Analysis of Seven Nearby Open Clusters Using Hipparcos Data

567

ANALYSIS OF SEVEN NEARBY OPEN CLUSTERS USING HIPPARCOS DATA

1 1 1 2 1

N. Robichon , F. Arenou ,C.Turon J.-C. Mermillio d , Y. Lebreton

DASGAL, URA CNRS 335, Observatoire de Paris, 92195 Meudon, France

Institut d'Astronomie, Universit e de Lausanne, Switzerland

calculate the cluster mean distance with Hipparcos ABSTRACT

parallaxes as well as the mean space velo city using

Hipparcos data and ground based radial velo cities.

From Hipparcos data in seven op en cluster elds

Praesep e, IC 4756, NGC 2516, NGC 3532, NGC

A eld star is considered as a memb er if its Hippar-

6475, NGC 6633 and Sto ck 2 we have computed

cos parallax and prop er motion are consistent with

the memb ership of stars. The mean cluster distances

the mean cluster values at a 3 level. Stars for which

have b een derived from intermediate Hipparcos data.

the p osition in the observational colour-magnitude

diagram was not in agreement with the cluster se-

quence were also rejected. Hipparcos double stars

Cluster sequences in the HR diagram have b een de-

were rejected when their duplicity could bias the

duced from their distances, the photometry coming

mean prop er motion and parallax values, i.e. when

from the `Base des Amas' Mermillio d 1988. Com-

the eld H59 of the Hipparcos Catalogue was equal

parison b etween the relative sequence p ositions shows

to G, O, V or X see ESA 1997.

that metallicity is probably not the only parameter

which in uences the p osition of the ZAMS.

The numb er of stars selected in each cluster is given

in Table 1. It varies b etween 6 and 24.

Key words: op en clusters; Hipparcos; Hertzsprung-

Russell diagram; distances; chemical comp osition.

3. CLUSTER MEAN PARALLAXES

1. INTRODUCTION

3.1. Hipparcos Intermediate Data

Op en clusters have b een used for a long time to cali-

The mean cluster parallaxes cannot be computed

brate the main sequences in the Hertzsprung-Russell

without caution. As was predicted b efore the satel-

diagram as a function of age and metallicity. They

lite launch Lindegren 1988, the estimation of the

also de ne one of the rst steps in the distance scaling

mean parallax or prop er motion of a cluster observed

of the Universe. The advent of the Hipparcos Cata-

by Hipparcos must takeinto account the observation

logue allows, for the rst time, to determine, without

mo de of the satellite. This is due to the fact that stars

anyphysical assumption, the lo cations of cluster se-

within a small area in the sky have frequently b een

quences in the HR diagram.

observed in the same eld of view of the satellite.

Consequently, one may exp ect correlations b etween

The comparison of the cluster sequences presented

measurements done on stars separated by a few de-

here and in Mermillio d et al. 1997 leads to amazing

grees, or with a separation b eing a multiple of the

results. The p ositions of cluster sequences are not

basic angle b etween the two elds of view.

correlated with metallicity as one could have thought

b efore.

This means that, when averaging the parallaxes or

prop er motions for these n stars, the improvement

factor do es not follow the exp ected 1= n law and will

2. MEMBER SELECTION

if is the mean not b e asymptotically b etter than

p ositive correlation between data. In the case of

0:35

clusters, the improvement is ab out n Lindegren

The selection of memb ers in an op en cluster is al-

1988. The straightaverage of individual parallaxes

ways a critical issue. The selection was done with

would not b e an optimal estimate of the mean cluster

the assumption that all stars b elonging to the cluster

parallax, and moreover its standard error would be

have the same space velo city and that they lie in a

seriously underestimated.

10 parsec radius sphere centred on the cluster centre.

The selection is iterative but converges after 2 or 3

The prop er way to take these correlations into ac-

iterations: with a set of well known memb ers, we

count is to come back to the reference great circle

568

Table 1. New cluster distances.

cluster N d { + m{M { + m{M EB V [Fe/H] age

[mas] [mas] [p c] [p c] [p c] [mag] [mag] [mag] [mag] [mag] [dex] [Myr]

