519

IDENTIFICATION OF MOVING GROUPS IN A SAMPLE OF EARLY-TYPE

MAIN-SEQUENCE STARS

1 3 1 1 2

F. Figueras ,A.E.G omez , R. Asiain , B. Chen , F. Comer on ,

3 3 4 3 1

S. Grenier , Y. Lebreton , M. Moreno , V. Sabas ,J.Torra

1

Departament d'Astronomia i Meteorologia, Universitat de Barcelona, Spain

2

Europ ean Southern Observatory, Garching b ei Munc  hen

3

DASGAL, URA 335 du CNRS, France

4

DepartamentdeF sica i Enginyeria Nuclear, U.P.C., Spain

ful compilation of radial velo cities have b een used for ABSTRACT

this study.

Di erent metho ds have b een used to characterize

The kinematic structure of young B5{F5 main-

moving groups in the 4-dimensional space of U,V,W,

sequence stars in the solar neighb ourho o d is analysed

age: a parametric approach SEMMUL algorithm,

using b oth accurate observational data { new astro-

Celeux & Dieb olt 1986; a non-parametric technic us-

metric Hipparcos data and complementary data from

ing a Kernel estimator Chen et al. 1997, a metho d

the ground { and several robust statistical metho ds.

based on the wavelet transform and a metho d based

The coherence of the results obtained from the di er-

on the aggregation of groups through moving centers.

ent metho ds SEMMUL, kernel estimator, wavelets,

In Section 2, we describ e the sample's compilation

dynamical clusters allows us to de nitively con rm

and its mean characteristics. Section 3 contains a

the existence of the Eggen's moving groups and to de-

brief description of the statistical metho ds used and

termine, without any a priori knowledge, their mean

the results obtained, and Section 4 is devoted to the

characteristics in the 4-dimensional space U,V,W,

analysis of the moving groups mean parameters.

age. We nd that mean velo city disp ersion in the

velo city comp onent in the direction of the galactic

rotation for Sirius, Pleiades, Hyades and Praesep e

1

moving groups are in the range 3{8 km s ,avalue

2. THE SAMPLE

larger than classically exp ected.

The working sample compiled by V. Sabas 1997

has b een selected from the global set of Hipparcos

Key words: young stars; galactic kinematics; moving

B5{F5 main-sequence stars with apparent magnitude

groups.

7.5 or brighter. In order not to bias the results when

lo oking for moving group memb ers among the eld

stars, the stars known as op en cluster's memb ers have

1. INTRODUCTION

b een rejected. To compute reliable physical parame-

ters and ages, double or susp ected double stars and

stars with p eculiarities in the sp ectra sp ectral typ es

The study of the irregularities in the velo city eld

from the Inca Catalogue have also b een rejected.

of young stars in the solar neighb ourho o d yields im-

The radial velo cities have b een taken from the recent

p ortant clues to understand the history of star for-

compilations of Barbier-Brossat 1997 and Du ot

mation and the dynamical pro cesses involved in the

et al. 1995, and from the Key-Programmes under-

evolution of our Galaxy. The detection and analysis

taken to complement the Hipparcos data OHP {

of features suchasmoving groups, the vertex devia-

Marly Sp ectrograph, ESO { Echelee Sp ectrograph:

tion, and gradients of the velo city eld demands the

Grenier 1997. Individual ages have b een obtained

use of robust statistical metho ds and highly accurate

Asiain et al. 1997 interp olation algorithm from

astrometric and physical data. Our pro ject attempts

Lebreton 1995 stellar evolutionary mo dels, taking

b oth to de nitively con rm the presence of moving

into account the metallicity, the e ective temp er-

groups and, through the kinematic and physical prop-

ature b eing computed from Stromgren photometry

erties of its memb ers, to constrain mo dels accounting

Hauck & Mermillio d 1996, Jordi et al. 1996, the

for their origin.

