Estimating a distance by inverting a parallax is only valid in the absence of noise. As most stars in the Gaia catalogue will have non-negligible fractional parallax errors, we must treat distance estimation as a constrained inference problem. Here we investigate the performance of various priors for estimating distances, using a simulated Gaia catalogue of one billion stars. We use three minimalist, isotropic priors, as well an anisotropic prior derived from the observability of stars in a Milky Way model. The two priors that assume a uniform distribution of stars--either in distance or in space density---give poor results: The root mean square fractional distance error, f_RMS, grows far in excess of 100% once the fractional parallax error, f_true, is larger than 0.1. A prior assuming an exponentially decreasing space density with increasing distance performs well once its single scale length parameter has been set to an appropriate value: f_RMS is roughly equal to f_true for f_true < 0.4, yet does not increase further as f_true increases up to to 1.0. The Milky Way prior performs well except towards the Galactic centre, due to a mismatch with the (simulated) data. Such mismatches will be inevitable (and remain unknown) in real applications, and can produce large errors. We therefore suggest to adopt the simpler exponentially decreasing space density prior, which is also less time-consuming to compute. Including Gaia photometry improves the distance estimation significantly for both the Milky Way and exponentially decreasing space density prior, yet doing so requires additional assumptions about the physical nature of stars.
We compare the parallaxes of stars from VLBI astrometry in the literature to those in the Gaia DR2 catalog. Our full sample contains young stellar objects, evolved AGB stars, pulsars and other radio stars. Excluding AGB stars, which show significant discrepancies between Gaia and VLBI parallaxes, and stars in binary systems, we obtain an average, systematic, parallax offset of $-75 \pm 29~μ$as for Gaia DR2, consistent with their estimate of a parallax zero-point between $-100$ and 0 $μ$as.
CONTEXT. Gaia EDR3 has produced parallaxes for 1.468x10^9 sources but there are calibration issues that require corrections to the published values and uncertainties. AIMS. We want to characterize the behavior of the uncertainties of the Gaia EDR3 parallaxes. We also aim to provide a procedure for the calculation of distances to stars and stellar clusters. METHODS. We reanalyze some of the data in the calibration papers for QSO and LMC parallaxes and combine those results with measurements for six bright GCs. We calculate the angular covariance of EDR3 parallaxes at small separations based on …
Context. The first release of astrometric data from Gaia will contain the mean stellar positions and magnitudes from the first year of observations, and proper motions from the combination of Gaia data with Hipparcos prior information (HTPM). Aims. We study the potential of using the positions from the Tycho-2 Catalogue as additional information for a joint solution with early Gaia data. We call this the Tycho-Gaia astrometric solution (TGAS). Methods. We adapt Gaia's Astrometric Global Iterative Solution (AGIS) to incorporate Tycho information, and use simulated Gaia observations to demonstra…
We reprise the analysis of Stassun & Torres (2016), comparing the parallaxes of the eclipsing binaries reported in that paper to the parallaxes newly reported in the Gaia second data release (DR2). We find evidence for a systematic offset of $-82 \pm 33$ micro-arcseconds, in the sense of the Gaia parallaxes being too small, for brightnesses $(G \lesssim 12)$ and for distances (0.03--3 kpc) in the ranges spanned by the eclipsing binary sample. The offset does not appear to depend strongly on distance within this range, though there is marginal evidence that the offset increases (becomes slightl…
For the vast majority of stars in the second Gaia data release, reliable distances cannot be obtained by inverting the parallax. A correct inference procedure must instead be used to account for the nonlinearity of the transformation and the asymmetry of the resulting probability distribution. Here we infer distances to essentially all 1.33 billion stars with parallaxes published in the second \gaia\ data release. This is done using a weak distance prior that varies smoothly as a function of Galactic longitude and latitude according to a Galaxy model. The irreducible uncertainty in the distanc…
We infer distances and their asymmetric uncertainties for two million stars using the parallaxes published in the Gaia DR1 (GDR1) catalogue. We do this with two distance priors: A minimalist, isotropic prior assuming an exponentially decreasing space density with increasing distance, and an anisotropic prior derived from the observability of stars in a Milky Way model. We validate our results by comparing our distance estimates for 105 Cepheids which have more precise, independently estimated distances. For this sample we find that the Milky Way prior performs better (the RMS of the scaled res…
