Periodic Orbits and Escapes in Dynamical Systems

We study the periodic orbits and the escapes in two different dynamical systems, namely (1) a classical system of two coupled oscillators, and (2) the Manko-Novikov metric (1992) which is a perturbation of the Kerr metric (a general relativistic system). We find their simple periodic orbits, their characteristics and their stability. Then we find their ordered and chaotic domains. As the energy goes beyond the escape energy, most chaotic orbits escape. In the first case we consider escapes to infinity, while in the second case we emphasize escapes to the central "bumpy" black hole. When the energy reaches its escape value a particular family of periodic orbits reaches an infinite period and then the family disappears (the orbit escapes). As this family approaches termination it undergoes an infinity of equal period and double period bifurcations at transitions from stability to instability and vice versa. The bifurcating families continue to exist beyond the escape energy. We study the forms of the phase space for various energies, and the statistics of the chaotic and escaping orbits. The proportion of these orbits increases abruptly as the energy goes beyond the escape energy.Comment: 28 pages, 23 figures, accepted in "Celestial Mechanics and Dynamical Astronomy

Large-scale environments of binary AGB stars probed by Herschel. II: Two companions interacting with the wind of pi1 Gruis

Context. The Mass loss of Evolved StarS (MESS) sample observed with PACS on board the Herschel Space Observatory revealed that several asymptotic giant branch (AGB) stars are surrounded by an asymmetric circumstellar envelope (CSE) whose morphology is most likely caused by the interaction with a stellar companion. The evolution of AGB stars in binary systems plays a crucial role in understanding the formation of asymmetries in planetary nebul{\ae} (PNe), but at present, only a handful of cases are known where the interaction of a companion with the stellar AGB wind is observed. Aims. We probe the environment of the very evolved AGB star $\pi^1$ Gruis on large and small scales to identify the triggers of the observed asymmetries. Methods. Observations made with Herschel/PACS at 70 $\mu$m and 160 $\mu$m picture the large-scale environment of $\pi^1$ Gru. The close surroundings of the star are probed by interferometric observations from the VLTI/AMBER archive. An analysis of the proper motion data of Hipparcos and Tycho-2 together with the Hipparcos Intermediate Astrometric Data help identify the possible cause for the observed asymmetry. Results. The Herschel/PACS images of $\pi^1$ Gru show an elliptical CSE whose properties agree with those derived from a CO map published in the literature. In addition, an arc east of the star is visible at a distance of $38^{\prime\prime}$ from the primary. This arc is most likely part of an Archimedean spiral caused by an already known G0V companion that is orbiting the primary at a projected distance of 460 au with a period of more than 6200 yr. However, the presence of the elliptical CSE, proper motion variations, and geometric modelling of the VLTI/AMBER observations point towards a third component in the system, with an orbital period shorter than 10 yr, orbiting much closer to the primary than the G0V star.Comment: 13 pages, 11 figures, accepted for publication in Astronomy & Astrophysic

Interplay Between Chaotic and Regular Motion in a Time-Dependent Barred Galaxy Model

We study the distinction and quantification of chaotic and regular motion in a time-dependent Hamiltonian barred galaxy model. Recently, a strong correlation was found between the strength of the bar and the presence of chaotic motion in this system, as models with relatively strong bars were shown to exhibit stronger chaotic behavior compared to those having a weaker bar component. Here, we attempt to further explore this connection by studying the interplay between chaotic and regular behavior of star orbits when the parameters of the model evolve in time. This happens for example when one introduces linear time dependence in the mass parameters of the model to mimic, in some general sense, the effect of self-consistent interactions of the actual N-body problem. We thus observe, in this simple time-dependent model also, that the increase of the bar's mass leads to an increase of the system's chaoticity. We propose a new way of using the Generalized Alignment Index (GALI) method as a reliable criterion to estimate the relative fraction of chaotic vs. regular orbits in such time-dependent potentials, which proves to be much more efficient than the computation of Lyapunov exponents. In particular, GALI is able to capture subtle changes in the nature of an orbit (or ensemble of orbits) even for relatively small time intervals, which makes it ideal for detecting dynamical transitions in time-dependent systems.Comment: 21 pages, 9 figures (minor typos fixed) to appear in J. Phys. A: Math. Theo

