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Astron. Astrophys. 350, 434-446 (1999)

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4. The Pleiades moving groups

In Paper I we used a method based on non-parametric density estimators to detect MGs among a sample of 2 061 B and A main sequence type stars in the four-dimensional space (U,V,W,log (age)). We used HIPPARCOS data as well as radial velocities from several sources (see Paper I for the details) to determine the stellar spatial velocities, and Strömgren photometry for the stellar ages. Tables 1 and 2 in Paper I show the main properties of the MGs when separated in the (U,V,W,log (age)) and (U,V,log (age)) spaces respectively. Since the W-velocity component is less discriminant than the other three variables, we will focus our study on the MGs in Table 2 of Paper I (Table 1 here). In particular, as already mentioned in the Sect. 1, we will deal with those MGS whose velocity components resemble those of Pleiades open cluster.


[TABLE]

Table 1. Number of members ([FORMULA]), velocity components and ages (along with their dispersions) of the Pleiades MGs found in Paper I


It is interesting to compare these results with those recently obtained by Chereul et al. (1998), who also found similar substructures in the Pleiades and other MGs by means of a wavelet analysis performed at different scales. The velocity dispersions of their substructures are quite a bit larger than those found for classical MGs, in agreement with our results. In their analysis, they did not consider the stellar age as a discriminant variable, which prevents them from detecting those substructures that are strongly defined in age but not so well defined in the velocity components. Another important difference between both methods is that Chereul et al. (1998) did not determine photometric ages for A0 to A3 stars, since no reliable metallicity is available for them. Instead, they computed a "paliative" age that produces an artificial peak in age of [FORMULA] yr, and a lack of other young stars (up to [FORMULA] yr). As mentioned in Asiain et al. (1997), a metallicity [FORMULA] is representative, in a statistical sense, of (normal) A type stars. Using this value, we did not observe any lack of stars in the young part of the age distribution (Paper I). On the other hand, since we do not use F type stars in our study because of the high uncertainties involved in the process to determine their ages, our data do not allow us to confirm the existence of the [FORMULA] yr old Pleiades substructure found by Chereul et al. (1998).

Using the numerical integration procedure described in Sect. 3.1, and the mean properties (nuclei) of the Pleiades substructures found in Paper I (Table 1), we have computed the trajectories of these substructures from the present up to the moment they were born (Fig. 3). This latter age is defined as the average age of the MGs constituent members. The youngest group, i.e. B1, is composed of Scorpio-Centaurus (Sco-Cen) OB association members (Paper I), and it was born in the interarm region. In Sect. 4.1 we study the evolution of this group. Since B1 is still too young to be affected by the disc heating effect or phase space mixing, we can determine its kinematic age with some confidence. The B2 group is considered separately in Sect. 4.2. This is also quite a young group and contains accurate information on some of the closest associations. The birthplace of the older groups, i.e. B3 and B4, is close to a minimum of the spiral arm potential, which seems consistent with their being born around this structure. Details on their spatial and velocity evolution are given in Sect. 4.3.

[FIGURE] Fig. 3. Trajectories of the MG's nuclei in Table 1 backwards in time, from present ([FORMULA]) until their mean age. The dashed lines represent spiral arms, as defined in Sect. 3.1. The reference system is rotating with the same angular velocity as the spiral arms ([FORMULA])

In recent studies based on the velocity field of Cepheids, Mishurov et al. (1997) and Mishurov & Zenina (1999) obtained a set of spiral arm parameters which clearly differ from those adopted here (e.g., in Mishurov & Zenina (1999), [FORMULA] and [FORMULA] km s- 1 kpc-1). When considering these new parameters, all Pleiades MG substructures turn out to be also placed, at birth, around the spiral arms. In this particular case, the Pleiades substructures appear, at birth, concentrated in a small area of the Galaxy. We also tested that the main conclusions of the current paper does not critically change with the selection of any of this two spiral arm patterns, as expected.

4.1. Scorpio-Centaurus association

Because of the short age of these stars and the quality of our data we are able to determine quite precisely these stars' kinematic age, defined as the time at which they were most concentrated in space - assuming that they are gravitationally unbound. We consider here only those stars in B1 that are concentrated in space (see Fig. 7 in Paper I). With the exception of HIP84970 and HIP74449, all of these stars were classified as members of Sco-Cen association by de Zeeuw et al. (de Zeeuw et al., 19992. Their position in the galactic and meridional planes as a function of time are shown in Fig. 4. It is quite evident that between around 4 and 12 Myr ago these stars were closer to each other than they are at present. However, observational errors produce additional dispersions on velocity and position, and therefore the maximum spatial concentration we find is shifted to the present. Fig. 4 also shows us that the last intersection of the Sco-Cen association with the galactic plane was between 8 and 16 million years ago.

