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. Medians of the standard errors at J1991.25 of the ve astrometric parameters as a function of the ecliptic

latitude top, declination midd le and galactic latitude bottom. The standard errors are expressed in mas for the

position and paral lax and in mas/yr for the components of the proper motion. Only the approximately 100 000 single stars

areconsidered in these plots.

2.3. Correlations the curves showing eventually the median precision

of the Hipparcos astrometry.

The covariance matrix of the ve astrometric param-

The median accuracies in Table 1 and in Figures 2

eters includes the ten correlation co ecients, which

are typical of the bulk of the catalogue, that is to

are necessary to express the standard errors and the

say apply directly to a star of 8.7 mag. The varia-

correlations in other co ordinates systems, or to prop-

tion of the median accuracy of the ve astrometric

agate the covariance matrix at an epoch di erent

parameters with the star magnitude is shown in Fig-

from T . The least correlation b etween the twopo-

ure 3. At the faint end the photon noise was the

0

sitional co ordinates app ears in ecliptic co ordinates,

limiting factor and the diagrams match the exp ected

with l; b 2 [0:2; 0:2] while in equatorial co ordi-

increase in the standard error with the magnitude.

nates  ;   2 [0:4; 0:4]. Again this is attributable

For stars brighter than 7 mag, the precision is more

to the natural symmetry of the scanning law with re-

or less indep endent of the brightness as the limiting

sp ect to the ecliptic. Similar values are found for

factor is chie y instrumental and weakly sensitiveto

the correlation between the two comp onents of the

the magnitude.

prop er motion. Regarding  ;   and ;  they



may b e quite large jj > 0:5 in some regions of the

Since many astrophysical applications of the Hippar-

sky. But this is not very signi cant, b ecause they

cos data will rest on samples of bright stars, it is

can b e made negligible simply by referring each star

imp ortant to notice that the precision in this range

to its mean observation time rather than the mean

of magnitude is much b etter than 1 mas or 1 mas/yr

catalogue ep o ch. Indeed the distribution of the corre-

on all the astrometric parameters. A useful rule of

lations is similar to that exp ected from the deviation

thumb of the astrometric accuracy applicable to the

of the individual mean observation time from T .

0

bright stars Hp < 7 is:

Only one correlation involving the parallax is notice-

 ' 0:55;  ' 0:45;  ' 0:75 in mas 1

  

able:  ;  . A sky chart would show a conspicuous

dip olar distribution with  '0:4 around =18h

and:

and  ' +0:4 around = 6 h from the equator to lat-

itude 60 degrees see ESA 1997, Vol. 1. This is the

 ' 0:65;  ' 0:55 in mas=yr 2

 



 largest single systematic e ect seen in the Hipparcos 8

mas mas/yr Positions - Parallax Proper Motions 1.25 1.25

1 1

0.75 σ π 0.75 σ µα ∗ σ α ∗ σµ 0.5 0.5 δ σ δ

0.25 0.25 02468101214 0 2 4 6 8 10 12 14

Hp Hp

Figure3. Medians of the standard errors at J1991.25 of the ve astrometric parameters as a function of the Hipparcos

magnitude. The standard errors are expressed in mas for the position and paral lax and in mas/yr for the components of

the proper motion. Only the approximately 100 000 single stars areconsidered in this plot.

rections to eliminate the risk of systematic e ects. Catalogue and it is well accounted for by the time

Numerous analyses of the Hipparcos parallaxes with distribution of the observations. While the e ective

the preliminary and nal solutions con rm this view observing p erio d lasted 37 months, it do es not cover

and indicate that the global zero-p oint o set, com- an integral number of years Table 1: the rst ob-

mon to all stars, is smaller than 0.1 mas Arenou servations were made in Novemb er 1989 and the last

et al. 1995, ESA 1997. A recent search of a global ones in March 1993, with an interruption of nearly

6

three months in fall 1992. Thus there is an imbal-

zero{p oint in the parallaxes in the 5:4  10 residuals

ance in the observations distribution in l l , which

of the astrometric data byFrschl e et al. 1997 sup-

is ultimately resp onsible for the correlation b etween

p orts also this claim with a non-signi cant o set of

the longitude or right ascension and the parallax.

0:010  0:010 mas.

