The Frequency of Intrinsic X-ray Weakness Among Broad Absorption Line
  Quasars
  We present combined $\approx 14-37~\rm ks$ Chandra observations of seven $z =
1.6-2.7$ broad absorption line (BAL) quasars selected from the Large Bright
Quasar Survey (LBQS). These seven objects are high-ionization BAL (HiBAL)
quasars, and they were undetected in the Chandra hard band ($2-8$ keV) in
previous observations. The stacking analyses of previous Chandra observations
suggested that these seven objects likely contain some candidates for
intrinsically X-ray weak BAL quasars. With the new Chandra observations, six
targets are detected. We calculate their effective power-law photon indices and
hard-band flux weakness, and find that two objects, LBQS $1203+1530$ and LBQS
$1442-0011$, show soft/steep spectral shapes ($\Gamma_{\rm eff}=
2.2^{+0.9}_{-0.9}$ and $1.9_{-0.8}^{+0.9}$) and significant X-ray weakness in
the hard band (by factors of $\approx$ 15 and 12). We conclude that the two
HiBAL quasars are good candidates for intrinsically X-ray weak BAL quasars. The
mid-infrared-to-UV spectral energy distributions (SEDs) of the two candidates
are consistent with those of typical quasars. We constrain the fraction of
intrinsically X-ray weak AGNs among HiBAL quasars to be $\approx 7-10\%$
($2/29-3/29$), and we estimate it is $\approx 6- 23\%$ ($2/35-8/35$) among the
general BAL quasar population. Such a fraction is considerably larger than the
fraction among non-BAL quasars, and we suggest that intrinsically X-ray weak
quasars are preferentially observed as BAL quasars. Intrinsically X-ray weak
AGNs likely comprise a small minority of the luminous type 1 AGN population,
and they should not affect significantly the completeness of these AGNs found
in deep X-ray surveys.
