Planck's Dusty GEMS. VIII. Dense-gas reservoirs in the most active dusty
  starbursts at z~3
  We present ALMA, NOEMA, and IRAM-30m/EMIR observations of the high-density
tracer molecules HCN, HCO+, and HNC in three of the brightest lensed dusty
star-forming galaxies at z~3-3.5, part of the Planck's Dusty GEMS sample, to
probe the gas reservoirs closely associated with their exceptional levels of
star formation. We obtain robust detections of ten emission lines between
J_up=4 and 6, as well as several additional flux upper limits. In
PLCK_G244.8+54.9, the brightest source at z=3.0, the HNC(5-4) line emission at
0.1" resolution, together with other spatially-integrated line profiles,
suggests comparable distributions of dense and more diffuse gas reservoirs, at
least over the most strongly magnified regions. This rules out any major effect
from differential lensing. The HCO+/HCN > 1 and HNC/HCN ~ 1 line ratios in our
sample are similar to those of nearby ULIRGs and consistent with
photon-dominated regions without any indication of important mechanical heating
or AGN feedback. We characterize the dense-gas excitation in PLCK_G244.8+54.9
using radiative transfer models assuming pure collisional excitation and find
that mid-J HCN, HCO+, and HNC lines arise from a high-density phase with H2
density n~10^5-6 cm^-3, although important degeneracies prevent determining the
exact conditions. The three GEMS are consistent with extrapolations of
dense-gas star-formation laws derived in the nearby Universe, adding further
evidence that the extreme star-formation rates observed in the most active
galaxies at z~3 are a consequence of their important dense-gas contents. The
dense-gas-mass fractions traced by HCN/[CI] and HCO+/[CI] line ratios are
elevated, but not exceptional compared to other lensed dusty star-forming
galaxies at z>2 and fall near the upper envelope of local ULIRGs. Our results
also favor constant dense-gas depletion times in these populations.
