89 research outputs found
A universal tool for determining the time delay and the frequency shift of light: Synge's world function
In almost all of the studies devoted to the time delay and the frequency
shift of light, the calculations are based on the integration of the null
geodesic equations. However, the above-mentioned effects can be calculated
without integrating the geodesic equations if one is able to determine the
bifunction giving half the squared geodesic distance between
two points and (this bifunction may be called Synge's world
function). In this lecture, is determined up to the order
within the framework of the PPN formalism. The case of a stationary
gravitational field generated by an isolated, slowly rotating axisymmetric body
is studied in detail. The calculation of the time delay and the frequency shift
is carried out up to the order . Explicit formulae are obtained for the
contributions of the mass, of the quadrupole moment and of the internal angular
momentum when the only post-Newtonian parameters different from zero are
and . It is shown that the frequency shift induced by the mass
quadrupole moment of the Earth at the order will amount to
in spatial experiments like the ESA's Atomic Clock Ensemble in Space mission.
Other contributions are briefly discussed.Comment: 18 pages, To appear in: "Lasers, Clocks and Drag-Free control:
Exploration of Relativistic Gravity in Space", Springer Series on
Astrophysics and Space Science Library, vol 349, p 15
Recommended from our members
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 3: The Galaxy in your preferred colours: Synthetic photometry from Gaia low-resolution spectra
Gaia Data Release 3 provides novel flux-calibrated low-resolution spectrophotometry for '220 million sources in the wavelength range 330 nm ≤ λ ≤ 1050 nm (XP spectra). Synthetic photometry directly tied to a flux in physical units can be obtained from these spectra for any passband fully enclosed in this wavelength range. We describe how synthetic photometry can be obtained from XP spectra, illustrating the performance that can be achieved under a range of different conditions - for example passband width and wavelength range - as well as the limits and the problems affecting it. Existing top-quality photometry can be reproduced within a few per cent over a wide range of magnitudes and colour, for wide and medium bands, and with up to millimag accuracy when synthetic photometry is standardised with respect to these external sources. Some examples of potential scientific application are presented, including the detection of multiple populations in globular clusters, the estimation of metallicity extended to the very metal-poor regime, and the classification of white dwarfs. A catalogue providing standardised photometry for 2.2×108sources in several wide bands of widely used photometric systems is provided (Gaia Synthetic Photometry Catalogue; GSPC) as well as a catalogue of '105 white dwarfs with DA/non-DA classification obtained with a Random Forest algorithm (Gaia Synthetic Photometry Catalogue for White Dwarfs; GSPC-WD)
Gaia Data Release 1: Open cluster astrometry: Performance, limitations, and future prospects
Context. The first Gaia Data Release contains the Tycho-Gaia Astrometric
Solution (TGAS). This is a subset of about 2 million stars for which, besides
the position and photometry, the proper motion and parallax are calculated
using Hipparcos and Tycho-2 positions in 1991.25 as prior information. Aims. We
investigate the scientific potential and limitations of the TGAS component by
means of the astrometric data for open clusters. Methods. Mean cluster parallax
and proper motion values are derived taking into account the error correlations
within the astrometric solutions for individual stars, an estimate of the
internal velocity dispersion in the cluster, and, where relevant, the effects
of the depth of the cluster along the line of sight. Internal consistency of
the TGAS data is assessed. Results. Values given for standard uncertainties are
still inaccurate and may lead to unrealistic unit-weight standard deviations of
least squares solutions for cluster parameters. Reconstructed mean cluster
parallax and proper motion values are generally in very good agreement with
earlier Hipparcos-based determination, although the Gaia mean parallax for the
Pleiades is a significant exception. We have no current explanation for that
discrepancy. Most clusters are observed to extend to nearly 15 pc from the
cluster centre, and it will be up to future Gaia releases to establish whether
those potential cluster-member stars are still dynamically bound to the
clusters. Conclusions. The Gaia DR1 provides the means to examine open clusters
far beyond their more easily visible cores, and can provide membership
assessments based on proper motions and parallaxes. A combined HR diagram shows
the same features as observed before using the Hipparcos data, with clearly
increased luminosities for older A and F dwarfs
Gaia Focused Product Release: Asteroid orbital solution: Properties and assessment
CONTEXT:
We report the exploitation of a sample of Solar System observations based on data from the third Gaia Data Release (Gaia DR3) of nearly 157 000 asteroids. It extends the epoch astrometric solution over the time coverage planned for the Gaia DR4, which is not expected before the end of 2025. This data set covers more than one full orbital period for the vast majority of these asteroids. The orbital solutions are derived from the Gaia data alone over a relatively short arc compared to the observation history of many of these asteroids.