Chaos and the continuum limit in the gravitational N-body problem II. Nonintegrable potentials

This paper continues a numerical investigation of orbits evolved in `frozen,' time-independent N-body realisations of smooth time-independent density distributions corresponding to both integrable and nonintegrable potentials, allowing for N as large as 300,000. The principal focus is on distinguishing between, and quantifying, the effects of graininess on initial conditions corresponding, in the continuum limit, to regular and chaotic orbits. Ordinary Lyapunov exponents X do not provide a useful diagnostic for distinguishing between regular and chaotic behaviour. Frozen-N orbits corresponding in the continuum limit to both regular and chaotic characteristics have large positive X even though, for large N, the `regular' frozen-N orbits closely resemble regular characteristics in the smooth potential. Viewed macroscopically both `regular' and `chaotic' frozen-N orbits diverge as a power law in time from smooth orbits with the same initial condition. There is, however, an important difference between `regular' and `chaotic' frozen-N orbits: For regular orbits, the time scale associated with this divergence t_G ~ N^{1/2}t_D, with t_D a characteristic dynamical time; for chaotic orbits t_G ~ (ln N) t_D. At least for N>1000 or so, clear distinctions exist between phase mixing of initially localised orbit ensembles which, in the continuum limit, exhibit regular versus chaotic behaviour. For both regular and chaotic ensembles, finite-N effects are well mimicked, both qualitatively and quantitatively, by energy-conserving white noise with amplitude ~ 1/N. This suggests strongly that earlier investigations of the effects of low amplitude noise on phase space transport in smooth potentials are directly relevant to real physical systems.Comment: 20 pages, including 21 FIGURES, uses RevTeX macro

Determination of masses of the central black holes in NGC524 and NGC2549 using Laser Guide Star Adaptive Optics

[abridged] We present observations of NGC524 and NGC2549 with LGS AO obtained at GEMINI North telescope using the NIFS IFU in the K band. The purpose of these observations, together with previously obtained observations with the SAURON IFU, is to determine the masses (Mbh) of the supermassive black holes (SMBH). The targeted galaxies were chosen to have central light profiles showing a core (NGC524) and a cusp (NGC2549), to probe the feasibility of using the galaxy centre as the NGS required for LGS AO. We employ an innovative `open loop' technique. The data have spatial resolution of 0.23" and 0.17" FWHM, showing that high quality LGS AO observations of these objects are possible. We construct axisymmetric three-integral dynamical models which are constrained with both the NIFS and SAURON data. The best fitting models yield Mbh=(8.3 +2.7 -1.3) x 10^8 Msun for NGC524 and Mbh=(1.4 +0.2 -1.3) x 10^7 Msun for NGC2549 (all errors are at the 3 sigma CL). We demonstrate that the wide-field SAURON data play a crucial role in the M/L determination increasing the accuracy of M/L by a factor of at least 5, and constraining the upper limits on Mbh. The NIFS data are crucial in constraining the lower limits of Mbh and in combination with the large scale data reducing the uncertainty by a factor of 2 or more. We find that the orbital structure of NGC524 shows significant tangential anisotropy, while at larger radii both galaxies are consistent with having almost perfectly oblate velocity ellipsoids. Tangential anisotropy in NGC524 coincides with the size of SMBH sphere of influence and the core region in the light profile. We test the accuracy to which Mbh can be measured using seeings obtained from typical LGS AO observations, and conclude that for a typical conditions and Mbh the expected uncertainty is of the order of 50%.Comment: 19 pages, 14 figure

<i>Gaia</i> Data Release 1. Summary of the astrometric, photometric, and survey properties