Pulsating stars, such as Cepheids, Miras, and RR Lyrae stars, are important distance indicators and calibrators of the "cosmic distance ladder", and yet their period-luminosity-metallicity (PLZ) relations are still constrained using simple statistical methods that cannot take full advantage of available data. To enable optimal usage of data provided by the Gaia mission, we present a probabilistic approach that simultaneously constrains parameters of PLZ relations and uncertainties in Gaia parallax measurements. We demonstrate this approach by constraining PLZ relations of type $ab$ RR Lyrae st…
With contemporary infrared spectroscopic surveys like APOGEE, red-giant stars can be observed to distances and extinctions at which Gaia parallaxes are not highly informative. Yet the combination of effective temperature, surface gravity, composition, and age - all accessible through spectroscopy - determines a giant's luminosity. Therefore spectroscopy plus photometry should enable precise spectrophotometric distance estimates. Here we use the APOGEE-Gaia-2MASS-WISE overlap to train a data-driven model to predict parallaxes for red-giant branch stars with $0<\log g\leq2.2$ (more luminous than…
Context. The Gaia satellite will measure highly accurate absolute parallaxes of hundreds of millions of stars by comparing the parallactic displacements in the two fields of view of the optical instrument. The requirements on the stability of the 'basic angle' between the two fields are correspondingly strict, and possible variations (on the microarcsec level) are therefore monitored by an on-board metrology system. Nevertheless, since even very small periodic variations of the basic angle might cause a global offset of the measured parallaxes, it is important to find independent verification …
We test the parallaxes reported in the Gaia first data release using the sample of eclipsing binaries with accurate, empirical distances from Stassun \& Torres (2016). We find an average offset of $-$0.25$\pm$0.05 mas in the sense of the Gaia parallaxes being too small (i.e., the distances too long). The offset does not depend strongly on obvious parameters such as color or brightness. However, we find with high confidence that the offset may depend on ecliptic latitude: the mean offset is $-$0.38$\pm$0.06 mas in the ecliptic north and $-$0.05$\pm$0.09 mas in the ecliptic south. The ecliptic l…
CONTEXT. 2MASS is the reference survey in the NIR part of the spectrum given its whole-sky coverage, large dynamic range, and proven calibration uniformity. However, previous studies disagree in the value of the zero points (ZPs) for its three bands JHK at the hundredth of a magnitude level. The disagreement should become more noticeable now that Gaia provides whole-sky optical photometry calibrated below that level. AIMS. We want to establish the value of the 2MASS ZPs based on NICMOS/HST spectrophotometry of the CALSPEC standard stars and test it with the help of Gaia DR2 parallaxes. METHODS…
The second Gaia data release (GDR2) provides precise five-parameter astrometric data (positions, proper motions and parallaxes) for an unprecedented amount of sources (more than $1.3$ billion, mostly stars). The use of this wealth of astrometric data comes with a specific challenge: how does one properly infer from these data the astrophysical parameters of interest? The main - but not only - focus of this paper is the issue of the estimation of distances from parallaxes, possibly combined with other information. We start with a critical review of the methods traditionally used to obtain dista…
Relativistic models of light propagation adopted for high-precision astrometry are based on the parametrised post-Newtonian formalism, which provides a framework for examining the effects of a hypothetical violation of general relativity on astrometric data. Astrometric observations are strongly affected by the post-Newtonian parameter $γ$ describing the strength of gravitational light deflection. We study both analytically and numerically how a deviation in the PPN parameter $γ$ from unity, which is the value predicted by general relativity, affects the parallax estimations in Gaia-like astro…
Context. Although the Gaia catalogue on its own is a very powerful tool, it is the combination of this high-accuracy archive with other archives that will truly open up amazing possibilities for astronomical research. The advanced interoperation of archives is based on cross-matching, leaving the user with the feeling of working with one single data archive. The data retrieval should work not only across data archives but also across wavelength domains. The first step for a seamless access to the data is the computation of the cross-match between Gaia and external surveys. Aims. We describe th…
In this contribution I provide a brief summary of the contents of Gaia DR1. This is followed by a discussion of studies in the literature that attempt to characterize the quality of the Tycho-Gaia Astrometric Solution parallaxes in Gaia DR1, and I point out a misconception about the handling of the known systematic errors in the Gaia DR1 parallaxes. I highlight some of the more unexpected uses of the Gaia DR1 data and close with a look ahead at the next Gaia data releases, with Gaia DR2 coming up in April 2018.
