Aperiodic quantum XXZ chains: Renormalization-group results

We report a comprehensive investigation of the low-energy properties of antiferromagnetic quantum XXZ spin chains with aperiodic couplings. We use an adaptation of the Ma-Dasgupta-Hu renormalization-group method to obtain analytical and numerical results for the low-temperature thermodynamics and the ground-state correlations of chains with couplings following several two-letter aperiodic sequences, including the quasiperiodic Fibonacci and other precious-mean sequences, as well as sequences inducing strong geometrical fluctuations. For a given aperiodic sequence, we argue that in the easy-plane anisotropy regime, intermediate between the XX and Heisenberg limits, the general scaling form of the thermodynamic properties is essentially given by the exactly-known XX behavior, providing a classification of the effects of aperiodicity on XXZ chains. We also discuss the nature of the ground-state structures, and their comparison with the random-singlet phase, characteristic of random-bond chains.Comment: Minor corrections; published versio

A symmetry group of a Thue-Morse quasicrystal

We present a method of coding general self-similar structures. In particular, we construct a symmetry group of a one-dimensional Thue-Morse quasicrystal, i.e., of a nonperiodic ground state of a certain translation-invariant, exponentially decaying interaction.Comment: 6 pages, Late

The Large Quasar Reference Frame (LQRF) - an optical representation of the ICRS

The large number and all-sky distribution of quasars from different surveys, along with their presence in large, deep astrometric catalogs,enables the building of an optical materialization of the ICRS following its defining principles. Namely: that it is kinematically non-rotating with respect to the ensemble of distant extragalactic objects; aligned with the mean equator and dynamical equinox of J2000; and realized by a list of adopted coordinates of extragalatic sources. Starting from the updated and presumably complete LQAC list of QSOs, the initial optical positions of those quasars are found in the USNO B1.0 and GSC2.3 catalogs, and from the SDSS DR5. The initial positions are next placed onto UCAC2-based reference frames, following by an alignment with the ICRF, to which were added the most precise sources from the VLBA calibrator list and the VLA calibrator list - when reliable optical counterparts exist. Finally, the LQRF axes are inspected through spherical harmonics, contemplating to define right ascension, declination and magnitude terms. The LQRF contains J2000 referred equatorial coordinates for 100,165 quasars, well represented across the sky, from -83.5 to +88.5 degrees in declination, and with 10 arcmin being the average distance between adjacent elements. The global alignment with the ICRF is 1.5 mas, and the individual position accuracies are represented by a Poisson distribution that peaks at 139 mas in right ascension and 130 mas in declination. It is complemented by redshift and photometry information from the LQAC. The LQRF is designed to be an astrometric frame, but it is also the basis for the GAIA mission initial quasars' list, and can be used as a test bench for quasars' space distribution and luminosity function studies.Comment: 23 pages, 23 figures, 6 tables Accepted for publication by Astronomy & Astrophysics, on 25 May 200

Ground-based astrometry calibrated by Gaia DR1: new perspectives in asteroid orbit determination

Context. The Gaia Data Release 1 (GDR1) is a first, important step on the path of evolution of astrometric accuracy towards a much improved situation. Although asteroids are not present in GDR1, this intermediate release already impacts asteroid astrometry. Aims. Our goal is to investigate how the GDR1 can change the approach to a few typical problems, including the determination of orbits from short-arc astrometry, the exploitation of stellar occultations, and the impact risk assessment. Methods.We employ optimised asteroid orbit determination tools, and study the resulting orbit accuracy and post-fit residuals. For this goal, we use selected ground-based asteroid astrometry, and occultation events observed in the past. All measurements are calibrated by using GDR1 stars. Results. We show that, by adopting GDR1, very short measurement arcs can already provide interesting orbital solutions, capable of correctly identifying near-Earth asteroids (NEAs) and providing a much more accurate risk rating. We also demonstrate that occultations, previously used to derive asteroid size and shapes, now reach a new level of accuracy at which they can be fruitfully used to obtain astrometry at the level of accuracy of Gaia star positions

<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

Gaia Data Release 1. Astrometry: one billion positions, two million proper motions and parallaxes

