Abstract
A procedure for calculating two-dimensional power spectra of microlensing magnification fields is presented. In the absence of a shift, the one-dimensional projections of the power spectra P(k) corresponding to the light curve of a point source moving in a linear trajectory can be approximated by the expression (a 2 + k 2)−1/2 (where a = const). The power spectrum of an extended source is treated like the product of the power spectrum of a point source and the power spectrum of the brightness distribution of the extended source. The effect of the extent of the source is that it acts like a filter, suppressing high-frequency components in the spectrum. Based on eight years of monitoring of the quad gravitational lens Q2237+0305 by the OGLE group, power spectra for all four images are constructed and the (temporal) size of the radiating region of the quasar in the V filter is estimated to be 24 ± 6 days; given the constraints on the transverse velocity of the lensing galaxy (<600 km/s), the linear size turns out to be <1015 cm.
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Original Russian Text © V.N. Shalyapin, 2006, published in Astronomicheskiĭ Zhurnal, 2006, Vol. 83, No. 9, pp. 784–793.