4 Discussion of the results

As we already mentioned, our results cannot be easily compared with those in the literature previous to the Hipparcos mission, since they use a different system. Glushkova et al. (1997) presents proper motion measurements for 181 clusters (and 21 open clusters in Glushkova et al. 1996). The differences found are compatible with our estimated errors. Note that although Glushkova et al. claim that they determine absolute proper motion, they do not refer to the Hipparcos system. Actually, the transformation from the 4M Catalogue (Gulyaev & Nesterov 1992) has to be done via the PPM Catalogue (Röser & Bastian 1991). We performed a quick comparison between the results of Glushkova et al. and those of BDW (187 objects in common), and we found a relative standard deviation of about of 5 mas/yr in both directions. This is larger than we would expect from the errors estimated in the two papers.

Figure 1: Comparison of our mean proper motions with BDW in $\mu_{\alpha}\cos{\delta}$.

Figure 2: Comparison of our mean proper motions with BDW in  $\mu _{\delta }$.

Our results can be compared with those of BDW, that were directly taken from the Hipparcos Catalogue. We present the differences for 86 common objects in Figs. 1 and 2. Gaussian fits to the histogram of differences (Figs. 3 and 4) give the mean proper motion differences of 0.1 mas/yr in $\mu_{\alpha}\cos{\delta}$ and 0 mas/yr in $\mu _{\delta }$; the root mean square differences are 1.2 mas/yr in $\mu_{\alpha}\cos{\delta}$ and 1.3 mas/yr in $\mu _{\delta }$.

Figure 3: Histogram of the mean proper motion differences of 86 common clusters with BDW in $\mu_{\alpha}\cos{\delta}$.

Figure 4: Histogram of the mean proper motion differences of 86 common clusters with BDW in $\mu _{\delta }$.

The differences between BDW and our work are within the precision of our measurements, in most cases. The mean of the differences show that there is no systematic trend, and the small value of the mean square difference assures that both sets of measurements are in agreement.

However, for 3 clusters, commented below, larger differences where found. In Fig. 1 we can see two discordant points and in Fig. 2 one discordant point, that present differences of about 3 mas/yr. The points refer to the clusters NGC 3228, Rup 98 and NGC 5822, respectively.

4.1 Ruprecht 98

One point that differs from BDW in Fig. 1 refers to Rup 98. For this cluster the proper motion of BDW was determined based on one star only (HIP 58432). This star is present in the Tycho 2 sample and our analysis shows that this star has a high membership probability ($P=93\%$). The difference obtained is due to the difference between Tycho2 ( $\mu_{\alpha}\cos{\delta} = -6.40$ mas/yr and $\mu_{\delta}= -9.30$ mas/yr) and Hipparcos ( $\mu_{\alpha}\cos{\delta} = -3.88$ mas/yr and $\mu_{\delta}= -8.57$ mas/yr) proper motion. Our statistical analysis confirms the membership of HIP 58432, but suggests that our proper motion determination, based on a large number of stars, is the correct one.

4.2 NGC 3228

We obtain a mean proper motion different from that of BDW. In this case, the proper motion given by BDW is based on 4 Hipparcos stars, and interestingly, 3 stars are present in our sample and were selected by our method. It seems that for this cluster our method is unable to distinguish the members from the background, which has approximately the same proper motion. We can see in Table 2 that the average proper motion of the background stars is quite different from zero. This cannot be explained by the reflex solar motion, since distant stars are expected to present negligible proper motion. Since the cluster is in the direction of the Carina spiral arm of the galaxy, it is possible that in the field studied, the population of stars belonging to the arm dominates over the more distant stars, and we get a biased background.

Based on this analysis, and considering the direction of the cluster and its small distance (529 pc), we expect NGC 3228 to present a large proper motion, and in this case, the result of BDW is probably correct.

4.3 NGC 5822

We could not find the origin of the problem for NGC 5822. In this case, many more stars were used in our statistical analysis and the Hipparcos proper motions agrees with the Tycho2 ones, for the two stars used by BDW. The selection of membership in our results is not reliable because there is no conspicuous separation of two populations in the investigated field.

It is possible that in this case, the large difference with respect to BDW could be explained by the large scattering of proper motions in $\mu _{\delta }$. The BDW mean proper motion of NGC 5822 may not express the real proper motion of the centroid of the cluster. A more detailed investigation using faint stars could be helpful to solve this doubt.

