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

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5. Space motion and Galactic orbit of Pal 5

Knowing the cluster's absolute proper motion and also its distance ([FORMULA]  kpc, Harris 1996) and radial velocity ([FORMULA]  km/s, Smith 1985) with respect to the Sun, we finally proceed to its motion in three-dimensional Galactic space. On the assumption of [FORMULA]  kpc for the distance Sun - Galactic center and [FORMULA]  km/s for the rotation of the local standard of rest (IAU 1986) and with the 'basic solar motion' of Delhaye (Mihalas & Binney 1981) as a reasonable estimate of the Sun's peculiar motion in the LSR , the cartesian components of the Galactocentric position and velocity of Pal 5 come out as shown in Table 2. As viewed from a point near the Sun the present location of the cluster lies on the opposite side of the Galaxy. It has a height of 16 kpc above the Galactic plane and a projected distance of 7 kpc from the Galactic center. While the direction of the velocity vector depends on the choice between the two different proper motion results given above (see the two cases in Table 2), the absolute value of the velocity is in both cases close to 130 km/s (see Table 3 b). This confirms that Pal 5 is indeed among the clusters with the lowest space velocity in the globular cluster system of the Galaxy.


Table 2. Galactocentric position and space velocity


Table 3. Orbital parameters for time interval [-10 ; 0] Gyr

Schweitzer, Cudworth & Majewski (1993) have pointed out that using their proper motion for Pal 5, the velocity vector is perpendicular to the position vector and hence the cluster is very close to apogalacticon. Our proper motion results do not confirm this particular orientation of the velocity vector. Nevertheless, the conclusion that Pal 5 is near apogalacticon remains true also with regard to the proper motions obtained in this paper. This can be anticipated from the fact that the total space velocity is much below the circular velocity of the Galaxy, and it is confirmed in a more precise manner by the results of a numerical calculation of the cluster's Galactic orbit.

[FIGURE] Fig. 8. Orbit of Pal 5 in the time interval [-10 ; 0] Gyr. Upper plot: Meridional Projection onto cylindrical coordinates [FORMULA]. Lower plot: Projection on the Galactic plane.

In analogy to our previous studies on other globular clusters we integrated the orbit of Pal 5 for the past 10 Gyrs, using the model by Allen & Santillan (1991) as a representation of the Galactic gravitational potential. The resulting orbital parameters are summarised in Table 3 and a plot of the orbital path is shown in Fig. 8. While with the proper motion from Schweitzer, Cudworth & Majewski (1993) the distance of the cluster from the Galactic center is limited by the current distance of 17 kpc, with our proper motion the orbit yields a maximum distance of 18.9 kpc and the most recent apogalacticon lies 0.05 Gyr (i.e. 1/8 of a mean orbital period) back from present. Perigalactic distances are found to be not smaller than 5.3 kpc. The eccentricity of the orbit (as measured by [FORMULA]) returns a value of 0.56. Naturally, the distribution of values of Galactocentric distance R is such that most of the time the cluster is seen at relatively large distances ([FORMULA]  kpc). Since the orbit is highly inclined, the distance from the Galactic plane can rise up to 18.5 kpc, but on the time average along the orbit this distance has only about half of the maximum size. The inclination of the (instantaneous) orbital plane with respect to the Galactic plane remains almost constant at about [FORMULA]. Following the proper motions of this paper, the cluster is in prograde rotation around the Galactic z -axis with an average rotation velocity of about 56 km/s, which is similar to the overall mean rotation velocity of the globular cluster system. On the other hand, with the proper motions found by Schweitzer, Cudworth & Majewski (1993) the cluster yields a z -angular momentum almost zero and hence a nearly polar orbit (i.e. [FORMULA] inclination) with an average rotational velocity component [FORMULA] of only 1 km/s. Despite these differences one finds agreement in the fact, that in both cases the cluster has a mean period of revolution of 0.4 Gyr (corresponding to 25 revolutions around the Galactic z -axis within 10 Gyrs).

In order to find out how much the orbital characteristics change within the estimated range of error in our proper motions, we modified the cluster's initial velocity accordingly and calculated a number of alternative orbits. The result of this test was, that the distance parameters do not undergo extreme changes, i.e. [FORMULA] and [FORMULA] fell within 18 and 20 kpc and [FORMULA] was between 3 and 8 kpc. The direction of rotation was in all cases prograde with average rotational velocities between 30 and 70 km/s. Although the z -angular momentum of Pal 5 is on a low level, (in the range 130 to 450 kpc [FORMULA] km/s) there was no indication for the appearance of chaotic motion, because all test orbits showed the characteristics of regular (quasiperiodic) motion, similar to the orbit of Fig. 8.

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© European Southern Observatory (ESO) 1998

Online publication: April 20, 1998