CO line emission from galaxies in the Epoch of Reionization
  We study the CO line luminosity ($L_{\rm CO}$), the shape of the CO Spectral
Line Energy Distribution (SLED), and the value of the CO-to-$\rm H_2$
conversion factor in galaxies in the Epoch of Reionization (EoR). To this aim,
we construct a model that simultaneously takes into account the radiative
transfer and the clumpy structure of giant molecular clouds (GMCs) where the CO
lines are excited. We then use it to post-process state-of-the-art zoomed, high
resolution ($30\, \rm{pc}$), cosmological simulation of a main-sequence
($M_{*}\approx10^{10}\, \rm{M_{\odot}}$, $SFR\approx 100\,\rm{M_{\odot}\,
yr^{-1}}$) galaxy, "Alth{\ae}a", at $z\approx6$. We find that the CO emission
traces the inner molecular disk ($r\approx 0.5 \,\rm{kpc}$) of Alth{\ae}a with
the peak of the CO surface brightness co-located with that of the [CII] 158$\rm
\mu m$ emission. Its $L_{\rm CO(1-0)}=10^{4.85}\, \rm{L_{\odot}}$ is comparable
to that observed in local galaxies with similar stellar mass. The high
($\Sigma_{gas} \approx 220\, \rm M_{\odot}\, pc^{-2}$) gas surface density in
Alth{\ae}a, its large Mach number (\mach$\approx 30$), and the warm kinetic
temperature ($T_{k}\approx 45 \, \rm K$) of GMCs yield a CO SLED peaked at the
CO(7-6) transition, i.e. at relatively high-$J$, and a CO-to-$\rm H_2$
conversion factor $\alpha_{\rm CO}\approx 1.5 \, \rm M_{\odot} \rm (K\, km\,
s^{-1}\, pc^2)^{-1} $ lower than that of the Milky Way. The ALMA observing time
required to detect (resolve) at 5$\sigma$ the CO(7-6) line from galaxies
similar to Alth{\ae}a is $\approx13$ h ($\approx 38$ h).
