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We report Atacama Large Millimeter/submillimeter Array (ALMA) observations ofCO $(8-7)$, $(9-8)$, $\rm H_{2}O (2_{0,2}-1_{1,1})$ and $\rm OH^{+}(1_{1}-0_{1})$ and NOrthern Extended Millimeter Array (NOEMA) observations ofCO $(5-4)$, $(6-5)$, $(12-11)$ and $(13-12)$ towards the $z = 6.003$ quasarSDSS J231038.88+185519.7, aiming to probe the physical conditions of themolecular gas content of this source. We present the best sampled CO spectralline energy distribution (SLED) at $z = 6.003$, and analyzed it with theradiative transfer code MOLPOP-CEP. Fitting the CO SLED to a one-componentmodel indicates a kinetic temperature $T_{\rm kin} = 228 \ \rm K$, moleculargas density $log (n(\rm H_{2})/\rm cm^{-3}$ )=4.75, and CO column density$log(N(\rm CO)/\rm cm^{-2}) =17.5$, although a two-component model better fitsthe data. In either case, the CO SLED is dominated by a "warm" and "dense"component. Compared to samples of local (Ultra) Luminous Infrared Galaxies((U)LIRGs), starburst galaxies and high redshift Submillimeter Galaxies (SMGs),J2310+1855 exhibits higher CO excitation at ($J \geq 8$), like other highredshift quasars. The high CO excitation, together with the enhanced $L_{\rmH_{2}O}/ L_{IR} $, $L_{\rm H_{2}O}/ L_{CO} $ and $L_{OH^{+}}/L_{\rm H_{2}O} $ratios, suggests that besides the UV radiation from young massive stars, othermechanisms such as shocks, cosmic rays and X-rays might also be responsible forthe heating and ionization of the molecular gas. In the nuclear region probedby the molecular emissions lines, any of these mechanisms might be present dueto the powerful quasar and the starburst activity.

Probing the full CO spectral line energy distribution (SLED) in the nuclear region of a quasar-starburst system at $z=6.003$