Diapositiva 1

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FIRST ANGLES SCHOOL MEASURING THE HUBBLE
CONSTANT AND LENS MASS MODELLING Santander
(Spain), 10 - 14 December 2004
OPTICAL MONITORING
by Luis J. Goicoechea (UC)
? The optical monitoring of GLQs began just after
the discovery of the first gravitational mirage
(Walsh, Carswell Weymann 1979, Nature 279, 381)
A
Q0957561 (Nordic Optical Telescope/GLITP)
B cD galaxy
?? The structure of the light curves of the
components A and B is an important tool to decide
on the nature of the phenomenon. Apart from an
offset in flux (magnitudes) and a time delay, the
macrolens scenario predicts similar light curves
of both components. The brightness record of B
must be a replica of the brightness record
corresponding to A.
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FIRST ANGLES SCHOOL MEASURING THE HUBBLE
CONSTANT AND LENS MASS MODELLING Santander
(Spain), 10 - 14 December 2004
I. OPTICAL MONITORING (OM) PROGRAMS

• THE FIRST DECADE (1980-1990)
• For Q0957561 (double), the first OM programs
  were conducted by Lloyd (1981, Nature 294, 727),
  Keel (1982, ApJ 255, 20), Florentin-Nielsen
  (1984, AA 138, L19), Schild Cholfin (1986, ApJ
  300, 209), Vanderriest et al. (1989, AA 215, 1)
  and Schild (1990, AJ 100, 1771). On the other
  hand, the system PG 1115080 (quad) was
  discovered in 1980 (Weymann et al. 1980, Nature
  285, 641), and the pioneering analyses of
  variability were carried out by Vanderriest and
  collaborators (Vanderriest et al. 1986, AA 158,
  L5 in French). The brightness changes in the
  double system UM 673 Q0142-100 (Surdej et al.
  1987, Nature 329, 695) was followed up by Surdej
  et al. (1988, AA 198, 49), and finally, the
  variability of the quad system Q22370305 (Huchra
  et al. 1985, AJ 90, 691) was studied by Irwin et
  al. (1989, AJ 98, 1989 microlensing!)

CASTLES (http//cfa-www.harvard.edu/glensdata)
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FIRST ANGLES SCHOOL MEASURING THE HUBBLE
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(Spain), 10 - 14 December 2004

• CfA-FLWO (USA) PROGRAM Q0957561 FOREVER
• Rudy Schild has devoted a big effort to follow up
  the flux fluctuations of the two components of
  Q0957561. All the data have been taken at Fred
  Lawrence Whipple Observatory (1.2 m telescope) in
  the R band. Although the light curves (Schild
  Thomson 1995, AJ 109, 1970) show a strange
  behaviour for no value of time delay do the
  fluctuations align (Schild 1996, ApJ 464, 125),
  they permit to obtain an average delay of about
  14 months 423 ? 6 days (Pelt et al. 1996, AA
  305, 97 dispersion method), 425 ? 17 days
  (Pijpers 1997, MNRAS 289, 933 SOLA method) and
  424.9 ? 1.2 days (Ovaldsen et al. 2003, AA 402,
  891 re-reduction of data dispersion c2
  methods).

• CALTECH-Princeton-APO (USA) PROGRAM Q0957561
  AND Q22370305
• The Gravitational Lens Monitoring Project at
  Apache Point Observatory (3.5 m telescope) was
  not successful with the Einstein Cross
  (Q22370305). However, the collaboration got to
  catch two very prominent twin events in the light
  curves of Q0957561A and Q0957561B (in the g
  band), which led to an accurate time delay
  estimation of 417 days (Kundic et al. 1997,
  ApJ 482, 75 c2, optimal reconstruction,
  dispersion cross-correlation methods).

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FIRST ANGLES SCHOOL MEASURING THE HUBBLE
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(Spain), 10 - 14 December 2004
A
B
??BA ? gravity (Shapiro effect) geometry

VERY PROMINENT TWIN EVENTS
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FIRST ANGLES SCHOOL MEASURING THE HUBBLE
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(Spain), 10 - 14 December 2004

• FLWO-Potsdam (USA/Germany) PROGRAM
• An ongoing program with the 1.2 m telescope (Fred
  Lawrence Whipple Observatory). Several
  gravitationally lensed quasars (Q0957561, SBS
  0909523, H1413117, B1422231, PG 1115080, RXJ
  09110551 and SDSS 10044112) are observed in
  different optical filters (wavelengths).

