8,198 research outputs found

    High-order half-integral conservative post-Newtonian coefficients in the redshift factor of black hole binaries

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    The post-Newtonian approximation is still the most widely used approach to obtaining explicit solutions in general relativity, especially for the relativistic two-body problem with arbitrary mass ratio. Within many of its applications, it is often required to use a regularization procedure. Though frequently misunderstood, the regularization is essential for waveform generation without reference to the internal structure of orbiting bodies. In recent years, direct comparison with the self-force approach, constructed specifically for highly relativistic particles in the extreme mass ratio limit, has enabled preliminary confirmation of the foundations of both computational methods, including their very independent regularization procedures, with high numerical precision. In this paper, we build upon earlier work to carry this comparison still further, by examining next-to-next-to-leading order contributions beyond the half integral 5.5PN conservative effect, which arise from terms to cubic and higher orders in the metric and its multipole moments, thus extending scrutiny of the post-Newtonian methods to one of the highest orders yet achieved. We do this by explicitly constructing tail-of-tail terms at 6.5PN and 7.5PN order, computing the redshift factor for compact binaries in the small mass ratio limit, and comparing directly with numerically and analytically computed terms in the self-force approach, obtained using solutions for metric perturbations in the Schwarzschild space-time, and a combination of exact series representations possibly with more typical PN expansions. While self-force results may be relativistic but with restricted mass ratio, our methods, valid primarily in the weak-field slowly-moving regime, are nevertheless in principle applicable for arbitrary mass ratios.Comment: 33 pages, no figure; minor correction

    Non-Parametric Direct Multi-step Estimation for Forecasting Economic Processes

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    We evaluate the asymptotic and finite-sample properties of direct multi-step estimation (DMS) for forecasting at several horizons. For forecast accuracy gains from DMS in finite samples, mis-specification and non-stationarity of the DGP are necessary, but when a model is well-specified, iterating the one-step ahead forecasts may not be asymptotically preferable. If a model is mis-specified for a non-stationary DGP, omitting either negative residual serial correlation or regime shifts, DMS can forecast more accurately. Monte Carlo simulations clarify the non-linear dependence of the estimation and forecast biases on the parameters of the DGP, and explain existing results.Adaptive estimation, multi-step estimation, dynamic forecasts, model mis-specification.

    Half-integral conservative post-Newtonian approximations in the redshift factor of black hole binaries

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    Recent perturbative self-force computations (Shah, Friedman & Whiting, submitted to Phys. Rev. {\bf D}, arXiv:1312.1952 [gr-qc]), both numerical and analytical, have determined that half-integral post-Newtonian terms arise in the conservative dynamics of black-hole binaries moving on exactly circular orbits. We look at the possible origin of these terms within the post-Newtonian approximation, find that they essentially originate from non-linear "tail-of-tail" integrals and show that, as demonstrated in the previous paper, their first occurrence is at the 5.5PN order. The post-Newtonian method we use is based on a multipolar-post-Minkowskian treatment of the field outside a general matter source, which is re-expanded in the near zone and extended inside the source thanks to a matching argument. Applying the formula obtained for generic sources to compact binaries, we obtain the redshift factor of circular black hole binaries (without spins) at 5.5PN order in the extreme mass ratio limit. Our result fully agrees with the determination of the 5.5PN coefficient by means of perturbative self-force computations reported in the previously cited paper.Comment: 18 pages, no figures, references updated and minor corrections include

    Exploring the reality of density substructures in the Palomar 5 stellar stream

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    We present an analysis of the presence of substructures in the stellar stream of the Palomar 5 globular cluster, as derived from Sloan Digital Sky Survey data. Using a matched filter technique, we recover the positions and sizes of overdensities reported in previous studies. To explore the reality of these structures, we also create an artificial model of the stream, in which we construct a realistic background on top of which we add a perfectly smooth stream structure, taking into account the effects of photometric completeness and interstellar extinction. We find that the smooth artificial stream then shows similarly-pronounced substructures as the real structure. Interestingly, our best-fit N-body simulation does display real projected density variations linked to stellar epicyclic motions, but these become less significant when taking into account the SDSS star-count constraints. The substructures found when applying our matched filter technique to the N-body particles converted into observable stars are thus mostly unrelated to these epicyclic motions. This analysis suggests that the majority of the previously-detected substructures along the tidal tail of Palomar 5 are artefacts of observational inhomogeneities.Comment: 10 pages, 9 figures, accepted for publication in MNRA

    Correlation functions of one-dimensional Bose-Fermi mixtures

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    We calculate the asymptotic behaviour of correlation functions as a function of the microscopic parameters for a Bose-Fermi mixture with repulsive interaction in one dimension. For two cases, namely polarized and unpolarized fermions the singularities of the momentum distribution functions are characterized as a function of the coupling constant and the relative density of bosons.Comment: RevTeX 4, 10 pages, 2 figure

    Stellar streams as gravitational experiments I. The case of Sagittarius

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    Tidal streams of disrupting dwarf galaxies orbiting around their host galaxy offer a unique way to constrain the shape of galactic gravitational potentials. Such streams can be used as leaning tower gravitational experiments on galactic scales. The most well motivated modification of gravity proposed as an alternative to dark matter on galactic scales is Milgromian dynamics (MOND), and we present here the first ever N-body simulations of the dynamical evolution of the disrupting Sagittarius dwarf galaxy in this framework. Using a realistic baryonic mass model for the Milky Way, we attempt to reproduce the present-day spatial and kinematic structure of the Sagittarius dwarf and its immense tidal stream that wraps around the Milky Way. With very little freedom on the original structure of the progenitor, constrained by the total luminosity of the Sagittarius structure and by the observed stellar mass-size relation for isolated dwarf galaxies, we find reasonable agreement between our simulations and observations of this system. The observed stellar velocities in the leading arm can be reproduced if we include a massive hot gas corona around the Milky Way that is flattened in the direction of the principal plane of its satellites. This is the first time that tidal dissolution in MOND has been tested rigorously at these mass and acceleration scales.Comment: 12 pages, 11 figures accepted for publication in A&A. The movie of Fig 6 can be watched at http://astro.unistra.fr/fileadmin/upload/DUN/observatoire/Images/GFThomas_MONDSgrstream_movie.mp
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