A new reduction of the astrometric data as produced by the Hipparcos mission has been published, claiming that the accuracies for nearly all stars brighter than magnitude $\mathrm{Hp}=8$ are improved, by up to a factor 4, compared to the original catalogue. As correlations between the underlying abscissa residuals have also been reduced by more than an order of magnitude to an insignificant level, our ability to determine reliable parallaxes and proper motions for open clusters should be improved. The new Hipparcos astrometric catalogue is used to derive mean parallax and proper motion estimat…
The second $Gaia$ Data Release (DR2) contains astrometric and photometric data for more than 1.6 billion objects with mean $Gaia$ $G$ magnitude $<$20.7, including many Young Stellar Objects (YSOs) in different evolutionary stages. In order to explore the YSO population of the Milky Way, we combined the $Gaia$ DR2 database with WISE and Planck measurements and made an all-sky probabilistic catalogue of YSOs using machine learning techniques, such as Support Vector Machines, Random Forests, or Neural Networks. Our input catalogue contains 103 million objects from the DR2xAllWISE cross-match tabl…
CONTEXT. The Gaia EDR3 parallaxes constitute the most detailed and accurate dataset that can be currently used to determine stellar distances in the solar neighborhood. Nevertheless, there is still room for improvement in their calibration and systematic effects can be further reduced in some circumstances. AIMS. The aim of this paper is to determine an improved Gaia EDR3 parallax bias as a function of magnitude, color, and ecliptic latitude using a single method applied to stars in open clusters, globular clusters, the LMC, and the SMC. METHODS. I study the behavior of the residuals or differ…
We present a sub-arcsecond cross-match of Gaia DR2 against the INT Photometric H-alpha Survey of the Northern Galactic Plane Data Release 2 (IPHAS DR2) and the Kepler-INT Survey (KIS). The resulting value-added catalogues (VACs) provide additional precise photometry to the Gaia photometry (r, i and H-alpha for IPHAS, with additional U and g for KIS). In building the catalogue, proper motions given in \gaia\ DR2 are wound back to match the epochs of IPHAS DR2, thus ensuring high proper motion objects are appropriately cross-matched. The catalogues contain 7,927,224 and 791,071 sources for IPHAS…
Aims: An effort has been undertaken to simulate the expected Gaia Catalogue, including the effect of observational errors. A statistical analysis of this simulated Gaia data is performed in order to better understand what can be obtained from the Gaia astrometric mission. This catalogue is used in order to investigate the potential yield in astrometric, photometric and spectroscopic information, and the extent and effect of observational errors on the true Gaia Catalogue. This article is a follow-up to Robin et. al. (2012), where the expected Gaia Catalogue content was reviewed but without the…
We present fits to the broadband photometric spectral energy distributions (SEDs) of 158 eclipsing binaries (EBs) in the Tycho-2 catalog. These EBs were selected because they have highly precise stellar radii, effective temperatures, and in many cases metallicities previously determined in the literature, and thus have bolometric luminosities that are typically good to $\lesssim$ 10%. In most cases the available broadband photometry spans a wavelength range 0.4-10 $μ$m, and in many cases spans 0.15-22 $μ$m. The resulting SED fits, which have only extinction as a free parameter, provide a virtu…
The Perseus Arm is the closest Galactic spiral arm from the Sun, offering an excellent opportunity to study in detail its stellar population. However, its distance has been controversial with discrepancies by a factor of two. Kinematic distances are in the range 3.9-4.2 kpc as compared to 1.9-2.3 kpc from spectrophotometric and trigonometric parallaxes, reinforcing previous claims that this arm exhibits peculiar velocities. We used the astrometric information of a sample of 31 OB stars from the star-forming W3 Complex to identify another 37 W3 members and to derive its distance from their Gaia…
Aims. We aim at creating a Bayesian model to infer the coefficients of PL or PLZ relations that propagates uncertainties in the observables in a rigorous and well founded way. Methods. We propose a directed acyclic graph to encode the conditional probabilities of the inference model that will allow us to infer probability distributions for the PL and PL(Z) relations. We evaluate the model with several semi-synthetic data sets and apply it to a sample of 200 fundamental mode and first overtone mode RR Lyrae stars for which Gaia DR1 parallaxes and literature Ks-band mean magnitudes are available…
