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We examine the effect that the shape of the source brightness profile has on the magnitude fluctuations of images in quasar lens systems due to microlensing. We do this by convolving a variety of accretion disk models (including Gaussian disks, uniform disks, "cones," and a Shakura-Sunyaev thermal model) with two magnification maps in the source plane, one with convergence kappa = 0.4 and shear gamma = 0.4 (positive parity) and the other with kappa = gamma = 0.6 ( negative parity). By looking at magnification histograms of the convolutions and using chi(2) tests to determine the number of observations that would be necessary to distinguish histograms associated with different disk models, we find that, for circular disk models, the microlensing fluctuations are relatively insensitive to all properties of the models except the half-light radius of the disk. Shakura-Sunyaev models are sufficiently well constrained by observed quasar properties that we can estimate the half-light radius at optical wavelengths for a typical quasar. If Shakura-Sunyaev models are appropriate, the half-light radii are very much smaller than the Einstein rings of intervening stars, and the quasar can be reasonably taken to be a point source except in the immediate vicinity of caustic-crossing events
We analyze the photometric data obtained by PLANET and OGLE on the caustic-crossing binary-lens microlensing event OGLE-2002-BLG-069. Thanks to the excellent photometric and spectroscopic coverage of the event, we are able to constrain the lens model up to the known ambiguity between close and wide binary lenses. The detection of annual parallax in combination with measurements of extended-source effects allows us to determine the mass, distance and velocity of the lens components for the competing models. While the model involving a close binary lens leads to a Bulge- Disc lens scenario with a lens mass of M = (0.51 ± 0.15) M-⊙ and distance of D-L = (2.9 ± 0.4) kpc, the wide binary lens solution requires a rather implausible binary black-hole lens ( M ≳ 126 M-⊙). Furthermore we compare current state-of-the-art numerical and empirical models for the surface brightness profile of the source, a G5III Bulge giant. We find that a linear limb-darkening model for the atmosphere of the source star is consistent with the data whereas a PHOENIX atmosphere model assuming LTE and with no free parameter does not match our observations
We discuss high-resolution, time-resolved spectra of the caustic exit of the binary microlensing event OGLE 2002-BLG-069 obtained with UVES on the VLT. The source star is a G5III giant in the Galactic Bulge. During such events, the source star is highly magnified, and a strong differential magnification around the caustic resolves its surface. Using an appropriate model stellar atmosphere generated by the PHOENIX v2.6 code we obtain a model light curve for the caustic exit and compare it with a dense set of photometric observations obtained by the PLANET microlensing follow up network. We further compare predicted variations in the Halpha equivalent width with those measured from our spectra. While the model and observations agree in the gross features, there are discrepancies suggesting shortcomings in the model, particularly for the Halpha line core, where we have detected amplified emission from the stellar chromosphere after the source star's trailing limb exited the caustic. This achievement became possible by the provision of the very efficient OGLE-III Early Warning System, a network of small telescopes capable of nearly-continuous round-the-clock photometric monitoring, on-line data reduction, daily near-real-time modelling in order to predict caustic crossing parameters, and a fast and efficient response of a 8 m class telescope to a "Target-of-Opportunity" observation request
The frequency of giant arcs - highly distorted and strongly gravitationally lensed background galaxies - is a powerful test for cosmological models. Previous comparisons of arc statistics for the currently favored concordance cosmological model ( lambda cold dark matter [LCDM]) with observations have shown an apparently large discrepancy in underpredicting cluster arcs. We present new ray-shooting results, based on a high-resolution (1024(3) particles in a 320 h(-1) Mpc box) large-scale structure simulation normalized to the Wilkinson Microwave Anisotropy Probe (WMAP) observations. We follow light rays through a pseudo - three-dimensional matter distribution approximated by up to 38 lens planes and evaluate the occurrence of arcs for various source redshifts. We find that the frequency of strongly lensed background galaxies is a steep function of source redshift: the optical depth for giant arcs increases by a factor of 5 when background sources are moved from redshift z(s) = 1.0 to 1.5. This is a consequence of a small decrease of the critical surface mass density for lensing, combined with the very steep cluster mass function at the high-mass end plus a modest contribution from secondary lens planes. Our results are consistent with those of Bartelmann et al. if we - as they did - restrict all sources to be at z(s) = 1. If we allow sources extending to or beyond z(s) greater than or equal to 1.5, the apparent discrepancy vanishes: the frequency of arcs increases by about a factor of 10 as compared to previous estimates, and results in roughly one arc per 20 deg(2) over the sky, in good agreement with the observed frequency of arcs
