Molecular gas in z~6 quasar host galaxies
  We investigate the molecular gas content of z~6 quasar host galaxies using
the IRAM / Northern Extended Millimeter Array. We target the 3mm dust
continuum, and the line emission from CO(6-5), CO(7-6), [CI]2-1 in 10
infra-red-luminous quasars that have been previously studied in their 1mm dust
continuum and [CII] line emission. We detect CO(7-6) at various degrees of
significance in all the targeted sources, thus doubling the number of such
detections in z~6 quasars. The 3mm to 1mm flux density ratios are consistent
with a modified black body spectrum with a dust temperature $T_{dust}$~47 K and
an optical depth $\tau_{\nu}$=0.2 at the [CII] frequency. Our study provides us
with four independent ways to estimate the molecular gas mass, $M_{H2}$, in the
targeted quasars. This allows us to set constraints on various parameters used
in the derivation of molecular gas mass estimates, such as the mass per
luminosity ratios $\alpha_{CO}$ and $\alpha_{[CII]}$, the gas-to-dust ratio
$\delta_{g/d}$, and the carbon abundance [C]/H2. Leveraging either on the dust,
CO, [CI], or [CII] emission yields mass estimates of the entire sample in the
range $M_{H2}$~$10^{10}$ to $10^{11}$ M$_{\odot}$. We compare the observed
luminosities of dust, [CII], [CI], and CO(7-6) with predictions from
photo-dissociation and X-ray dominated regions. We find that the former provide
better model fits to our data, assuming that the bulk of the emission arises
from dense ($n_H>10^4$ cm$^{-3}$) clouds with a column density
$N_{H}$~$10^{23}$ cm$^{-2}$, exposed to a radiation field with intensity
$G_0$~$10^3$ (in Habing units). Our analysis reiterates the presence of massive
reservoirs of molecular gas fueling star formation and nuclear accretion in
$z$~6 quasar host galaxies. It also highlights the power of combined 3mm and
1mm observations for quantitative studies of the dense gas content in massive
galaxies at cosmic dawn.