In this work, we use $13$ microlensing candidates with dark lenses from OGLE III catalogue \cite{2016MNRAS.458.3012W} and cross-match them with the GAIA catalogue. We identify the microlensing source stars in the GAIA catalogue by comparing the coordinate and the magnitude of stars and using the proper motion and the parallax parameters of the source stars. Combining with the microlensing light curves as well as the microlensing parallax effect, we determine the mass and the distance of lenses from Earth. We conclude that the lens for this set of microlensing events for the massive lenses are …
We present a comparison of Gaia Data Release 1 (DR1) parallaxes with photometric parallaxes for a sample of 212 Galactic Cepheids at a median distance of 2~kpc, and explore their implications on the distance scale and the local value of the Hubble constant H_0. The Cepheid distances are estimated from a recent calibration of the near-infrared Period-Luminosity P-L relation. The comparison is carried out in parallax space, where the DR1 parallax errors, with a median value of half the median parallax, are expected to be well-behaved. With the exception of one outlier, the DR1 parallaxes are in …
We compared positions of the Gaia first data release (DR1) secondary data set at its faint limit with CCD positions of stars in 20 fields observed with the VLT/FORS2 camera. The FORS2 position uncertainties are smaller than one milli-arcsecond (mas) and allowed us to perform an independent verification of the DR1 astrometric precision. In the fields that we observed with FORS2, we projected the Gaia DR1 positions into the CCD plane, performed a polynomial fit between the two sets of matching stars, and carried out statistical analyses of the residuals in positions. The residual RMS roughly mat…
We derive Bayesian distances for all stars in the RV sample of Gaia DR2, and use the statistical method of Schoenrich, Binney & Asplund(2012) to validate the distances and test the Gaia parallaxes. In contrast to other methods, which rely on special sources, our method directly tests the distances to all stars in our sample. We find clear evidence for a near-linear trend of distance bias f with distance s, proving a parallax offset delta p. On average, we find delta p = -0.054 mas (parallaxes in Gaia DR2 need to be increased) when accounting for the parallax uncertainty under-estimate in the G…
Astrometric surveys such as Gaia and LSST will measure parallaxes for hundreds of millions of stars. Yet they will not measure a single distance. Rather, a distance must be estimated from a parallax. In this didactic article, I show that doing this is not trivial once the fractional parallax error is larger than about 20%, which will be the case for about 80% of stars in the Gaia catalogue. Estimating distances is an inference problem in which the use of prior assumptions is unavoidable. I investigate the properties and performance of various priors and examine their implications. A supposed u…
The second Gaia data release (DR2) is scheduled for April 2018. While Gaia DR1 had increased the number of stars with parallaxes by a factor 20 with respect to the Hipparcos catalogue, Gaia DR2 will bring another factor 500 increase, with parallaxes (and proper motions) for more than a billion stars. In addition, Gaia DR2 will deliver improved accuracy and precision for the astrometric and photometric data, $G$, $G_\mathrm{BP}$, $G_\mathrm{RP}$ magnitudes, radial velocities, identification and characterisation of variable stars and asteroids as well as stellar parameters for stars down to $G =…
Gaia DR2 provides a unique all-sky catalogue of 550'737 variable stars, of which 151'761 are long-period variable (LPV) candidates with G variability amplitudes larger than 0.2 mag (5-95% quantile range). About one-fifth of the LPV candidates are Mira candidates, the majority of the rest are semi-regular variable candidates. For each source, G, BP , and RP photometric time-series are published, together with some LPV-specific attributes for the subset of 89'617 candidates with periods in G longer than 60 days. We describe this first Gaia catalogue of LPV candidates, and present various validat…
We present estimates of distances, ages and masses for over 6 million stars. These estimates are derived from the combination of spectrophotometric data and Gaia eDR3 parallaxes. For that, we used the previously published Unified tool to estimate Distances, Ages, and Masses (UniDAM).