• Wise Observatory (Israel) PROGRAM
• Using the Wise Observatory 1m telescope, the
  Tel-Aviv University astronomers are monitoring in
  the V and R bands about 30 systems of lensed
  quasars, in order to detect the time-delay
  between the images. Recently, they measured the
  time delay between the two components of
  HE1104-1805 (Ofek Maoz 2003, ApJ 594, 101 c2
  cross-correlation methods). The new value of
  160 days strongly disagrees with the previous one
  of about 310 days (Gil-Merino, Wisotzki
  Wambsganss 2002, AA 381, 42 dispersion
  cross-correlation methods), and this system
  merits more attention. There is significant
  uncorrelated variability, and it seems that most
  of the uncorrelated (extrinsic) variability
  occurs in component A (the one nearest to the
  lens) microlensing fluctuations?

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FIRST ANGLES SCHOOL MEASURING THE HUBBLE
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A red , B blue time delay linear gradient
in the flux ratio B/A
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FIRST ANGLES SCHOOL MEASURING THE HUBBLE
CONSTANT AND LENS MASS MODELLING Santander
(Spain), 10 - 14 December 2004
? Belgian-Nordic Group The Belgian-Nordic group
carried out a very intense activity during the
past five years. They participated in several
monitoring projects and measured several time
delays at optical wavelengths. PG 1115080
(quad) DtBC 23.7 ? 3.4 days, DtAC 9.4 days
(Schechter et al. 1997, ApJ 475, L85)
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FIRST ANGLES SCHOOL MEASURING THE HUBBLE
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B1600434 (double) 51 ? 4 days (Burud et al.
2000, ApJ 544, 117 SOLA, dispersion, c2
iterative methods). They used the Nordic Optical
Telescope (NOT) and the I optical filter.

• Problems
• Time dependent offset microlensing?
• Main event in B another microlensing?
• Main events seem to be shifted in time

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FIRST ANGLES SCHOOL MEASURING THE HUBBLE
CONSTANT AND LENS MASS MODELLING Santander
(Spain), 10 - 14 December 2004
HE 2149-2745 (double) 103 ? 12 days (Burud et
al. 2002, AA 383, 71 c2 method). Using the
Danish 1.5 m telescope at La Silla Observatory
(ESO, Chile) and the V optical filter.
No problems!
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FIRST ANGLES SCHOOL MEASURING THE HUBBLE
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(Spain), 10 - 14 December 2004
RXJ 0911.40551 (quad) time delay of 146 ? 8
days between A A1 A2 A3 and B (Hjorth et
al. 2002, ApJ 572, L11 iterative method). Using
the NOT at Roque de Los Muchachos Observatory
(Spain) and the I optical filter.
Offset by values between -1.95 mag and 2.05 mag
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FIRST ANGLES SCHOOL MEASURING THE HUBBLE
CONSTANT AND LENS MASS MODELLING Santander
(Spain), 10 - 14 December 2004
SBS 1520530 (double) 130 ? 3 days (Burud et al.
2002, AA 391, 481 iterative method). Using the
NOT at Roque de Los Muchachos Observatory (Spain)
and the R optical filter.
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FIRST ANGLES SCHOOL MEASURING THE HUBBLE
CONSTANT AND LENS MASS MODELLING Santander
(Spain), 10 - 14 December 2004
FBQ 09512635 (double) 16 ? 2 days (Jakobsson et
al. 2004, astro-ph/0409444). Using the NOT at
Roque de Los Muchachos Observatory (Spain) and
the R optical filter.
Problems linear gradients more problems
Only the last 300 days are consideredproblems in
the beginning microlensing, multiple delays?
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FIRST ANGLES SCHOOL MEASURING THE HUBBLE
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(Spain), 10 - 14 December 2004
? Maidanak Collaboration (Russia/Ukraine/Uzbekista
n Germany) The former Soviet Union group and
the Potsdam group carry out an important activity
at the Maidanak Observatory (Uzbekistan), by
using the 1.5 m telescope. Joint efforts in
Potsdam (Germany), Tashkent (Uzbekistan), Moscow
(Russia) and Kharkov (Ukraine) permit to develop
a GLQ monitoring program. The targets are
Q22370305 (microlensing!), SBS 1520530,
Q0957561, SBS 0909523, H1413117, B1422231, PG
1115080, RXJ 09214528 and UM 673 Q0142-100.

• Spanish Collaboration
• The Spanish collaboration began in the summer of
  1995, and it is currently conducted by the IAC
  (Tenerife), UC (Santander) and UV (Valencia)
  groups.