Microlensing is the only known direct method to measure the masses of stars that lack visible companions. In terms of microlensing observables, the mass is given by M (c(2)/4G)(r) over tilde (E)theta(E) and so requires the measurement of both the angular Einstein radius theta(E) and the projected Einstein radius (r) over tilde (E). Simultaneous measurement of these two parameters is extremely rare. Here we analyze OGLE-2003-BLG-238, a spectacularly bright (I-min 10.3), high-magnification (A(max) 170) microlensing event. Pronounced finite-source effects permit a measurement of theta(E) = 650 muas. Although the timescale of the event is only t(E) 38 days, one can still obtain weak constraints on the microlens parallax: 4.4 AU < <(r)over tilde>(E) < 18 AU at the 1 σ level. Together these two parameter measurements yield a range for the lens mass of 0.36 M-&ODOT; < M < 1.48 M-&ODOT;. As was the case for MACHO- LMC-5, the only other single star (apart from the Sun) whose mass has been determined from its gravitational effects, this estimate is rather crude. It does, however, demonstrate the viability of the technique. We also discuss future prospects for single-lens mass measurements
It has been conjectured that the distribution of magnifications of a point source microlensed by a randomly distributed population of intervening point masses is independent of its mass spectrum. We present gedanken experiments that cast doubt on this conjecture and numerical simulations that show it to be false
A small fraction of all quasars are strongly lensed and multiply imaged, with usually a galaxy acting as the main lens. Some, or maybe all of these quasars are also affected by microlensing, the effect of stellar mass objects in the lensing galaxy. Usually only the photometric aspects of microlensing are considered: the apparent magnitudes of the quasar images vary independently because the relative motion between source, lens and observer leads to uncorrelated magnification changes as a function of time. However, stellar microlensing on quasars has yet another effect, which was first explored by Lewis & lbata (1998): the position of the quasar - i.e. the center-of-light of the many microimages - can shift by tens of microarcseconds due to the relatively sudden (dis-)appearance of a pair of microimages when a caustic is being crossed. Here we explore quantitatively the astrometric effects of microlensing on quasars for different values of the lensing parameters kappa and gamma (surface mass density and external shear) covering most of the known multiple quasar systems. We show examples of microlens-induced quasar motion (i.e. astrometric changes) and the corresponding light curves for different quasar sizes. We evaluate statistically the occurrence of large "jumps" in angular position and their correlation with apparent brightness fluctuations. We also show statistical relations between positional offsets and time from random starting points. As the amplitude of the astrometric offset depends on the source size, astrometric microlensing signatures of quasars - combined with the photometric variations - will provide. very good constraints on the sizes of quasars as a function of wavelength. We predict that such signatures will be detectable for realistic microlensing scenarios with near future technology in the infrared/optical (Keck- Interferometry, VLTI, SIM, GAIA). Such detections will show that not even high redshift quasars define a "fixed" coordinate system
We present a detailed study of the effects of gravitational microlensing on compact and distant gamma-ray blazars. These objects have gamma-ray-emitting regions that are small enough to be affected by microlensing effects produced by stars lying in intermediate galaxies. We compute the gravitational magnification taking into account effects of the lensing and show that, whereas the innermost gamma-ray spheres can be significantly magnified, there is little magnification either for very high gamma-ray energies or for lower (radio) frequencies (because these wavelengths are emitted from larger regions). We analyse the temporal evolution of the gamma-ray magnification for sources moving in a caustic pattern field, where the combined effects of thousands of stars are taken into account using a numerical technique. We propose that some of the unidentified gamma-ray sources (particularly some of those lying at high galactic latitude with gamma-ray statistical properties that are very similar to detected gamma-ray blazars) are indeed the result of gravitational lensing magnification of background undetected active galactic nuclei (AGN). This is partly supported from a statistical point of view: we show herein as well, using the latest information from the third EGRET catalogue, that high-latitude gamma-ray sources have similar averaged properties to already detected gamma-ray AGN. Some differences between both samples, regarding the mean flux level, could also be understood within the lensing model. With an adequate selection of lensing parameters, it is possible to explain a variety of gamma-ray light curves with different time-scales, including non-variable sources. The absence of strong radio counterparts could be naturally explained by differential magnification in the extended source formalism.
Due to their extremely small luminosity compared to the stars they orbit, planets outside our own Solar System are extraordinarily difficult to detect directly in optical light. Careful photometric monitoring of distant stars, however, can reveal the presence of exoplanets via the microlensing or eclipsing effects they induce. The international PLANET collaboration is performing such monitoring using a cadre of semi-dedicated telescopes around the world. Their results constrain the number of gas giants orbiting 1-7 AU from the most typical stars in the Galaxy. Upgrades in the program are opening regions of ''exoplanet discovery space'' - toward smaller masses and larger orbital radii - that are inaccessible to the Doppler velocity technique.
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.