4. Comparison of binary source and blended single source
where the blending parameter f gives the contribution of the light of the source at unlensed state to the total light (source and component which does not undergo any lensing).
In the case of large , one has and therefore
i.e. the light curve for a binary source approaches that for a blended single source (object 2), and , where the blended single source is the exact limit of the binary source for . Similarly, for large , one has and
so that one approaches the light curve for a blended single source which now is object 1, and . For , one obtains , so that for (), the light curves for a blended single source object 2 (1) and for a binary source differ by less than 6%. This shows that any blended event will have a successful fit with a binary source, where large uncertainties in some of the fit parameters are expected, because the binary source model involves more parameters than that for a blended single source, namely for n spectral bands the distance parameter (), the point of time () and the luminosity offset ratios (altogether parameters) are convolved into n blending parameters .
Griest & Hu (1992) have performed a comprehensive study on the types of events which arise for binary sources. Depending on the type of the primary star of the binary system and the lens mass, they find that among the binary source events, 60-95% have a light curve which is mainly effected by one of the objects only. They call these events "offset bright" event if this object is the brighter one and "offset dim" or "merged offset dim" of this object is the dimmer one 2, where 50-80% of the binary source events fall into the category "offset bright", 7-20% into the category "offset dim" and 0.3-2% into the category "merged offset dim". The large fraction of these types of events among the binary source events means that it is likely that events due to binary sources can be successfully fitted with the model of a blended single source.
© European Southern Observatory (ESO) 1998
Online publication: April 28, 1998