Context. Gaia Data Release 1 (DR1) contains astrometric results for more than 1 billion stars brighter than magnitude 20.7 based on observations collected by the Gaia satellite during the first 14 months of its operational phase. Aims. We give a brief overview of the astrometric content of the data release and of the model assumptions, data processing, and validation of the results. Methods. For stars in common with the Hipparcos and Tycho-2 catalogues, complete astrometric single-star solutions are obtained by incorporating positional information from the earlier catalogues. For other stars only their positions are obtained, essentially by neglecting their proper motions and parallaxes. The results are validated by an analysis of the residuals, through special validation runs, and by comparison with external data. Results. For about two million of the brighter stars (down to magnitude ∼11.5) we obtain positions, parallaxes, and proper motions to Hipparcos-type precision or better. For these stars, systematic errors depending for example on position and colour are at a level of ±0.3 milliarcsecond (mas). For the remaining stars we obtain positions at epoch J2015.0 accurate to ∼10 mas. Positions and proper motions are given in a reference frame that is aligned with the International Celestial Reference Frame (ICRF) to better than 0.1 mas at epoch J2015.0, and non-rotating with respect to ICRF to within 0.03 mas yr−1 . The Hipparcos reference frame is found to rotate with respect to the Gaia DR1 frame at a rate of 0.24 mas yr−1 . Conclusions. Based on less than a quarter of the nominal mission length and on very provisional and incomplete calibrations, the quality and completeness of the astrometric data in Gaia DR1 are far from what is expected for the final mission products. The present results nevertheless represent a huge improvement in the available fundamental stellar data and practical definition of the optical reference frame

Gaia Data Release 2: The celestial reference frame (Gaia -CRF2)

Context. The second release of Gaia data (Gaia DR2) contains the astrometric parameters for more than half a million quasars. This set defines a kinematically non-rotating reference frame in the optical domain. A subset of these quasars have accurate VLBI positions that allow the axes of the reference frame to be aligned with the International Celestial Reference System (ICRF) radio frame. Aims. We describe the astrometric and photometric properties of the quasars that were selected to represent the celestial reference frame of Gaia DR2 (Gaia-CRF2), and to compare the optical and radio positions for sources with accurate VLBI positions. Methods. Descriptive statistics are used to characterise the overall properties of the quasar sample. Residual rotation and orientation errors and large-scale systematics are quantified by means of expansions in vector spherical harmonics. Positional differences are calculated relative to a prototype version of the forthcoming ICRF3. Results. Gaia-CRF2 consists of the positions of a sample of 556 869 sources in Gaia DR2, obtained from a positional cross-match with the ICRF3-prototype and AllWISE AGN catalogues. The sample constitutes a clean, dense, and homogeneous set of extragalactic point sources in the magnitude range G ≈ 16 to 21 mag with accurately known optical positions. The median positional uncertainty is 0.12 mas for G < 18 mag and 0.5 mas at G = mag. Large-scale systematics are estimated to be in the range 20 to 30 μas. The accuracy claims are supported by the parallaxes and proper motions of the quasars in Gaia DR2. The optical positions for a subset of 2820 sources in common with the ICRF3-prototype show very good overall agreement with the radio positions, but several tens of sources have significantly discrepant positions. Conclusions. Based on less than 40% of the data expected from the nominal Gaia mission, Gaia-CRF2 is the first realisation of a non-rotating global optical reference frame that meets the ICRS prescriptions, meaning that it is built only on extragalactic sources. Its accuracy matches the current radio frame of the ICRF, but the density of sources in all parts of the sky is much higher, except along the Galactic equator

Gaia Data Release 2: The astrometric solution

Gaia Data Release 2 (Gaia DR2) contains results for 1693 million sources in the magnitude range 3 to 21 based on observations collected by the European Space Agency Gaia satellite during the first 22 months of its operational phase. We describe the input data, models, and processing used for the astrometric content of Gaia DR2, and the validation of these results performed within the astrometry task. Some 320 billion centroid positions from the pre-processed astrometric CCD observations were used to estimate the five astrometric parameters (positions, parallaxes, and proper motions) for 1332 million sources, and approximate positions at the reference epoch J2015.5 for an additional 361 million mostly faint sources. Special validation solutions were used to characterise the random and systematic errors in parallax and proper motion. For the sources with five-parameter astrometric solutions, the median uncertainty in parallax and position at the reference epoch J2015.5 is about 0.04 mas for bright (G<14 mag) sources, 0.1 mas at G=17 mag, and 0.7 mas at G=20 mag. In the proper motion components the corresponding uncertainties are 0.05, 0.2, and 1.2 mas/yr, respectively. The optical reference frame defined by Gaia DR2 is aligned with ICRS and is non-rotating with respect to the quasars to within 0.15 mas/yr. From the quasars and validation solutions we estimate that systematics in the parallaxes depending on position, magnitude, and colour are generally below 0.1 mas, but the parallaxes are on the whole too small by about 0.03 mas. Significant spatial correlations of up to 0.04 mas in parallax and 0.07 mas/yr in proper motion are seen on small (<1 deg) and intermediate (20 deg) angular scales. Important statistics and information for the users of the Gaia DR2 astrometry are given in the appendices.Includes STFC