4.4 The analyses of the stars in Collinder 399 and Roslund 5

Two controversial objects (Col 399 $\alpha=19^{\rm h}25^{\rm m}$; $\delta=+20^{\rm o}11^{\prime}$ and Ros 5 $\alpha=20^{\rm h}10^{\rm m}$; $\delta=+33^{\rm o}46^{\prime}$ in J2000), discussed by Baumgardt (1998, hereinafter B98) were investigated with the help of Tycho2 proper motions.

An area of two times the area covered by the clusters (centered on the coordinates below) was examined and no clear concentration of stars in the vector proper motion diagram (VPD) of Col 399 were found (see Fig. 5). Although the statistical solution could be compatible with the existence of an open cluster, the VPD and the large standard deviation in mean proper motion indicate that Col 399 is only a concentration of bright stars and not a real cluster, as suggested by B98.

Figure 5: Vector proper motion diagram of the stars in the region of the Collinder 399.

Also in the case of Ros 5, we do not see two separated populations. Tycho2 proper motions suggest the existence of a loose concentration of stars at $\mu_{\alpha}\cos{\delta}=2.5$ mas/yr and $\mu_{\delta}=-1.5$ mas/yr.

B98 gives some arguments that corroborate the real existence of Ros 5. It is important to keep in mind that the Ros 5 is situated relatively far from the galactic plane ( $b = +71.4^{\rm o}$) corresponding to Z = 160 pc for a distance of 500 pc. This distance to the plane may seem surprising for a young cluster ( $\log t = 7.8$ years); a possible explanation could be star formation by the impact of a high-velocity cloud with the gas of the galactic plane (Lépine & Duvert 1994).

 

 

Table 3: Comparison between our results of mean proper motions of the clusters (Cols. 2 and 3) and those obtained in the literature (Cols. 4 and 5). Note that in the both sets the values are in the Hipparcos system, in mas/yr. In less two columns are given the difference (in modulus) that shows the coincidence of the results. To the clusters Col 135, Col 132 and Ros 5 the paper gives only the values of the concentration of proper motions in VPD. The references are given in text.

Cluster	$\mu_{\alpha}\cos{\delta}$	$\mu _{\delta }$	$\mu_{\alpha}\cos{\delta}$	$\mu _{\delta }$	$\Delta\mu_{\alpha}\cos{\delta}$	$\Delta\mu_{\delta}$	REF
Bla 1	$20.2 \pm 2.6$	$3.1 \pm 2.6$	$19.2 \pm 2.0$	$2.8 \pm 2.0$	1.0	0.3	a
Bla 1	$20.2 \pm 2.6$	$3.1 \pm 2.6$	$19.15 \pm 0.50$	$3.21 \pm 0.27$	1.0	0.1	c
Col 121$^{\star}$	$-5.7 \pm 3.2$	$3.7 \pm 3.2$	$-5.1 \pm 0.1$	$-1.5 \pm 0.1$	0.6	5.2	e
Col 121	$-5.7 \pm 3.2$	$3.7 \pm 3.2$	$-3.88 \pm 0.16$	$4.35 \pm 0.19$	1.8	0.6	c
Col 132	$-2.0 \pm 3.6$	$3.0 \pm 3.6$	$-3.57 \pm 0.24$	$4.16 \pm 0.31$	1.6	1.2	c
Col 132	$-2.0 \pm 3.6$	$3.0 \pm 3.6$	-3.0	4.0	1.0	1.0	d
Col 135	$-10.7 \pm 1.1$	$5.3 \pm 1.1$	-10.5	6.0	0.2	0.7	d
Col 140	$-7.3 \pm 1.8$	$2.7 \pm 1.8$	$-8.52 \pm 0.22$	$4.60 \pm 0.28$	1.2	1.9	c
IC 2391	$-25.0 \pm 1.2$	$22.8 \pm 1.2$	$-24.6 \pm 1.1$	$23.2 \pm 1.1$	2.5	0.2	a
IC 2391	$-25.0 \pm 1.2$	$22.8 \pm 1.2$	$-25.06 \pm 0.25$	$22.73 \pm 0.22$	0.1	0.1	c
NGC 1662	$-1.9 \pm 1.2$	$-2.2 \pm 1.2$	$-3.2 \pm 0.6$	$-1.6 \pm 0.6$	1.3	0.6	b
Pleiades (Mel 22)	$19.9 \pm 1.7$	$-45.0 \pm 1.7$	$20.0 \pm 1.8$	$-45.1 \pm 1.8$	0.1	0.1	a
Pleiades (Mel 22)	$19.9 \pm 1.7$	$-45.0 \pm 1.7$	$19.15 \pm 0.23$	$-45.72 \pm 0.18$	0.7	0.7	c
Ros 5	$2.3 \pm 2.7$	$-1.5 \pm 2.7$	3.0	1.0	0.7	2.5	d
Sto 2	$17.3 \pm 2.3$	$-13.2 \pm 2.3$	$17.1 \pm 4.6$	$-12.9 \pm 4.6$	0.2	0.3	a
Sto 2	$17.3 \pm 2.2$	$-13.2 \pm 2.2$	$15.97 \pm 0.75$	$-13.56 \pm 0.54$	1.3	0.4	c
Tru 10$^{\star}$	$-14.5 \pm 1.5$	$-3.4 \pm 1.5$	$-14.3 \pm 0.2$	$-4.9 \pm 0.2$	0.2	1.5	e
Tru 10	$-12.1 \pm 1.5$	$6.7 \pm 1.5$	$-13.29 \pm 0.25$	$7.32 \pm 0.24$	1.2	0.6	c
Tru 37	$-1.6 \pm 2.7$	$-1.8 \pm 2.7$	$-3.75 \pm 0.35$	$-3.48 \pm 0.33$	2.1	1.7	c

