The ALPINE-ALMA [CII] Survey: Investigation of 10 Galaxies at $z\sim4.5$
  with [OII] and [CII] Line Emission $-$ ISM Properties and [OII]$-$SFR
  Relation
  We present $10$ main-sequence ALPINE galaxies (log($M/M_{\odot}$) = 9.2-11.1
and ${\rm SFR}=23-190\,{\rm M_{\odot}\,yr^{-1}}$) at $z\sim4.5$ with optical
[OII] measurements from Keck/MOSFIRE spectroscopy and Subaru/MOIRCS narrow-band
imaging. This is the largest such multi-wavelength sample at these redshifts,
combining various measurements in the ultra-violet, optical, and far-infrared
including [CII]$_{158{\rm \mu m}}$ line emission and dust continuum from ALMA
and H$\alpha$ emission from Spitzer photometry. For the first time, this unique
sample allows us to analyze the relation between [OII] and total star-formation
rate (SFR) and the interstellar medium (ISM) properties via [OII]/[CII] and
[OII]/\halpha luminosity ratios at $z\sim4.5$. The [OII]$-$SFR relation at
$z\sim4.5$ cannot be described using standard local descriptions, but is
consistent with a metal-dependent relation assuming metallicities around $50\%$
solar. To explain the measured dust-corrected luminosity ratios of
$L[OII]/L[CII] \sim 0.98^{+0.21}_{-0.22}$ and $L[OII]/LHa \sim
-0.22^{+0.13}_{-0.15}$ for our sample, ionization parameters $\log(U)< -2$ and
electron densities $\log(\rm n_e / {\rm [cm^{-3}]}) \sim 2.5-3$ are required.
The former is consistent with galaxies at $z\sim2-3$, however lower than at
$z>6$. The latter may be slightly higher than expected given the galaxies'
specific SFR. The analysis of this pilot sample suggests that typical log($
M/M_{\odot})$ > 9 galaxies at $z\sim4.5$ to have broadly similar ISM properties
as their descendants at $z\sim2$ and suggest a strong evolution of ISM
properties since the Epoch of Reionization at $z>6$.
