5 Comparison with other proper motion catalogues

 

5.1 PPM

  From the PPM catalogue (Röser & Bastian 1991), the standard catalogue of positions and proper motions before Hipparcos, we found 49 stars in a circular region with a radius of 85arcmin centered on IC348 (see Fig. 8, PPM stars drawn as +). For these 49 stars which are brighter than 12.5 (the PPM lists visual or photographic magnitudes) the average proper motion errors are 4.2mas/yr.

The proper motions of the PPM stars have been transformed to the Hipparcos system using the 20 Hipparcos stars in the field. All these Hipparcos stars were also found in the PPM catalogue. The accuracy of this transformation (Eq. (5) in mas/yr) was estimated as the mean error of the mean proper motion differences for these 20 stars.

 $\parbox{7.5cm}{\begin{eqnarray} \mu_x({\r... ...m PPM} \rightarrow {\rm Hipp}) = \mu_y({\rm PPM}) + 2.7 \pm 1.1.\end{eqnarray}}$

The proper motion diagram of the PPM stars after the transformation to the Hipparcos system is shown in Fig. 7a. There are 10 PPM stars within 30arcmin from the cluster center drawn as filled circles. These stars show a remarkable concentration in the proper motion diagram compared to the remaining stars outside this region. If we exclude one outlier (number 22 in Fredrick 1956, which is a clear nonmember), the remaining group of 9 stars shows a proper motion dispersion of 4.0mas/yr and 4.5mas/yr, respectively in $\mu_x$ and $\mu_y$, which is in good agreement with the catalogue errors. Therefore, from the PPM proper motions this group of 9 stars can be considered as a cluster with common proper motion (cf. Table 5).

  

Figure 7: Proper motions in Hipparcos system from different catalogues: PPM, ACT and Hipparcos stars within 85arcmin from IC348 are shown in a), b) and c). PPM and ACT stars with smaller distances from cluster centre (r < 30arcmin) are shown as filled circles in a) and b). Hipparcos stars with bold, normal and thin error bars, have parallaxes $\pi \gt 5$, $3 < \pi < 5$ and $\pi < 3$mas, respectively. There is a remarkable separation of three groups of stars seen in the Hipparcos data: foreground stars with large proper motion dispersion, a group of stars at intermediate distances between 200pc and 320pc with small proper motion dispersion (comparable to Hipparcos errors) and a third group of more distant stars which show again a larger proper motion dispersion. For comparison all stars from Fredrick (1956) are shown in d). Dashed lines show standard antapex direction

5.2 Starnet

  The Starnet catalogue (Röser 1996) gives proper motions determined from the combination of the improved Guide Star Catalogue (GSC1.2, Röser et al. 1997) and the Astrographic Catalogue (AC). Unless the large epoch difference of about 80 years, the GSC1.2 positions are only of moderate accuracy and, moreover, the accuracy of proper motions in the region of IC348 suffers also from the low accuracy of AC positions in the declination zone north $+30\deg$.Nevertheless, we have selected Starnet data in the same large region around IC348 (radius 85arcmin) yielding an overall number of 214 stars with GSC magnitudes < 13.5. For these stars the average proper motion errors were 6.6mas/yr, i.e. significantly larger than the errors of the present proper motion study and of other catalogue data used in this work. Therefore, we did not include these data in the discussion and a proper motion diagram is not shown here.

5.3 ACT catalogue

  The Tycho catalogue (ESA 1997) provides positions of about 25mas accuracy (at epoch 1991.25), for about one million stars with V < 11.5 but only low accurate proper motions ($\sim$25mas/yr). Combining the accurate positions (compared to other catalogues as PPM or GSC) with the measurements of the Astrographic Catalogue, made at the beginning of the century, one can get proper motions about ten times more accurate than the Tycho proper motions. This was done by Urban et al. (1998b), constructing the ACT catalogue after transforming the AC to the AC2000 on the Hipparcos system (Urban et al. 1998a).

From 69 Tycho stars within a 85arcmin search radius around IC348 ACT data are available for 65 stars. These stars plotted as $\times$ in Fig. 8 have average proper motion errors of 2.6mas/yr and 3.0mas/yr, respectively for $\sigma_{\mu_x}$ and $\sigma_{\mu_y}$.The proper motions of these ACT stars (already in the Hipparcos system) are shown in Fig. 7b with the stars of the central region around IC348 (r<30arcmin) being plotted as filled circles. If we further exclude from the six stars in the central region one outlier in the proper motion diagram, the remaining five stars are well concentrated with a proper motion dispersion of 2.5mas/yr and 2.8mas/yr, respectively in $\sigma_{\mu_x}$ and $\sigma_{\mu_y}$. This proper motion dispersion is in very good agreement with the catalogue errors so that from the ACT data these five stars can be interpreted as members of a cluster. Table 5 shows the mean proper motion and dispersion of the 5 ACT stars in comparison to different member selections from other catalogues.

