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Astron. Astrophys. 325, 613-622 (1997)

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3. Kinematics

3.1. Velocity dispersion

Positions and proper motions of the stars from Tables [FORMULA] are shown in Figs. 1 and 2. We exclude stars with proper motions clearly off the Taurus mean motion from the discussion in this section; they are discussed separately in Sect. 4. Clustering of the remaining stars around the overall mean values [FORMULA] mas/y is visible in the proper motion diagram, and we immediately note that there is a relatively large scatter around the mean motion. Also, there is a slight difference in motion between the stars in the central region (Tables 1 and 2) with a mean proper motion of (2.4, -21.1) mas/y and those from the southern region (upper part of Table 3) with a mean of (10.1, -9.8) mas/y. The difference in [FORMULA] ([FORMULA]) is significant with confidence level larger than 95 [FORMULA] (99.9 [FORMULA]) in a t -test for distributions with different dispersions.

[FIGURE] Fig. 2. Proper motions of all the stars in the centre (Tables 1 and 2) and of the youngest stars in the south (upper part of Table 3). The coding of the different stars is the same as in Fig. 1. Note that the proper motion of LkCa 14 is too large to be shown in this diagram (it maybe wrong anyway, see Sect. 4).

We first discuss the velocity dispersion inferred from the scatter in proper motions. The distance of the Tau-Aur clouds is determined to be 140 pc (Elias 1978, Kenyon et al. 1994). Recently Preibisch & Smith (1997) have determined a best fit distance of [FORMULA] pc on the basis of rotational properties of 25 WTTS, in good agreement with previous determinations of the distance of the whole cloud. At a distance of 140 pc the scatter in proper motion corresponds to a velocity dispersion in one coordinate of 6.5 km s-1 for the whole complex. Splitting the sample into stars in the central and the southern region, we find a velocity dispersion in the central part of Tau-Aur of 5.4 km s-1, while the stars in the southern region exhibit a velocity dispersion of 7.6 km s-1.

The mean error of the STARNET proper motions of 5 mas/y (Röser 1996) corresponds to 3.3 km s-1 at a distance of 140 pc. Subtracting this from the observed scatter we get an intrinsic scatter of 4.3 km s-1 for the stars in the central part and 6.8 km s-1 for the stars in the southern region. These values appear very large compared to previous investigations. Jones & Herbig (1979) derive an overall intrinsic velocity dispersion of 3.2 km s-1 and 2.2 km s-1 in their x - and y -direction (x essentially parallel to right ascension, y parallel to declination), respectively, but the region investigated by Jones & Herbig (1979) is smaller than our 'central region' which is roughly the same as in Wichmann et al. (1996).

There is a significant difference in the determination of proper motions in Jones & Herbig (1979) and proper motions from STARNET. The region in Jones & Herbig (1979) is separated into subregions each corresponding to plate pairs. Proper motions are determined differentially from these plate pairs. This minimizes the effect of projection of the space motions over large areas of the sky, which is inherent in our proper motions because they are absolute proper motions (on the system of FK5).

The mean proper motion of [FORMULA] mas/y and [FORMULA] mas/y given by Jones & Herbig (1979) is comparable to our mean motion, indicating that the difference of the two astrometric systems is small. A thorough conversion of the proper motions between the Jones-Herbig system of relative proper motions and the FK5 system of STARNET proper motions is not possible because only few stars are in common.

Jones & Herbig (1979) subdivided the complex into smaller subregions, as they had a fainter limiting magnitude and a larger number of stars. Within these subgroups they determine the intrinsic velocity dispersion in the following way. From the measured scatter of the proper motions they subtract the scatter expected from the accuracy of their measurements. However, these two quantities are almost equal. So, they derive an upper limit of 1-2 km s-1 in most of their subgroups. The size of our sample does not allow for a further subdivision. We can only study the velocity dispersion of the complex as a whole. A velocity dispersion of 5.4 km s-1 would disintegrate the Tau-Aur complex in a time of the order [FORMULA] years, but typically smaller than the ages of the PMS stars. We suppose that a large part of the measured velocity dispersion can be attributed to the ad hoc assumption that all stars are situated at a distance of 140 pc, and we discuss this in the next section.

3.2. Space velocities

As the stars of our sample populate a large region on the sky the influence on proper motions caused by projection effects has to be taken into account. It is necessary to consider the total space velocities for a discussion of the velocity dispersion. In the literature (see Table 1 in Neuhäuser et al. 1995a for references) we found radial velocity measurements for 28 stars in the central area of Table 1.

Space velocities of 26 of these stars (omitting the 2 stars with zero proper motion components) calculated under the assumption of a fixed distance of 140 pc for all stars are shown in Fig. 3 (upper panel). The corresponding velocity dispersions are [FORMULA] km s-1, [FORMULA] km s-1 and [FORMULA] km s-1. The low dispersion in U is caused mainly by the distance-independent radial velocities. The large dispersion in V and W cannot be explained by the mean errors of STARNET proper motions, and we suggest that it is (at least partly) due to the lack of knowledge of the true distances.

[FIGURE] Fig. 3. Space velocities for 26 TTS of Table 1 with radial velocities available. In the upper panel space velocities are calculated assuming fixed distances of 140 pc for all stars, in the lower panel distances are adjusted so that the resulting space velocity for every star is as close as possible to the mean space velocity of the upper panel. U points in the direction of the galactic centre, V in the direction of galactic rotation and W towards the north galactic pole. The highest peak in the V velocities based on fitted distances is due to 11 stars.

