An Isolated Stellar-Mass Black Hole Detected Through Astrometric Microlensing

We report the first unambiguous detection and mass measurement of an isolated stellar-mass black hole (BH). We used the Hubble Space Telescope (HST) to carry out precise astrometry of the source star of the long-duration (t_E ~ 270 days), high-magnification microlensing event MOA-2011-BLG-191/OGLE-2011-BLG-0462, in the direction of the Galactic bulge. HST imaging, conducted at eight epochs over an interval of six years, reveals a clear relativistic astrometric deflection of the background star's apparent position. Ground-based photometry shows a parallactic signature of the effect of the Earth's motion on the microlensing light curve. Combining the HST astrometry with the ground-based light curve and the derived parallax, we obtain a lens mass of 7.1 +/- 1.3 M_Sun and a distance of 1.58 +/- 0.18 kpc. We show that the lens emits no detectable light, which, along with having a mass higher than is possible for a white dwarf or neutron star, confirms its BH nature. Our analysis also provides an absolute proper motion for the BH. The proper motion is offset from the mean motion of Galactic-disk stars at similar distances by an amount corresponding to a transverse space velocity of ~45 km/s, suggesting that the BH received a modest natal 'kick' from its supernova explosion. Previous mass determinations for stellar-mass BHs have come from radial-velocity measurements of Galactic X-ray binaries, and from gravitational radiation emitted by merging BHs in binary systems in external galaxies. Our mass measurement is the first ever for an isolated stellar-mass BH using any technique

Geometric operator and approximation theory Final scientific report

In the study of hilbertian subspaces of Banach spaces and lower estimates of norms by hilbertian norms, entropy numbers and Gelfand numbers are important tools which were further developed in this research. Some new applications were found, e.g. studying the growth of polynomials in several variables or regularizing general convex bodies or its polars after a few rotations. Some of the results can also be formulated in terms of entropy or Gelfand numbers. A general formula for the entropy numbers of operators between weak type 2 and weak type 2 dual spaces in terms of other s-numbers was found, which yielded a partial positive result on the duality problem for entropy numbers. Studying this duality problem further, it was found that euclidean balls may - in an isomorphic sense - produce a tiling of R"n. Also, entropy numbers and volume estimates for k-codimensional sections of convex bodies are related. Concerning spherical functions, a very precise formula for the rate of best approximation E_k_,_n(f) of continuous functions on the sphere S"n"-"1 by (restrictions of) polynomials of degree k in n variables was shown, estimating E_k_,_n(f) by #omega#(f,n/(n+k)), #omega# the modulus of continuity. The factor n is the best possible, as can be seen by choosing f to be a certain norm restriction. (orig.)SIGLEAvailable from TIB Hannover: DtF QN1(23,43) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekGerman-Israeli Foundation for Scientific Research and Development (GIF), Oberschleissheim (Germany)DEGerman

Study of interfacial pattern formation in diffusion-controlled systems Final report

Available from TIB Hannover: F95B462 / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEGerman-Israeli Foundation for Scientific Research and Development (GIF), Oberschleissheim (Germany)DEGerman

An investigation of the potential of multi-sensor imaging spectroscopy data for the analysis of natural surface properties

SIGLEAvailable from TIB Hannover: RR 6134(2000,17) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Theory of charged and multi-component membranes, vesicles and other lamellar systems Final scientific report

Available from TIB Hannover: F98B1589 / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEGerman-Israeli Foundation for Scientific Research and Development (GIF), Oberschleissheim (Germany)DEGerman

Electronic states of isolated clusters Final scientific report

SIGLEAvailable from TIB Hannover: DtF QN1(23,58) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekGerman-Israeli Foundation for Scientific Research and Development (GIF), Oberschleissheim (Germany)DEGerman

Electronic properties of granular and mesoscopic point contact structures Final scientific report

The research project involved static and dynamic properties of small systems which are of great fundamental and practical importance for the understanding of the physics of microstructures (small metal particles, electronic states in confined geometries, etc.). Our study concentrated on properties of the electronic wave functions of such structures with emphasis on electronic correlations, electron-phonon interactions, electron interference effects and tunneling processes. Special attention was paid to experimentally accessible quantities. Part of the research dealt with properties of superconductors of complicated electronic and magnetic structures. (orig.)SIGLEAvailable from TIB Hannover: DtF QN1(23,14) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekGerman-Israeli Foundation for Scientific Research and Development (GIF), Oberschleissheim (Germany)DEGerman