Comparison between the photometric lightcurves illustrated in Figs. 2 (click here) and 3 (click here) for the A, B, C and D lensed components of H1413+117 reveals a remarkably good match between the measurements derived using the two independent image analysis methods described in the previous section. Figure 4 (click here) compares the photometric measurements and their uncertainties derived using the two independent methods. Except for a few isolated data points, there is a very good overall agreement between these independent photometric determinations.
Figure 4: Relative magnitudes for the A, B, C and D lensed
components of H1413+117 (all filters), with respect to the reference
photometric star, derived using the
automatic image decomposition technique (1) and the interactive CLEAN algorithm
(2). The diagonal lines represent curves of perfect match between the two
methods. Note that for the sake of clarity, the measurements pertaining to
B, C, D and their associated diagonal lines have
been translated by constant values with respect to the results for A
From our two observations in the B band (see Table 1), we note
that the B component is weaker than the C component, while being almost
equal in the V band (see Fig. 2 (click here) and Fig. 3 (click here)).
Image B is also markedly stronger than image C in the I band than in
the R band (see Table 1 for the independent photometric
measurements). This is consistent with differential reddening
caused by dust in the lensing galaxy along the different light paths of the
lensed components. The prominence of absorption lines at redshifts z = 1.44,
1.66 in the spectrum of component B supports this interpretation (Magain
et al. 1988) and
suggests searching for the lensing object(s) at
those redshifts, in the vicinity of the B component.
The lightcurves for the A, B and C components clearly vary in a
parallel fashion in all filters, starting at a
minimum luminosity in 1988,
at the beginning of the ESO observation series, and peaking in 1991.
The time delay for this system is expected to be shorter than one month
(Kayser et al. 1990), so the quasi-simultaneous variations
observed for these three components are consistent with intrinsic
variations, as previously
noted by Arnould et al. (1993) and Remy et al.
(1996).
In order to avoid windowing effects on the time delay determinations (see
Kayser 1993), the V and R lightcurves of component A,
derived with method 1, have been smoothed using a simple low-pass spline
with cut-off frequency of about (2 weeks)-1. The magnitude
differences between the data and the smoothed curve fall approximately within
the 
limit. Nevertheless, the 
for those magnitude
differences, in a given filter, is found to be too high by a factor 4, at
least. This could indicate the existence of photometric variations at higher
frequencies but also of non-Gaussian errors or an oversmoothing of the data. In
the next step of the analysis, the two smoothed lightcurves for component
A (one for R and one for V) have been numerically translated in the
epoch-magnitude diagram (
, 
).
For a given value of (, ), the corresponding
between the observations of a given component and the point of the
translated smoothed lightcurve at the same epoch has been computed. As the
high frequency variations disallow a direct statistical interpretation of the
values, the latter ones have been normalized in two ways.
If we assume that the smoothed lightcurve of A should be compatible with
the A data, the for each component have been normalized to the
minimum of A (solid contours in Fig. 5 (click here)). Considering the
A data points, the derived 
contour at the 99%
confidence level (combined for the V and R filters in Fig. 5 (click here)),
extends to about 
days. This sets a lower limit on the accuracy of
the time delay determination based on this technique with the present data.
For the B and C components, the time delays corresponding to a minimum
computed independently for the two filters (not represented) are
found to be non-consistent. This accounts for the relatively smaller size of
the 99% compatibility domain of the combined for components B
and C (see Fig. 5 (click here)). No acceptable values for the were
found for the D component at the 99% confidence level. This is a definite
indication for an abnormal behavior of the D lightcurve, incompatible with
the simple interpretation in terms of time delay.
The for each component has also been normalized to the local minimum
of that component (dashed contours in Fig. 5 (click here)). With this
normalization, differences in the curves which would be
incompatible with the hypothesis of the time
delay phenomenon are hidden. An upper limit of about 150 days on the
absolute value for the time delays remains. All the curves are thus
also compatible with zero time delay.
Figure 5: 99% confidence level contours for the of the differences
between a smoothed lightcurve of component A, translated by in
epoch and in magnitude, and the measurements of the
four components, as derived by method 1. The smoothed lightcurve has been
defined by a spline interpolation of the A measurements; hence the
differences in epoch and magnitudes are relative to A. The
computed independently for the V and R data have been combined in the
present diagram and normalized to the minimum for A (solid
contours) or to the minimum for the given component (dashed
contours). Crosses indicate the positions of the minima
We conclude that the present lightcurves of the Cloverleaf quasar are not sufficiently well sampled and/or accurate in order to estimate precise values for the time delays, only upper limits can be set. However, given the noticeable intrinsic photometric variability of H1413+117, we feel confident that a better sampling of the lightcurves will lead to an accurate determination of the time delays for this system.
Analysis of our observations does not show any clear sign of micro-lensing
activity for the A, B and C components. The photometric variations for
the D component, however, deviate somewhat from the parallel behavior
seen for the other three lensed QSO images. Particularly during the 1992
season, there is a steep decrease in the
flux of this component by approximately 0.1 magnitude during three months,
while the other components remain relatively constant. The event is seen in
both the I and R bands, whereas the V and B bands have insufficient
observations to substantiate this. Variations during 1988 for the D
component reported by Remy et al. (1996) in the V band were
also interpreted as being possibly caused by micro-lensing. Angonin et al.
concluded from spectra obtained on March 7, 1989 that the continuum of
image D was slightly bluer than the other three images. From our
observations in 1988 and 1994 we find no significant blue excess in the D
component to within
0.03 mag. Unfortunately the observations from 1989 are
not of sufficient quality to draw any definite conclusions.
In conclusion, pending a direct identification of the lensing galaxy, the
multiply imaged QSO H1413+117
constitutes a very good candidate for a direct and independent determination of the Hubble parameter H0. A photometric monitoring of this optical source, with optimal time coverage, should be organized in the near future. International collaboration will be essential for its success.
Acknowledgements
RØ would like to thank the STScI, the Norwegian Research Council and the Stockholm Observatory for financial support during a two month stay at STScI. MR and JS would like to thank B. Revenaz for his help at STScI and the PRODEX grant "Gravitational Lensing with HST'' for financial support. AS thanks for financial support under grant no 781-73-058 from the Netherlands Foundation for Research in Astronomy (ASTRON) which receives its funds from the Netherlands Organisation for Scientific Research (NWO).