F. de Felice

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

Gaia Data Release 1 (Gaia 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. 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. 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 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 e.g. 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. The Hipparcos reference frame is found to rotate with respect to the Gaia DR1 frame at a rate of 0.24 mas/yr. 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 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 astrometric solution

Context. 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. Aims. We describe the input data, models, and processing used for the astrometric content of Gaia DR2, and the validation of these resultsperformed within the astrometry task. Methods. 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. These data were calculated in two steps. First, the satellite attitude and the astrometric calibration parameters of the CCDs were obtained in an astrometric global iterative solution for 16 million selected sources, using about 1% of the input data. This primary solution was tied to the extragalactic International Celestial Reference System (ICRS) by means of quasars. The resulting attitude and calibration were then used to calculate the astrometric parameters of all the sources. Special validation solutions were used to characterise the random and systematic errors in parallax and proper motion. Results. 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 masat G = 20 mag. In the proper motion components the corresponding uncertainties are 0.05, 0.2, and 1.2 mas yr−1, 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−1. 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−1 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.

A General Relativistic Model of Light Propagation in the Gravitational Field of the Solar System: The Static Case

Modern astrometry is based on angular measurements at the microarcsecond level. At this accuracy, a fully general relativistic treatment of the data reduction is required. This paper concludes a series of articles dedicated to the problem of relativistic light propagation, presenting the final, microarcsecond version of a relativistic astrometric model that enables us to trace back a light path to its source through the nonstationary gravitational field of the moving bodies in the solar system. The previous model is used as test bed for numerical comparisons with the present one. We also test different versions of the computer code implementing the model at different levels of complexity to start exploring the best trade-off between numerical efficiency and the microarcsecond accuracy that needs to be reached.

Time Machine and Geodesic Motion in Kerr Metric

The existence of nontrivial causality violation is a peculiar property of the space-time around a naked singularity. In the case of Kerr metric witha > m we have found that for a particular class of geodesies that could in principle violate causality, the conditions for causality violation are never satisfied.

Globally noncausal space-times. II: Naked singularities and curvature conditions

In this paper we prove that if there is a naked singularity, then there will be some null geodesic, reaching ℐ+ from the singularity, which does not satisfy the strong curvature condition regardless of whether causality is violated or not. Assuming that a naked singularity is a strong curvature singularity only sufficiently far to the future, we prove that strong causality is violated arbitrarily close to ℐ+.

Causality violation in the Kerr metric

The conjecture that geodesics in the Kerr matric witha > m cannot violate causality in the sense of meeting a turning point before making up for lost time, is found to be untrue for null geodesics.

Vortical null orbits, repulsive barriers, energy confinement in Kerr metric

We give the complete analytical description of the null trajectories in the field of a Kerr naked singularity. Two peculiar phenomena are described: the existence of repulsive barbiers in ther < 0 world and the existence of null circular bound orbits which surround the singularity in “shells.” They distribute around the surface atr = m, which is the position of the horizon in the extreme black-hole case; this suggests that a naked singularity “remembers” the position of the last horizon.

The angular momentum behavior in the dissipationless collapse of triaxial systems

We present N-body simulations of the collapse of six triaxial systems having the angular momentum aligned with one of their principal axes. Two different initial density distributions are chosen. The final relaxed states of the simulations show (1) a net outflow of angular momentum from the inner regions to the outer halo, consistent with the loss expected during the formation of elliptical galaxies; (2) a general misalignment of the average spin of the internal mass fractions with respect to that of the total system. Finally, some considerations are given concerning the occurrence of the necessary condition for the formation of a black hole at the center of these systems

On the pre-horizon regime in the Kerr metric

Sufficiently close to an event horizon an increase in the angular velocity induces more gravitational attraction than centrifugal repulsion on a circularly orbiting particle. At the same time the local compass of inertia tends to precess forward with respect to the sense of the orbital rotation, rather than backwards. A spacetime which gives rise to these effects is termed to be in a pre-horizon regime. The authors investigate the occurrence of this regime in the Kerr metric.

General relativistic satellite astrometry - II. Modeling parallax and proper motion

The non-perturbative general relativistic approach to global astrometry introduced by de Felice et al. ([CITE]) is here extended to account for the star motions on the Schwarzschild celestial sphere. A new expression of the observables, i.e. angular distances among stars, is provided, which takes into account the effects of parallax and proper motions. This dynamical model is then tested on an end-to-end simulation of the global astrometry mission GAIA. The results confirm the findings of our earlier work, which applied to the case of a static (angular coordinates only) sphere. In particular, measurements of large arcs among stars (each measurement good to ~