The ALPINE-ALMA [CII] Survey: Obscured Star Formation Rate Density and
  Main Sequence of star-forming galaxies at z>4
  Star formation rate (SFR) measurements at z>4 have relied mostly on
rest-frame far-ultraviolet (FUV) observations. The corrections for dust
attenuation based on IRX-$\beta$ relation are highly uncertain and are still
debated in the literature. Hence, rest-frame far-infrared (FIR) observations
are necessary to constrain the dust-obscured component of the SFR. In this
paper, we exploit the rest-frame FIR continuum observations collected by the
ALMA Large Program to INvestigate [CII] at Early times (ALPINE) to directly
constrain the obscured SFR in galaxies at 4.4<z<5.9. We use stacks of continuum
images to measure average infrared (IR) luminosities taking into account both
detected and undetected sources. Based on these measurements, we measure the
position of the main sequence of star-forming galaxies and the specific SFR
(sSFR) at $z\sim4.5$ and $z\sim5.5$. We find that the main sequence and sSFR do
not evolve significantly between $z\sim4.5$ and $z\sim5.5$, as opposed to lower
redshifts. We develop a method to derive the obscured SFR density (SFRD) using
the stellar masses or FUV-magnitudes as a proxy of FIR fluxes measured on the
stacks and combining them with the galaxy stellar mass functions and FUV
luminosity functions from the literature. We obtain consistent results
independent of the chosen proxy. We find that the obscured fraction of SFRD is
decreasing with increasing redshift but even at $z\sim5.5$ it constitutes
around 61\% of the total SFRD.
