Subaru High-z Exploration of Low-Luminosity Quasars (SHELLQs) III. Star
  formation properties of the host galaxies at $z \gtrsim 6$ studied with ALMA
  We present our ALMA Cycle 4 measurements of the [CII] emission line and the
underlying far-infrared (FIR) continuum emission from four optically
low-luminosity ($M_{\rm 1450} > -25$) quasars at $z \gtrsim 6$ discovered by
the Subaru Hyper Suprime Cam (HSC) survey. The [CII] line and FIR continuum
luminosities lie in the ranges $L_{\rm [CII]} = (3.8-10.2) \times 10^8~L_\odot$
and $L_{\rm FIR} = (1.2-2.0) \times 10^{11}~L_\odot$, which are at least one
order of magnitude smaller than those of optically-luminous quasars at $z
\gtrsim 6$. We estimate the star formation rates (SFR) of our targets as
$\simeq 23-40~M_\odot ~{\rm yr}^{-1}$. Their line and continuum-emitting
regions are marginally resolved, and found to be comparable in size to those of
optically luminous quasars, indicating that their SFR or likely gas mass
surface densities (key controlling parameter of mass accretion) are accordingly
different. The $L_{\rm [CII]}/L_{\rm FIR}$ ratios of the hosts, $\simeq
(2.2-8.7) \times 10^{-3}$, are fully consistent with local star-forming
galaxies. Using the [CII] dynamics, we derived their dynamical masses within a
radius of 1.5-2.5 kpc as $\simeq (1.4-8.2) \times 10^{10}~M_\odot$. By
interpreting these masses as stellar ones, we suggest that these faint quasar
hosts are on or even below the star-forming main sequence at $z \sim 6$, i.e.,
they appear to be transforming into quiescent galaxies. This is in contrast to
the optically luminous quasars at those redshifts, which show starburst-like
properties. Finally, we find that the ratios of black hole mass to host galaxy
dynamical mass of the most of low-luminosity quasars including the HSC ones are
consistent with the local value. The mass ratios of the HSC quasars can be
reproduced by a semi-analytical model that assumes merger-induced black
hole-host galaxy evolution.
