Revealing the Accretion Physics of Supermassive Black Holes at Redshift
  z~7 with Chandra and Infrared Observations
  X-ray emission from quasars has been detected up to redshift $z=7.5$,
although only limited to a few objects at $z>6.5$. In this work, we present new
Chandra observations of five $z>6.5$ quasars. By combining with archival
Chandra observations of six additional $z>6.5$ quasars, we perform a systematic
analysis on the X-ray properties of these earliest accreting supermassive black
holes (SMBHs). We measure the black hole masses, bolometric luminosities
($L_{\rm bol}$), Eddington ratios ($\lambda_{\rm Edd}$), emission line
properties, and infrared luminosities ($L_{\rm IR}$) of these quasars using
infrared and sub-millimeter observations. Correlation analysis indicates that
the X-ray bolometric correction (the factor that converts from X-ray luminosity
to bolometric luminosity) decreases with increasing $L_{\rm bol}$, and that the
UV/optical-to-X-ray ratio, $\alpha_{\rm ox}$, strongly correlates with $L_{\rm
2500}$, and moderately correlates with $\lambda_{\rm Edd}$ and blueshift of CIV
emission lines. These correlations are consistent with those found in lower-$z$
quasars, indicating quasar accretion physics does not evolve with redshift. We
also find that $L_{\rm IR}$ does not correlate with $L_{\rm 2-10 keV}$ in these
luminous distant quasars, suggesting that the ratio of the SMBH growth rate and
their host galaxy growth rate in these early luminous quasars are different
from those of local galaxies. A joint spectral analysis of the X-ray detected
$z>6.5$ quasars yields an average X-ray photon index of $
\Gamma=2.32^{+0.31}_{-0.30}$, steeper than that of low-$z$ quasars. By
comparing it with the $\Gamma-\lambda_{\rm Edd}$ relation, we conclude that the
steepening of $\Gamma$ for quasars at $z>6.5$ is mainly driven by their higher
Eddington ratios.
