Truth or delusion? A possible gravitational lensing interpretation of
  the ultra-luminous quasar SDSS J010013.02+280225.8 at $z=6.30$
  Gravitational lensing sometimes dominates the observed properties of
apparently very bright objects. We present morphological properties in the
high-resolution (FWHM $\sim0.''15$) Atacama Large Millimeter/submillimeter
Array (ALMA) 1-mm map for an ultra-luminous quasar (QSO) at $z=6.30$, SDSS
J010013.02+280225.8 (hereafter J0100+2802), whose black hole mass $M_{\rm BH}$
is the most massive ($\sim$ 1.2$\times10^{10}M_{\odot}$) at $z>6$ ever known.
We find that the continuum emission of J0100+2802 is resolved into a quadruple
system within a radius of $0.''2$, which can be interpreted as either multiple
dusty star-forming regions in the host galaxy or multiple images due to strong
gravitational lensing. The Mg$_{\rm II}$ absorption and the potential
Ly$\alpha$ line features have been identified at $z=2.33$ in the near-infrared
spectroscopy towards J0100+2802, and a simple mass model fitting well
reproduces the positions and flux densities of the quadruple system, both of
which are consistent with the latter interpretation. Although a high-resolution
map taken in the Advanced Camera for Survey (ACS) on board Hubble Space
Telescope (HST) shows a morphology with an apparently single component, in our
fiducial lens mass model it can simply be explained by a $\sim50$ pc scale
offset between the ALMA and HST emission regions. In this case, the
magnification factor for the observed HST emission is obtained to $\sim450$,
reducing the intrinsic $M_{\rm BH}$ estimate to even below $10^{9}\,M_{\odot}$.
The confirmation or the rejection of the gravitational lensing scenario is
important for our understanding of the super-massive black holes in the early
Universe.