BEFORE 1995
IN A NEAR FUTURE
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FIRST ANGLES SCHOOL MEASURING THE HUBBLE
CONSTANT AND LENS MASS MODELLING Santander
(Spain), 10 - 14 December 2004
From two prominent twin events in the light
curves of Q0957561A and Q0957561B (in the R
band), the collaboration estimated an accurate
time delay of 425 ? 4 days (Serra-Ricart et al.
1999, ApJ 526, 40 d2 method). They used the
Spanish 82 cm (IAC-80) telescope at Teide
Observatory (Tenerife, Spain).
A (time delay-advanced) green circles B
(magnitude-shifted) red squares
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FIRST ANGLES SCHOOL MEASURING THE HUBBLE
CONSTANT AND LENS MASS MODELLING Santander
(Spain), 10 - 14 December 2004
What is the time delay in Q0957561? averaged
IAC events 423-425 days or APO main events
417 days?
417 days
424 days
417 days
Coming back to the APO data in the g band
(Goicoechea 2002, MNRAS 334, 905)
432 days
d(DtBA) (Dd/cDds) (1 zd) (qA qB) . dr
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FIRST ANGLES SCHOOL MEASURING THE HUBBLE
CONSTANT AND LENS MASS MODELLING Santander
(Spain), 10 - 14 December 2004
Other things
? GLITP monitoring of Q22370305 (Alcalde et al.
2002, ApJ 572, 729) and Q0957561 (Ullán et al.
2003, MNRAS 346, 415). Using the NOT, and the V
and R filters
?? The UC group also observed Q0957561 and SBS
0909523 from 2003 March to 2003 June. The new VR
observations were made with the 1.52-m Spanish
Telescope at Calar Alto Observatory, Almeria
(Spain). The analysis and interpretation of the
VR light curves are in progress (in collaboration
with the Oslo group)
??? Finally, the Spanish groups are involved in
two monitoring programs with the 2.00-m Liverpool
Telescope, which is a fully robotic telescope at
the Observatorio del Roque de Los Muchachos, La
Palma (Spain). P1 Daily monitoring of SBS
0909523 and Q0957561 P2 Photometry and
spectroscopy of several GLQs
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FIRST ANGLES SCHOOL MEASURING THE HUBBLE
CONSTANT AND LENS MASS MODELLING Santander
(Spain), 10 - 14 December 2004
II. OPTICAL PHOTOMETRY (or MAGIC?)
Due to the usual small angular separation between
the lensed components and the proximity of one or
several components to the lens galaxy, from
ground-based frames, the photometry of a multiple
QSO is remarkably complex (a magical task?). The
size of the seeing disk (atmospheric effect) is
of about 1-2, i.e., similar to the typical
angular size of the gravitational mirages.
Double star Z Aquarii, which has a separation of
2 (Sky Telescope, Beating the Seeing by A.
M. MacRobert)
Q0957561
Q22370305
2
6
A1A2A3Lens
BLens
ABCDLens
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FIRST ANGLES SCHOOL MEASURING THE HUBBLE
CONSTANT AND LENS MASS MODELLING Santander
(Spain), 10 - 14 December 2004
SOME PHOTOMETRIC TECHNIQUES (sorry if your own
technique is not included here)

• Deconvolution (Magain, Courbin Sohy 1998, ApJ
  494, 472 Belgian-Nordic group). This task
  combine all the frames (optical images) obtained
  at different epochs to determine the numerical
  light distribution of the extended source (lens
  galaxy) as well as the positions of the point
  sources (QSO components), since these parameters
  do not vary with time. The flux of the point
  sources are allowed to vary from image to image,
  which produces the light curves.

• Aperture/PSF photometry (Serra-Ricart et al.
  1999, ApJ 526, 40 Ovaldsen et al. 2003, AA 402,
  89 large separation double systems, i.e., gtgt
  1). For example, the PHO2COM task (by Miquel
  Serra) works in the following way if the FWHM of
  the seeing disk is q, we initially take two
  circles of radius q, which are centered on the
  two components A and B. A reference star
  (reference candle) S is also encircled by a ring
  of radius q.

