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Extracting the lag from the simulations

 

figure306


Figure 7: Results for the simulated light curves: tex2html_wrap_inline893 surfaces and confidence contours resulting from applying trial transfer functions tex2html_wrap_inline895 and tex2html_wrap_inline917 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 tex2html_wrap_inline897 as the ordinate in order to display the topography of the region near the minimum. Contours are shown the following levels: tex2html_wrap_inline899 . The first three of these contours correspond to tex2html_wrap_inline923 , 90% and 95% for two interesting parameters and are shown in bold. In both cases, the existence of a deep hole in tex2html_wrap_inline893 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

eqnarray315

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 tex2html_wrap_inline893 surfaces and confidence contours that result from passing the simulated light curves through the trial transfer functions tex2html_wrap_inline895 and tex2html_wrap_inline917 , 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 tex2html_wrap_inline893 surface at approximately the right time delay, delay fraction and delay width. Note that the tex2html_wrap_inline1039 dimension, which has been suppressed in the tex2html_wrap_inline917 plots, has a value of tex2html_wrap_inline1199 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.


next up previous
Next: Discussion Up: Applications to simulations Previous: Constructing the simulated light

Chris Reynolds
Tue Jan 11 17:27:37 MST 2000