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Astron. Astrophys. 333, 893-896 (1998)

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3. Point-mass lens and binary source

For a binary source, according to Griest & Hu (1992), two values of [FORMULA] and [FORMULA] defining the closest approach to the first and to the second source object are used, which imply two functions [FORMULA] and [FORMULA]. With [FORMULA] and [FORMULA] being the luminosities of the two parts and the luminosity offset ratio

[EQUATION]

the light amplification is given by

[EQUATION]

so that the light curve is a superposition of two light curves for point sources behind point-mass lenses.

Since the two components of the binary source may be located on the same side or on opposite sides of the lens trajectory without changing the distance functions [FORMULA] and [FORMULA], two different physical configurations producing the same light curve exist. I call the case where the components are on the same side the cis -configuration, the case where the components are on opposite sides the trans -configuration.

Let [FORMULA] denote the distance between the closest approaches of the lens to the two components and [FORMULA] denote the distance between the source components, both measured in projected Einstein radii [FORMULA]. It follows that

[EQUATION]

The angle [FORMULA] between the direction from source component 1 to source component 2 and the lens trajectory is given by

[EQUATION]

where the upper sign refers to the trans-configuration and the lower sign refers to the cis-configuration. The half-distance between the components follows as

[EQUATION]

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© European Southern Observatory (ESO) 1998

Online publication: April 28, 1998

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