The dense molecular gas in the $\mathrm{z}\sim 6$ QSO SDSS J231038.88+185519.7 resolved by ALMA

Abstract

We present ALMA observations of the CO(6-5) and [CII] emission lines and the sub-millimeter continuum of the $z\sim 6$ quasi-stellar object (QSO) SDSS J231038.88+185519.7. Compared to previous studies, we have analyzed a synthetic beam that is ten times smaller in angular size, we have achieved ten times better sensitivity in the CO(6-5) line, and two and half times better sensitivity in the [CII] line, enabling us to resolve the molecular gas emission. We obtain a size of the dense molecular gas of $2.9\pm 0.5$ kpc, and of $1.4\pm 0.2$ kpc for the 91.5 GHz dust continuum. By assuming that CO(6-5) is thermalized, and by adopting a CO--to--$H_2$ conversion factor ${\alpha }_{\mathrm{CO}}=0.8{\mathrm{M}}_{\odot }{\mathrm{K}}^{-1}(km/s{)}^{-1}\mathrm{p}{\mathrm{c}}^2$, we infer a molecular gas mass of $\mathrm{M}({\mathrm{H}}_2)=(3.2\pm 0.2)\times 10^{10}{\mathrm{M}}_{\odot }$. Assuming that the observed CO velocity gradient is due to an inclined rotating disk, we derive a dynamical mass of ${\mathrm{M}}_{\mathrm{dyn}}\mathrm{si}{\mathrm{n}}^2(\mathrm{i})=(2.4\pm 0.5)\times 10^{10}{\mathrm{M}}_{\odot }$, which is a factor of approximately two smaller than the previously reported estimate based on [CII]. Regarding the central black hole, we provide a new estimate of the black hole mass based on the C~IV emission line detected in the X-SHOOTER/VLT spectrum: ${\mathrm{M}}_{\mathrm{BH}}=(1.8\pm 0.5)\times 10^9{\mathrm{M}}_{\odot }$. We find a molecular gas fraction of $\mu =\mathrm{M}({\mathrm{H}}_2)/{\mathrm{M}}^{\ast }\sim 4.4$, where ${\mathrm{M}}^{\ast }\approx {\mathrm{M}}_{\mathrm{dyn}}-\mathrm{M}({\mathrm{H}}_2)-\mathrm{M}(\mathrm{BH})$. We derive a ratio $v_{rot}/\sigma \approx 1-2$ suggesting high gas turbulence, outflows/inflows and/or complex kinematics due to a merger event. We estimate a global Toomre parameter $Q\sim 0.2-0.5$, indicating likely cloud fragmentation. We compare, at the same angular resolution, the CO(6-5) and [CII] distributions, finding that dense molecular gas is more centrally concentrated with respect to [CII]. We find that the current BH growth rate is similar to that of its host galaxy.

arXiv commentA&A in press

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