C ii] sources with L [C II] > 2.0 108 L o˙ (5σ) to be less than 1.8 10-4 Mpc-3 (90% confidence level). At this luminosity depth and volume coverage, we present an observed evolution of the [C ii] luminosity function from z = 6-8 to z ∼ 0 by comparing the ASPECS measurement to literature results at lower redshift.
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