ALMA Lensing Cluster Survey: Deep 1.2 mm Number Counts and Infrared Luminosity Functions at z ≃ 1–8

<jats:title>Abstract</jats:title> <jats:p>We present a statistical study of 180 dust continuum sources identified in 33 massive cluster fields by the Atacama Large Millimeter/submillimeter Array Lensing Cluster Survey (ALCS) over a total of 133 arcmin<jats:sup>2</jats:sup> area, homogeneously observed at 1.2 mm. ALCS enables us to detect extremely faint millimeter sources by lensing magnification, including near-infrared (NIR) dark objects showing no counterparts in existing Hubble Space Telescope and Spitzer images. The dust continuum sources belong to a blind sample (<jats:italic>N</jats:italic> = 141) with signal-to-noise ratio (S/N) ≳ 5.0 (a purity of >0.99) or a secondary sample (<jats:italic>N</jats:italic> = 39) with S/N = 4.0–5.0 screened by priors. With the blind sample, we securely derive 1.2 mm number counts down to ∼7 <jats:italic>μ</jats:italic>Jy, and find that the total integrated 1.2 mm flux is <jats:inline-formula> <jats:tex-math> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mn>20.7</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>6.5</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>8.5</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> </jats:inline-formula> Jy deg<jats:sup>−2</jats:sup>, resolving ≃80% of the cosmic infrared background light. The resolved fraction varies by a factor of 0.6–1.1 due to the completeness correction depending on the spatial size of the millimeter emission. We also derive infrared (IR) luminosity functions (LFs) at <jats:italic>z</jats:italic> = 0.6–7.5 with the <jats:inline-formula> <jats:tex-math> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>1</mml:mn> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:msub> <mml:mrow> <mml:mi>V</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>max</mml:mi> </mml:mrow> </mml:msub> </mml:math> </jats:inline-formula> method, finding the redshift evolution of IR LFs characterized by positive luminosity and negative density evolution. The total (= UV + IR) cosmic star formation rate density (SFRD) at <jats:italic>z</jats:italic> > 4 is estimated to be <jats:inline-formula> <jats:tex-math> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mn>161</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>21</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>25</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> </jats:inline-formula>% of the Madau and Dickinson measurements mostly based on rest-frame UV surveys. Although our general understanding of the cosmic SFRD is unlikely to change beyond a factor of 2, these results add to the weight of evidence for an additional (≈60%) SFRD component contributed by the faint millimeter population, including NIR-dark objects.</jats:p>