a) Sanner & Geffert (2001), A&A, 2001, 310, 87; b) Dias et al. (2000), A&A, 357, 149; c) Robicon et al. (1999), A&A, 345, 471;
d) Baumgardt (1998), A&A, 340, 402; e) De Zeeuw et al. (1999), AJ, 117, 354

$^{\star}$ Mean proper motions are in ( $\mu_{l}\cos{b}$, $\mu_{b}$)

 

 

Table 4: Hipparcos data of the stars in the region of the cluster Rup 147, Sto 10, VDBH 23, VDBH 34 respectively. In Cols. 1 and 2 are given the equatorial coordinates in J2000. Then are given: Hipparcos number, visual magnitude, the parallax (in mas) the proper motion in $\mu_{\alpha}\cos{\delta}$ and $\mu _{\delta }$ (in mas/yr), the parallax error (in mas), B-V, and the membership probability obtained using our data (in $\%$).

$\alpha_{2000}$	$\delta_{2000}$	num HIP	V	parallax($\pi$)	$\mu_{\alpha}\cos{\delta}$	$\mu _{\delta }$	$\sigma_{\pi}$	B-V	P
19 15 26.117	-16 05 57.07	94635	7.43	3.57	-1.98	-27.84	1.01	1.259	100
19 17 23.845	-16 04 24.35	94803	7.65	3.75	-2.00	-27.33	1.04	1.396	100
05 39 04.270	+37 58 35.90	26585	7.51	3.74	-1.88	-1.27	0.99	0.043	69
05 39 36.800	+37 59 20.00	26632	6.96	2.60	-2.20	-0.81	0.99	0.015	87
05 41 31.090	+38 11 18.00	26803	8.18	2.68	-0.93	-3.05	1.16	0.308	80
08 12 50.710	-36 13 41.34	40218	7.62	3.20	-7.62	7.40	0.69	-0.129	92
08 13 18.194	-36 20 30.26	40255	7.32	2.67	-6.77	7.21	0.61	-0.120	92
08 13 22.654	-36 18 37.50	40268	7.34	2.51	-7.59	7.18	0.63	-0.143	92
08 13 29.517	-35 53 58.26	40274	4.78	3.33	-7.30	10.07	0.51	-0.110	36
08 13 58.312	-36 19 20.21	40321	5.09	2.77	-8.66	7.89	0.54	-0.184	85
08 13 58.700	-36 20 26.80	40324	6.11	2.20	-7.21	7.69	0.55	-0.185	75
08 15 58.823	-35 54 11.49	40485	6.15	1.72	-8.11	6.59	0.55	1.549	90
08 16 12.582	-35 52 55.74	40506	7.29	13.15	15.24	35.14	0.68	0.890	0
08 16 24.995	-36 12 09.35	40519	7.18	2.83	-10.50	7.03	0.65	-0.137	84
08 29 51.237	-44 44 36.40	41684	8.72	1.55	-1.42	2.81	0.84	0.042	76
08 30 39.230	-44 44 14.35	41737	6.30	1.46	-9.65	4.90	0.67	-0.007	69

4.5 Comparison with other astrometric studies

Some open clusters in our sample are in common with other individual astrometric studies. In this comparison we use only results of mean proper motion of the clusters given in the Hipparcos system. Comparison between the selected members with others selected by photometric criteria will be presented in a forthcoming paper.

