IRREGULARITIES of the VELOCITY FIELD J. Torra1

Home , Gould Belt

513

YOUNG STARS: IRREGULARITIES OF THE VELOCITY FIELD

1 2 1 3

J. Torra ,A.E.G omez , F. Figueras , F. Comer on ,

2 4 1 1

S. Grenier , M.O. Mennessier , M. Mestres ,D.Fern andez

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

Observatoire de Paris-Meudon, D.A.S.G.A.L., France

Europ ean Southern Observatory, Garching b ei Munc hen, Germany

GRAAL. Universit e de Montp ellier I I, France

interpreted as a lo cal e ect of the spiral arm Lind- ABSTRACT

blad 1973, by energetic event on the galactic disk

Olano 1982, Elmegreen 1982, corrugation waves in

the galactic disk Nelson 1976 or by an halo-disk

We present here a rst review of the structure and

interaction Comer on 1992, Lepine & Duvert 1995.

kinematics of the lo cal system of young stars. Hip-

parcos astrometric data for a large sample of O and

The velo city eld of young stars is describ ed to rst

B stars have b een complemented with a careful com-

order by the Oort's formulae Ogoro dnikov 1965

pilation of available radial velo cities and Stromgren

relating the observed radial velo city, distance and

photometry thus providing reliable distance, spatial

prop er motion with the solar motion and the gra-

velo city and age for each star in the sample. The

dients of the velo city eld. Several works have b een

fundamental parameters characterizing the structure

devoted to the determination of the Oort's constants

of the Gould Belt, inclination, size and age are deter-

considering only di erential rotation or including

mined. The velo city eld is studied by means of the

other e ects such as spiral structure or expanding

classical rst order approach. Oort's constants A, B,

motions Lindblad 1980, Cr ez e et al. 1973, Byl et al.

C, K are determined for several subsamples selected

1981, Comer on et al. 1991 among others.

by age and the results explained by the presence of

the Gould Belt.

2. THE CATALOGUE

Key words: galactic kinematics; young stars; Gould

Belt.

Our initial sample contains 6922 O-B typ e stars Hip-

parcos Internal proposal, INCA060, of which 5846

b elong to the Hipparcos Survey. The sources of ra-

1. INTRODUCTION

dial velo cities have b een the Barbier-Brossat 1997

and the Du ot et al. 1995 compilations. Priority

has b een given to the rst one, and only stars with

O and B stars in the solar neighb ourho o d have b een

quality A, B or C in the last compilation have b een

traditionally used as prob es of galactic structure and

considered Grenier 1997. Using these sources, only

kinematics. Their intrinsic brightness allows their

3182 stars of our total sample have known radial ve-

observations to great distances from the Sun, and

lo city, this parameter b eing, at present, the most im-

due to their youth, their motions can be exp ected

p ortant limitation to undertake the study of the ve-

to hold imp ortant clues to the pro cesses that formed

lo city eld in the solar neighb ourho o d.

them. An imp ortant characteristic of the distribu-

Stromgren photometry has b een used to compute tion of young stars were recognized more than one

photometric distances and ages. 3031 stars from our century ago when J. Herschel realized that the lo-

sample have complete photometry in the Hauck & cal system of young stars shows a concentration of

Mermillio d 1996 catalogue. From these, we have stars along a great circle tilted resp ect to the galac-

rejected the stars b eing double or multiple from Hip- tic equator. Since the pioneering work by Gould in

parcos <10 arcsec and m<3 mag, the variable 1874-1879 a great number of studies have b een de-

stars m > 0:6 mag and the stars showing p ecu- voted to the Gould Belt trying to explain its struc-

liarities in the sp ectral typ e or in the photometric ture and kinematics, characterized by the existence

indices Masana 1994. Crawford 1978 calibration of a expanding motion Lesh 1968, Stothers & Frogel,

has b een used to derive photometric distances which 1974, Frogel & Stothers 1977. More recently Westin

are compared to the Hipparcos distances { computed 1985, Comer on et al. 1991, Comer on 1992,

as the inverse of the parallax { in Figure 1. Al- Palous 1995 and Lindblad et al. 1997 have studied

though no systematic trend seems to b e present, an the Belt and determined its orientation, age and kine-

exp ected large scattering is observed for stars at dis- matics. Several mo dels have b een presented in order

tances higher than 200 pc. Other photometric cal- to explain the origin of the Gould Belt: it has b een 514

1000 250

200 750

150

500

100 Number of stars Hipparcos distance (pc)

250 50

0 0 0 250 500 750 1000 6.0 6.5 7.0 7.5 8.0 8.5 9.0

Photometric distance (pc) Log(Age)

Figure1. Comparison between photometric and Hippar- Figure 2. Age distribution of the working sample 2139

cos distances for the working sample 2139 stars. Pho- stars. Ages computedfrom Bressan et al. 1993 evolu-

tometric distances computed from Crawford 1978 cali- tionary models.

brations.

