The Galactic Center stellar cluster: The central arcsecond

With 10 years of high-resolution imaging data now available on the stellar cluster in the Galactic Center, we analyze the dynamics of the stars at projected distances $\leq1.2''$ from the central black hole candidate Sagittarius A* (Sgr A*). We find evidence for radial anisotropy of the cluster of stars surrounding Sgr A*. We confirm/find accelerated motion for 6 stars, with 4 stars having passed the pericenter of their orbits during the observed time span. We calculated/constrained the orbital parameters of these stars. All orbits have moderate to high eccentricities. The center of acceleration coincides with the radio position of Sgr A*. From the orbit of the star S2, the currently most tightly constrained one, we determine the mass of Sgr A* to $3.3\pm0.7\times10^{6}$M$_{\odot}$ and its position to $2.0\pm2.4$ mas East and $2.7\pm4.5$ mas South of the nominal radio position. The data provide compelling evidence that Sgr A* is a single supermassive black hole.Comment: 7 pages, 3 Figures; to be published in Astron. Nachr., Vol. 324, No. S1 (2003), Special Supplement "The central 300 parsecs of the Milky Way", Eds. A. Cotera, H. Falcke, T. R. Geballe, S. Markof

Asymptotic Analysis of Inpainting via Universal Shearlet Systems

Recently introduced inpainting algorithms using a combination of applied harmonic analysis and compressed sensing have turned out to be very successful. One key ingredient is a carefully chosen representation system which provides (optimally) sparse approximations of the original image. Due to the common assumption that images are typically governed by anisotropic features, directional representation systems have often been utilized. One prominent example of this class are shearlets, which have the additional benefitallowing faithful implementations. Numerical results show that shearlets significantly outperform wavelets in inpainting tasks. One of those software packages, www.shearlab.org, even offers the flexibility of usingdifferent parameter for each scale, which is not yet covered by shearlet theory. In this paper, we first introduce universal shearlet systems which are associated with an arbitrary scaling sequence, thereby modeling the previously mentioned flexibility. In addition, this novel construction allows for a smooth transition between wavelets and shearlets and therefore enables us to analyze them in a uniform fashion. For a large class of such scaling sequences, we first prove that the associated universal shearlet systems form band-limited Parseval frames for $L^2(\mathbb{R}^2)$ consisting of Schwartz functions. Secondly, we analyze the performance for inpainting of this class of universal shearlet systems within a distributional model situation using an $\ell^1$-analysis minimization algorithm for reconstruction. Our main result in this part states that, provided the scaling sequence is comparable to the size of the (scale-dependent) gap, nearly-perfect inpainting is achieved at sufficiently fine scales

The Galactic Center

In the past decade high resolution measurements in the infrared employing adaptive optics imaging on 10m telescopes have allowed determining the three dimensional orbits stars within ten light hours of the compact radio source at the center of the Milky Way. These observations show the presence of a three million solar mass black hole in Sagittarius A* beyond any reasonable doubt. The Galactic Center thus constitutes the best astrophysical evidence for the existence of black holes which have long been postulated, and is also an ideal `lab' for studying the physics in the vicinity of such an object. Remarkably, young massive stars are present there and probably have formed in the innermost stellar cusp. Variable infrared and X-ray emission from Sagittarius A* are a new probe of the physical processes and space-time curvature just outside the event horizon.Comment: Write up of the talk at IAU Symposium No. 238 (21-25 August 2006, Prague), to appear in Proceedings of "Black Holes: from Stars to Galaxies" (Cambridge University Press), p. 17

ℓ1\ell^1-Analysis Minimization and Generalized (Co-)Sparsity: When Does Recovery Succeed?

This paper investigates the problem of signal estimation from undersampled noisy sub-Gaussian measurements under the assumption of a cosparse model. Based on generalized notions of sparsity, we derive novel recovery guarantees for the $\ell^{1}$-analysis basis pursuit, enabling highly accurate predictions of its sample complexity. The corresponding bounds on the number of required measurements do explicitly depend on the Gram matrix of the analysis operator and therefore particularly account for its mutual coherence structure. Our findings defy conventional wisdom which promotes the sparsity of analysis coefficients as the crucial quantity to study. In fact, this common paradigm breaks down completely in many situations of practical interest, for instance, when applying a redundant (multilevel) frame as analysis prior. By extensive numerical experiments, we demonstrate that, in contrast, our theoretical sampling-rate bounds reliably capture the recovery capability of various examples, such as redundant Haar wavelets systems, total variation, or random frames. The proofs of our main results build upon recent achievements in the convex geometry of data mining problems. More precisely, we establish a sophisticated upper bound on the conic Gaussian mean width that is associated with the underlying $\ell^{1}$-analysis polytope. Due to a novel localization argument, it turns out that the presented framework naturally extends to stable recovery, allowing us to incorporate compressible coefficient sequences as well

Haemoglobinopathies and newborn haemoglobinopathy screening in Germany.

Germany has been an immigration country since the early 1950s. In December 2007, 6.7 million non-German citizens lived in the country. However, the total number of citizens with a migration background is 15–20 million, about 9 million of whom come from countries where sickle cell disease and thalassaemias are frequent. In a country with 82 million inhabitants health authorities are not worried by the presence of probably 1000–1500 sickle cell and 450 transfusion-dependent thalassaemia patients, and therefore no screening or preventive measures have been taken so far on a national scale. There are plans for a pilot project (1 year) to screen all newborns for sickle cell disease in obstetric hospitals in 4–5 cities with more than 20% migrants. Funding and lack of an infrastructure to provide counselling are major problems

Star Formation and Dynamics in the nuclei of AGN

Using adaptive optics on Keck and the VLT in the H- and K-bands, we have begun a project to probe the dynamics and star formation around AGN on scales of 0.1arcsec. The stellar content of the nucleus is traced through the 2.29micron CO2-0 and 1.62micron CO6-3 absorption bandheads. These features are directly spatially resolved, allowing us to measure the extent and distribution of the nuclear star forming region. The dynamics are traced through the 2.12micron H_2 1-0S(1) and 1.64micron [FeII] emission lines, as well as stellar absorption features. Matching disk models to the rotation curves at various position angles allows us to determine the mass of the stellar and gas components, and constrain the mass of the central black hole. In this contribution we summarise results for the two type~1 AGN Mkn231 and NGC7469.Comment: contribution to "The interplay among Black Holes, Stars and ISM in Galactic Nuclei", March 200

Weighing the young stellar discs around Sgr A*

It is believed that young massive stars orbiting Sgr A* in two stellar discs on scales of 0.1-0.2 parsecs were formed either farther out in the Galaxy and then quickly migrated inward, or in situ in a massive self-gravitating disc. Comparing N-body evolution of stellar orbits with observational constraints, we set upper limits on the masses of the two stellar systems. These masses turn out to be few times lower than the expected total stellar mass estimated from the observed young high-mass stellar population and the standard galactic IMF. If these stars were formed in situ, in a massive self-gravitating disc, our results suggest that the formation of low-mass stars was suppressed by a factor of at least a few, requiring a top-heavy initial mass function (IMF) for stars formed near sgr A*.Comment: accepted to MNRAS. 6 pages, 5 figure