Star Formation and ISM Properties in Host Galaxies of Three Far-infrared
  Luminous Quasars at $z\sim6$
  We present Karl G. Jansky Very Large Array (VLA) observations of the CO
(2$-$1) line emission towards three far-infrared luminous quasars at $z\sim6$:
SDSS J231038.88$+$185519.7 and SDSS J012958.51$-$003539.7 with $\sim0\farcs6$
resolution and SDSS J205406.42$-$000514.8 with $\sim2\farcs1$ resolution. All
three sources are detected in the CO (2$-$1) line emission -- one source is
marginally resolved, and the other two appear as point sources. Measurements of
the CO (2$-$1) line emission allow us to calculate the molecular gas mass even
without a CO excitation model. The inferred molecular gas masses are
(0.8$-$4.3) $\times$ 10$^{10}$ $M_{\odot}$. The widths and redshifts derived
from the CO (2$-$1) line are consistent with previous CO (6$-$5) and
[\ion{C}{2}] measurements. We also report continuum measurements using the
Herschel for SDSS J231038.88$+$185519.7 and SDSS J012958.51$-$003539.7, and for
SDSS J231038.88+185519.7, data obtained at $\sim140$ and $\sim300$ GHz using
the Atacama Large Millimeter/submillimeter Array (ALMA). In the case of SDSS
J231038.88+185519.7, we present a detailed analysis of the spectral energy
distribution and derive the dust temperature ($\sim40$ K), the dust mass
($\sim10^{9}$ $M_{\odot}$), the far-infrared luminosity (8$-$1000 $\mu$m;
$\sim10^{13}$ $ L_{\odot}$) and the star formation rate (2400$-$2700
$M_{\odot}$ yr$^{-1}$). Finally, an analysis of the photo-dissociation regions
associated with the three high redshift quasars indicates that the interstellar
medium in these sources has similar properties to local starburst galaxies.
