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We reformulate the transport equation which determines the size, shape and orientation of infinitesimal light beams in arbitrary spacetimes. The behaviour of such light beams near vertices and conjugate points is investigated, with special attention to the singular behaviour of the optical scalars. We then specialize the general transport equation to the case of an approximate metric of an inhomogeneous universe, which is a Friedmann metric `on average' with superposed isolated weak matter inhomogeneities. In a series of well-defined approximations, the equations of gravitational lens theory are derived. Finally, we derive a relative optical focusing equation which describes the focusing of light beams relative to the case that the beam is unaffected by matter inhomogeneities in the universe, from which it follows immediately that no beam can be focused less than one which is unaffected by matter clumps, before it propagates through its first conjugate point., Comment: 31 pages, uuencoded compressed postscript; preprint MPA 787

In a recent paper by Rodrigues-Williams \& Hogan (RH94), a correlation between high-redshift, optically-selected QSOs and Zwicky clusters was reported at a very high significance level. Due to the fairly bright flux threshold of the cluster sample, these correlations cannot be interpreted as being due to an environmental effect of the clusters on the quasar activity. The most likely interpretation employed in RH94 was the effect of gravitational lensing by the foreground clusters, though the required magnification to explain the observed correlations has to be considerably higher than obtained from simple mass models for the clusters. We have repeated the analysis of RH94 using a different QSO sample, namely radio quasars and radio galaxies from the 1-Jy sample. In accordance with RH, we detect a statistically significant correlation between Zwicky clusters and 1-Jy sources with intermediate redshift ($z\approx 1$), but fail to detect significant effects for higher-redshift sources. In addition, we detect a highly significant underdensity of low-redshift radio sources around Zwicky clusters, for which an environmental interpretation seems to be most reasonable. Our result for the overdensity of $z\sim 1$ sources is in good agreement with previous results and can possibly be interpreted as a lensing effect, though we have not tried to quantitatively investigate a lensing model. Other interpretations, such as patchy dust obscuration, can not explain the observed effect and its tendency with redshift., Comment: 21 pages, uudecoded postscriptfile, figures included, MPA preprint number 828

We present a novel method to recontruct the mass distribution of galaxy clusters from their gravitational lens effect on background galaxies. The method is based on a least-chisquare fit of the two-dimensional gravitational cluster potential. The method combines information from shear and magnification by the cluster lens and is designed to easily incorporate possible additional information. We describe the technique and demonstrate its feasibility with simulated data. Both the cluster morphology and the total cluster mass are well reproduced., Comment: 9 pages including 2 figures, submitted to ApJ Letters

The image distortions of high-redshift galaxies caused by gravitational light deflection of foreground clusters of galaxies can be used to reconstruct the two-dimensional surface mass density of these clusters. We apply an unbiased parameter-free reconstruction technique to the cluster CL0939+4713 (Abell 851), observed with the WFPC2 on board of the HST. We demonstrate that a single deep WFPC2 observation can be used for cluster mass reconstruction despite its small field of view and the irregular shape of the data field (especially for distant clusters). For CL0939, we find a strong correlation between the reconstructed mass distribution and the bright cluster galaxies indicating that mass follows light on average. The detected anti-correlation between the faint galaxies and the reconstructed mass is most likely an effect of the magnification (anti) bias, which was detected previously in the cluster A1689. Because of the high redshift of CL0939 (z_d=0.41), the redshift distribution of the lensed, faint galaxies has to be accounted for in the reconstruction technique. We derive an approximate global transformation for the surface mass density which leaves the mean image ellipticities invariant, resulting in an uncertainty in the normalization of the mass. From the non-negativity of the surface mass density, we derive lower limits on the mass inside the observed field. We can break the invariance transformation for the mass using the magnification effect on the observed number density of the background galaxies. Assuming a mean redshift of 0.8 and a fraction of 15 % (20 %) of cluster galaxies in the observed galaxy sample with 23

A new method for the reconstruction of the projected mass distribution of clusters of galaxies from the image distortion of background galaxies is discussed. This method is essentially equivalent to the one we developed previously, i.e., the noise-filtering method, but has several practical advantages: (1) It is much easier to implement; (2) it can be easily applied to wide-field images, since the constraints on the number of gridpoints are much weaker than for the previous method, and (3) it can be easily generalized to more complicated field geometries, such as that of the Wide Field Planetary Camera 2 (WFPC2) onboard HST. We have tested the performance of our new inversion method (for which a FORTRAN-77 implementation is available from the authors) using simulated data, demonstrating that it fares very favourably., Comment: 13 pages, 6 figures included; Fortran subroutines can be requested after paper will be accepted

We present WeCAPP, a long term monitoring project searching for microlensing events towards M 31. Since 1997 the bulge of M 31 was monitored in two different wavebands with the Wendelstein 0.8 m telescope. In 1999 we extended our observations to the Calar Alto 1.23 m telescope. Observing simultaneously at these two sites we obtained a time coverage of 53 % during the observability of M 31. To check thousands of frames for variability of unresolved sources, we used the optimal image subtraction method (OIS) by Alard & Lupton (1998) This enabled us to minimize the residuals in the difference image analysis (DIA) and to detect variable sources with amplitudes at the photon noise level. Thus we can detect microlensing events with corresponding amplifications A > 10 of red clump giants with M_I = 0., Comment: 10 pages, 21 figures, published in Astronomy & Astrophysics (2001)

