5 ASTROMETRIC PROPERTIES OF THE HIPPARCOS CATALOGUE F. Mignard Observatoire de la C^ote d'Azur, CERGA, UMR CNRS 6527, Avenue Cop ernic, F06130 Grasse, France ABSTRACT of stars formed a pre{de ned observing programme selected after a wide consultation of the astronomi- cal community ab out their scienti c interest and the The main statistical astrometric prop erties of the p ossibility to allo cate sucient observational time to Hipparcos Catalogue are reviewed. This includes the each selected star. The median magnitude of the Cat- overall gures useful to characterize the content of alogue is Hp =8:7 and half of the Catalogue lies in the Hipparcos Catalogue, meaningful for an average the interval 8 < Hp < 9:5. The exact distribution star of 9 mag. The formal errors of the ve astro- is shown in Figure 1, drawn with a logarithmic scale metric parameters are discussed in di erent co ordi- to show the small p opulations at the bright and faint nate systems as a function of the p osition on the sky ends. and of the magnitude of the stars. While there is almost no sizeable e ect with the ecliptic longitude, The Catalogue completeness dep ends on the Galactic the formal errors of the ecliptic longitude and paral- latitude and sp ectral typ e and varies from Hp =7:3 lax display large variations with the ecliptic latitude. near the galactic plane to Hp = 9 in the p olar re- For the other co ordinate systems the precision of all gions. The stellar density is ' 3 stars per square the astrometric parameters is a function of b oth p o- degree on the average, with lo cal densities as large sitional co ordinates. A more detailed investigation of as 5.5 stars per square degree in the galactic plane the distribution of the parallaxes and their exp ected and close to 2 stars p er square degree in many iso- errors as a function of the magnitude and of the lo- lated sp ots. Because of the selection of stars in the cation of the star on the sky is also carried out with Input Catalogue, a zone a few degrees wide, and in a particular emphasis on the relative error = . the direction of the galactic anti-centre l = 180 deg is ab ove the average sky density. Keywords: Astrometry, Hipparcos, Parallaxes. 100000 INTRODUCTION 1. 10000 1000 The ESA astrometric mission Hipparcos was the rst space exp eriment fully dedicated to astrometry. The ation program came to an end in August 1993 observ 100 after 37 months of e ective observation. This was fol- wed by three more years of data pro cessing ending lo 10 up with the merging of the two solutions pro duced, to a large extent, indep endently by the NDAC and 1 FAST Consortia. One more year was necessary to 0123456789101112Hp arrange all the results into a consistent pro duct and write an extensive do cumentation, including a user guide of the Catalogue and detailed chapters on the Figure1. Magnitude distribution of the 118 218 entries of construction of the Hipparcos and Tycho solutions. the Hipparcos Catalogue. The vertical scale is logarithmic and the labels indicate the beginning of a class 0.5 mag The primary result is an astrometric catalogue of wide. The linear envelope of the distribution on the bright 118 218 entries nearly evenly distributed over the sky side indicates that the Catalogue is comprehensive up to with an astrometric precision in p osition, prop er mo- Hp= 7.5. tion and parallax of 1 mas or mas/yr, or b etter for the brightest stars. The p ositions and prop er mo- tions of the Catalogue de ne an optical reference The observational pro cedure and the principles of the frame with a likely global accuracy of ab out 0.1 mas data reduction have b een presented in the scienti c and 0.1 mas/yr and no regional distortion. This set literature in many instances. The most detailed and up dated presentation is in any case available in Vol- Based on observations made with the ESA Hipparcos satellite. umes 1{4 of the published catalogue ESA 1997. 6 Table 1. Summary of the astrometric solution Catalogue ep o ch 1991.25 Measurement p erio d 1989.85{1993.21 Reference system ICRS 2 Mean sky density ' 3 stars/deg cos Median precision of p ositions Hp < 9 mas 0.77 0.64 Median precision of prop er motions Hp < 9mas/yr 0.88 0.74 Median precision of parallaxes Hp < 9mas 0.97 Numb er of stars with = < 0:1 17 900 single stars 3 000 double or multiple stars Numb er of stars with = < 0:2 49 500 for each of the comp onents. The Catalogue entries 2. THE HIPPARCOS ASTROMETRIC which needed a more elab orate mo deling, such as the CATALOGUE acceleration solution, are usually not included in the subsequent statistical analysis. 