- Data & Software
Q0957+561
PROGRAMS
Simple FORTRAN programs to apply the d2 test (accurate and robust time delay measurements)
QSO size ratios from multiband monitoring of a microlensing high-magnification event
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What is the d2 test?
We can accurately and robustly measure the time delay between the
intrinsic features that appear in two images A and B of a multiple QSO (with
relation to A, we assume that B is delayed in TBA). As it was discussed by
Lehar et al. (1992, ApJ 384, 453), the irregular delay-peak of the AB
cross-correlation function should be closely traced by the symmetrical
central peak (around the lag t = 0) of the
AA (or BB) autocorrelation function. Moreover, other features of
the cross-correlation function around lags t1,
t2,... will be closely reproduced in
the autocorrelation function around lags t1-TBA,
t2-TBA,...,
respectively. Therefore, if the shifted discrete autocorrelation
(DAC) is matched to the discrete cross-correlation (DCC), in
principle, one derives an
accurate
and robust value
of the time delay. This self-consistent methodology is called the
delta-square test, and it was successfully applied to some golden
datasets for QSO 0957+561 (e.g., Goicoechea et al. 1998, Ap&SS 261, 341;
Serra-Ricart et al. 1999, ApJ 526, 40). The technique belongs to a "second
generation" of methodologies to infer time delays, since it only works
when one knows a rough value of the delay. The rough estimation T may be
done from a simpler technique ("first generation"). Before to apply the
d2 test, we need to make a
golden dataset.
A golden dataset contains an ACTIVE and FREE FROM LONG GAPS
light curve A during a period [ti,tf]
and an ACTIVE and FREE FROM LONG GAPS light curve B
during a period [ti + T,tf + T]. It is also
required the HOMOGENEOUS MONITORING of both images. In some cases (if
there are microlensing events, observational problems,...), the intrinsic
variability is corrupted and important distortions in the features of the
cross-correlation function appear as compared with the corresponding
features in the autocorrelation functions. Therefore, as a final analysis,
we must compare the AA (or BB) autocorrelation and the AB cross-correlation.
IF THERE ARE NO IMPORTANT DIFFERENCES BETWEEN AA (OR BB) AND AB,
then all is ok and we can apply the technique. While some "first
generation" methods give delays mainly based on the dominant features of
the light curves, our methodology is sensitive to the whole information.
Do you want to play with d2?
We invite you to use the Q0957+561A, B data by Kundic et al. You may take the main event in A-1995 (95P.DAT) and the main event in B-1996 (96P.DAT), or alternatively, the secondary event in A-1995 (95S.DAT) and the secondary event in B-1996 (96S.DAT). For the main events, cross-correlations and autocorrelations are described in CROSP.FOR (outputs: CROSP5.DAT and CROSP15.DAT) and AUTOP.FOR (outputs: AUTOP5.DAT and AUTOP15.DAT). For the secondary events: CROSS.FOR (CROSS5.DAT, CROSS15.DAT), AUTOS.FOR (AUTOS5.DAT, AUTOS15.DAT). In order to compare AA and AB, one could use ACCP5FIG.FOR/ACCP15FIG.FOR (main) or/and ACCS5FIG.FOR/ACCS15FIG.FOR (secondary). Are you ready to apply the test?. The d2 technique appears in DELTAP.FOR (outputs: DELTAP5.DAT, DELTAP15.DAT) and DELTAS.FOR (outputs: DELTAS5.DAT, DELTAS15.DAT) for the main and secondary events, respectively....and the errors?. The programs to derive errors are: (1) ERRORP5SIM.FOR (output: ERRORP5SIM.DAT) for the main events, and (2) ERRORS5SIM.FOR (output: ERRORS5SIM.DAT) for the secondary events. A comparison of results (main events vs. secondary events) is really instructive.
QSO SIZE RATIOS FROM MULTIBAND MONITORING OF A MICROLENSING HIGH-MAGNIFICATION EVENT
We and our collaborators have developed a new scheme to study the nature of the central engine in a microlensed QSO. The compact emission regions could have different sizes in different optical wavelengths, and our framework permits to obtain the source size ratios when a special HME (e.g., a caustic crossing event, a two--dimensional maximum crossing event and so on) is produced in one of the QSO components. To infer the source size ratios, only cross-correlations between the brightness records in different optical bands are required. While the deconvolution method gets a richer information (1D intrinsic luminosity profiles), the new approach is free of the technical problems with complex inversion procedures. Using simulations related to VR GLITP data of QSO 2237+0305A, we have tested the ability of the scheme in the determination of the visible-to-red ratio q = RV/RR. Our synthetic light curves indicate that extremely accurate fluxes (with a few µJy uncertainties, or equivalently, a few milli-magnitudes errors) can lead to about 10% measurements of q. Taking into account the errors in the fluxes of QSO 2237+0305A from a normal ground-based telescope (of about 10 µJy, or equivalently, 10 mmag), it must be possible the achievement of smaller errors from the current superb-telescopes, and thus, an accurate determination of q. The whole paper is HERE. Several simple FORTRAN programs (some of them use the IMSL or PGPLOT libraries):
● MAKING
SYNTHETIC LCs: different samplings and accuracies
LightCurves.for LightCurvesC.for (tr.dat, tv.dat) LightCurvesA.for LightCurvesHA.for
● LCs: syn08r.dat and syn08v.dat
Figure including the syn08ha(r,v) LCs and the GLITP ones (glitpr.dat and glitpv.dat): SLChafig.for
● From the syn08ha(r,v) LCs:
chi2 technique ® Chi2.for (a = 2 days)
Chi2sim.for (BOOTSTRAP: a = 2 days, 3-point filter)
Chi2simN.for (NORMAL: a = 2 days)
D2 technique ® Disp.for (d = 2 days)
Dispsim.for (BOOTSTRAP: d = 2 days, 3-point filter)
DispsimN.for (NORMAL: d = 2 days)
Histogram of the simulations: Simhahist.for
NOTE: These FORTRAN codes are not the final ones that were used in our A&A paper (see here above)!