We have studied the zero-point offset of Gaia early Data Release 3 (EDR3) parallaxes based on a sample of 0.3 million giant stars built from the LAMOST data with distance accuracy better than 8.5\%. The official parallax zero-point corrections largely reduce the global offset in the Gaia EDR3 parallaxes: the global parallax offsets are $-$27.9 $μ$as and $-$26.5 $μ$as (before correction) and $+$2.6 $μ$as and $+$2.9 $μ$as (after correction) for the five- and six-parameter solutions, respectively. The bias of the raw parallax measurements is significantly dependent on the $G$ magnitudes, spectral…
Parallaxes measured by the Gaia mission have huge significance for astronomy, but parallaxes in Gaia DR2 are known to have systematic errors that depend on the source position and other quantities. We use the abundant information in faint Milky Way stars, along with the GOG simulation of the Gaia catalog, to probe the spatial dependence of Gaia DR2 parallax systematic errors in an empirical way. The parallax signal, concentrated in thick disk turnoff stars with magnitude G ~ 17, is sufficient to construct maps of the parallax systematic error over the majority of the sky. These maps show a loc…
Although the Gaia catalogue on its own will be a very powerful tool, it is the combination of this highly accurate archive with other archives that will truly open up amazing possibilities for astronomical research. The advanced interoperation of archives is based on cross-matching, leaving the user with the feeling of working with one single data archive. The data retrieval should work not only across data archives, but also across wavelength domains. The first step for seamless data access is the computation of the cross-match between Gaia and external surveys. The matching of astronomical c…
Interpreting and modelling astronomical catalogues requires an understanding of the catalogues' completeness or selection function: objects of what properties had a chance to end up in the catalogue. Here we set out to empirically quantify the completeness of the overall Gaia DR3 catalogue. This task is not straightforward because Gaia is the all-sky optical survey with the highest angular resolution to date and no consistent ``ground truth'' exists to allow direct comparisons. However, well-characterised deeper imaging enables an empirical assessment of Gaia's $G$-band completeness across par…
Context. This study has been developed in the framework of the computational simulations executed for the preparation of the ESA Gaia astrometric mission. Aims. We focus on describing the objects and characteristics that Gaia will potentially observe without taking into consideration instrumental effects (detection efficiency, observing errors). Methods. The theoretical Universe Model prepared for the Gaia simulation has been statistically analyzed at a given time. Ingredients of the model are described, giving most attention to the stellar content, the double and multiple stars, and variabili…
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…
We extend the SDSS Stripe 82 Standard Stars Catalog with post-2007 SDSS imaging data. This improved version lists averaged SDSS ugriz photometry for nearly a million stars brighter than r~22 mag. With 2-3x more measurements per star, random errors are 1.4-1.7x smaller than in the original catalog, and about 3x smaller than for individual SDSS runs. Random errors in the new catalog are ~< 0.01 mag for stars brighter than 20.0, 21.0, 21.0, 20.5, and 19.0 mag in u, g, r, i, and z-bands, respectively. We achieve this error threshold by using the Gaia Early Data Release 3 (EDR3) Gmag photometry to …
We have developed a general statistical procedure for analysis of 2D and 3D finite patterns, which is applied to the data from recently released Gaia-ESA catalogue DR2. The 2D analysis clearly confirms our former results on the presence of binaries in the former DR1 catalogue. Our main objective is the statistical 3D analysis of DR2. For this, it is essential that the DR2 catalogue includes parallaxes and data on the proper motion. The analysis allows us to determine for each pair of stars the probability that it is the binary star. This probability is represented by the function \b{eta}(Δ) de…