2.1. Main Features The distributions of the formal standard errors of the astrometric parameters are shown in Figure 2 for the The main characteristics of the astrometric solution three main co ordinate systems: ecliptic, equatorial are summarised in Table 1. The Catalogue epoch, and galactic. The plots are based on the 100 038 `sin- T = J1991:25, is close to the mean ep o ch of all the 0 gle stars', or to b e more precise, all the catalogue en- observations. The true mean observation ep o chofa tries which do not b elong to the Double and Multiple particular star may di er from the Catalogue ep o ch Systems Annex hereafter DMSA. One must b ear in by up to six months in the worst cases, although it mind that the transformation of the errors from one usually ranges within two months of the Catalogue system to another is not simply the distribution of epoch. This was a delib erate choice p ermitted by a mean error on the sky expressed in two di erent the publication of the full covariance matrix of the systems, but a full transformation of the comp onents astrometric parameters of every star. The Hipparcos of the covariance matrix from one system to another. Catalogue is aligned with the extragalactic reference Only the standard errors of the parallaxes are invari- frame and constitutes a materialisation of the Inter- antinachange of co ordinate system. national Celestial Reference System in the visible. The ecliptic system is the most appropriate to show The absolute astrometry with atypical accuracy of the Hipparcos standard errors and correlations. In 1 mas, provides an improvementby nearly two orders this system there is virtually no dep endence of the of magnitude with resp ect to the b est fundamental standard errors with the longitude, as a consequence catalogue available b efore Hipparcos and more than of the ecliptic-driven scanning law, and a plot as a two orders of magnitude when compared to compila- function of latitude pro duces meaningful results with tion catalogues of similar size, like the SAO and the no averaging along a small circle of latitude. In con- PPM. As for the prop er motions, the improvementis trast, in the equatorial system, and ab ove all, in the not so large as a result of the very limited timebase on galactic system, the standard errors are function of which the Hipparcos measurements were p erformed, the two p ositional co ordinates = l; b and x x compared to the several tens of years used for the a plot as a function of b involves an averaging over ground-based prop er motions. This implies in par- the longitudes. In these two cases, only sky charts ticular, that the quality of the Hipparcos reference can convey visually and without distortion the full frame will degrade rather quickly, if no e ort is done prop erties of the astrometric precision. to maintain it in the years to come. Basically, the error in ecliptic latitude is fairly con- stant on the sky, while the errors in longitude and 2.2. Standard Errors of the Astrometric parallax exhibit marked variations with the ecliptic Parameters latitude. These features are a mere and foreseen consequence of the scanning law which yields less ob- servations in the ecliptic plane that in the higher lat- For the vast ma jority of the single stars the astro- itude, and a b etter geometrical con guration to de- metric mo del adopted assumes a uniform space mo- termine the latitude near the ecliptic plane than at tion relative to the barycentre of the solar system. b = 50 degrees, and just the opp osite for the longi- The complete description of the apparent star p osi- tude. The two e ects cancel each other for the lati- tion is then given by the ve astrometric parame- tude while they add for the longitude. ters, namely two co ordinate p ositions at the Cata- logue reference ep o ch for the barycentric direction of In the equatorial system, the situation is quite simi- a star, the parallax and the two comp onents of the lar, just slightly smo othed out, b ecause the obliquity tangential motion expressed in angular measures as is not very large. In the case of the galactic co ordi- ; . In the case of comp ound sources with twoor nates, the averaging over the galactic longitudes on a more comp onents, the treatmentwas somewhat more small circle of constant galactic latitude, attens all complex but at the end led to a similar description 7 mas mas/yr 1.25 1.25 σ π σ µ l * 1 σ 1 l * 0.75 0.75 σ µ σ b b 0.5 0.5 0.25 0.25 -1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1 sin b sin b mas mas/yr 1.25 1.25 σ π σ µ α ∗ 1 1 σ α ∗ 0.75 0.75 σ µ δ σ δ 0.5 0.5 0.25 0.25 -1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1 sin δ sin δ mas mas/yr 1.25 1.25 σ π σ 1 1 µβ σ β 0.75 0.75 σ µ λ∗ σ λ ∗ 0.5 0.5 0.25 0.25 -1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1 sin β sin β Figure 2.