stellar luminosity from Hipparcos M and the b olo-

v

metric correction of Malagnini 1966. Only stars

with logage larger than 7.5 have b een retained. A selection of 2588 young B5{F5 main sequence Hip-

Distances have b een computed directly from Hip- parcos stars within ab out 250 p c from the Sun, with

parcos parallaxes for the stars with
=  0:15, known individual ages, computed from Stromgren

and with a weighted mean between Hipparcos and photometry and Hipparcos parallaxes, and a care-

520

photometric distance for the rest few stars. Meil-

lon 1996 algorithm has b een used to compute the

U,V,W comp onents of the helio centric space ve-

lo city U directed towards the galactic center, V

towards the galactic rotation direction and W to-

wards the north galactic p ole and the corresp ond-

ing errors considering the Hipparcos correlation co-

ecients among variables. Finally, the stars with

1

residual velo city larger than 65 km s have b een

rejected b ecause they probably do not b elong to the

galactic disk p opulation. The sample contains 2588

stars with a mean velo city comp onents U; V ; W =

1

11:72  0:06; 11:38  0:06; 7:03  0:05 km s

o o

and a vertex deviation of  = 22:5  1:2 . The

mean observational errors in the velo city comp onents

1

are  ; ;  = 2.4,2.3,1.9 km s and the dis-

U V W

tribution of the relative error in age is presented in

Figure 1.

Figure 2. The distribution of the total sample in the U,V plane.

300

the U,V,W comp onents of the helio centric space ve-

lo city and the individual ages  . As will be seen,

this last parameter give imp ortant clues to the de -

200

nition of the moving groups physical prop erties

3.1. SEMMUL Algorithm

Number of stars 100

SEMMUL algorithm Sto chatique, Estimation, Max-

imisation, MULtidimensionnel, develop ed by Celeux

& Dieb olt 1986, is a parametric metho d allowing

0 ts inside a sam- 0.00 0.25 0.50 0.75 1.00 the separation of Gaussian comp onen

relative error in age

ple. It do es not need to adopt a set of initial condi-

tions and can work without a predetermined knowl-

edge of the numb er of comp onents only needs a max-

imum numb er. Adapted by Arenou 1993, it takes

Figure 1. Relative errors in age for the total sample

into account a Gaussian distribution of the observa-

tional errors.

computed using Monte Carlo simulations, Asiain et al.

1997.

It has b een applied to the whole sample in the four-

dimensional space of U,V,W, log  and ab out 50

runs have b een p erformed assuming a maximum of

3. STATISTICAL METHODS

6,7, and 8 groups Sabas 1997. The results are pre-

sented in Table 1.

Figure 2 shows the distribution of the total sample in

the U,V plane. De nitively, and as already noticed

by Palous and Hauck 1986, the observed velo city

3.2. Wavelet Transform

distribution in these sp ectral ranges cannot be de-

scrib ed by a unique velo city ellipsoid, indicating that

The wavelet transform provides an easily inter-

a mixture of several kinematic structures is present.

pretable visual representation of a signal sx,y,z.

Moreover, it allows to detect structures working at Four di erent statistical metho ds have b een applied

di erent scales detection of hierarchic classes, in- to the total sample to determine which are the mean

cluding voids in the distribution. The wavelet co e- characteristics of these kinematic structures. They

cients are computed from: are based on di erenthyp othesis Gaussian distribu-

tion of the sub-structures, Gaussian distribution for

the remaining eld without imp osing any prede ned

knowledge of the substructures, clustering metho ds

O

without previous hyp othesis, etc, so the coherence

WCx; y ; z ;  =gx; y ; z ;   sx; y ; z  1

among the obtained results will give us a wide under-

standing of the real phenomena.

The adopted wavelet function g x; y ; x;   is the ra- The p osition of the stars around the Sun do es not

dial Mexican Hat Murenzi 1990 which in the 3- provide any discriminant information for the detec-

Dimensional space takes the form: tion of moving groups, so the working parameters are

521

Table 1. The means and dispersions of the groups found using the SEMMUL algorithm in the 4-dimensional space: U,

1

V,Wcomponents Units: km s  and log  .