We report the detection of the first 2 microlensing candidates from the Wendelstein Calar Alto Pixellensing Project (WeCAPP). Both are detected with a high signal-to-noise-ratio and were filtered out from 4.5 mill. pixel light curves using a variety of selection criteria. Here we only consider well-sampled events with timescales of 1 d < t_fwhm < 20 d, high amplitude, and low chi^2 of the microlensing fit. The two-color photometry (R,I) shows that the events are achromatic and that giant stars with colors of (R-I) ~ 1.1 mag in the bulge of M31 have been lensed. The magnification factors are 64 and 10 which are obtained for typical giant luminosities of M_I = -2.5 mag. Both lensing events lasted for only a few days (t_fwhm^GL1 = 1.7 d and t_fwhm^GL2 = 5.4 d). The event GL1 is likely identical with PA-00-S3 reported by the POINT-AGAPE project. Our calculations favor in both cases the possibility that MACHOs in the halo of M31 caused the lensing events. The most probable masses, 0.08 M_sun for GL1 and 0.02 M_sun for GL2, are in the range of the brown dwarf limit of hydrogen burning. Solar mass objects are a factor of two less likely., Comment: Accepted for publication in ApJ Letters (28 Oct 2003), 4 pages, 2 color figures, uses emulateapj style

In this paper we present the WeCAPP variable star catalogue towards the bulge of M31. The observations of the WeCAPP microlensing survey (optical R and I bands) during three years (2000-2003) result in a database with unprecedented time coverage for an extragalactic variable star study. We detect 23781 variable sources in a 16.1' x 16.6' field centered on the nucleus of M31. The catalogue of variable stars contains the positions, the periods and the variations in the R and I bands. We classify the variables according to their position in the R-band period-amplitude plane. Three groups can be distinguished; while the first two groups can be mainly associated with Cepheid-like variables (population I Cepheids in group I, type II Cepheids and RV Tauri stars in group II), the third one consists of Long Period Variables (LPVs). We detect 37 RV Tauri stars and 11 RV Tauri candidates which is one of the largest collections of this class of stars to date. The classification scheme is supported by Fourier decomposition of the light curves. Our data shows a correlation of the low-order Fourier coefficients Phi_21 with Phi_31 for classical Cepheids, as well for type II Cepheids and RV Tauri stars. Correlating our sample of variable stars with the X-ray based catalogues of Kaaret (2002) and Kong et al. (2002) results in 23 and 31 coincidences, 8 of which are M31 globular clusters. The number density of detected variables is clearly not symmetric, which has to be included in the calculations of the expected microlensing event rate towards M31. This asymmetry is due to the enhanced extinction in the spiral arms superimposed on the bulge of M31 which reduces the number of sources to about 60%, if compared to areas of equivalent bulge brightness (without enhanced extinction being present)., Comment: 22 pages, re-submitted to A&A after referee comments have been taken into account

Highly magnified lensed galaxies allow us to probe the morphological and spectroscopic properties of high-redshift stellar systems in great detail. However, such objects are rare, and there are only a handful of lensed galaxies which are bright enough for a high-resolution spectroscopic study with current instrumentation. We report the discovery of a new massive lensing cluster, SDSS J120923.7+264047, at z=0.558. Present around the cluster core, at angular distances of up to ~40'', are many arcs and arc candidates, presumably due to lensing of background galaxies by the cluster gravitational potential. One of the arcs, 21'' long, has an r-band magnitude of 20, making it one of the brightest known lensed galaxies. We obtained a low-resolution spectrum of this galaxy, using the Keck-I telescope, and found it is at redshift of z=1.018., Comment: MNRAS, in press

We report observations of three gravitationally lensed supernovae (SNe) in the Cluster Lensing And Supernova survey with Hubble (CLASH) Multi-Cycle Treasury program. These objects, SN CLO12Car (z = 1.28), SN CLN12Did (z = 0.85), and SN CLA11Tib (z = 1.14), are located behind three different clusters, MACSJ1720.2+3536 (z = 0.391), RXJ1532.9+3021 (z = 0.345), and A383 (z = 0.187), respectively. Each SN was detected in Hubble Space Telescope optical and infrared images. Based on photometric classification, we find that SNe CLO12Car and CLN12Did are likely to be Type Ia supernovae (SNe Ia), while the classification of SN CLA11Tib is inconclusive. Using multi-color light-curve fits to determine a standardized SN Ia luminosity distance, we infer that SN CLO12Car was approx. 1.0 +/- 0.2 mag brighter than field SNe Ia at a similar redshift and ascribe this to gravitational lens magnification. Similarly, SN CLN12Did is approx. 0.2 +/- 0.2 mag brighter than field SNe Ia. We derive independent estimates of the predicted magnification from CLASH strong+weak-lensing maps of the clusters (in magnitude units, 2.5 log10 μ): 0.83 +/- 0.16 mag for SN CLO12Car, 0.28 +/- 0.08 mag for SN CLN12Did, and 0.43 +/- 0.11 mag for SN CLA11Tib. The two SNe Ia provide a new test of the cluster lens model predictions: we find that the magnifications based on the SN Ia brightness and those predicted by the lens maps are consistent. Our results herald the promise of future observations of samples of cluster-lensed SNe Ia (from the ground or space) to help illuminate the dark-matter distribution in clusters of galaxies, through the direct determination of absolute magnifications.