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Astron. Astrophys. 333, 531-539 (1998)

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4. Mean absolute proper motion of the cluster

Due to the large heliocentric distance of Pal 5 and the moderate accuracy in the proper motions of individual stars (in comparison to the high accurate relative proper motion studies of many Galactic globular clusters by Cudworth and coworkers, e.g. Schweitzer, Cudworth & Majewski 1993) we have not tried to obtain membership probabilities. For the determination of the mean absolute cluster proper motion [FORMULA] we averaged the proper motions of all stars within a given cluster radius [FORMULA] and corrected the result [FORMULA] for the contamination with field stars in the selected cluster region:

[EQUATION]

The number of contaminating field stars in the cluster region [FORMULA] was estimated from the comparison of the number density in the cluster region with that of the field stars outside the cluster region. The mean absolute proper motion of the field stars [FORMULA] can be determined very accurately due to their large numbers in a sufficiently large sky region between [FORMULA] and [FORMULA] outside the globular cluster ([FORMULA]).

Systematic errors are always a significant concern in proper motion reductions. Therefore, several selection criteria for the objects used in the determination of the mean absolute cluster proper motion were tested and the results from different samples of objects compared:

  • number of observations per star
  • internal proper motion accuracy
  • image classification
  • radius of the cluster region [FORMULA]
  • field region between [FORMULA] and [FORMULA]
  • magnitude interval (in order to investigate possible systematic errors as function of magnitude)

Fig. 6 shows as an example the mean absolute proper motion as a function of cluster radius for all objects in the magnitude interval [FORMULA], classified as stars on the reference plate, measured on at least 5 plates, with proper motion errors less than 12 mas/yr.

[FIGURE] Fig. 6. Mean proper motion of all star-like objects in the magnitude interval [FORMULA] measured on at least 5 plates with internal proper motion errors [FORMULA]  12 mas/yr as a function of the distance from the cluster centre. The data were binned in radial annuli of 2 arcmin width around the cluster. Error bars show the error of the mean proper motion in an annulus.

According to the observed radial density profile of the globular cluster (Fig. 7a and b) the cluster region with [FORMULA]  arcmin contains almost all cluster stars. On the other side, the number of cluster stars in a sufficiently large field region, e.g. between [FORMULA]  arcmin and [FORMULA]  arcmin can be neglected in the determination of the mean absolute proper motion of the field stars [FORMULA]. However, a contamination of the field star sample with galaxies has to be considered.

The tidal radii of Pal 5 given in the literature are relatively large: 18.2 arcmin according to Webbink (1985) and 15.9 arcmin according to Trager, King & Djorgovski (1995). However, the slightly increased number density from 10 arcmin to 18 arcmin in comparison to the region outside [FORMULA] is obviously not an indication of the tidal radius of Pal 5 but caused by the galaxy cluster Abell 2050. This can be seen in the comparison of the radial density profile for objects with stellar classification with those for objects with non-stellar classification and for merged objects (Fig. 7a and b a). The image classification near the plate limits is problematic so that a relatively large fraction of galaxies can be expected among the faint objects measured on the deep Schmidt plates with stellar classification.

[FIGURE] Fig. 7. Radial density profile obtained from counts in annuli around Pal 5 with a width of 2 arcmin. a in dependence on image classification: all objects measured on the reference plate (open circles), objects with stellar classification with additional measurements on at least two other plates ([FORMULA]), non-stellar classification ([FORMULA]), merged objects (triangles). b all faint objects measured on the reference plate and at least two other plates: [FORMULA] ([FORMULA]), [FORMULA] (triangles), [FORMULA] (open boxes), [FORMULA] (open circles), [FORMULA] ([FORMULA]). The dashed lines show the cluster region ([FORMULA]  arcmin) used in the determination of the mean cluster motion and the tidal radius of 18 arcmin according to Webbink (1985).

Due to strong image crowding in dense globular clusters, such as M 3 or M 5, there is a central minimum in the density profiles of these clusters measured on deep Schmidt plates, i.e. the core region can not be resolved into single objects. Unless the Pal 5 cluster centre can be resolved on the Schmidt plates, the image crowding causes some problems. As seen in Fig. 7a, there is a concentration of objects with non-stellar and merged classification, which is in the sum even larger than the central density of stellar objects. On the other hand, as a result of image crowding there is no concentration of the faintest objects toward the cluster centre (Fig. 7b).

In order to reduce systematic effects in the determination of the mean absolute proper motion of the cluster due to image crowding and different contamination of the cluster and field stars with galaxies, the objects with non-stellar classification and all faint objects ([FORMULA]) were not used. In dependence on further parameters describing the reliability of the proper motion determination of single stars the number of cluster stars [FORMULA] in the magnitude interval [FORMULA] and with [FORMULA]  arcmin varied from 250 to 100. The ratio [FORMULA] varied between 1/2.5 and 1/1.

The mean result of the absolute cluster proper motion from about 20 alternative computations changing the selection criteria - internal proper motion errors of single stars, number of plates they were measured on, smaller magnitude intervals - was: [FORMULA]  mas/yr. All single runs yielded a result within the given errors which were also comparable to the formal errors of each computation. No systematic magnitude dependent effects were found.

Our results and the results of Schweitzer, Cudworth & Majewski (1993) [FORMULA]  mas/yr look superficially similar in heliocentric terms. However, the results differ at the 4-sigma level in both [FORMULA] and [FORMULA], using the quadratically combined errors to estimate sigma. If we compare the results in Galactocentric terms, i.e. ours: [FORMULA]  mas/yr versus theirs: [FORMULA]  mas/yr we see that the direction of the space motion we derive is completely different from theirs.

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© European Southern Observatory (ESO) 1998

Online publication: April 20, 1998
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