Context. At about 1000 days after the launch of Gaia we present the first Gaia data release, Gaia DR1, consisting of astrometry and photometry for over 1 billion sources brighter than magnitude 20.7. Aims. A summary of Gaia DR1 is presented along with illustrations of the scientific quality of the data, followed by a discussion of the limitations due to the preliminary nature of this release. Methods. The raw data collected by Gaia during the first 14 months of the mission have been processed by the Gaia Data Processing and Analysis Consortium (DPAC) and turned into an astrometric and photometric catalogue. Results. Gaia DR1 consists of three components: a primary astrometric data set which contains the positions, parallaxes, and mean proper motions for about 2 million of the brightest stars in common with the HIPPARCOS and Tycho-2 catalogues – a realisation of the Tycho-Gaia Astrometric Solution (TGAS) – and a secondary astrometric data set containing the positions for an additional 1.1 billion sources. The second component is the photometric data set, consisting of mean G-band magnitudes for all sources. The G-band light curves and the characteristics of ∼3000 Cepheid and RR-Lyrae stars, observed at high cadence around the south ecliptic pole, form the third component. For the primary astrometric data set the typical uncertainty is about 0.3 mas for the positions and parallaxes, and about 1 mas yr−1 for the proper motions. A systematic component of ∼0.3 mas should be added to the parallax uncertainties. For the subset of ∼94 000 HIPPARCOS stars in the primary data set, the proper motions are much more precise at about 0.06 mas yr−1. For the secondary astrometric data set, the typical uncertainty of the positions is ∼10 mas. The median uncertainties on the mean G-band magnitudes range from the mmag level to ∼0.03 mag over the magnitude range 5 to 20.7. Conclusions. Gaia DR1 is an important milestone ahead of the next Gaia data release, which will feature five-parameter astrometry for all sources. Extensive validation shows that Gaia DR1 represents a major advance in the mapping of the heavens and the availability of basic stellar data that underpin observational astrophysics. Nevertheless, the very preliminary nature of this first Gaia data release does lead to a number of important limitations to the data quality which should be carefully considered before drawing conclusions from the data

The effectiveness of e-&amp; mHealth interventions to promote physical activity and healthy diets in developing countries: a systematic review

Background: Promoting physical activity and healthy eating is important to combat the unprecedented rise in NCDs in many developing countries. Using modern information-and communication technologies to deliver physical activity and diet interventions is particularly promising considering the increased proliferation of such technologies in many developing countries. The objective of this systematic review is to investigate the effectiveness of e-&amp; mHealth interventions to promote physical activity and healthy diets in developing countries.Methods: Major databases and grey literature sources were searched to retrieve studies that quantitatively examined the effectiveness of e-&amp; mHealth interventions on physical activity and diet outcomes in developing countries. Additional studies were retrieved through citation alerts and scientific social media allowing study inclusion until August 2016. The CONSORT checklist was used to assess the risk of bias of the included studies.Results: A total of 15 studies conducted in 13 developing countries in Europe, Africa, Latin-and South America and Asia were included in the review. The majority of studies enrolled adults who were healthy or at risk of diabetes or hypertension. The average intervention length was 6.4 months, and text messages and the Internet were the most frequently used intervention delivery channels. Risk of bias across the studies was moderate (55.7 % of the criteria fulfilled). Eleven studies reported significant positive effects of an e-&amp; mHealth intervention on physical activity and/or diet behaviour. Respectively, 50 % and 70 % of the interventions were effective in promoting physical activity and healthy diets.Conclusions: The majority of studies demonstrated that e-&amp; mHealth interventions were effective in promoting physical activity and healthy diets in developing countries. Future interventions should use more rigorous study designs, investigate the cost-effectiveness and reach of interventions, and focus on emerging technologies, such as smart phone apps and wearable activity trackers.Trial registration: The review protocol can be retrieved from the PROSPERO database (Registration ID: CRD42015029240)

MELCHIORS: The Mercator Library of High Resolution Stellar Spectroscopy

Aims. Over the past decades, libraries of stellar spectra have been used in a large variety of science cases, including as sources of reference spectra for a given object or a given spectral type. Despite the existence of large libraries and the increasing number of projects of large-scale spectral surveys, there is to date only one very high-resolution spectral library offering spectra from a few hundred objects from the southern hemisphere (UVES-POP). We aim to extend the sample, offering a finer coverage of effective temperatures and surface gravity with a uniform collection of spectra obtained in the northern hemisphere.Methods. Between 2010 and 2020, we acquired several thousand echelle spectra of bright stars with the Mercator-HERMES spectrograph located in the Roque de Los Muchachos Observatory in La Palma, whose pipeline offers high-quality data reduction products. We have also developed methods to correct for the instrumental response in order to approach the true shape of the spectral continuum. Additionally, we have devised a normalisation process to provide a homogeneous normalisation of the full spectral range for most of the objects.Results. We present a new spectral library consisting of 3256 spectra covering 2043 stars. It combines high signal-to-noise and high spectral resolution over the entire range of effective temperatures and luminosity classes. The spectra are presented in four versions: raw, corrected from the instrumental response, with and without correction from the atmospheric molecular absorption, and normalised (including the telluric correction)