We have established a mixture model approach to derive the parallax of the Milky Way globular clusters. It avoids the problem of cluster membership determination and provides a completely independent astrometrical solution by purely using the parallax data. This method is validated with simulated clusters of \cite{2017MNRAS.467..412P}. We have resolved 120 real globular clusters by the mixture model using parallaxes of the second data release of \gaia. They construct the largest direct parallax sample up to now. In comparing with other direct parallax results based on cluster members, includin…
Aims. The catalog of Stars With ExoplanETs (SWEET-Cat) was originally introduced in 2013. Since then many more exoplanets have been confirmed, increasing significantly the number of host stars listed there. A crucial step toward a comprehensive understanding of these new worlds is the precise and homogeneous characterization of their host stars. Better spectroscopic stellar parameters along with new results from Gaia eDR3 provide updated and precise parameters for the discovered planets. A new version of the catalog, whose homogeneity in the derivation of the parameters is key to unraveling st…
Recent works have made strong efforts to produce standardised photometry in RGB bands. For this purpose, we carefully defined the transmissivity curves of RGB bands and defined a set of standard sources using the photometric information present in Gaia EDR3. This work aims not only to significantly increase the number and accuracy of RGB standards but also to provide, for the first time, reliable uncertainty estimates using the BP and RP spectrophotometry published in Gaia DR3 instead of their integrated photometry to predict RGB photometry. Furthermore, this method allows including calibrated…
Gaia Early Data Release 3 (Gaia EDR3) gives trigonometric parallaxes for nearly 1.5 billion sources. Inspection of the EDR3 data for sources identified as quasars reveals that their parallaxes are biased, that is systematically offset from the expected distribution around zero, by a few tens of microarcsec. We attempt to map the main dependencies of the parallax bias in EDR3. In principle this could provide a recipe for correcting the EDR3 parallaxes. For faint sources the quasars provide the most direct way to estimate parallax bias. In order to extend this to brighter sources and a broader r…
We employ differential astrometric methods to establish a small field reference frame stable at the micro-arcsecond ($μ$as) level on short timescales using high-cadence simulated observations taken by Gaia in February 2017 of a bright star close to the limb of Jupiter, as part of the relativistic experiment on Jupiter's quadrupole. We achieve sub$μ$as-level precision along scan through a suitable transformation of the field angles into a small-field tangent plane and a least-squares fit over several overlapping frames for estimating the plate and geometric calibration parameters with tens of r…
TOPCAT, and its command line counterpart STILTS, are powerful tools for working with large source catalogues. ESA's Gaia mission, most recently with its second data release, is producing source catalogues of unprecedented quality for more than a billion sources. This paper presents some examples of how TOPCAT and STILTS can be used for analysis of Gaia data.
Determination of absolute parallaxes by means of a scanning astrometric satellite such as Hipparcos or Gaia relies on the short-term stability of the so-called basic angle between the two viewing directions. Uncalibrated variations of the basic angle may produce systematic errors in the computed parallaxes. We examine the coupling between a global parallax shift and specific variations of the basic angle, namely those related to the satellite attitude with respect to the Sun. The changes in observables produced by small perturbations of the basic angle, attitude, and parallaxes are calculated …
755 new CCD observations during the years 2014-2016 have been reduced to derive the precise positions of Triton, the first satellite of Neptune. The observations were made by the 1 m telescope at Yunnan Observatory over fifteen nights. The positions of Triton are measured with respect to the stars in Gaia DR1 star catalogue. The theoretical position of Triton was retrieved from the Jet Propulsion Laboratory (JPL) ephemeris nep081xl, while the position of Neptune was obtained from the JPL ephemeris DE431mx. Our results show that the mean O-Cs (observed minus computed) are 0.042 and -0.006 arcse…
