Pinpointing the massive black hole in the Galactic Center with gravitationally lensed stars

A new statistical method for pinpointing the massive black hole (BH) in the Galactic Center on the IR grid is presented and applied to astrometric IR observations of stars close to the BH. This is of interest for measuring the IR emission from the BH, in order to constrain accretion models; for solving the orbits of stars near the BH, in order to measure the BH mass and to search for general relativistic effects; and for detecting the fluctuations of the BH away from the dynamical center of the stellar cluster, in order to study the stellar potential. The BH lies on the line connecting the two images of any background source it gravitationally lenses, and so the intersection of these lines fixes its position. A combined search for a lensing signal and for the BH shows that the most likely point of intersection coincides with the center of acceleration of stars orbiting the BH. This statistical detection of lensing by the BH has a random probability of ~0.01. It can be verified by deep IR stellar spectroscopy, which will determine whether the most likely lensed image pair candidates (listed here) have identical spectra.Comment: 4 pages, 2 figures, submitted to ApJ

Reliability demonstration for safety-critical systems

This paper suggests a new model for reliability demonstration of safety-critical systems, based on the TRW Software Reliability Theory. The paper describes the model; the test equipment required and test strategies based on the various constraints occurring during software development. The paper also compares a new testing method, Single Risk Sequential Testing (SRST), with the standard Probability Ratio Sequential Testing method (PRST), and concludes that: • SRST provides higher chances of success than PRST • SRST takes less time to complete than PRST • SRST satisfies the consumer risk criterion, whereas PRST provides a much smaller consumer risk than the requirement

Wavelength-independent coupler from fiber to an on-chip cavity, demonstrated over an 850nm span

A robust wide band (850 nm) fiber coupler to a whispering-gallery cavity with ultra-high quality factor is experimentally demonstrated. The device trades off ideality for broad-band, efficient input coupling. Output coupling efficiency can remain high enough for practical applications wherein pumping and power extraction must occur over very broad wavelength spans

Level-crossing and modal structure in microdroplet resonators

We fabricate a liquid-core liquid-clad microcavity that is coupled to a standard tapered fiber, and then experimentally map the whispering-gallery modes of this droplet resonator. The shape of our resonator is similar to a thin prolate spheroid, which makes space for many high-order transverse modes, suggesting that some of them will share the same resonance frequency. Indeed, we experimentally observe that more than half of the droplet's modes have a sibling having the same frequency (to within linewidth) and therefore exhibiting a standing interference-pattern

Spectroscopic Binary Mass Determination using Relativity

High-precision radial-velocity techniques, which enabled the detection of extrasolar planets are now sensitive to relativistic effects in the data of spectroscopic binary stars (SBs). We show how these effects can be used to derive the absolute masses of the components of eclipsing single-lined SBs and double-lined SBs from Doppler measurements alone. High-precision stellar spectroscopy can thus substantially increase the number of measured stellar masses, thereby improving the mass-radius and mass-luminosity calibrations.Comment: 10 pages, 1 figure, accepted for publication by the Astrophysical Journal Letter

On the existence of 0/1 polytopes with high semidefinite extension complexity

In Rothvo\ss{} it was shown that there exists a 0/1 polytope (a polytope whose vertices are in \{0,1\}^{n}) such that any higher-dimensional polytope projecting to it must have 2^{\Omega(n)} facets, i.e., its linear extension complexity is exponential. The question whether there exists a 0/1 polytope with high PSD extension complexity was left open. We answer this question in the affirmative by showing that there is a 0/1 polytope such that any spectrahedron projecting to it must be the intersection of a semidefinite cone of dimension~2^{\Omega(n)} and an affine space. Our proof relies on a new technique to rescale semidefinite factorizations

Stellar Dynamics of Extreme-Mass-Ratio Inspirals

Inspiral of compact stellar remnants into massive black holes (MBHs) is accompanied by the emission of gravitational waves at frequencies that are potentially detectable by space-based interferometers. Event rates computed from statistical (Fokker-Planck, Monte-Carlo) approaches span a wide range due to uncertaintities about the rate coefficients. Here we present results from direct integration of the post-Newtonian N-body equations of motion descrbing dense clusters of compact stars around Schwarzschild MBHs. These simulations embody an essentially exact (at the post-Newtonian level) treatment of the interplay between stellar dynamical relaxation, relativistic precession, and gravitational-wave energy loss. The rate of capture of stars by the MBH is found to be greatly reduced by relativistic precession, which limits the ability of torques from the stellar potential to change orbital angular momenta. Penetration of this "Schwarzschild barrier" does occasionally occur, resulting in capture of stars onto orbits that gradually inspiral due to gravitational wave emission; we discuss two mechanisms for barrier penetration and find evidence for both in the simulations. We derive an approximate formula for the capture rate, which predicts that captures would be strongly disfavored from orbits with semi-major axes below a certain value; this prediction, as well as the predicted rate, are verified in the N-body integrations. We discuss the implications of our results for the detection of extreme-mass-ratio inspirals from galactic nuclei with a range of physical properties.Comment: 28 pages, 16 figures. Version 2 is significantly revised to reflect new insights into J and Q effects, to be published late

Kepler423b: a half-Jupiter mass planet transiting a very old solar-like star

We report the spectroscopic confirmation of the Kepler object of interest KOI-183.01 (Kepler-423b), a half-Jupiter mass planet transiting an old solar-like star every 2.7 days. Our analysis is the first to combine the full Kepler photometry (quarters 1-17) with high-precision radial velocity measurements taken with the FIES spectrograph at the Nordic Optical Telescope. We simultaneously modelled the photometric and spectroscopic data-sets using Bayesian approach coupled with Markov chain Monte Carlo sampling. We found that the Kepler pre-search data conditioned (PDC) light curve of KOI-183 exhibits quarter-to-quarter systematic variations of the transit depth, with a peak-to-peak amplitude of about 4.3 % and seasonal trends reoccurring every four quarters. We attributed these systematics to an incorrect assessment of the quarterly variation of the crowding metric. The host star KOI-183 is a G4 dwarf with $M_\star=0.85\pm0.04$ M_\rm{Sun}, $R_\star=0.95\pm0.04$ R_\rm{Sun}, $T_\mathrm{eff}=5560\pm80$ K, $[M/H]=-0.10\pm0.05$ dex, and with an age of $11\pm2$ Gyr. The planet KOI-183b has a mass of $M_\mathrm{p}=0.595\pm0.081$ M$_\mathrm{Jup}$ and a radius of $R_\mathrm{p}=1.192\pm0.052$ R$_\mathrm{Jup}$, yielding a planetary bulk density of $\rho_\mathrm{p}=0.459\pm0.083$ g/cm$^{3}$. The radius of KOI-183b is consistent with both theoretical models for irradiated coreless giant planets and expectations based on empirical laws. The inclination of the stellar spin axis suggests that the system is aligned along the line of sight. We detected a tentative secondary eclipse of the planet at a 2-$\sigma$ confidence level ($\Delta F_{\mathrm{ec}}=14.2\pm6.6$ ppm) and found that the orbit might have a small non-zero eccentricity of $e=0.019^{+0.028}_{-0.014}$. With a Bond albedo of $A_\mathrm{B}=0.037\pm0.019$, KOI-183b is one of the gas-giant planets with the lowest albedo known so far.Comment: 13 pages, 13 figures, 5 tables. Accepted for publication in A&A. Planet designation changed from KOI-183b to Kepler-423