200

ibrations Balona et al. 1984, Jakobsen 1985 have

b een also considered for the computation of photo-

metric distances, thus checking that the kinematic

results do not dep end of the calibration used. 150

Individual ages have b een computed from the evo-

lutionary mo dels of Bressan et al. 1993 for solar

following Asiain et al. 1997 interp o-

comp osition 100

lation algorithm, which considers, as input parame-

ters, the T and log g derived from the photometric e

Number of stars

indices Mo on et al. 1985, grids. The stars show-

ing a relative error on age larger than 100 p er cent

have b een rejected these are stars near or b elow the

ZAMS for which the obtained age is not reliable.

The histograms of the age distribution and the com-

puted individual errors are presented in Figure 2 and

ely. Figure 3 resp ectiv 0 102030405060708090100

Relative error in Age

According to the physical information available we

Figure3. Distribution of the relative errors in age 2139

have de ned twoworking samples:

stars.

Sample 1: 2139 stars with good = 100

stars clearly showing the galactic b elt and the in-

p er cent ages and photometric distances. Useful

clined and assymetric structure of the Gould Belt.

to determine the fundamental parameters of the

Gould Belt.

Wehave not tried to individually separate the stars

b elonging to the Gould Belt from the ones in the

Sample 2: 1539 stars, a subsample of Sample 1,

galactic plane; otherwise we will follow the metho d

containing the stars with known radial velo cities

develop ed by Comer on et al. 1994, well suited for

having 7 km/s, well suited for the analysis

large samples, which allows a statistical determina-

of the systematic velo city eld.

tion of the parameters characterizing the geometry of

b oth b elts. We assume that the density distribution

of the sample in the celestial sphere can b e writen as:

3. FUNDAMENTAL PARAMETERS OF THE

GOULD BELT

l; b= l; b+ l; b 1

G g

We can see in Figure 4 where X,Y,Z are the galac-

tic helio centric co ordinates with X directed towards

the galactic center, Y in the direction of the galactic where and are the density distributions around

G g

rotation and Z directed towards the north galactic the Gould Belt and the galactic equator resp ectively.

p ole, the well known spatial distribution of young For each one of these distributions we assume that: 515

500

a) individual ages, to b e complete, our sample is limited

to stars brighter than 6.5 mag.

In Table 1 we show the results obtained for several

subsamples of sample 1 selected by age and photo-

Assuming q > 0 as an indicator of

−500500 metric distance. e see that it is de-

b) the presence of the Gould Belt, w

ned by i =17 20 and = 278 290 , in good

t with previous results. We found the high- 0 agreemen

Z (pc)

est q value, 0.94, for stars younger than 30 million

years and distances between 400 and 600 pc; some ears establish the limits

−500500 older stars up to 60 million y

the Gould Belt at 400 pc, and very few, if any,

c) of

stars older than 60 million years indicate also a limit

Tsioumis & Fricke 1979 considered the

0 of 400 p c.

extent to b e 450{600 p c, and Westin 1985 consid-

ered 250{500 p c dep ending on the galactic longitude.

e can see the relationship b etween age −500 In Figure 4 w

−1500 −1000 −500 0 500 1000 1500

and structure in the X, Z plane. Wewant to remark

X (pc)

that when the metho d is applied to the complete sam-

Figure4. Spatial distribution in the X,Z plane: a total

ple of OB Survey stars with V 7:9 see Figure 5

the same conclusions are reached, although in this

sample of 2139 stars; b 1120 stars with 60 Myr; c

case only sp ectral typ es are available as indicators of

1019 stars with >60 Myr.

evolution.

sin

4. SYSTEMATIC MOTION OF YOUNG STARS

/ exp 2

2 sin =2

4.1. Distribution of Residual Velo cities

b eing the angular distance to the equator of the

corresp onding distribution and its halfwidth. The

The sample of 1539 O-B typ e stars used to derive the

geometric parameters: inclination, i, longitude of the

systematic motion of young stars in the solar neigh-

ascending no de, , halfwidths of b oth b elts ;

G g

b ourho o d shows see Figure 6 an irregular distribu-

as well as the fraction of the stars, q , b elonging to

tion in the U,V plane, U,V,W b eing the comp o-

the Gould Belt which enters in the prop ortionality

nents of the velo city in the system de ned in Sec-

constant in Equation 2 are determined by an iterative

tion 3. The sample is reduced to 1417 stars when

maximum likeliho o d metho d.

those with residual velo city exceding 65 km s are

eliminated. Mean velo city and disp ersions of the

1000

working sample are:

6.5 7.9

U ;V ;W = -12.7, -14.6, -8.1 km s

o o

800 o

; ; = 16.0, 11.5, 8.0 km s

U V W

600

The values obtained for the solar motion when age

groups are considered see Table 2 are a ected 400 Number of stars

200

0 02468101214

V magnitude

Figure 5. Distribution of apparent magnitudes: 6922

stars from INCA060 proposal empty histogram and 2139

stars with good ages and photometric distances l led his-

togram.