[FIGURE] Fig. 4. Spatial distribution of the 27 stars in B1 sub-group that are spatially concentrated in space as a function of time. Numbers in the upper right corners indicate the time in Myr

The evolution of the errors or dispersions in the stellar position and velocity can be calculated more precisely by means of the epicycle approximation (Eqs. A2). We now consider the fact that the observed dispersion in position inside a given MG ([FORMULA], where [FORMULA] is the distance from the LSR to a given star) can be decomposed into two parts, i.e.

[EQUATION]

where

[FORMULA] is the MG intrinsic dispersion at the time t, and
[FORMULA] is the MG mean observational error.

Since both [FORMULA] and [FORMULA] can be easily determined at different epochs ([FORMULA] can be calculated by integrating the stellar orbits until time t, and [FORMULA] can be propagated from present using Eqs. A2), we can also derive the time [FORMULA] at which [FORMULA] was minimum. In Fig. 5 we show the evolution of [FORMULA], [FORMULA] and [FORMULA]. We observe a clear minimum in [FORMULA] around [FORMULA] yr, which corresponds to B1 kinematic age. At the minimum spatial concentration we find the intrinsic spatial dispersions are [FORMULA] = 20 pc, [FORMULA] = 22 pc, and [FORMULA] = 15 pc, smaller than their current values of [FORMULA] = 30 pc, [FORMULA] = 33 pc, and [FORMULA] = 16 pc. Also, their intrinsic velocity dispersions were smaller at [FORMULA], and [FORMULA] 2 km s-1 in each component.

[FIGURE] Fig. 5. Evolution of the observed dispersion (dot-dashed line ), mean propagated error (dashed line ) and intrinsic dispersion (solid darker line ) in [FORMULA] (distance to the Sun), determined from the most spatially concentrated stars in the B1 group

There is a clear discrepancy between the kinematic and the "photometric" age of B1. This could be due to several reasons. First of all, most of the stars in B1 are massive, and their atmospheres are probably rotating very quickly. Thus, the observed photometric colors are affected by this rotation, and so are the derived atmospheric parameters. The photometric ages, determined from these atmospheric parameters and stellar evolutionary models (Asiain et al., 1997), are systematically overestimated because of this effect. In order to evaluate this effect, we have corrected the observed photometric colors for rotation by considering a constant angle of inclination between the line of sight and the rotation angle ([FORMULA]), and a constant atmospheric angular velocity ([FORMULA], where [FORMULA] is the critical angular velocity). In this way we obtain a mean age [FORMULA] yr, and even smaller values for [FORMULA]. More details on the correction for atmospheric rotation can be found in Figueras & Blasi (1998). Second, before applying our method to detect moving groups (Paper I) we eliminated all stars with relative errors in age bigger than 100%, which slightly bias the age of young groups to larger values.

In a recent study de Zeeuw et al. (1999) carried out a census of nearby OB associations using HIPPARCOS astrometric measurements and a procedure that combines both a convergent point method and a method that uses parallaxes in addition to positions and proper motions. Their sample of neighbouring stars is much larger than ours, since radial velocities and Strömgren photometry are needed for our analysis. They found 521 stars in the Sco-Cen association, of which only 65 were in our sample. From these stars we have determined the mean velocity components of each association, which are in close agreement to those of B1 (Table 2). However, their dispersions and ages are quite a bit larger than expected for a typical association. A deeper analysis revealed to us the presence of some stars in de Zeeuw et al.'s (1999) associations whose peculiar velocities are responsible for their large velocity dispersion. Consistently, the ages of these stars are also peculiar ([FORMULA] yr). Removing these stars and a few others with anomalously large ages 3, all of which probably belong to the field, we find a more reasonable kinematic properties and ages for these associations (Table 3).


[TABLE]

Table 2. Number of members ([FORMULA]), spatial velocity components and ages (along with their dispersions) of the Sco-Cen associations found by de Zeeuw et al. (1999), determined from those members present in our sample



[TABLE]

Table 3. Same as Table 2, now removing a few stars with peculiar velocity components and ages