Lynga

Praesep e 24 5.65 0.31 177.0 9.2 10.3 6.24 0.12 0.12 5.99 0.00 0.07 830

IC 4756 9 3.46 0.30 289.0 23.1 27.4 7.30 0.18 0.20 8.58 0.20 0.04 830

NGC 6475 21 3.43 0.30 291.5 23.4 27.9 7.32 0.18 0.20 7.08 0.06 0.03 130

NGC 6633 6 3.43 0.53 291.5 39.0 53.3 7.32 0.31 0.36 8.01 0.17 -0.11 630

Sto ck02 8 3.16 0.47 316.5 41.0 55.3 7.50 0.30 0.35 8.62 0.38 -0.14 170

NGC 2516 15 2.87 0.20 348.4 22.7 26.1 7.71 0.15 0.16 8.49 0.13 -0.23 70

NGC 3532 7 2.40 0.40 416.7 59.5 83.3 8.10 0.33 0.40 8.53 0.04 -0.10 290

from Piatti et al. 1995

from Claria & Piatti 1996

variations of the normalised di erences = level, to calibrate the correlation b etween the refer-

as a function of apparent magnitude V b ottom and ence great circle abscissae, so that the full covariance

colour index B V top are represented in Fig- matrix b etween observations allows to nd the opti-

ure 1. The indep endence between these normalised mal astrometric parameters. As part of the least-

di erences and apparent magnitudes or colour indices squares pro cedure, the nal covariance matrix be-

was not rejected byaPearson or Kendall statistical tween astrometric parameters is also found. The

test. adopted metho d is similar to that of van Leeuwen

& Evans 1997 with the exception that the cali-

B - V

bration of correlation co ecients has b een done on

0.0 0.5 1.0 1.5 2.0

h reference great circle. This has b een done us-

eac 3

ulae by Lindegren 1988 to

ing the theoretical form 2

which harmonics were added through the use of co- 1

π sine transform Press et al. 1992. σ )/

moy 0 π −

(

or a given cluster, either the mean parallax or the F -1

Praesepe

prop er motion or b oth may b e considered to b e the

-2 IC 4756

unknowns for the cluster, the other astro- same NGC 6475

-33 NGC 6633

parameters of cluster stars remaining deter- metric Stock 02

NGC 2516

individually. In our case, only the parallax mined 2

NGC 3532

b een considered constant, the resulting values has 1 π

b eing given Table 1. From these mean parallaxes )/

moy 0

, and asso ciated standard errors, the distance and π −

( -1

distance mo duli are also indicated, together with a

1 variation. In the right part of Table 1, the dis-

-2

tance mo duli, colour excesses, and ages, quoted by -3

56789101112

a 1987, and metallicities from Lynga 1987,

Lyng V

Piatti et al. 1995 or Claria & Piatti 1996 are also

indicated. Figure1. Normalised di erences of the 94 cluster mem-

bers versus B-V top and V bottom.

3.2. Accuracy of the Results

4. CLUSTER COLOUR{MAGNITUDE

The distances and the distance mo duli given in Ta- DIAGRAMS

ble 1 deserve some more comments. Since the trans-

formation from parallax to distance is not linear, a

bias in the quoted distances could b e exp ected. How-

In each cluster, Johnson BV photo electric photom-

ever, the relative error = is small b etween 6 and

etry compiled in the `Base des Amas' was used to

17 p er cent so the e ect is probably negligible see

build well de ned cluster sequences in the observa-

Brown et al. 1997.

tional Hertzsprung-Russell diagram. For IC 4756

and Sto ck 2, not enough photo electric photometry

When computing the mean cluster parallax, one im-

was available to obtain a clean sequence. Redden-

plicitly assumes that the disp ersion in individual par-

ing of each cluster from Lynga 1987 and Hippar-

allaxes is only due to the measurements errors. The

cos mean cluster parallaxes were used to obtain the

depth of the cluster should be taken into account;

absolute magnitude M and the dereddened colour

however, except p erhaps for Praesep e, it is small

indices B V . The higher part of the Figure 2

compared to the quoted error on distance and may

shows the sup erp osition of the 5 cluster sequences in

b e neglected.

the M ; B V diagram. The lower part repro-

V 0

duces the sequences of Praesep e and NGC 2516 with

Finally one may ask whether there could b e a mag- the error bars on absolute magnitudes derived from

nitude or colour e ect in the Hipparcos parallaxes Hipparcos data see Table 1. The cluster sequences

which could bias the mean parallax estimation. The separate into two groups: Praesep e and NGC 6475 569

-2 -1 0 1

V 2 M 3 Praesepe 4 NGC 6475 NGC 3532 5 NGC 6633 6 NGC 2516

-2 -1 0 1

V 2 M 3 4 5 6

-0.25 0 0.25 0.5 0.75 1 1.25

(B-V)0

Figure2. Colour-Magnitude diagram of ve open clusters using Hipparcos mean paral laxes.