The metho d has the advantage that the helio centric

distance of the stars are only used to de ne the limit

of the subsamples considered. The metho d will pro-

Figure6. U,V distribution of the 1539 stars with good

duce accurate results only if the sample is complete

enough. As can b e seen in Figure 5, if wewant to use kinematical data.

516

Table 1. Geometrical parameters of the Gould Belt as a function of distance and age: inclination i , longitude of the

ascending node , fraction of stars belonging to the Gould Belt q, angular width of the Gould Belt and the

G G

galactic belt , and number of stars N.

p c i q N

G G

0-30 10 years

r < 400 19.98.2 278.041.9 0.860.03 14.17 10.91 103

400 r < 600 17.615.2 287.862.4 0.940.03 10.06 11.79 56

600 r < 800 13.54.0 301.413.8 0.500.09 15.37 9.19 31

600 r < 2000 13.94.8 322.021.9 91

30-60 10 years

r < 400 20.810.3 290.425.2 0.650.03 8.43 23.39 201

400 r < 600 9.52.1 283.85.5 37

600 r < 800 13.75.4 283.78.9 0.190.13 43.57 6.99 9

600 r < 2000 18.59.5 282.310.9 0.460.09 28.32 6.25 31

60 10 years

r < 400 24.011.5 278.831.7 0.350.02 23.92 20.35 596

400 r < 600 21.25.2 178.320.3 20

1 @U @V

by the presence of moving groups as describ ed by

B =

Figueras et al. 1997.

2 @y @x

Thanks to the go o d qualityofthe Hipparcos astro-

1 @U @V

metric data and the accurate compilation of radial

C =

2 @x @y

velo cities, the mean errors are ; ; = 3.8,

U V W

1 1

3.8, 3.0 km s ,between1and2kms b etter than

previous studies.

1 @U @V

K = +

2 @x @y

4.2. Derivation of the Oort's Constants

where no systematic motion p erp endicular to the

plane is considered other than that arising from the

The Oort's constants have b een derived using a rst- solar p eculiar motion. The conversion factor k =4:74

order approximation of the systematic velo city eld if velo cities are expressed in km/s, prop er motions in

Ogoro dnikov 1965: arsec/yr, and distances in parcecs.

The three equations { radial velo city and prop er mo-

2 2 2

tion in longitude and latitude { have b een simultan-

V = Ar sin 2l cos b + Cr cos 2l cos b + Kr cos b

iously solved using an unweighted least square t. In

Table 2 we show the results obtained when di erent

U cos l cos b V sin l cos b W sin b 3

subsamples selected in distance and age are consid-

ered. The results for stars with distances 70 r

< 400 p c are summarized in Figure 7 where we can

appreciate the monotonic b ehaviour of the A and B

rk cos b = Ar cos 2l cos b + Br cos b Cr sin 2l cos b+

Oort's constants against age. The classical values of

1 1

+U sin l V cos l 4

A 15 and B 12 km s kp c are obtained for

the oldest sample, while values as lowasA=0 km

1 1 1 1

s kp c and B = 26 km s kp c are found for

the youngest stars. The K term shows, as exp ected,

rk = Ar sin 2l sin b cos b Cr cos 2l sin b cos b

a strong decrease with increasing age and disap ears

for ages b etween 40 and 60 million years, thus con-

Kr sin b cos b + U cos l sin b+

rming its relationship with the expanding motion

of the Gould Belt. On the contrary, the C constant

+V sin l sin b W cos b 5

shows a rather erratic and not explained b ehaviour

that could b e related to the spiral arms. The same

where l , b are the galactic co ordinates, r the distance,

trends app ear in Figure 8 where wehave plotted, for

V the radial velo city, and the prop er motions.

r l b

broad age groups, the values of the Oort's constants

U , v and W are the comp onents of the p eculiar

against the distance. We see that for the youngest

motion of the Sun in km s resp ect to the circular

age group A and B take low values for the nearest

velo city and A; B ; C and K are the Oort's constants,

region asso ciated with the Gould Belt, reaching the

linear combinations of the gradients of the systematic

classical values for distant stars, whereas for the old-

velo city:

est group quite stable classical values are found. The

K constant reaches the zero values at a distane of

ab out 500 p c which could indicate the extend of the

Belt in agreement with the determination we did in

the previous paragraph. Now again the C constant

1 @U @V

b ehaves rather di erent b eing the intermediate group

A = +

30{60 Myr the one showing the maximum variation.