2q
A

Blens
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FIRST ANGLES SCHOOL MEASURING THE HUBBLE
CONSTANT AND LENS MASS MODELLING Santander
(Spain), 10 - 14 December 2004
PHO2COM The reference star total flux is
extracted through aperture photometry with an
aperture of radius 2q, i.e., we integrate the
instrumental flux (counts) within a circle of
radius 2q (using a clean frame, without
background signal).
2q
central axis
FS(2q) ?pixels ? 2q FS(pixel)
S
CCD pixels
PSF (point spread function) fitting photometry,
within the initial circle of radius q, is applied
to all the objects (QSO components and reference
star).
Fit in 2D (e.g., Gaussian) ? Integration in 2D ?
FS(q), Fi(q) (i A,B)
1D central axis for S (FS)

We compute an aperture correction f
FS(2q)/FS(q) and QSO total fluxes Fi(2q) f ?
Fi(q).
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FIRST ANGLES SCHOOL MEASURING THE HUBBLE
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(Spain), 10 - 14 December 2004
PHO2COM Finally, one can compare the QSO
component fluxes with that of the reference star.
As the magnitude of an object is defined by m
- 2.5 logF k, the component-to-star flux ratios
are equivalent to magnitude differences mi mS
- 2.5 logFi(2q)/FS(2q).
Although we dealth with a large separation
(between components) system, one of its
components could be close to the lens galaxy. If
the component B and the deflector are close
enough, and the lens galaxy is relatively bright,
then the PHO2COM flux of the contaminated
component (B) will be overestimated.
q
Excess of flux!
central axis
Fit in 2D ? Integration in 2D ? FB(q) FB(q)
contamination
B Lens

Therefore, FB(2q) f ? FB(q) c and mB mS
- 2.5 logFi(2q)/FS(2q) c/FS(2q) mS - 2.5
logFi(2q)/FS(2q) C (C gt 0)
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FIRST ANGLES SCHOOL MEASURING THE HUBBLE
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For example, the contamination of Q0957561B in
the R band at the NOT is given by a law C
mB(true) mB(PHO2COM) a ? q b.
Both the galaxy/component B confusion and the
bias in the component flux from PHO2COM will
depend on the seeing (FWHM q). The
contamination by galactic light can be derived
from simulations or from another data processing
technique (which avoids that contamination).

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FIRST ANGLES SCHOOL MEASURING THE HUBBLE
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• Image subtraction (Alard 2000, AAS 144, 363
  Wozniak et al. 2000, ApJ 529, 88 Alcalde et al.
  2002, ApJ 572, 729 bright galaxy lens).
  Observations of a multiply imaged QSO with a
  bright lens galaxy are well adapted for optimal
  image subtraction designed to efficiently remove
  the galaxy contribution without modeling its
  photometric profile. This task co-adds the frames
  to built up a deep reference frame (reference
  image). This reference frame is subtracted
  subsequently from each of the individual CCD
  frames in order to obtain differential images.
  The lens galaxy disappears totally after the
  optimal subtraction, and the observed residuals
  essentially correspond to the variable lensed QSO
  images. In the last steps (apart from the
  comparison with the reference star and the error
  estimates), one must perform a simultaneous N-PSF
  fitting photometry (N is the number of QSO
  components) of all differential frames obtained
  by optimal subtraction in order to measure for
  each of the N lensed components the respective
  flux differences between each individual frame
  and the reference one. In order to get the
  absolute fluxes at all observing epochs for each
  of the N components, we also need to perform
  direct photometry on the reference frame.

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FIRST ANGLES SCHOOL MEASURING THE HUBBLE
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(Spain), 10 - 14 December 2004
OGLE collaboration nine difference images of
Q22370305 at various epochs (V-band)
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FIRST ANGLES SCHOOL MEASURING THE HUBBLE
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(Spain), 10 - 14 December 2004

• PSF fitting (e.g., McLeod et al. 1998, AJ 115,
  137 Ullán et al. 2003, MNRAS 346, 415 CASTLES
  and Spanish collaborations). For example, the
  PSFPHOT task is useful for extracting clean QSO
  fluxes (free of background signal,
  cross-contamination between the components and
  contamination by the galaxy light). The technique
  uses an observationally motivated 2D galaxy
  profile (e.g., de Vaucouleurs profile), which is
  convolved with a PSF to reproduce the observed
  lens galaxy profile. Thus the instrumental fluxes
  of the N QSO components and the reference star
  (S) can be measured by means of PSF fitting.
  Obviously, constant backgrounds are included to
  model the two regions of interest the lens
  system and the S star. In this photometric
  procedure, the clean two-dimensional profiles of
  the field stars are used as empirical PSFs.
  Analytical PSFs are not considered (e.g.,
  Gaussian law and so on).

