Figure 7: Results for the simulated light curves:
surfaces and
confidence contours resulting from applying trial transfer functions
and
to the reconstructed continuum light curves and
comparing with the line band light curve (allowing for an additive offset
between the bands). Surfaces are plotted using
as the ordinate in order to display
the topography of the region near the minimum. Contours are shown the
following levels:
. The
first three of these contours correspond to
, 90% and 95% for
two interesting parameters and are shown in bold. In both cases, the
existence of a deep hole in
space demonstrates that the imposed
lag has been clearly detected and its parameters recovered.
We use the method of Section 2.1 and 2.2 to form an optimally reconstructed, evenly-sampled continuum lightcurve. The covariance model used is given by eqn (13) and (14) with
A total of N=3000 simulated data points were used to form the reconstruction which spans a simulated observation time of 400000s. A portion of the simulated dataset and its reconstruction are presented in Fig. 6. Note how well the reconstruction algorithm recovers the real signal during the times with data, and brackets the real signal during other times.
Figure 7 presents the
surfaces and confidence contours that result
from passing the simulated light curves through the trial transfer
functions
and
, including minimization over any additive
offset between the continuum and line band light curves. Both trial
transfer functions clearly detect the imposed lag in so far as a a deep and
isolated hole is present in the
surface at approximately the right
time delay, delay fraction and delay width. Note that the
dimension, which has been suppressed in the
plots, has a value of
at the global minimum. This demonstrates the power of
this technique for finding and characterizing subtle time lags or leads
that are present in such data.