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When a gravitationally lensed source crosses a caustic, a pair of images is created or destroyed. We calculate the mean number of such pairs of microimages <n> for a given macroimage of a gravitationally lensed point source due to microlensing by the stars of the lensing galaxy. This quantity was calculated by Wambsganss, Witt, and Schneider in 1992 for the case of zero external shear, ;=0, at the location of the macroimage. Since in realistic lens models a nonzero shear is expected to be induced by the lensing galaxy, we extend this calculation to a general value of ;. We find a complex behavior of <n> as a function of ; and the normalized surface mass density in stars, ;*. Specifically, we find that at high magnifications, where the average total magnification of the macroimage is <;>=|(1-;*)2- ;2|-1>>1, <n> becomes correspondingly large and is proportional to <;>. The ratio <n>/ <;> is largest near the line ;=1-;*, where the magnification <;> becomes infinite, and its maximal value is 0.306. We compare our semianalytic results for <n> with the results of numerical simulations and find good agreement. We find that the probability distribution for the number of extra microimage pairs is reasonably described by a Poisson distribution with a mean value of <n> and that the width of the macroimage magnification distribution tends to be largest for <n>~1.

The gravitationally lensed quasar Q2237+0305 in X-rays: ROSAT/HRI detection of the "Einstein Cross"
(1999)

We report the first detection of the gravitationally lensed quasar Q2237+0305 in X-rays. With a ROSAT/HRI exposure of 53 ksec taken in Nov./Dec. 1997, we found a count rate of 0.006 counts per second for the combined four images. This corresponds to an X-ray flux of 2.2*E(-13) erg/cm(2) /sec and an X-ray luminosity of 4.2*E(45) erg/sec (in the ROSAT energy window 0.1-2.4 keV). The ROSAT/HRI detector is not able to resolve spatially the four quasar images (maximum separation 1.8 arcsec). The analysis is based on about 330 source photons. The signal is consistent with no variability, but with low significance. This detection is promising in view of the upcoming X-ray missions with higher spatial/spectral resolution and/or collecting power (Chandra X-ray Observatory, XMM and ASTRO-E).

We present a new determination of the time delay of the gravitational lens system HE 1104-1805 (``Double Hamburger'') based on a previously unpublished dataset. We argue that the previously published value of Delta tA-B=0.73 years was affected by a bias of the employed method. We determine a new value of Delta tA-B=0.85+/-0.05 years (2sigma confidence level), using six different techniques based on non interpolation methods in the time domain. The result demonstrates that even in the case of poorly sampled lightcurves, useful information can be obtained with regard to the time delay. The error estimates were calculated through Monte Carlo simulations. With two already existing models for the lens and using its recently determined redshift, we infer a range of values of the Hubble parameter: H0=48+/-4 km s-1 Mpc-1 (2sigma ) for a singular isothermal ellipsoid (SIE) and H0=62+/-4 km s-1 Mpc-1 (2sigma ) for a constant mass-to-light ratio plus shear model (M/L+gamma ). The possibly much larger errors due to systematic uncertainties in modeling the lens potential are not included in this error estimate.

Contrary to naive expectation, diluting the stellar component of the lensing galaxy in a highly magnified system with smoothly distributed ``dark'' matter increases rather than decreases the microlensing fluctuations caused by the remaining stars. For a bright pair of images straddling a critical curve, the saddle point (of the arrival time surface) is much more strongly affected than the associated minimum. With a mass ratio of smooth matter to microlensing matter of 4:1, a saddle point with a macromagnification of ;=9.5 will spend half of its time more than a magnitude fainter than predicted. The anomalous flux ratio observed for the close pair of images in MG 0414+0534 is a factor of 5 more likely than computed by Witt, Mao, & Schechter, if the smooth matter fraction is as high as 93%. The magnification probability histograms for macroimages exhibit a distinctly different structure that varies with the smooth matter content, providing a handle on the smooth matter fraction. Enhanced fluctuations can manifest themselves either in the temporal variations of a light curve or as flux ratio anomalies in a single epoch snapshot of a multiply imaged system. While the millilensing simulations of Metcalf & Madau also give larger anomalies for saddle points than for minima, the effect appears to be less dramatic for extended subhalos than for point masses. Moreover, microlensing is distinguishable from millilensing because it will produce noticeable changes in the magnification on a timescale of a decade or less.

Quasar Microlensing
(2001)