Non-integrability of density perturbations in the FRW universe

We investigate the evolution equation of linear density perturbations in the Friedmann-Robertson-Walker universe with matter, radiation and the cosmological constant. The concept of solvability by quadratures is defined and used to prove that there are no "closed form" solutions except for the known Chernin, Heath, Meszaros and simple degenerate ones. The analysis is performed applying Kovacic's algorithm. The possibility of the existence of other, more general solutions involving special functions is also investigated.Comment: 13 pages. The latest version with added references, and a relevant new paragraph in section I

Effective algorithm of analysis of integrability via the Ziglin's method

In this paper we continue the description of the possibilities to use numerical simulations for mathematically rigorous computer assisted analysis of integrability of dynamical systems. We sketch some of the algebraic methods of studying the integrability and present a constructive algorithm issued from the Ziglin's approach. We provide some examples of successful applications of the constructed algorithm to physical systems.Comment: a figure added, version accepted to JDC

Bound and unbound substructures in Galaxy-scale Dark Matter haloes

We analyse the coarse-grained phase-space structure of the six Galaxy-scale dark matter haloes of the Aquarius Project using a state-of-the-art 6D substructure finder. Within r_50, we find that about 35% of the mass is in identifiable substructures, predominantly tidal streams, but including about 14% in self-bound subhaloes. The slope of the differential substructure mass function is close to -2, which should be compared to around -1.9 for the population of self-bound subhaloes. Near r_50 about 60% of the mass is in substructures, with about 30% in self-bound subhaloes. The inner 35 kpc of the highest resolution simulation has only 0.5% of its mass in self-bound subhaloes, but 3.3% in detected substructure, again primarily tidal streams. The densest tidal streams near the solar position have a 3-D mass density about 1% of the local mean, and populate the high velocity tail of the velocity distribution.Comment: Submitted to MNRAS on 12/10/2010, 11 pages, 10 figure

No variations in transit times for Qatar-1 b

The transiting hot Jupiter planet Qatar-1 b was presented to exhibit variations in transit times that could be of perturbative nature. A hot Jupiter with a planetary companion on a nearby orbit would constitute an unprecedented planetary configuration, important for theories of formation and evolution of planetary systems. We performed a photometric follow-up campaign to confirm or refute transit timing variations. We extend the baseline of transit observations by acquiring 18 new transit light curves acquired with 0.6-2.0 m telescopes. These photometric time series, together with data available in the literature, were analyzed in a homogenous way to derive reliable transit parameters and their uncertainties. We show that the dataset of transit times is consistent with a linear ephemeris leaving no hint for any periodic variations with a range of 1 min. We find no compelling evidence for the existence of a close-in planetary companion to Qatar-1 b. This finding is in line with a paradigm that hot Jupiters are not components of compact multi-planetary systems. Based on dynamical simulations, we place tighter constraints on a mass of any fictitious nearby planet in the system. Furthermore, new transit light curves allowed us to redetermine system parameters with the precision better than that reported in previous studies. Our values generally agree with previous determinations.Comment: Accepted for publication in A&

Supernova Remnant in a Stratified Medium: Explicit, Analytical Approximations for Adiabatic Expansion and Radiative Cooling

We propose simple, explicit, analytical approximations for the kinematics of an adiabatic blast wave propagating in an exponentially stratified ambient medium, and for the onset of radiative cooling, which ends the adiabatic era. Our method, based on the Kompaneets implicit solution and the Kahn approximation for the radiative cooling coefficient, gives straightforward estimates for the size, expansion velocity, and progression of cooling times over the surface, when applied to supernova remnants (SNRs). The remnant shape is remarkably close to spherical for moderate density gradients, but even a small gradient in ambient density causes the cooling time to vary substantially over the remnant's surface, so that for a considerable period there will be a cold dense expanding shell covering only a part of the remnant. Our approximation provides an effective tool for identifying the approximate parameters when planning 2-dimensional numerical models of SNRs, the example of W44 being given in a subsequent paper.Comment: ApJ accepted, 11 pages, 2 figures embedded, aas style with ecmatex.sty and lscape.sty package