The centre of the missing observations is very nearly

the autumn equinox when the longitude of the Sun

is 180 degrees. Therefore the parts of the sky not ob-

3.2. Distribution of the Parallaxes

served are in the vicinityofl = 90 deg or l = 270 deg,

b ecause the scanning law implies that the observa-

tions are centred at 90 deg from the Sun. The

The distribution of the parallaxes measured by Hip-

observed correlations match quite precisely the the-

parcos is plotted in Figure 4 for all the entries of the

oretical values exp ected from this asymmetry with

Catalogue, including double and multiple stars. Half

resp ect to the Sun.

of the stars are closer than 230 p c. This average de-

p ends however on the region of the celestial sphere:

the median parallax for Hipparcos stars lying close

to the galactic plane is of the order of 2.5 mas, while

3. PROPERTIES OF THE HIPPARCOS

it reaches 6 mas at mid-galactic latitude, b eing lo-

PARALLAXES

cally as large as 9 mas. This re ects essentially the

initial selection of stars from their astrophysical in-

terest, rather than a true physical distribution. In

3.1. Construction of the Parallaxes

any case, this is a basic prop erty of the Catalogue

that one must b e aware of in future investigations.

There is little doubt that the Hipparcos parallaxes

will play a ma jor role for many years to come in

Only 4100 stars in 118 000 or 3.3 p er cent, are found

with negative parallaxes, primarily between 0 and the applications of the Hipparcos results to stellar

2 mas. Most of this negative tail is of statistical physics and galactic astronomy. Recent and much

origin, as the parallaxes were not constrained to b e heralded investigations have shown already the im-

p ositive. The statistical distribution of the measured pact of the Hipparcos parallaxes in the revision of

parallaxes of the distant stars, those with true par- the cosmic distance scale and in the re-evaluation of

allaxes < 1 mas, has a tail of typical width equal to the ages of the oldest stars, although the discussion

two to three times the standard deviation, ' 3 mas, is not closed yet. The construction of a high resolu-

extending into the negative region. The  200 par- tion Hertzsprung-Russell diagram, is already a vivid

allaxes more negative than ' 3 mas are more likely and app ealing illustration of the impact of accurate

to b elong to unreliable solutions, multiple stars or stellar distances in the mere description of where the

sto chastic solutions, and should not b e considered a stars lie in a magnitude-colour diagram Perryman

part of the statistics. et al. 1995, Perryman et al. 1997.

The right plot in Figure 4 refers to the same data The Hipparcos parallaxes are trigonometric and by

as the left one but with a scale in log  and bins construction are virtually absolute, in that sense they

of width 0.1 dex. The distribution is remarkably do not use reference background stars. Truly abso-

symmetric from  = 0:1 mas to the largest paral- lute parallaxes would have needed to refer the tiny

laxes. The dashed line sup erimp osed is a Gaussian parallactic motion to a xed direction, while in fact

distribution of mean  = 0:68 and standard devia- Hipparcos tied pairs of stars at wide angle. How-

tion  =0:38 and indicates that the distribution of ever, the numb er of ob jects asso ciated to a particu-

the measured parallaxes is very close to log{normal lar star is large enough and in suciently many di- 9

15000 14000

12000

10000 10000 8000

6000 5000 4000

2000

0 0 - 8 - 4 0 4 8 12 16 20 24 28 32 36 40 44 48 -1 -0.6 -0.2 0.2 0.6 1 1.4 1.8 2.2 2.6 Log π Parallax in mas

0.10.5 12 5 10 20 50 100 200 π (mas)

Figure4. Distribution of the paral laxes measured by Hipparcos. The plots arebased on the ful l content of the Hipparcos

Catalogue: single stars, doubles and multiples, acceleration and stochastic solutions. Alogarithmic scale in the right plot

shows that the paral laxes fol low nearly a log-normal distribution. The best normal distribution is superimposed as a dashed line.

30000 100000

25000 10000

20000 1000 15000 100 10000

10 5000

0 1 0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 4 4.4 4.8 0123456789

σ(π) in mas σ(π) in mas

Figure5. Histogram of the standard errors of the Hipparcos paral laxes for the 118 000 entries of the Catalogue. The same

distribution is shown in the left and right plots, with a logarithmic vertical axis in the latter to reveal the smal l population

at the extremes of the distribution.

6000 600 Single Stars Double Stars 5000 500

4000 400 7200 1600

3000 300

2000 200

1000 100

0 0 0 102030405060708090 0 102030405060708090 σ π (%) σ π (%)

π / π /

Figure6. Relative standard errors of the Hipparcos paral laxes for the entries of the Catalogue with a positive paral lax.

The left plot refers to the 96 700 single stars and the right one to the 12 600 double and multiple systems of Annex C.