2 @y @x

517

Table 2. Oort's constants and residual solar motion as a function of distance and age. Units: A, B, C, K in km s

1 1

kpc ;U ,V ,W in km s .

Age 10 yrs A B C K U V W N

70 p c r < 400 p c

< 2 -0.44.6 -26.04.6 3.14.6 14.34.6 10.21.1 17.91.1 7.61.0 57

2 E < 4 7.52.8 -17.42.8 9.02.8 10.12.8 10.10.7 16.50.7 8.00.6 114

4 E < 6 7.13.2 -15.13.2 6.83.2 3.83.2 13.40.7 15.30.7 7.70.7 134

6 E < 8 12.03.4 -13.63.4 7.53.4 -1.13.4 12.60.8 15.70.8 7.60.7 107

8 E < 10 14.14.0 -12.24.0 2.04.0 -1.54.0 14.60.9 15.00.9 7.70.9 94

< 3 3.73.1 -22.63.1 3.73.1 16.13.1 10.40.7 17.20.7 8.10.7 107

3 E < 6 6.92.4 -15.52.4 8.62.4 4.12.4 12.30.6 15.70.6 7.60.5 198

6 13.71.9 -9.81.9 -3.71.9 -0.21.9 12.40.4 14.40.4 7.20.2 625

400 p c r < 800 p c

< 2 14.12.1 -21.22.1 1.32.1 -2.42.1 9.71.2 15.41.2 6.51.1 73

2 E < 4 9.52.0 -23.82.0 -1.32.0 -0.92.0 9.11.1 13.91.1 9.70.9 78

4 E < 6 -0.13.2 -15.13.2 -1.43.2 0.73.2 17.31.6 13.31.6 7.81.5 45

6 E < 8 15.04.4 -10.94.4 2.54.4 -9.74.4 13.72.3 13.72.3 10.42.2 26

< 3 12.51.7 -21.41.7 -0.41.7 -3.91.7 9.91.0 14.91.0 7.50.8 117

3 E < 6 4.72.2 -18.62.2 0.12.2 2.82.2 14.01.2 13.41.2 9.21.1 79

6 11.93.6 -8.33.6 -2.03.6 -6.93.6 12.61.8 12.11.8 8.61.7 49

400 p c r < 1500 p c

< 2 14.51.1 -14.91.1 -0.41.1 -4.01.1 10.61.0 14.31.0 7.81.0 136

2 E < 4 10.21.6 -18.11.6 -1.21.6 -1.11.6 9.41.2 13.01.2 9.51.0 107

4 E < 6 2.52.3 -13.52.3 -5.72.3 0.52.3 18.71.5 12.51.5 9.51.4 61

6 E < 8 11.64.3 -11.74.3 0.34.3 -8.34.3 11.42.4 15.82.4 9.02.3 30

< 3 14.11.0 -14.81.0 -0.61.0 -4.31.0 10.20.8 13.80.8 8.10.8 191

3 E < 6 4.51.6 -16.01.6 -3.01.6 0.31.6 15.51.2 12.91.2 9.91.1 113

6 10.23.3 -10.23.3 -1.93.3 -6.73.3 10.71.8 14.11.8 7.21.8 55

15 15

10 10 A 5 A 5 0

−15 −10 B −20 B −15

−25 −20

8 5 C 6 C 0

4 −5

15 10 10 K 5 K 5 0 0 −5

0246810 0 200 400 600 800 1000

Age Distance (pc)

Figure7. Variation of A,B,C,K Oort's constants against Figure8. Variation of A,B,C,K Oort's constants against

age for stars within 70 pc r < 400 pc. Units: 10 yr distance. Dots: stars with ages between 0{30 Myr;

1 1

and km s kpc squares: ages between 30{60 Myr and triangles: ages

1 1

larger than 60 Myr. Units: km s kpc .

ACKNOWLEDGEMENTS

Balona, L.A., Shobbro ok, R.R. 1984, MNRAS 211,

973

This work has b een supp orted by CICYT ESP95-

Barbier-Brossat, M. 1997, private communication

180, PICASSO program and PICS-348.

Bressan, A., Fagotto, F., Bertelli, G., Chiosi, C. 1993,

A&AS 100, 647

Byl, J., Ovenden, M.W. 1981, MNRAS 196, 659

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