On the HU Aquarii planetary system hypothesis

In this work, we investigate the eclipse timing of the polar binary HU Aquarii that has been observed for almost two decades. Recently, Qian et al. attributed large (O-C) deviations between the eclipse ephemeris and observations to a compact system of two massive jovian companions. We improve the Keplerian, kinematic model of the Light Travel Time (LTT) effect and re-analyse the whole currently available data set. We add almost 60 new, yet unpublished, mostly precision light curves obtained using the time high-resolution photo-polarimeter OPTIMA, as well as photometric observations performed at the MONET/N, PIRATE and TCS telescopes. We determine new mid--egress times with a mean uncertainty at the level of 1 second or better. We claim that because the observations that currently exist in the literature are non-homogeneous with respect to spectral windows (ultraviolet, X-ray, visual, polarimetric mode) and the reported mid--egress measurements errors, they may introduce systematics that affect orbital fits. Indeed, we find that the published data, when taken literally, cannot be explained by any unique solution. Many qualitatively different and best-fit 2-planet configurations, including self-consistent, Newtonian N-body solutions may be able to explain the data. However, using high resolution, precision OPTIMA light curves, we find that the (O-C) deviations are best explained by the presence of a single circumbinary companion orbiting at a distance of ~4.5 AU with a small eccentricity and having ~7 Jupiter-masses. This object could be the next circumbinary planet detected from the ground, similar to the announced companions around close binaries HW Vir, NN Ser, UZ For, DP Leo or SZ Her, and planets of this type around Kepler-16, Kepler-34 and Kepler-35.Comment: 20 pages, 18 figures, accepted to Monthly Notices of the Royal Astronomical Society (MNRAS

Departure from the constant-period ephemeris for the transiting exoplanet WASP-12 b

Most hot Jupiters are expected to spiral in towards their host stars due to transfering of the angular momentum of the orbital motion to the stellar spin. Their orbits can also precess due to planet-star interactions. Calculations show that both effects could be detected for the very-hot exoplanet WASP-12 b using the method of precise transit timing over a timespan of the order of 10 yr. We acquired new precise light curves for 29 transits of WASP-12 b, spannning 4 observing seasons from November 2012 to February 2016. New mid-transit times, together with literature ones, were used to refine the transit ephemeris and analyse the timing residuals. We find that the transit times of WASP-12 b do not follow a linear ephemeris with a 5 sigma confidence level. They may be approximated with a quadratic ephemeris that gives a rate of change in the orbital period of -2.56 +/- 0.40 x 10^{-2} s/yr. The tidal quality parameter of the host star was found to be equal to 2.5 x 10^5 that is comparable to theoretical predictions for Sun-like stars. We also consider a model, in which the observed timing residuals are interpreted as a result of the apsidal precession. We find, however, that this model is statistically less probable than the orbital decay.Comment: Accepted for publication in A&A Letter

A Quadratic Programming Approach to Quasi-Static Whole-Body Manipulation

This paper introduces a local motion planning method for robotic systems with manipulating limbs, moving bases (legged or wheeled), and stance stability constraints arising from the presence of gravity. We formulate the problem of selecting local motions as a linearly constrained quadratic program (QP), that can be solved efficiently. The solution to this QP is a tuple of locally optimal joint velocities. By using these velocities to step towards a goal, both a path and an inverse-kinematic solution to the goal are obtained. This formulation can be used directly for real-time control, or as a local motion planner to connect waypoints. This method is particularly useful for high-degree-of-freedom mobile robotic systems, as the QP solution scales well with the number of joints. We also show how a number of practically important geometric constraints (collision avoidance, mechanism self-collision avoidance, gaze direction, etc.) can be readily incorporated into either the constraint or objective parts of the formulation. Additionally, motion of the base, a particular joint, or a particular link can be encouraged/discouraged as desired. We summarize the important kinematic variables of the formulation, including the stance Jacobian, the reach Jacobian, and a center of mass Jacobian. The method is easily extended to provide sparse solutions, where the fewest number of joints are moved, by iteration using Tibshirani’s method to accommodate an l_1 regularizer. The approach is validated and demonstrated on SURROGATE, a mobile robot with a TALON base, a 7 DOF serial-revolute torso, and two 7 DOF modular arms developed at JPL/Caltech