AIMS:
The work aims to produce orbital elements for a large set of asteroids based on 66 months of accurate astrometry provided by Gaia and to assess the accuracy of these orbital solutions with a comparison to the best available orbits derived from independent observations. A second validation is performed with accurate occultation timings.
METHODS:
We processed the raw astrometric measurements of Gaia to obtain astrometric positions of moving objects with 1D sub-mas accuracy at the bright end. For each asteroid that we matched to the data, an orbit fitting was attempted in the form of the best fit of the initial conditions at the median epoch. The force model included Newtonian and relativistic accelerations to derive the observation equations, which were solved with a linear least-squares fit.
RESULTS:
Orbits are provided in the form of state vectors in the International Celestial Reference Frame for 156 764 asteroids, including near-Earth objects, main-belt asteroids, and Trojans. For the asteroids with the best observations, the (formal) relative uncertainty σa/a is better than 10-10. Results are compared to orbits available from the Jet Propulsion Laboratory and MPC. Their orbits are based on much longer data arcs, but from positions of lower quality. The relative differences in semi-major axes have a mean of 5 × 10-10 and a scatter of 5 × 10-
Gaia Early Data Release 3: The celestial reference frame (Gaia-CRF3)
CONTEXT:
Gaia-CRF3 is the celestial reference frame for positions and proper motions in the third release of data from the Gaia mission, Gaia DR3 (and for the early third release, Gaia EDR3, which contains identical astrometric results). The reference frame is defined by the positions and proper motions at epoch 2016.0 for a specific set of extragalactic sources in the (E)DR3 catalogue.
AIMS:
We describe the construction of Gaia-CRF3 and its properties in terms of the distributions in magnitude, colour, and astrometric quality.
METHODS:
Compact extragalactic sources in Gaia DR3 were identified by positional cross-matching with 17 external catalogues of quasi-stellar objects (QSO) and active galactic nuclei (AGN), followed by astrometric filtering designed to remove stellar contaminants. Selecting a clean sample was favoured over including a higher number of extragalactic sources. For the final sample, the random and systematic errors in the proper motions are analysed, as well as the radio-optical offsets in position for sources in the third realisation of the International Celestial Reference Frame (ICRF3).
RESULTS:
Gaia-CRF3 comprises about 1.6 million QSO-like sources, of which 1.2 million have five-parameter astrometric solutions in Gaia DR3 and 0.4 million have six-parameter solutions. The sources span the magnitude range G = 13–21 with a peak density at 20.6 mag, at which the typical positional uncertainty is about 1 mas. The proper motions show systematic errors on the level of 12 µas yr–1 on angular scales greater than 15 deg. For the 3142 optical counterparts of ICRF3 sources in the S/X frequency bands, the median offset from the radio positions is about 0.5 mas, but it exceeds 4 mas in either coordinate for 127 sources. We outline the future of Gaia-CRF in the next Gaia data releases. Appendices give further details on the external catalogues used, how to extract information about the Gaia-CRF3 sources, potential (Galactic) confusion sources, and the estimation of the spin and orientation of an astrometric solution
Gaia Data Release 3: Exploring and mapping the diffuse interstellar band at 862 nm
Context. Diffuse interstellar bands (DIBs) are common interstellar absorption features in spectroscopic observations but their origins remain unclear. DIBs play an important role in the life cycle of the interstellar medium (ISM) and can also be used to trace Galactic structure. Aims. Here, we demonstrate the capacity of the Gaia-Radial Velocity Spectrometer (RVS) in Gaia DR3 to reveal the spatial distribution of the unknown molecular species responsible for the most prominent DIB at 862 nm in the RVS passband, exploring the Galactic ISM within a few kiloparsecs from the Sun. Methods. The DIBs are measured within the GSP-Spec module using a Gaussian profile fit for cool stars and a Gaussian process for hot stars. In addition to the equivalent widths and their uncertainties, Gaia DR3 provides their characteristic central wavelength, width, and quality flags. Results. We present an extensive sample of 476 117 individual DIB measurements obtained in a homogeneous way covering the entire sky. We compare spatial distributions of the DIB carrier with interstellar reddening and find evidence that DIB carriers are present in a local bubble around the Sun which contains nearly no dust. We characterised the DIB equivalent width with a local density of 0.19 ± 0.04 kpc1 and a scale height of 98.60 8.46+11.10 pc. The latter is smaller than the dust scale height, indicating that DIBs are more concentrated towards the Galactic plane. We determine the rest-frame wavelength with unprecedented precision (?0 = 8620.86 ± 0.019 in air) and reveal a remarkable correspondence between the DIB velocities and the CO gas velocities, suggesting that the 862 nm DIB carrier is related to macro-molecules. Conclusions. We demonstrate the unique capacity of Gaia to trace the spatial structure of the Galactic ISM using the 862 nm DIB
Gaia Focused Product Release: Radial velocity time series of long-period variables
Context: The third Gaia Data Release (DR3) provided photometric time series of more than 2 million long-period variable (LPV) candidates. Anticipating the publication of full radial-velocity data planned with Data Release 4, this Focused Product Release (FPR) provides radial-velocity time series for a selection of LPV candidates with high-quality observations.