Using recent positions obtained by meridian circle observations combined with other astrometric Catalogues, Dias et al. (2000) determined accurate mean proper motions of stars with $V \leq 15$ in the region of the open cluster NGC 1662. The membership determination was obtained applying the Zhao & He (1990) method. Our present results are in agreement with Dias et al. (2000), the small difference being within the errors of our study.

We have in common with the work of De Zeeuw et al. (1999) the open clusters Trumpler 10 and Collinder 121. In that paper the proper motions are given in galactic coordinates ( $\mu_{l}\cos \it b$, $\mu_{\it b}$), and we transformed our mean proper motions to galactic coordinates ( $\mu_{l}\cos \it b$, $\mu_{\it b}$). We can see that our mean proper motions are in agreement with those of de Zeeuw et al., both results being different from those of BDW. The nature of a number of open clusters was investigated by B98 using the Hipparcos data. In many cases B98 gives the values of proper motion of the concentration of the stars in the VPD. If we use these values as the mean proper motion of the clusters, it is possible to compare them with our results (Table 3), in spite of the small distances of these objects. Except for the difference of 2.5 mas/yr in Ros 5, our results are in good agreement with the literature. The difference are still within our errors and may be caused if the value of B98 (based only in two stars) does not well represent the real mean proper motion of the centroid of the cluster.

In another study, Robichon et al. (1999, hereinafter RAMT) determined the mean astrometric parameters of nearby ( $d \leq 500$ pc) open clusters using data from the Hipparcos Catalogue. In this study two different member selections were applied to distinguish members from the field stars. For all clusters closer than 300 pc (and for 8 clusters closer than 500 pc) the parallaxes and proper motions of the stars were used and for the other clusters (farther than 500 pc or with less than 8 members in Hipparcos) the preselected stars in the Hipparcos Imput Catalogue (HIC) (Turon et al. 1992) were taken into account.

Figure 6: Comparison of our results of mean proper motions with those provided by Robichon et al. (1999). The differences as a function of the Robichon et al. results are presented. Note that $\bullet$ represents the values in $\mu_{\alpha}\cos{\delta}$ and ${\ast }$ in $\mu _{\delta }$.

Our sample and that of RAMT have 32 objects in common and using this set we checked the quality of our mean proper motions. We determined the differences of each result (see Fig. 6) and the mean square difference in $\mu_{\alpha}\cos{\delta}$ and $\mu _{\delta }$ (0.2 mas/yr). Clearly, no large differences can be seen and all of the differences are within 2.5 mas/yr, the typical error of our study.

4.6 Mean parallaxes of 4 clusters obtained from membership determination

We investigated the open clusters Ruprecht 147 ( $\alpha=19^{\rm h}16^{\rm m}$; $\delta=-16^{\rm o}17^{\prime}$; J2000, Stock 10 ( $\alpha=05^{\rm h}39^{\rm m}$; $\delta=+37^{\rm o}56^{\prime}$; J2000, vdB-Hagen 23 ( $\alpha=08^{\rm h}14^{\rm m}$; $\delta=-36^{\rm o}23^{\prime}$; J2000) and vdB-Hagen 34 ( $\alpha=08^{\rm h}31^{\rm m}$; $\delta=-44^{\rm o}30^{\prime}$; J2000) that have no distance determined. The identification of the members of the cluster allows us to use the data from the Hipparcos Catalogue to derive the distance of these objects (see Table 4). The parameters obtained from the Sanders method for these clusters are given in Table 2; using 2 stars for Rup 147, 3 stars for Sto 10, 7 stars for VDBH 23 and 2 star for VDBH 34 we derive the mean parallax of $3.7 \pm 0.2$, $3.0 \pm 0.6$, $2.6 \pm 0.5$ and $1.5 \pm 0.05$ respectively. We can see that these clusters are within 1 kpc with distances of roughly 250 pc, 333 pc, 384 pc and 666 pc, respectively.

This constitutes the first estimation of the distance of these clusters but a more rigorous photometric investigation is of interest to confirm these values.