A complete sample of bright Swift Gamma-Ray Bursts: X-ray afterglow
  luminosity and its correlation with the prompt emission
  We investigate wheter there is any correlation between the X-ray afterglow
luminosity and the prompt emission properties of a carefully selected
sub-sample of bright Swift long Gamma-Ray Bursts (GRBs) nearly complete in
redshift (~90%). Being free of selection effects (except flux limit), this
sample provides the possibility to compare the rest frame physical properties
of GRB prompt and afterglow emission in an unbiased way. The afterglow X-ray
luminosities are computed at four different rest frame times (5 min, 1 hr, 11
hr and 24 hr after trigger) and compared with the prompt emission isotropic
energy E_iso, the isotropic peak luminosity L_iso and the rest frame peak
energy E_peak. We find that the rest frame afterglow X-ray luminosity do
correlate with these prompt emission quantities, but the significance of each
correlation decreases over time. This result is in agreement with the idea that
the GRB X-ray light curve can be described as the result of a combination of
different components whose relative contribution and weight change with time,
with the prompt and afterglow emission dominating at early and late time,
respectively. In particular, we found evidence that the plateau and the shallow
decay phase often observed in GRB X-ray light curves are powered by activity
from the central engine. The existence of the L_X-E_iso correlation at late
times (t_rf > 11 hr) suggests a similar radiative efficiency among different
bursts with on average about 6% of the total kinetic energy powering the prompt
emission.
