Unveiling the warm and dense ISM in z > 6 quasar host galaxies via water vapor emission

Water vapor (H2O) is one of the brightest molecular emitters after carbon monoxide (CO) in galaxies with high infrared (IR) luminosity, allowing us to investigate the warm and dense phase of the interstellar medium (ISM) where star formation occurs. However, due to the complexity of its radiative spectrum, H2O is not frequently exploited as an ISM tracer in distant galaxies. Therefore, H2O studies of the warm and dense gas at high-z remain largely unexplored. In this work, we present observations conducted with the Northern Extended Millimeter Array (NOEMA) toward three z > 6 IR-bright quasars J2310+1855, J1148+5251, and J0439+1634 targeted in their multiple para- and ortho-H2O transitions (3(12) - 3(03), 1(11) - 0(00), 2(20) - 2(11), and 4(22) - 4(13)), as well as their far-IR (FIR) dust continuum. By combining our data with previous measurements from the literature, we estimated the dust masses and temperatures, continuum optical depths, IR luminosities, and star formation rates (SFR) from the FIR continuum. We modeled the H2O lines using the MOLPOP-CEP radiative transfer code, finding that water vapor lines in our quasar host galaxies are primarily excited in the warm, dense (with a gas kinetic temperature and density of T-kin = 50 K, n(H2) similar to 10(4.5) - 10(5) cm(-3)) molecular medium with a water vapor column density of N-H2O similar to 2 x 10(17) - 3 x 10(18) cm(-3). High-J H2O lines are mainly radiatively pumped by the intense optically-thin far-IR radiation field associated with a warm dust component at temperatures of T-dust similar to 80 - 190K that account for <5 - 10% of the total dust mass. In the case of J2310+1855, our analysis points to a relatively high value of the continuum optical depth at 100 mu m (tau(100) similar to 1). Our results are in agreement with expectations based on the H2O spectral line energy distribution of local and high-z ultra-luminous IR galaxies and active galactic nuclei (AGN). The analysis of the Boltzmann diagrams highlights the interplay between collisions and IR pumping in populating the high H2O energy levels and it allows us to directly compare the excitation conditions in the targeted quasar host galaxies. In addition, the observations enable us to sample the high-luminosity part of the H2O-total-IR (TIR) luminosity relations (L-H2O - L-TIR). Overall, our results point to supralinear trends that suggest H2O-TIR relations are likely driven by IR pumping, rather than the mere co-spatiality between the FIR continuum- and line-emitting regions. The observed L-H2O/L-TIR ratios in our z > 6 quasars do not show any strong deviations with respect to those measured in star-forming galaxies and AGN at lower redshifts. This supports the notion that H2O can be likely used to trace the star formation activity buried deep within the dense molecular clouds.