570

sequences are ab out 0:5 0:7 magnitude ab ove those of 0.7 magnitude between two sequences, would be

of NGC 3532, NGC 6633 and NGC 2516. higher than 1.1 dex! Although metallicity determi-

nations are quite uncertain, such a di erence b etween

NGC 2516 and Praesep e is probably to b e excluded.

In the other hand, if the di erence between the se-

5. ZAMS

quences of NGC 2516 and Praesep e of 0.25 magnitude

is due to metallicity di erence, the di erence of 0.45

magnitudes 0:7 0:25 between the two sequences

The helium abundance Y is very dicult to measure

is very unlikely compared with the errors on the dis-

directly and is only observable in B stars. Thus, Y is

tance mo dulus derived from the Hipparcos mean par-

usually supp osed to vary with the metal abundance

allaxes.

Z according to the law: DY=DZ = DY=DZ i.e.

Y =2:8Z+0:227 where 2.8 is derived from the cali-

This is a con rmation of what has b een found for 6

bration in luminosity of a solar mo del calculated with

other clusters in Mermillio d et al. 1997. This seems

up dated input physics Lebreton 1997 and 0.227 is

to indicate that helium abundance variations b etween

the primordial helium abundance Balges et al. 1993.

clusters may be larger than thought b efore, or, at

Figure 3 shows ZAMS for di erentvalues of Z with

least, that another parameter added to metallicity,

values of Y following the previous law. For metallic-

plays an imp ortant role in the p osition of sequences

ities in the range of those of the 5 clusters presented

in the HR diagram.

in this p oster 0:23 < [Fe=H] < 0:07, the shift

in magnitude b etween sequences is smaller than 0.25

This result is, however, to be con rmed with more

magnitude.

photo electric data, more precise reddenings and ho-

mogeneous [Fe/H] determination.

3 REFERENCES Fe/H = -0.254 ; Z = 0.01 ; Y = 0.255 Fe/H = -0.066 ; Z = 0.015 ; Y = 0.269

Fe/H = +0.070 ; Z = 0.02 ; Y = 0.283 yd, R.N., Mathews, G.J., 1993, ApJ,

4 Balges, M.J., Bo

418, 229

wn, A.G.A., Arenou, F., van Leeuwen, F., Linde-

5 Bro

gren, L., Luri, X., 1997, ESA SP{402, this volume

Claria J.J., Piatti E.P., 1996, PASP, 108, 672

bol 6

1997, The Hipparcos and Tycho Catalogues, M ESA,

Volume 1, Intro duction and Guide to the Data,

7 ESA SP{1200

Lebreton, Y., 1997, in preparation

an Leeuwen, F., Evans, D., 1997, A&A, submitted

8 v

Lindegren, L., 1988, Scienti c asp ects of the Input

Catalogue Preparation II, January 1988, Sitges,

orra, C. Turon, eds. 3.8 3.7 3.6 3.5 J. T

log(T )

a, G., 1987, Catalogue, 5th edition Strasb ourg

eff Lyng

Mermillio d, J.-C., Turon, C., Robichon, N., Arenou,

F., Lebreton, Y., 1997, ESA SP{402, this volume

Mermillio d, J.-C., 1988, Bull. Inf. Centre Donn ees

Figure3. ZAMS computed for di erent values of Z and

Stellaires, 35, 77-91

Y fol lowing Y = 2.8 Z + 0.227.

Piatti, E.P., Claria, J.J., Abadi, M.G., 1995, AJ, 110,

2813

Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flan-

6. CONCLUSION

nery, B.P., 1992, Numerical Recip es, Cambridge

University Press

Relative p osition of cluster sequences in the

M ; B V diagram are qualitatively but not

V 0

quantitatively in agreement with [Fe/H] variations.

Praesep e and NGC 6475, with a metallicity higher

than the solar one, have sequences higher than

NGC 3532, NGC 6633 and NGC 2516 which are de-

cient. But the magnitude shift between sequences

is larger than exp ected. The NGC 2516 sequence,

for example, is 0.8 magnitude b elow the Praesep e

one. According to the ZAMS presented in the pre-

vious paragraph, this cannot be explained only by

the metallicity di erence between the two clusters

[Fe=H] = 0:23 for NGC 2516 and [Fe=H] = 0:07

for Praesep e. Assuming a usual helium variation,

the metallicity di erence required to explain a shift