The connecting health and technology study: A 6-month randomized controlled trial to improve nutrition behaviours using a mobile food record and text messaging support in young adults

© 2016 Kerr et al. Background: Early adulthood represents the transition to independent living which is a period when changes in diet and body weight are likely to occur. This presents an ideal time for health interventions to reduce the effect of health problems and risk factors for chronic disease in later life. As young adults are high users of mobile devices, interventions that use this technology may improve engagement. The Connecting Health and Technology study aimed to evaluate the effectiveness of tailored dietary feedback and weekly text messaging to improve dietary intake of fruit, vegetables and junk food over 6 months among a population-based sample of men and women (aged 18-30 years). Methods: A three-arm, parallel, randomized control trial was conducted. After baseline assessments, participants were randomized to one of three groups: A) dietary feedback and weekly text messages, B) dietary feedback only or C) control group. Dietary intake was assessed using a mobile food record App (mFR) where participants captured images of foods and beverages consumed over 4-days at baseline and post-intervention. The primary outcomes were changes in serves of fruits, vegetables, energy-dense nutrient-poor (EDNP) foods and sugar-sweetened beverages (SSB). The intervention effects were assessed using linear mixed effect models for change in food group serves. Results: Young adults (n = 247) were randomized to group A (n = 82), group B (n = 83), or group C (n = 82). Overall, no changes in food group serves for either intervention groups were observed. An unanticipated outcome was a mean weight reduction of 1.7 kg (P = .02) among the dietary feedback only. Men who received dietary feedback only, significantly reduced their serves of EDNP foods by a mean of 1.4 serves/day (P = .02). Women who received dietary feedback only significantly reduced their intake of SSB (P = .04) by an average of 0.2 serves/day compared with controls. Conclusions: Tailored dietary feedback only resulted in a decrease in EDNP foods in men and SSB in women, together with a reduction in body weight. Using a mobile food record for dietary assessment and tailored feedback has great potential for future health promotion interventions targeting diet and weight in young adults. Trial Registration: Australian Clinical Trials Registry Registration number: ACTRN12612000250831

Gaia Data Release 2 Mapping the Milky Way disc kinematics

Context. The second Gaia data release (Gaia DR2) contains high-precision positions, parallaxes, and proper motions for 1.3 billion sources as well as line-of-sight velocities for 7.2 million stars brighter than G(RVS) = 12 mag. Both samples provide a full sky coverage. Aims. To illustrate the potential of Gaia DR2, we provide a first look at the kinematics of the Milky Way disc, within a radius of several kiloparsecs around the Sun. Methods. We benefit for the first time from a sample of 6.4 million F-G-K stars with full 6D phase-space coordinates, precise parallaxes (sigma((omega) over bar)/(omega) over bar Results. Gaia DR2 allows us to draw 3D maps of the Galactocentric median velocities and velocity dispersions with unprecedented accuracy, precision, and spatial resolution. The maps show the complexity and richness of the velocity field of the galactic disc. We observe streaming motions in all the components of the velocities as well as patterns in the velocity dispersions. For example, we confirm the previously reported negative and positive galactocentric radial velocity gradients in the inner and outer disc, respectively. Here, we see them as part of a non-axisymmetric kinematic oscillation, and we map its azimuthal and vertical behaviour. We also witness a new global arrangement of stars in the velocity plane of the solar neighbourhood and in distant regions in which stars are organised in thin substructures with the shape of circular arches that are oriented approximately along the horizontal direction in the U - V plane. Moreover, in distant regions, we see variations in the velocity substructures more clearly than ever before, in particular, variations in the velocity of the Hercules stream. Conclusions. Gaia DR2 provides the largest existing full 6D phase-space coordinates catalogue. It also vastly increases the number of available distances and transverse velocities with respect to Gaia DR1. Gaia DR2 offers a great wealth of information on the Milky Way and reveals clear non-axisymmetric kinematic signatures within the Galactic disc, for instance. It is now up to the astronomical community to explore its full potential.Peer reviewe