  

Figure 8: Catalogue stars in an extended region around IC348. The large dashed circle shows the search radius of 85arcmin, the smaller one the cluster region with a radius of 30arcmin. The dashed box indicates the one square degree field of the present study. 49 PPM stars found within 85arcmin from IC348 are drawn as +, 64 ACT stars are drawn as $\times$. The 20 Hipparcos stars within 85arcmin are drawn as circles of different size and line thickness in dependence on their measured parallaxes: large and bold circles for stars with $\pi \gt 5$mas, circles with medium size and line width for stars with $3 < \pi < 5$mas, small and weak circles for stars with $\pi < 3$mas. One can see that the Hipparcos stars with intermediate distances, i.e. $3 < \pi < 5$mas, which were also found as a common proper motion group (see Fig. 7d) are not concentrated in the cluster region with a radius of 30arcmin but distributed over a larger field

  

Table 5: Comparison of mean proper motions (with their dispersions given in parentheses) for different membership criteria applied to some catalogues

5.4 Hipparcos

  Only five stars from the Hipparcos catalogue (ESA 1997) fall into the one square degree field of our investigation. Four of these stars were also included in the proper motion catalogue of Fredrick (1956). These stars are oPersei, the brightest (V=3.8, B1 III) star in the one square degree field around IC348, BD$+31\hbox{$^\circ$}643$a and BD$+31\hbox{$^\circ$}643$b (Fredrick numbers 17 and 18) generally accepted as the brightest members of IC348, and HD281157 (V=10.2, B5) which is number 24 of Fredrick and according to its proper motion also a member of IC348. Unfortunately, the Hipparcos proper motions and parallaxes of BD$+31\hbox{$^\circ$}643$a and BD$+31\hbox{$^\circ$}643$b are identical with large common errors of $\ge 3.5$mas/yr and 3.3mas, respectively. These errors are much larger than those of the other stars in the field (compare proper motion error bars in Fig. 7c).

The average proper motion errors of all 20 Hipparcos stars found within 85arcmin from IC348 are 1.5mas/yr and 1.3mas/yr, respectively in $\mu_x$ and $\mu_y$. The average parallax error of these 20 Hipparcos stars is 1.5mas. If we select among these relatively bright stars in an extended region around IC348 three groups with $\pi \gt 5$mas (8 stars), 3mas$< \pi <$5mas (7 stars) and $\pi < 3$mas (5 stars) and plot them in a proper motion diagram we can see a remarkable correlation between the proper motion dispersion and the distance (Fig. 7c). Whereas both foreground and background stars show larger proper motion dispersions, the group at intermediate distance shows a proper motion dispersion which is comparable to the Hipparcos proper motion errors. This is a strong indication that these 7 stars are members of a cluster.

Using all stars concentrated in the proper motion diagram shown in Fig. 7c at $(\mu_x,\mu_y)=(+5,-8)$ mas/yr within a circle of 6 mas/yr radius (i.e. 9 Hipparcos stars, see also Table 5) we calculate a mean distance of 261_-23⁺²⁷pc. This value for the cluster distance considering 9 Hipparcos stars with a mean proper motion of $(\mu_x,\mu_y)=(+4.6,-8.3)$ mas/yr within 85arcmin from IC348 is in good agreement with the recent discussion of the distance of the Per OB 2 association by de Zeeuw et al. (1999). They obtained on the basis of Hipparcos data mean distances of $318\pm27$ for the early-type members and $282\pm21$ for the late-type members of the association covering more than $15 \times 10$ square degrees on the sky.

We may conclude on the basis of these distance estimates that the cluster IC 348 is a part of the Per OB 2 association. From the comparison of the mean proper motion we get an additional argument for this assumption: The mean proper motion of 12 stars with >95% membership probability in the Per OB 2 association (de Zeeuw et al. 1999) is $(\mu_x,\mu_y)=(+4.9,-7.5)$ mas/yr, respectively with a dispersion of 1.5,2.0) mas/yr. This result for the Per OB 2 association agrees well with our mean proper motion of the IC 348 cluster stars given in Table 4.

In Table 5 mean proper motions and their dispersions for the Hipparcos cluster stars selected on the basis of parallax and location in the field around IC348 or only of their proper motion are shown in comparison to other cluster member selections from different catalogues. From all results in Table 5 the Hipparcos results are in best agreement with our membership determination (group A in Table 4).

5.5 The catalogue of Fredrick

  The proper motion catalogue of Fredrick (1956) contains 38 stars with visual magnitudes smaller than 13.5 covering a field around IC348 which is nearly equal to the one square degree field selected for this study (see Fig. 1). His catalogue consists of two parts based on the observations made with the Sproul 24-inch refractor (34 plates with a scale of 18.87arcsec/mm and a time baseline of 38 years) and with the McCormick 26-inch refractor (21 plates with a scale of 20.75arcsec/mm and a time baseline of 32 years). The proper motion error of the averaged Sproul and McCormick data (21 stars) was given as 0.3mas/yr, whereas the proper motion errors of the stars based on either Sproul or McCormick data were estimated as 0.5mas/yr.