U V W    log    

U V W

log  

16:8 10:3 6:5 7:2 7:6 4:2 8:0 0:2 6:4

0:6 0:6 0:3 0:4 0:4 0:2 3:4

9:7 23:9 5:5 6:4 4:6 4:4 8:2 0:2 13:8 Pleiades

0:3 0:3 0:3 0:3 0:2 0:2 5:2

9:7 6:0 8:4 4:4 3:1 6:3 8:5 0:2 8:2

0:3 0:2 0:5 0:2 0:2 0:3 5:2

26:5 14:5 5:3 6:4 4:8 6:7 8:6 0:3 10:3

0:4 0:3 0:4 0:3 0:2 0:3 3:5

10:0 2:8 7:0 7:5 5:2 6:5 8:7 0:2 15:1 Sirius

0:4 0:3 0:3 0:3 0:2 0:2 2:3

37:4 15:2 7:9 6:0 5:2 7:6 8:9 0:2 7:7 Hyades

0:4 0:4 0:5 0:3 0:3 0:4 3:7

10:9 12:4 8:0 16:9 13:4 10:2 8:8 0:4 38:5 eld

0:6 0:4 0:3 0:4 0:3 0:2 12:9

2 2 2

2 2 2

x +y +z

x +y +z

2

2

2 g x; y ; z ;  = 3 e

2



where  is the scale variable: its biggest value is con-

strained by the extent of the sample and the lowest

1

by the observational errors  2kms . With this

metho d a given structure is detected when its char-

acteristic size is of the same order than the wavelet

scale  ,even if it is sup erimp osed on constant back-

ground or at gradient.

In this work, the metho d has b een applied in the 2-

dimensional space of U,V and in the 3-dimensional

case using U,V,log  . We have checked that the

W comp onent of the space velo city do es not give ad-

ditional information.

Figure 3 shows the contour map of the wavelet co e-

1

Figure3. Comparison of the contour map of the wavelet

cients obtained in the U,V space for  = 5 km s ,

1

coecients at  = 5 km s and the results obtained using

together with the results given by the SEMMUL al-

1

gorithm for comparison. Di erent scales have also

SEMMUL Units: km s .

b een computed { according to Daub echies 1990 a

correct sampling is obtained by increasing  with a

p

1

factor 2 { b eing  = 5 km s a go o d compromise

n

X

1 x x

between the obtained substructures and the observa-

i

p^ x= K   3

real

tional errors involved.

d

nh h

i=1

Due to the diculty of plotting the wavelet co e-

cients in the 3-dimensional case, Figure 4 shows the

where as Kernel function K we use the multivariate

maximum wavelet co ecient obtained for each log 

normal density function Fukunaga 1972. This p df

value. The U,V,log   values for each maxima are

can b e expressed as a sum of eld stars and moving

indicated in the top of the gure.

groups memb ers:

p x=p x+p x 4

real eld mov

3.3. Non-parametric Approach using KERNEL

Estimators

where the p df of the eld stars has b een expressed by

amultivariate Gaussian function with unknown mean

and covariance matrix. Moving groups memb ers are

The non-parametric kernel approach used in this then separated by means of a two hyp othesis tests

work Chen et al. 1997 is based on the hyp othesis using two thresholds parameters C1 and C2 Chen

that the presence of the moving groups is indicated et al. 1997. An automatic pro cedure is used to de-

by a concentration over the ellipsoidal velo city dis- termine the b est C1 and C2 applying a Kolmogorov-

tribution of the eld stars. It has the advantage that Smirnov test to the rst main axis of the Principal

there is no a prede ned hyp othesis ab out the kine- Comp onent Analysis. After the separation of moving

matics of the substructures asso ciated to the moving groups memb ers from eld stars, cluster analysis is

groups. The real probability density function p df  used to assign each star to a moving group. Their

of the total sample is computed from: means and disp ersions are presented in Table 2.