10

Table 2. Number and fraction of the population of single

ter quality for the single stars than for the multiples,

and multiple stars with a relative error of the paral lax less

a fact not very surprising. The cumulative distri-

than the limit set in the rst column. About 8500 entries

butions given in Table 2 show that the degradation

with negative paral laxes or which are in the DMSA G, O,

is not very large, with for example 18 per cent of

the single stars with  = < 0:1versus 13 p er cent

VorXare not included in the statistics.



for the multiples. More striking is the fact that the

 = Number Fraction p er cent



level of 18 per cent of the multiples is reached at

 = < 0:125 instead of 0.10 for the singles. This is

p er cent Singles Multiples Singles Multiples



the result of a fortunate circumstance to the extent

< 1 140 16 0.1 0.1

that among the astrometric parameters, the p ositions

< 2 710 50 0.7 0.4

and prop er motions are sensitive to the mo delling of

< 5 5200 450 5.4 3.6

the double star, whereas the parallax is not. Thus,

one can say, that despite a small di erence of qual-

< 10 17900 1600 18.5 12.8

ity, the Hipparcos parallaxes are statistically homoge-

< 20 42800 4200 44.2 33.3

neous irresp ective of whether the star was pro cessed

< 50 78000 8800 80.6 70.0

as single or not.

4. CONCLUSION

over a wide range of distances. This is a further hint

that the Hipparcos parallaxes are free of systematic

e ect down to 0.1 mas and are statistically meaning-

The Hipparcos mission was initially planned to p er-

ful even for stars much farther than 1 kp c. The slight

form global astrometry with a precision of 2 mas for

bump in the rst class includes also all the p ositive

a representative Hipparcos star. The astrometric re-

parallaxes less than 0.1 mas.

sults after 37 months of e ective observation and sev-

eral years of data analysis surpass signi cantly this

already ambitious goal, thanks to the intrinsic qual-

3.3. Distribution of the Standard Errors

ityof the instrument and the resources deployed in

the pro cessing. One must keep in mind that having

measured the parallaxes to within 1 mas instead of

The distribution of the standard errors of the paral-

2 mas, makes the accessible universe eight times as

laxes is shown in Figure 5 with a linear ordinate in the

large as exp ected from the nominal mission. The ex-

left plot and a logarithmic scale on the right useful

amination of the 17 volumes of the printed version

to visualise the content of the less p opulated classes.

of the Catalogue and all the ASCI I les shows that

The main distribution is as regular as p ossible, with

Hipparcos has b een much more than an astrometric

an average at  ' 0:9 mas. There are just ab ove



mission, but a genuine advance in stellar astronomy,

1600 stars with standard errors of the parallax larger

adding to the astrometric parameters a photometric

than 5 mas, as seen in the right plot. This number is

survey of unprecedented quality and coverage and a

in any case rather small and concerns ab out 100 very

renewal in the astronomy of the visual double stars.

faint single stars Hp > 11:5 with normal solution,

The Hipparcos legacy will b e visible for manyyears

ab out 1000 double or multiple stars of the DMSA-

through its far reaching astrophysical applications.

C, quite often the faint comp onent ofatwo-p ointing

double, and 500 with sto chastic solutions. All these

entries are noted in the Catalogue for the p o or qual-

ity of the astrometric solution as a whole.

ACKNOWLEDGMENTS

More relevant for many astrophysical applications is

the relative precision of the distances measured by

Thanks are due to all the p eople in the industry or

 = . The distributions are plotted in Figure 6 sep-

in scienti c institutions who have allowed the reali-



arately for the single and non-single stars. All the

sation of this remarkable landmark in science. This

entries 96 731 not included in the Double and Multi-

overview re ects b ehind the name of a single author

ple Systems Annex and with a non-negative parallax

their full dedication to the pro ject over manyyears.

make the set of single stars, whereas the set multiple

Full names are given in the Hipparcos do cumenta-

stars comprises the entries 12 569 of the DMSA-C

tion.

with non negative parallax. The 8500 missing entries

are equally distributed between the solutions with

negative parallaxes and the entries in the parts G,

REFERENCES

O, V or X of the DMSA.

Arenou, F., Lindegren, L., Frschl e, M. et al., 1995,

The two distributions in Figure 6 are very alike

A&A, 304, 52

with a maximum at  = ' 12 per cent, although



less marked for the double stars than for the sin-

ESA, 1997, The Hipparcos and Tycho Catalogues,

gles. However the fraction of entries with  = >

SP{1200, Vols. 1{4



100 p er cent, is much larger for the multiples than for

Frschl e, M., Mignard, F., Arenou, F., 1997, ESA

the singles resp ectively 12 p er cent and 7 p er cent.

SP{402, this volume

Perryman, M., Lindegren, L., Kovalevsky, J. et al.,

1995, A&A, 304, 69

The vertical scales in Figure 6 di er by a factor 10,

which is slightly larger than the ratio of the two p op-

Perryman, M., Lindegren, L., Kovalevsky, J. et al.,

ulations. This proves that the distribution of the

1997, A&A Letters, in press

relative error of the parallaxes tends to be of b et-