## Institut für Physik und Astronomie

We present results of the analysis of 70 RR Lyrae stars located in the bar of the Large Magellanic Cloud (LMC). Combining the spectroscopically determined metallicity of these stars from the literature with precise periods from the OGLE III catalog and multi-epoch K-s photometry from the VISTA survey of the Magellanic Clouds system, we derive a new near-infrared period-luminosity-metallicity (PLKsZ) relation for RR Lyrae variables. In order to fit the relation we use a fitting method developed specifically for this study. The zero-point of the relation is estimated two different ways: by assuming the value of the distance to the LMC and by using Hubble Space Telescope parallaxes of five RR Lyrae stars in the Milky Way (MW). The difference in distance moduli derived by applying these two approaches is similar to 0.2 mag. To investigate this point further we derive the PL(Ks)Z relation based on 23 MW RR Lyrae stars that had been analyzed in Baade-Wesselink studies. We compared the derived PL(Ks)Z relations for RR Lyrae stars in the MW and LMC. Slopes and zero-points are different, but still consistent within the errors. The shallow slope of the metallicity term is confirmed by both LMC and MW variables. The astrometric space mission Gaia is expected to provide a huge contribution to the determination of the RR Lyrae PL(Ks)Z relation; however, calculating an absolute magnitude from the trigonometric parallax of each star and fitting a PL(Ks)Z relation directly to period and absolute magnitude leads to biased results. We present a tool to achieve an unbiased solution by modeling the data and inferring the slope and zero-point of the relation via statistical methods.

When Galactic microlensing events of stars are observed, one usually measures a symmetric light curve corresponding to a single lens, or an asymmetric light curve, often with caustic crossings, in the case of a binary lens system. In principle, the fraction of binary stars at a certain separation range can be estimated based on the number of measured microlensing events. However, a binary system may produce a light curve which can be fitted well as a single lens light curve, in particullary if the data sampling is poor and the errorbars are large. We investigate what fraction of microlensing events produced by binary stars for different separations may be well fitted by and hence misinterpreted as single lens events for various observational conditions. We find that this fraction strongly depends on the separation of the binary components, reaching its minimum at between 0.6 and 1.0 Einstein radius, where it is still of the order of 5% The Einstein radius is corresponding to few A.U. for typical Galactic microlensing scenarios. The rate for misinterpretation is higher for short microlensing events lasting up to few months and events with smaller maximum amplification. For fixed separation it increases for binaries with more extreme mass ratios. Problem of degeneracy in photometric light curve solution between binary lens and binary source microlensing events was studied on simulated data, and data observed by the PLANET collaboration. The fitting code BISCO using the PIKAIA genetic algorithm optimizing routine was written for optimizing binary-source microlensing light curves observed at different sites, in I, R and V photometric bands. Tests on simulated microlensing light curves show that BISCO is successful in finding the solution to a binary-source event in a very wide parameter space. Flux ratio method is suggested in this work for breaking degeneracy between binary-lens and binary-source photometric light curves. Models show that only a few additional data points in photometric V band, together with a full light curve in I band, will enable breaking the degeneracy. Very good data quality and dense data sampling, combined with accurate binary lens and binary source modeling, yielded the discovery of the lowest-mass planet discovered outside of the Solar System so far, OGLE-2005-BLG-390Lb, having only 5.5 Earth masses. This was the first observed microlensing event in which the degeneracy between a planetary binary-lens and an extreme flux ratio binary-source model has been successfully broken. For events OGLE-2003-BLG-222 and OGLE-2004-BLG-347, the degeneracy was encountered despite of very dense data sampling. From light curve modeling and stellar evolution theory, there was a slight preference to explain OGLE-2003-BLG-222 as a binary source event, and OGLE-2004-BLG-347 as a binary lens event. However, without spectra, this degeneracy cannot be fully broken. No planet was found so far around a white dwarf, though it is believed that Jovian planets should survive the late stages of stellar evolution, and that white dwarfs will retain planetary systems in wide orbits. We want to perform high precision astrometric observations of nearby white dwarfs in wide binary systems with red dwarfs in order to find planets around white dwarfs. We selected a sample of observing targets (WD-RD binary systems, not published yet), which can possibly have planets around the WD component, and modeled synthetic astrometric orbits which can be observed for these targets using existing and future astrometric facilities. Modeling was performed for the astrometric accuracy of 0.01, 0.1, and 1.0 mas, separation between WD and planet of 3 and 5 A.U., binary system separation of 30 A.U., planet masses of 10 Earth masses, 1 and 10 Jupiter masses, WD mass of 0.5M and 1.0 Solar masses, and distances to the system of 10, 20 and 30 pc. It was found that the PRIMA facility at the VLTI will be able to detect planets around white dwarfs once it is operating, by measuring the astrometric wobble of the WD due to a planet companion, down to 1 Jupiter mass. We show for the simulated observations that it is possible to model the orbits and find the parameters describing the potential planetary systems.