On bare masses in time-symmetric initial-value solutions for two black holes

The Brill-Lindquist time-symmetric initial-value solution for two uncharged black holes is rederived using the Hamiltonian constraint equation with Dirac delta distributions as a source for the binary black-hole field. The bare masses of the Brill-Lindquist black holes are introduced in a way which is applied, after straightforward modification, to the Misner-Linquist binary black-hole solution.Comment: LaTeX, 4 page

The binary black-hole problem at the third post-Newtonian approximation in the orbital motion: Static part

Post-Newtonian expansions of the Brill-Lindquist and Misner-Lindquist solutions of the time-symmetric two-black-hole initial value problem are derived. The static Hamiltonians related to the expanded solutions, after identifying the bare masses in both solutions, are found to differ from each other at the third post-Newtonian approximation. By shifting the position variables of the black holes the post-Newtonian expansions of the three metrics can be made to coincide up to the fifth post-Newtonian order resulting in identical static Hamiltonians up the third post-Newtonian approximation. The calculations shed light on previously performed binary point-mass calculations at the third post-Newtonian approximation.Comment: LaTeX, 9 pages, to be submitted to Physical Review

Modelling the Galactic Bar Using Red Clump Giants

The color-magnitude diagrams of $\sim 7 \times 10^5$ stars obtained for 12 fields across the Galactic bulge with the OGLE project reveal a well-defined population of bulge red clump giants. We find that the distributions of the apparent magnitudes of the red clump stars are systematically fainter when moving towards lower galactic $l$ fields. The most plausible explanation of this distinct trend is that the Galactic bulge is a bar, whose nearest end lies at positive galactic longitude. We model this Galactic bar by fitting for all fields the observed luminosity functions in the red clump region of the color-magnitude diagram. We find that almost regardless of the analytical function used to describe the 3-D stars distribution of the Galactic bar, the resulting models have the major axis inclined to the line of sight by $20-30\deg$, with axis ratios corresponding to $x_0:y_0:z_0=3.5:1.5:1$. This puts a strong constraint on the possible range of the Galactic bar models. Gravitational microlensing can provide us with additional constrains on the structure of the Galactic bar.Comment: submitted to the New Astronomy, 27 pages, 11 figures; also available at ftp://www.astro.princeton.edu/stanek/Barmodel and through WWW at http://www.astro.princeton.edu/~library/prep.htm

Dynamical modelling of the elliptical galaxy NGC 2974

In this paper we analyse the relations between a previously described oblate Jaffe model for an ellipsoidal galaxy and the observed quantities for NGC 2974, and obtain the length and velocity scales for a relevant elliptical galaxy model. We then derive the finite total mass of the model from these scales, and finally find a good fit of an isotropic oblate Jaffe model by using the Gauss-Hermite fit parameters and the observed ellipticity of the galaxy NGC 2974. The model is also used to predict the total luminous mass of NGC 2974, assuming that the influence of dark matter in this galaxy on the image, ellipticity and Gauss-Hermite fit parameters of this galaxy is negligible within the central region, of radius $0.5R_{\rm e}.$Comment: 7 figure

Contextual cropping and scaling of TV productions

This is the author's accepted manuscript. The final publication is available at Springer via http://dx.doi.org/10.1007/s11042-011-0804-3. Copyright @ Springer Science+Business Media, LLC 2011.In this paper, an application is presented which automatically adapts SDTV (Standard Definition Television) sports productions to smaller displays through intelligent cropping and scaling. It crops regions of interest of sports productions based on a smart combination of production metadata and systematic video analysis methods. This approach allows a context-based composition of cropped images. It provides a differentiation between the original SD version of the production and the processed one adapted to the requirements for mobile TV. The system has been comprehensively evaluated by comparing the outcome of the proposed method with manually and statically cropped versions, as well as with non-cropped versions. Envisaged is the integration of the tool in post-production and live workflows

Transition from antibunching to bunching for two dipole-interacting atoms

It is known that there is a transition from photon antibunching to bunching in the resonance fluorescence of a driven system of two two-level atoms with dipole-dipole interaction when the atomic distance decreases and the other parameters are kept fixed. We give a simple explanation for the underlying mechanism which in principle can also be applied to other systems. PACS numbers 42.50.Ar, 42.50FxComment: Submitted to Phys. Rev. A; 15 pages Latex + 4 figure

Eccentric-disk models for the nucleus of M31

We construct dynamical models of the ``double'' nucleus of M31 in which the nucleus consists of an eccentric disk of stars orbiting a central black hole. The principal approximation in these models is that the disk stars travel in a Kepler potential, i.e., we neglect the mass of the disk relative to the black hole. We consider both ``aligned'' models, in which the eccentric disk lies in the plane of the large-scale M31 disk, and ``non-aligned'' models, in which the orientation of the eccentric disk is fitted to the data. Both types of model can reproduce the double structure and overall morphology seen in Hubble Space Telescope photometry. In comparison with the best available ground-based spectroscopy, the models reproduce the asymmetric rotation curve, the peak height of the dispersion profile, and the qualitative behavior of the Gauss-Hermite coefficients h_3 and h_4. Aligned models fail to reproduce the observation that the surface brightness at P1 is higher than at P2 and yield significantly poorer fits to the kinematics; thus we favor non-aligned models. Eccentric-disk models fitted to ground-based spectroscopy are used to predict the kinematics observed at much higher resolution by the STIS instrument on the Hubble Space Telescope (Bender et al. 2003), and we find generally satisfactory agreement.Comment: 45 pages, 18 figures, accepted by Ap

Dark matter and non-Newtonian gravity from General Relativity coupled to a fluid of strings

An exact solution of Einstein's field equations for a point mass surrounded by a static, spherically symmetric fluid of strings is presented. The solution is singular at the origin. Near the string cloud limit there is a $1/r$ correction to Newton's force law. It is noted that at large distances and small accelerations, this law coincides with the phenomenological force law invented by Milgrom in order to explain the flat rotation curves of galaxies without introducing dark matter. When interpreted in the context of a cosmological model with a string fluid, the new solution naturally explains why the critical acceleration of Milgrom is of the same order of magnitude as the Hubble parameter.Comment: 12 pages, REVTeX, no figure