Using 12 common stars of the catalogue of Fredrick (1956) and our study we transformed our proper motion system to the Fredrick system by applying the corrections given in Eq. (6) (in mas/yr).

$$\begin{eqnarray} \mu_x(\rightarrow {\rm Fredrick}) &=& \mu_x + 0.8 \pm 0.8 \nonumber\\ \mu_y(\rightarrow {\rm Fredrick}) &=& \mu_y - 1.6 \pm 0.7.\end{eqnarray}$$ (6)

  

Figure 9: Central part of proper motion diagram of our sample (in Hipparcos proper motion system) showing all measured proper motions as dots, the foreground stars with small proper motion membership probabilities of cluster and distant field stars ($P_{\rm cl} < 10$% and $P_{\rm df} < 10$%) overplotted as open circles, the distant field stars ($P_{\rm df} \gt 90$%) as small $\times$ and the cluster stars ($P_{\rm cl} \gt 90$%) as small +. In addition, the stars of Fredrick (1956) are shown including all highly probable (small filled circles) and other possible (open triangles) and some nonmembers (open squares) according to his proper motion study. As one can see the Fredrick members are located just in between the two distributions for cluster stars and distant field stars found in this study

In dependence on the different selection criteria (proper motion, position and location in the CMD) there are 17 possible members among the 38 stars of Fredrick (1956). These 17 possible members were also considered as cluster stars in Preibisch et al. (1996). Based on a more rigorous selection, particularly allowing only a small region for the cluster stars in their projected position, Fredrick (1956) discussed 8 highly probable members. Figure 9 shows the central region of the proper motion diagram with small dots representing our proper motion sample, overplotted open circles for the foreground stars (small proper motion membership probabilities for cluster and distant field stars, $P_{\rm cl} < 10$% and $P_{\rm df} < 10$%), small $\times$ for the distant field stars ($P_{\rm df} \gt 90$%) and small + for the cluster stars ($P_{\rm cl} \gt 90$%). Also shown are the stars of Fredrick (1956) falling into this region of the proper motion diagram, including the 8 highly probable members (small filled circles), other 9 possible members (filled lozenges) and 10 nonmembers (filled squares).

The location of the cluster members according to Fredrick (1956) just in between the distributions of cluster stars and distant field stars determined in this study can not be explained by the accuracy of the transformation of our proper motions to the Fredrick system (Eq. (7)) which was sufficiently high. We are also quite sure about the significance of the two different distributions which we interpret as cluster stars and distant field stars (see Sects. 4.2 and 4.3). The elongated proper motion distribution even of the highly probable members of Fredrick (1956) may indicate somewhat larger errors in his $\mu_y$ proper motion components. On the other hand, this distribution of the possible proper motion members of Fredrick (1956) may also be an indication of two overlapping distributions instead of only one for the cluster stars. The elongation becomes even stronger and changes its direction from north-south to that of the standard apex direction if some additional stars near to the highly probable cluster stars in the proper motion diagram are included (compare Figs. 7d and 9).

There are 4 Hipparcos stars and 8 ACT stars among the 38 stars of the catalogue of Fredrick (1956) with one star having both Hipparcos and ACT proper motion measurements. We have used 4 Hipparcos plus 7 ACT proper motions to compute the corrections of the Fredrick proper motions to the Hipparcos system (given by Eq. (7) in mas/yr).

$$\begin{eqnarray} \mu_x({\rm Fredrick} \rightarrow {\rm Hipp}) &=& \mu_x({\rm Fre... ...} \rightarrow {\rm Hipp}) &=& \mu_y({\rm Fredrick}) - 4.9 \pm 0.7.\end{eqnarray}$$ (7)

Before that we have checked whether the ACT proper motions in the larger field around IC348 (radius of 85arcmin) show any residual deviation from the Hipparcos proper motion system and found no significant deviations (Eq. (8), in mas/yr) from 16 common stars in Hipparcos and ACT.

$$\begin{eqnarray} \mu_x({\rm Hipp}) - \mu_x({\rm ACT})& =& - 0.3 \pm 0.7 \nonumber\\ \mu_y({\rm Hipp}) - \mu_y({\rm ACT}) &=& - 0.1 \pm 0.8.\end{eqnarray}$$ (8)

The relatively large error of the $\mu_x$ correction in Eq. (7) comes from the wide spread in the proper motion differences between Fredrick and ACT stars. Nevertheless, we did not use the alternative correction (Eq. (9) in mas/yr) obtained from only 4 Hipparcos stars.

$$\begin{eqnarray} \mu_x({\rm Fredrick} \rightarrow {\rm Hipp}) &=& \mu_x({\rm Fre... ...} \rightarrow {\rm Hipp}) &=& \mu_y({\rm Fredrick}) - 6.7 \pm 0.7.\end{eqnarray}$$ (9)

In spite of the smaller formal errors of this correction, we decided that it would be less reliable due to the small number of 4 stars from which two (the double star BD$+31\hbox{$^\circ$}643$) have relatively large Hipparcos proper motion errors ($\ge 3.5$mas/yr).