The interstellar medium distribution, gas kinematics, and system dynamics of the far-infrared luminous quasar SDSS J2310+1855 at $z=6.0$

We present ALMA sub-kpc- to kpc-scale resolution observations of the [CII], CO(9-8), and OH$^{+}$\,($1_{1}$--$0_{1}$) lines along with their dust continuum emission toward the FIR luminous quasar SDSS J231038.88+185519.7 at $z = 6.0031$. The [CII] brightness follows a flat distribution with a Sersic index of 0.59. The CO(9-8) line and the dust continuum can be fit with an unresolved nuclear component and an extended Sersic component with a Sersic index of ~1. The dust temperature drops with distance from the center. The effective radius of the dust continuum is smaller than that of the line emission and the dust mass surface density, but is consistent with that of the star formation rate surface density. The OH$^{+}$\,($1_{1}$--$0_{1}$) line shows a P-Cygni profile with an absorption, which may indicate an outflow with a neutral gas mass of $(6.2\pm1.2)\times10^{8} M_{\odot}$ along the line of sight. We employed a 3D tilted ring model to fit the [CII] and CO(9-8) data cubes. The two lines are both rotation dominated and trace identical disk geometries and gas motions. We decompose the circular rotation curve measured from the kinematic model fit to the [CII] line into four matter components (black hole, stars, gas, and dark matter). The quasar-starburst system is dominated by baryonic matter inside the central few kiloparsecs. We constrain the black hole mass to be $2.97^{+0.51}_{-0.77}\times 10^{9}\,M_{\odot}$; this is the first time that the dynamical mass of a black hole has been measured at $z\sim6$. A massive stellar component (on the order of $10^{9}\,M_{\odot}$) may have already existed when the Universe was only ~0.93 Gyr old. The relations between the black hole mass and the baryonic mass of this quasar indicate that the central supermassive black hole may have formed before its host galaxy. [Abridged version. Please see the full abstract in the manuscript.]