5. OGLE#5 as an example
The points mentioned above can be illustrated using the event OGLE#5 as an example. Table 1 shows the result of a fit for a single source with and without blending, while Table 2 shows the result of a fit with a binary source.
Table 1. OGLE #5: Fits for a single source with and without blending
Table 2. OGLE #5: Binary source fit
For the fits, amplification values have been used rather than the magnification values as obtained from the OGLE collaboration. These amplification values refer to a baseline, which has been obtained by fitting the tail region to a constant brightness. One obtains also a scaling factor , which corresponds to the most-likely size of the errors. Table 3 shows the results.
Table 3. OGLE #5: fixing of the baseline and scaling factor
For the fits of the light curve, the errors have been increased by the factor . The need for rescaling arises from the fact that the assumption of a constant tail does not hold for the original data. The error bounds shown correspond to projections of the hypersurface .
Note that the single source fit without blending is not acceptable. The error bounds on are large for the fit with blending: The boundaries of the 1- -intervals differ by a factor of 1.5 so that the expectation values for the masses would differ by a factor of about 2.
The differences between the fits with and without blending can be seen in the light curves of the peak region in Fig. 1. The magnitudes are shown as the ordinate, which allows to see the data and the light curve in the peak better, though the fits have been performed using the amplification values. One sees a dramatic improvement of the fit with blending compared with fit without. For the fit without blending, one has many discrepant points in the wings of the light curve, which is not the case for the fit with blending.
The light curve for a binary source (Fig. 1) is similar to that for a single source with blending. The lens passes close to object 1, whereas the minimal separation to the position of object 2 projected onto the lens plane is about 0.7-1.2 . The luminosity offset ratio is in agreement with the blending parameter if one considers the quoted 1- -bounds - so that the binary source corresponds to a single source object 1 event with blending -, the values meet at about . For the binary source fit, there are large uncertainties in the event time scale , the minimal distance to object 2, , the time of closest approach to object 2, , and in the luminosity offset ratio . The extremely large upper bound on is due to the lack of data points for , since light curves are possible which involve another peak in this region. However, this bound is not arbitrarily large because this peak still has some influence to the right wing of the peak near . If this peak would move to infinity one would approach the fit for a single source with blending which however has a which is larger by about 7.
Fig. 2 shows the lens trajectory and the magnification contours for the binary source fit for both the cis- and the trans-configuration. All distances are measured in Einstein radii projected to the source plane .
This example demonstrates that a blended event can successfully be explained by a binary source model and that the error bounds on the parameters which are convolved into the blending parameter are large. However, since the binary source model corresponds to a "merged offset dim" event which should not occur frequently (around 1% of the binary source events) it does not show the other direction clearly.
© European Southern Observatory (ESO) 1998
Online publication: April 28, 1998