522

Table 2. Means and dispersions of the groups found using KERNEL algorithm in the 4-dimensional space U,V,W,log  

1

Units = km s .

U V W    log    

U V W

log  

-10.4 -22.9 -6.3 6.7 5.3 3.9 8.01 0.20 10 Pleiades

11.1 3.5 -6.4 7.5 4.9 6.9 8.81 0.19 11 Sirius

-16.1 -11.9 -6.4 6.4 7.1 3.9 8.34 0.26 17 IC 2391 ?

-44.7 -18.1 -6.1 2.5 2.4 8.5 9.18 0.08 0.5 Hyades

-34.3 -15.5 -4.7 3.2 2.6 5.4 8.77 0.17 3 Praesep e

Table 3. Means and dispersions of the groups found using the BMDP K-means algorithm in the 3-dimensional space U,

1

V, log   Units: km s .

U V   log    

U V

log  

-7.1 -26.3 8.7 6.2 8.37 0.31 14 Pleiades

+11.7 +0.5 9.4 7.5 8.81 0.28 20 Sirius

-30.5 -20.1 12.3 8.8 9.01 0.22 18 Hyades ?

-22.7 -16.4 8.3 5.3 8.31 0.24 16 IC 2391 ?

-13.2 -3.9 8.6 6.8 8.81 0.28 19

-11.3 -7.2 8.5 7.3 7.95 0.30 13

with Hyades and Praesep e op en clusters. Here we 3.4. BMDP K-means Clustering

must emphasize that the metho ds have not consid-

ered any knowledge of the center of the structure

The program K-means clustering of cases develop ed

obtained. Another new substructure seems to be

by BMDP Statistical Software Inc. is a particular

present in the Sirius moving group when using the

case of the dynamical clusters algorithm. Based on

wavelet-3D metho d, although it has not b een p os-

the aggregation of groups through moving centers, it

sible to asso ciate with any known kinematic struc-

do es not need the knowledge of the lo cation of the

ture. The existence of this substructure cannot be

groups although the numb er of groups must b e xed.

con rmed when simulated samples are analysed to

The results obtained when applying the metho d to

derive the threshold of signi cance of the irregulari-

the total sample in the U,V,log   space are pre-

ties obtained with the wavelet-3D metho d. The ex-

sented in Table 3.

istence of substructures in Sirius has also b een found

by Sabas 1997 and interpreted according to Weide-

mann 1992 mo del.

4. MEAN PARAMETERS OF THE MOVING

More doubtful is the asso ciation of the moving groups

GROUPS

we have obtained with the IC 2391 op en cluster.

1

Eggen 1992c obtained 20:8, 15:9, 8:3 km s

for the IC 2391 moving group, whereas Palous 1997

The centers of the substructures obtained using the

1

derived 18:3, 13:5, 5:9 km s for the mean

four statistical metho ds are presented in Table 4 for

velo cityof the op en cluster. As can b e seen in Ta-

comparison. The mean velo city comp onents and age

ble 4, SEMMUL and kernel metho ds can detect this

of some of the obtained groups can be clearly asso-

structure but, wavelet metho d and BMDP can not.

ciated with op en clusters present in the solar neigh-

The diculty comes from the fact that this structure

b ourho o d. Let us remind that known op en clusters

is placed near the center of the remaining eld stars

memb ers have b een rejected. In particular, the co-

distribution, its identi cation b ecoming in this case

herence obtained among SEMMUL, WAVELET and

more con ictive. Finally, no op en cluster counter-

KERNEL metho ds for the moving groups of Pleiades,

part has b een found for the young structure obtained

Sirius, and Hyades is excellent, de nitively con rm-

1

around U,V,W = 10; 6; 8 km s and the

ing the presence of such stellar streams and their as-

1

structure placed around U,V = 26, 15 km s ,

so ciation with the corresp onding op en clusters. Our

although three of our metho ds indicate their exis-

results show good agreement with those obtained

tence.

