Astronomy & Astrophysics

All Figures

$\begin{figure} \par\includegraphics[width=8.2cm,clip]{2422_01.eps}\end{figure}$ Figure 1: Expected quasar variations $\delta m$ in magnitudes as a function of the time interval $\delta t$ (see text). The curves are plotted for 2 different absolute magnitudes M_B and for 3 quasar redshifts.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=8.2cm,clip]{2422_02.eps}\end{figure}$ Figure 2: Example of simulated light curve, for a 2-year long observation and a peak-to-peak amplitude A=0.1 mag. The continuous light curve is shown as a solid line. It has been smoothed on a length scale of 30 days. The four samplings used in the simulations are shown (plus the logarithmic sampling, see text), along with the error bars of 0.01 mag. The figure is constructed for an object with a visibility of 8 consecutive months, hence the size of the gap in the center of the curves is 4 months. The curve plotted for the logarithmic sampling has the same number of data points as the curve for the 7-day sampling.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=15.25cm,clip]{2422_03.eps} % \end{figure}$ Figure 3: Histograms exploring the observational parameter space described in the text for the determination of a time delay of 80 days. Each curve is the probability density function for the time delay, obtained from 100 000 simulations, for a particular combination of the three variables. These are: 1- sampling interval, four columns, from left to right: irregular, 15 days, 7 days, 3 days; 2- visibility period, three bands from top to bottom: 12, 8, and 5 months; 3- peak-to-peak variation, A, three rows within each band, from top to bottom: 0.3, 0.2, 0.1 mag. Each panel is labeled with the mean and standard deviation of the measured time delay, as well as the percentage error. The effect of microlensing is not included in these simulations, and is treated later.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=14.5cm,clip]{2422_04.eps}\end{figure}$ Figure 4: Summary of the estimated percentage error on the measured time delay as a function of the observational parameters: 1- peak-to-peak variation, A; 2- sampling interval (x-axis of each panel); 3- visibility period. Each panel corresponds to one value of the input time delay $\Delta t_{{\rm in}}$ . The percentage error on the time delay, plotted on the y-axis, is calculated from 100 000 simulations. The lines connecting the points correspond to different periods of visibility. The solid lines are for circumpolar objects, the dotted lines are for the 8-month visibility, and the long dashed lines are for the 5-month visibility. We have used three peak-to-peak values of the amplitudes A for the simulated light curves, which increases from left to right in the three columns. The curve for the 5-month visibility and 120-day time delay has not been computed, as there are almost no data points in common between the curves of image A and image B. The star-shaped symbols plot the percentage errors for quasars with real measured optical time delays published in the literature. See text for further details.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=14.4cm,clip]{2422_05.eps}\end{figure}$ Figure 5: Histograms exploring the observational parameter space described in the text for the determination of a time delay of 80 days, including the effects of microlensing. Each curve is the probability density function for the time delay, obtained from 100 000 simulations, for a sampling interval of 3 days, and for a particular combination of the variables. These are: 1- microlensing amplitude, $A_{\mu } = \alpha \cdot A$ , four columns, from left to right: $\alpha =0, 0.01,0.05, 0.1$ ; 2- visibility period, three bands from top to bottom: 12, 8, and 5 months); 3- peak-to-peak variation, A, three rows within each band, from top to bottom: 0.3, 0.2, 0.1 mag. Each panel is labeled with the mean and standard deviation of the measured time delay, as well as the percentage error. While no strong systematic drifts of the histograms are seen relative to the input time delay $\Delta t_{{\rm in}}=80$ days, the width of the histograms are significantly broadened as microlensing increases.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=11cm,clip]{2422_06.ps}\vspace*{3mm} \includegraphics[width=11cm,clip]{2422_07.ps}\end{figure}$ Figure 6: Top: percentage error on the time delay for the irregular sampling and for three amplitudes A. In each column the results are shown for four microlensing amplitudes $A_{\mu } = \alpha \cdot A$ , starting on the left with $\alpha =0$ , i.e., no microlensing. The different types of curves correspond to the three visibilities, as in Fig. 4. The solid lines are for circumpolar objects, the dotted lines are for the 8-month visibility, and the long dashed lines are for the 5-month visibility. Bottom: same plot as above but for the 3-day sampling.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=11cm,clip]{2422_08.ps}\vspace*{6mm} \par\includegraphics[width=11cm,clip]{2422_09.ps}\end{figure}$ Figure 7: Same as Fig. 6, but for the 7-day sampling ( top) and for the 15-day sampling ( bottom).
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=6cm,clip]{2422_10.ps}\hspace*{8mm} \in... ...422_12.ps}\hspace*{8mm} \includegraphics[width=6cm,clip]{2422_13.ps}\end{figure}$ Figure 8: Time delay distributions for four different values of $\Delta t_{{\rm in}}$ , each time for 3 visibilities and a peak-to-peak variation A=0.3. We compare the distributions obtained for the logarithmic sampling (without microlensing), with the results for the 7-day sampling. Clear distortions of the histograms are seen when the time delay is close to the visibility window of the object, when a regular sampling is adopted (left column in the four panels). The histograms obtained with the logarithmic sampling are well symmetrical and narrow. The systematic error is also reduced. This effect is not so evident when the time delay is much shorter than the visibility window, where the logarithmic sampling even degrades the results.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=8.2cm,clip]{2422_01.eps}\end{figure}$	Figure 1: Expected quasar variations $\delta m$ in magnitudes as a function of the time interval $\delta t$ (see text). The curves are plotted for 2 different absolute magnitudes M_B and for 3 quasar redshifts.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=11cm,clip]{2422_08.ps}\vspace*{6mm} \par\includegraphics[width=11cm,clip]{2422_09.ps}\end{figure}$	Figure 7: Same as Fig. 6, but for the 7-day sampling ( top) and for the 15-day sampling ( bottom).
Open with DEXTER