We tested this hypothesis by varying the distance of each star in order to minimize the difference between the corresponding space velocity and the mean space velocity of the complex at a fixed distance of 140 pc. By this, the dispersion in the velocity components is significantly reduced to 2.1 km s-1, 3.3 km s-1 and 2.8 km s-1 (Fig. 3 ; lower panel). The resulting velocity dispersion is now almost equal in all three components, an indication for the correctness of our hypothesis. A velocity dispersion of about 3 km s-1 in one component is very close to the formal error of STARNET proper motions. This sets an upper limit to the intrinsic velocity dispersion. This upper limit must be small compared to 3 km s-1 in order to have no influence on the measured velocity dispersion. This result is consistent with the result of Jones & Herbig (1979) for the smaller subgroups within their sample.

The distances calculated in the manner described above are shown in Fig. 4. The mean of these distances is 127 pc, close to 140 pc. Furthermore our sample is biased towards brighter stars, i. e. nearer and/or earlier type stars, so a slightly lower value than the distance to the whole cloud complex is expected for these stars. The dispersion of the distances is 39 pc which is comparable to the extent of the association in the tangential plane of at least [FORMULA] or 49 pc at a distance of 140 pc.

[FIGURE] Fig. 4. Distance histogram for the stars shown in Fig. 3. Distances are calculated requiring that the resulting space velocities are close to the mean. The mean of the distances is 127 pc with a dispersion of 39 pc.

It is impossible to solve for the mean motion of the cluster and the distances of the stars simultaneously. Minimizing the velocity dispersion always favours lower distances and a lower mean cluster motion, so all these values would tend to zero. Minimizing only the relative dispersion, normalized to the absolute value of the space velocity, yielded a velocity dispersion which was much lower than expected from the errors of the STARNET proper motions and in turn an unbelievably high dispersion in the resulting distances.

These kinematically determined individual distances of the stars are not to be taken too literally; for this the method is too coarse. However, the method yields a general tendency for the distribution of the radial distances of the TTS in Taurus-Auriga.

3.3. Relation of the southern stars to Taurus-Auriga

We discuss different scenarios for the origin of the youngest stars in the southern region and their possible relation to the Taurus molecular clouds.

(a) First we assume that the young stars in the southern region belong to the Taurus-Auriga complex and share the same mean space motion. Because of their different proper motions the southern stars cannot fulfill the requirement of the same space motion if they are at a distance of 140 pc. Varying their distances as described above (with a solution in the distance interval between 50 pc and 300 pc for only 11 out of 16 stars), we find that they would be located at lower distances than the stars in the central area with a mean distance of 88 pc. This however leads to a conflict in the HR diagram (Fig. 5): Nearly all the stars in the south would lie below the main sequence for 88 pc which is in contradiction to their zero-age main sequence or even pre-main sequence nature. The velocity dispersions calculated with these distances are [FORMULA] km s-1, [FORMULA] km s-1 and [FORMULA] km s-1. The dispersions in V and W are close to the values derived for the stars in the central region, but the dispersion in U (which is more or less independent of the distances) is higher than expected for members of a common star forming region.

[FIGURE] Fig. 5. Hertzsprung Russell diagram for the stars of Tables 1 and 2 and the youngest stars of Table 3 without the high proper motion stars discussed separately in section 4. Apparent V -magnitudes are taken from GSC (typical errors 0.3 mag) without corrections for extinction. Spectral types are taken from SIMBAD for stars of Table 1, from Wichmann et al. (1996) for stars of Table 2 and from Magazzù et al. (1997) for the stars of Table 3. The ZAMS is calculated for a distances of 140 pc and 88 pc, respectively. Some pre-ROSAT CTTS and WTTS appear below the ZAMS because we did not correct for absorption.

(b) If we assume that the stars are located at comparable distances to the Taurus-Auriga association of about 140 pc, this would make their location in the HR diagram comparable to the Taurus member stars. Kinematically they would not be related to the Taurus clouds, but the two complexes would rather approach each other with a relative velocity of [FORMULA] km s-1 and were adjacent to each other now only by chance. It might be possible that the Taurus clouds originated in a high-velocity cloud impact, so that the Taurus clouds oscillate around the galactic plane. During the last passage through the plane, the stars were separated (combing-out) from the Taurus clouds, and now move ahead and already begin to fall back to the plane. Alternatively, all the young stars south of Taurus may just be Gould's belt members with typical ages of 3-5 [FORMULA] yrs; see Neuhäuser et al. (1997) for a discussion.

(c) If the stars were more distant than 140 pc the HR diagram would constrain them to be really very young pre-main sequence stars. At the same time they would show a velcocity dispersion higher than expected for a group of very young stars, and likewise very high X-ray luminosities. In the tangential plane the two complexes would pass more or less closely depending on the distance difference.

Neither of the above scenarios is completely convincing. Maybe the stars in the southern area do not have a common origin and are not located at approximately similar distances. Brice no et al. (1997) suggest that the population discoverd by ROSAT south of the Taurus clouds is not made up of pre-main sequence but rather main-sequence stars for which we do not expect that they share a common kinematic behaviour. On the other hand only a small fraction of the youngest stars in Table 3 are really PMS stars; about half of the PMS stars in Neuhäuser et al. (1997) are too faint for STARNET. None of the younger stars appear to be ejected from the northern Tau-Aur region. It should be kept in mind, however, that dynamically ejection mechanisms favour low-mass escapers (Sterzik & Durisen 1995). These stars are absent in this magnitude limited subsample.

Our kinematical findings indicate most probable that the PMS stars in the southern extension move towards the central Tau-Aur region. This implies a larger separation of the two complexes in the past. From the kinematical point of view a common star formation process seems therefore excluded. The larger ages of the southern stars support our conclusion that star formation in the two complexes must have been triggered by different events.

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© European Southern Observatory (ESO) 1997

Online publication: April 28, 1998

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