5 The space motion of M 10

The first absolute proper motion of M 10 based on the Hipparcos system was given in Geffert et al. (1997), which was later used in Odenkirchen et al. (1997) and Dinescu et al. (1999). However, as mentioned in Odenkirchen et al. (1997), the result of M 10 was only preliminary due to the small number of Hipparcos stars used for the reduction of the plates. The use of additional plates from Shanghai has led to a significant lower proper motion in declination. However, even for this sample of plates the solution is only moderately stable: omitting one reference star leads to an absolute proper motion of M 10, which differs from the original solution by about more than the mean uncertainties of the absolute proper motions. Fortunately, this is not the case for the denser ACT catalogue. In summary, the use of the ACT catalogue resulted in a more stable solution, while the use of Hipparcos stars provided the more direct link to an extragalactic reference frame. The catalogues based on the ACT catalogue (Urban et al. 1998) and on the Hipparcos catalogue (ESA 1997) contributed therefore with equal weight to the final absolute proper motion of the globular cluster M 10. We obtained a mean absolute proper motion of $\mbox{$\mu_{\alpha}\cos\delta$ }= -5.5 \mbox{ $\pm$\space }1.2\;$mas/yr and $\mbox{$\mu_{\delta}$ }= -6.2 \mbox{ $\pm$\space }1.2\;$mas/yr. Together with the distance from the Sun of 4.3 kpc and a radial velocity of $+76\;$ km s^-1 (Harris 1996) we have calculated the velocity components in a system of galactic standard at rest (U,V,W), peri- and apogalactic distances $R_{\rm p}$, $R_{\rm a}$, eccentricity e and the z-component of the angular momentum of the orbit using a simple logarithmic galactic mass model (see e.g. Dauphole et al. 1996). These data are shown in Table 7. Figure 2 gives the orbit of M 10 integrated over 10 Gyr backwards according to the method of Allen & Santillán (1991) using the programme of Odenkirchen et al. (1997).

   

Table 7: Velocity components in a system of galactic standard at rest and kinematical data of the orbit of globular cluster M 10. A simple logarithmic galactic mass model was used (see e.g. Dauphole et al. 1996). (Note that U points from Sun to galactic centre! A positive z component of the angular momentum indicates a prograde rotation in the Galaxy)

Object	U	V	W	$R_{\rm a}$	$R_{\rm p}$	e	Iz
	[km s-1]	[km s-1]	[km s-1]	[kpc]	[kpc]		[kpc km s-1]
M 10	$+111 \pm 10$	$+90 \pm 18$	$+63 \pm 18$	$5.4 \pm 0.2$	$2.3 \pm 0.4$	$0.41 \mbox{ $\pm$\space }0.08$	$+533 \mbox{ $\pm$\space }70$

Figure 2: The meridional section of the orbit of M 10 calculated backwards over 10 Gyr