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Astron. Astrophys. 325, 877-880 (1997)

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1. Introduction

The most spectacular effects of microlensing occur when the angular radius of the source ([FORMULA]) is much smaller than that of the Einstein ring ([FORMULA]) for the microlens, and this case has therefore been investigated theoretically in most detail up till now. Although microlensing of large sources ([FORMULA]) may cause significant effects (RS), it has been much less considered till now. The reason for this may be the long timescales for these effects when the lenses have about one solar mass. However, when comparing flux ratios of the different images in multiply lensed quasars, the timescale is of no importance.

For large sources ([FORMULA]) RS derived a usefull analytical approximation for the standard deviation of the variations in magnitude due to microlensing:

[EQUATION]

Here [FORMULA] is the optical depth for microlensing. The shear [FORMULA] was assumed to be zero, and the surface luminosity was constant over the source. One lens plane with a random star distribution was also assumed. The variations in the magnitude m are mainly due to fluctuations in the average surface mass density projected in front of the source caused by Poisson fluctuations in the number of stars. Numerical calculations showed that for [FORMULA] -values equal to 0.1 and 0.4 the standard deviation [FORMULA] was always less than [FORMULA] given by Eq. (1), (up to 20% for sources with [FORMULA]), the difference getting smaller for larger sources, hence;

[EQUATION]

We have carried out more extensive calculations for various values of [FORMULA] and [FORMULA] and also included shear terms ([FORMULA]). Since, for the large sources we are considering, [FORMULA]), the timescale of variability is normally rather long ([FORMULA] years), we shall not here be simulating lightcurves, but concentrate on determining by numerical simulations the standard deviation [FORMULA] in the magnitude variation caused by microlensing. This is particularly important in the case of lensed quasars with multiple images, since [FORMULA] can then often be estimated by measuring flux ratios between the images in different wavebands, or the equivalent widths of an emission line in the different images, see discussion in Section 4. A few details on the numerical method is briefly commented upon in Section 2, and the results are presented in Section 3.

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© European Southern Observatory (ESO) 1997

Online publication: April 28, 1998

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