STEP-TO-STEP 1.- To determine the relevant
information on the galaxy, the method uses the
best images in terms of seeing values
(superbimages). Therefore, the code is applied to
each image with a seeing (FWHM) better than qlim,
considering the PSF of the brightest field star
and allowing all parameters to be free.
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FIRST ANGLES SCHOOL MEASURING THE HUBBLE
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For some frames, the method could not be able to
accurately extract several physical parameters of
the lens galaxy, leading to results in apparent
disagreement with the global distributions. Thus,
in the estimation of each parameter, it is
followed a scheme with two parts. First, the
values with a deviation ( value - average)
exceeding the standard one are dropped. Second,
the parameter is inferred from the average of the
"surviving" values. Finally, one obtains the
morphological parameters of the galaxy (e.g., the
effective radius, Reff, the ellipticity, e, and
the position angle, P.A.), the relative position
of the galaxy (position relative to the brightest
QSO component) and the relative flux G Flens/FS.

• 2.- The code is applied to all images (whatever
  their seeings), setting the galaxy parameters to
  those derived in the previous step (e.g., Reff,
  e, P.A., relative position and G), using galaxy
  fluxes given by Flens G ? FS and allowing the
  remaining parameters to vary. In this last
  iteration, although all the available PSFs are
  used, the fluxes from the PSF of the brightest
  field star are regarded as the standard ones. For
  the i-component (i 1,N)
• yi mi mS - 2.5 log(Fi/FS).

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FIRST ANGLES SCHOOL MEASURING THE HUBBLE
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(Spain), 10 - 14 December 2004
The light curves yi(t) show global behaviours
gi(t) that are caused by true intrinsic or
extrinsic phenomena (e.g., linear trends or
prominent events), as well as day-to-day
variabilities, ri(t) yi(t) gi(t), whose
interpretation is not easy true daily
fluctuations or observational noise?. For example

eA ? ltrA2gt1/2 5 mmag (in principle, the
residual signal contains both observational noise
and true variability)
gA(t)
rA(t)
eE lt(yE - ltyEgt)2gt1/2 4 mmag
NO true variability eA 5 mmag
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FIRST ANGLES SCHOOL MEASURING THE HUBBLE
CONSTANT AND LENS MASS MODELLING Santander
(Spain), 10 - 14 December 2004
In some systems, the situation is relatively
simple. If the gravitational mirage consists of
two QSO components, and the lens galaxy is
clearly fainter than the multiple QSO, each
frame (region including the system) can be
explained in terms of the background signal (free
parameter 1) and two light distributions with
the shape of a stellar PSF free parameters flux
of A (2), flux of B (3), 2D position of A
(4-5) and 2D position of B (6-7).
Each night, to estimate a reliable error, one may
take several consecutive frames, and obtain the
average value and the standard deviation of the
consecutive measurements yi(1), , yi(M). This is
a statistically and physically conservative
approach, because the s value is not divided by
M1/2 and any possible true intraday (hourly)
variation is neglected. Of course, the intrinsic
uncertainty only can be tested by using
complementary photometric tasks.
SBS 0909523 CASTLES (http//cfa-www.harvard.edu/g
lensdata) - HST image
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FIRST ANGLES SCHOOL MEASURING THE HUBBLE
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The system SBS 0909523 frame taken with the
1.52-m Spanish Telescope at Calar Alto
Observatory, Spain
c2 fit
The code starts with a set of seven initial
values (initial model) ptsrc0.intens        
ptsrc1.intens         ptsrc1.x             
ptsrc1.y              background            
  x0                      y0                 
    
Model frame
Difference frame
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III. TIME DELAY ESTIMATION
? DISPERSION METHOD (D2) Pelt and collaborators
(Pelt et al. 1994, AA 256, 775 1996, AA 305,
97) developed this statistical technique that is
based on the minimum dispersion between the two
brightness records
? ITERATIVE METHOD the two light curves are
correlated through an iterative procedure (e.g.,
Burud et al. 2000, ApJ 544, 117)
? CROSS-CORRELATION METHODS there are several
variants. The most sophisticated are discrete
cross-correlation function (Edelson Krolik
1988, ApJ 333, 646), ZDCF (Alexander 1997, in
Astronomical Time Series, Kluwer, p. 163) and d2
test (e.g., Serra-Ricart et al. 1999, ApJ 526,
40). This last technique (d2) is based on the
expected similarity between the discrete
autocorrelation function (DAC) of the light curve
of one component and the discrete
cross-correlation function (DCC), and it is
useful to derive a very accurate delay, provided
that a first (rough) estimate is known. Updated
information on the d2 test and other UC group
materials (software, images and so on) is
available at https//grupos.unican.es/glendama/