//
Aims: We describe the production and content of the Gaia catalog of LPV radial-velocity time series, and the methods used to compute the variability parameters published as part of the Gaia FPR.
//
Methods: Starting from the DR3 catalog of LPV candidates, we applied several filters to construct a sample of sources with high-quality radial-velocity measurements. We modeled their radial-velocity and photometric time series to derive their periods and amplitudes, and further refined the sample by requiring compatibility between the radial-velocity period and at least one of the G, GBP, or GRP photometric periods.
//
Results: The catalog includes radial-velocity time series and variability parameters for 9614 sources in the magnitude range 6 ≲ G/mag ≲ 14, including a flagged top-quality subsample of 6093 stars whose radial-velocity periods are fully compatible with the values derived from the G, GBP, and GRP photometric time series. The radial-velocity time series contain a mean of 24 measurements per source taken unevenly over a duration of about three years. We identify the great majority of the sources (88%) as genuine LPV candidates, with about half of them showing a pulsation period and the other half displaying a long secondary period. The remaining 12% of the catalog consists of candidate ellipsoidal binaries. Quality checks against radial velocities available in the literature show excellent agreement. We provide some illustrative examples and cautionary remarks.
//
Conclusions: The publication of radial-velocity time series for almost ten thousand LPV candidates constitutes, by far, the largest such database available to date in the literature. The availability of simultaneous photometric measurements gives a unique added value to the Gaia catalog
Recommended from our members
Gaia Data Release 1: Summary of the astrometric, photometric, and survey properties
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. We summarize Gaia DR1 and provide
illustrations of the scientific quality of the data, followed by a discussion
of the limitations due to the preliminary nature of this release. Gaia DR1
consists of: 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 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 for the proper motions. A systematic component of ~0.3 mas
should be added to the parallax uncertainties. For the subset of ~94000
Hipparcos stars in the primary data set, the proper motions are much more
precise at about 0.06 mas/yr. 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. 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 Early Data Release 3: The Gaia Catalogue of Nearby Stars
Aims. We produce a clean and well-characterised catalogue of objects within 100 pc of the Sun from the Gaia Early Data Release 3. We characterise the catalogue through comparisons to the full data release, external catalogues, and simulations. We carry out a first analysis of the science that is possible with this sample to demonstrate its potential and best practices for its use.
Methods. Theselection of objects within 100 pc from the full catalogue used selected training sets, machine-learning procedures, astrometric quantities, and solution quality indicators to determine a probability that the astrometric solution is reliable. The training set construction exploited the astrometric data, quality flags, and external photometry. For all candidates we calculated distance posterior probability densities using Bayesian procedures and mock catalogues to define priors. Any object with reliable astrometry and a non-zero probability of being within 100 pc is included in the catalogue.
Results. We have produced a catalogue of 331 312 objects that we estimate contains at least 92% of stars of stellar type M9 within 100 pc of the Sun. We estimate that 9% of the stars in this catalogue probably lie outside 100 pc, but when the distance probability function is used, a correct treatment of this contamination is possible. We produced luminosity functions with a high signal-to-noise ratio for the main-sequence stars, giants, and white dwarfs. We examined in detail the Hyades cluster, the white dwarf population, and wide-binary systems and produced candidate lists for all three samples. We detected local manifestations of several streams, superclusters, and halo objects, in which we identified 12 members of Gaia Enceladus. We present the first direct parallaxes of five objects in multiple systems within 10 pc of the Sun.
Conclusions. We provide the community with a large, well-characterised catalogue of objects in the solar neighbourhood. This is a primary benchmark for measuring and understanding fundamental parameters and descriptive functions in astronomy.</jats:p
- …