by Eggen 1991, 1992a, 1992b using the FK5 cat-

alogue: 11:6, 20:7, 10:4, 14.9, 1.3, 11:2,

1

KERNEL metho d allows, in addition to the determi- 40:0, 17:0, 2:0 km s for the moving groups

nation of the mean kinematic prop erties, the identi- of Pleiades, Sirius and Hyades resp ectively. Further-

cation of the moving group memb ers in the fourth more, thanks to the good quality of the data pro-

dimensional space of U,V,W,log  . In Figure 5 the vided by Hipparcos, Kernel and wavelet-3D meth-

spatial distribution of the obtained memb ers is plot- o ds allow, for the rst time, to sub divide the Hyades

ted, con rming the fact that the stars b elonging to moving group in two di erent structures with mean

moving groups are disseminate around the Sun with- kinematic and age parameters in excellent agreement

523

Table 4. Comparison between di erent methods: obtained moving groups and their association with open clusters.

SEMUL 4D WAVELETS WAVELETS 3D KERNEL BMDP Asso ciated

U,V,W,log   2D - U,V U,V,log  4D + CA U,V,log  op en cluster

 =5  =3 U,V,W,log  G omez et al. 1990

-10,-24,-5 8.2 -10,-23 -15,-24 8.13 -10,-22,-6 8.01 -7,-26 8.38 Pleiades: -5.8,-24.0, -12.4

-14,-21 7.78

+10, +3,-7 8.7 +10, +2 +13, +2 8.63 +11, +4,-6 8.81 +11,+0 8.81 Sirius: +14.5,+2.5,-8.5

 +7, +6 9.04

-37,-15,-8 8.9 -40,-17 -44,-19 9.20 -44,-18,-6 9.18 -30, -20 9.01 Hyades: -44.4, -17.0, -5.0

-33,-16 8.82 -34,-15,-5 8.77 Praesep e: -37.1,-23.5,-7.0

-16,-10,-6 8.0 -16,-12,-6 8.34 IC 2391: -18.3,-13.5, -5.9

-26,-14,-5 8.6 -26,-17 -26,-17 8.50 -22,-16 8.31

-10, -6,-8 8.5 -11, -6  -9, -6 8.00 -11,-7 7.9

-13,-4 8.8

-17, -5 8.22

1 1

 = 5.84 km s ,  = 4.80 km s and  = 5.85

U V W

1

km s . A slight trend on ages seems to b e present

although wehave not physical explanation for it and

will deserve further studies. Taking into account that

the distribution of the observational errors in our to- (−15,−24,8.13) ( −9, −6,8.00) (−14,−21,7.78) (−17, −4,8.22) (−26,−17,8.50) ( +7, +6,9.04) (−44,−19,9.20)

(+13, +2,8.63) (−33,−16,8.82)

1

 ,  ,   = 2.4, 2.4, 1.9 km s is

150.0 tal sample 

U V W

contributing to the velo city disp ersion of the moving

Pleiades 1

Praesepe Hyades

Sirius

groups in no more than 0.5{0.6 km s , the classi-

cal p oint of view that a moving group should havea

small disp ersion in the V comp onentmust b e de ni-

tively rejected. Other interpretations in terms of a

100.0

lo cal concentration of dark matter Casertano et al.

1993 or a mo del assuming the origin of these groups

to lie in large scale spiral sho cks asso ciated to the

spiral densitywaves Comer on et al. 1997 must b e considered.

50.0

maximum Wavelet Coefficient

ACKNOWLEDGMENTS

This work has b een supp orted by CICYT ESP95-

0.0 180, PICASSO program and PICS-348. 7.0 8.0 9.0

log(age)

REFERENCES

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100

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8

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