4.2. B2 group

Even though B2 is quite a young group, the propagation of age uncertainties over time prevents us from determining the group's kinematic age by means of the procedure developed for the B1 group. Instead, we have determined the trajectories of each star in B2, and that of the MG's nucleus itself. The spatial concentration of these stars is propagated back in time by counting the number of stars found in 300 pc around the MG nucleus (Fig. 6). We do not find any maximum in spatial concentration during the last [FORMULA] yr. To better understand the structure of this group we plot in Fig. 7 the position of these stars and their velocity components on the galactic and meridional plane, referred to the LSR and corrected for galactic differential rotation. We observe that it is actually composed of several spatial stellar clumps , each of which has its own kinematic behaviour, although certain degree of mixture is also evident. In particular, one of these clumps (most of the filled circles in Fig. 7) perfectly overlaps with the Sco-Cen association mentioned above (20 of these stars are classified as members of this association by de Zeeuw et al. 1999). This clumps's velocity components, and kinematic age, are also very similar to those found for the B1 group. Once again, the photometric age of these stars is probably overestimated because of the high rotation velocity of their atmospheres 4. A second clump is coincident with the Cassiopeia-Taurus (Cas-Tau) association in both position and velocity spaces (most of the empty circles in Fig. 7). There are two dominant streams among these stars. In the heliocentric system, corrected for galactic differential rotation, their velocities are (U,V)[FORMULA](-10,-18) km s-1 and (-13,-23) km s-1 respectively (they share a common W component [FORMULA] km s-1). Their ages are [FORMULA] yr. These values are in good agreement with those found by de Zeeuw et al. (1999) for Cas-Tau association, i.e. (U,V,W) = (-13.24,-19.69,-6.38) km s-1 with an age of [FORMULA] yr (actually, about half of them are classified as Cas-Tau members by these authors). Finally, we observe a less concentrated group of stars at [FORMULA] kpc and [FORMULA] kpc, or [FORMULA] (diamonds in Fig. 7). The kinematic properties and age of this clump are very similar to those of the Cas-Tau association, whereas its position quite well agrees with that of the recently discovered Cepheus OB6 association (Hoogerwerf et al., 1997).

[FIGURE] Fig. 6. Number of MG stars placed around their nucleus (at a distance [FORMULA] 300 pc) as a function of time, for MGs B2, B3 and B4

[FIGURE] Fig. 7. Position of B2 stars at present and their velocities referred to the LSR and corrected for galactic differential rotation. Different symbols are used for three galactic longitude ranges. The size of the symbols is inversely proportional to the age of the stars they represent

Thus, B2 seems to be the superposition of several OB associations from the Gould Belt, which are mixing with each other in the process of disintegration. These stars were classified as belonging to the same MG in Paper I since they roughly share the same kinematics and age, a consequence of their being formed from the same material.

4.3. Older Pleiades subgroups

Groups B3 and B4 in Table 1 are considerably older than B1 and B2, and therefore only few details on the conditions in which they were formed can be recovered. In particular, the uncertainties in [FORMULA] due to observational error increase almost monotonically with time. Though this increase can be closely approximated by Eq. 3 for an axysimmetric galactic potential, when considering the terms [FORMULA] and [FORMULA] this approximation breaks (it only works during the first [FORMULA] yr). To estimate the effect of typical errors in both the position ([FORMULA] 10-15 pc) and velocity ([FORMULA] 2-3 km s-1) components of moving groups on [FORMULA] as a function of time, we have simulated a stellar group whose dispersions in the phase space equals those errors, then determined their orbits. We obtain a dispersion in [FORMULA] due to these errors of [FORMULA] 500 pc after [FORMULA] yr. Moreover, we cannot know the way in which individual orbits have been perturbed due to the disc heating effect, producing additional spatial and velocity dispersions.

As mentioned above, these older groups seem to have been born in the vicinity of the spiral arms. The position at birth of groups B3 and B4 are especially interesting: on the one hand, the trajectories followed by these groups show a maximum galactocentric distance at the moment they were born, which corresponds to a minimum kinematic energy (Figs. 3 and 8); on the other hand, by determining the trajectories of the B3 members we observe two focusing points close to the B3 and B4 birthplaces (Fig. 8). An identical result is obtained when using B4 stars. Following Yuan (1977), these points could be interpreted as the birthplace of B3 and B4. For spatially concentrated groups of stars with small velocity dispersions epicycle theory predicts (Sect. 2) the focusing phenomenon will be produced every [FORMULA]. Since the Pleiades groups oscillate around a guiding center placed at [FORMULA] 8.0-8.2 kpc, the corresponding epicycle frequency is [FORMULA] 38-40 km s- 1 kpc-1 (determined from [FORMULA], Sect. 3.1), with [FORMULA] 1.5-1.6 [FORMULA] yr. This period [FORMULA] is compatible with the ages of B3 and B4.

[FIGURE] Fig. 8. Stellar trajectories of the B3 members during the last 3.5[FORMULA] yr. The position of the B3 nucleus at t = 0, -1.5 and -3 [FORMULA] yr (in units of [FORMULA] yr) is indicated with an open circle. The reference system is the same as in Fig. 3

By following the same procedure used for the B2 group we study the spatial concentration of the older groups (Fig. 6). For B4 there is a maximum concentration at [FORMULA], which corresponds to this MG's age, whereas we observe two peaks in concentration for B3 at [FORMULA] and [FORMULA] respectively, the first one corresponding to the last focusing event, and the second one corresponding to the average age of its members.

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© European Southern Observatory (ESO) 1999

Online publication: October 4, 1999
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