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Astron. Astrophys. 359, 907-931 (2000)

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5. Discussion

The detection of stars tidally stripped from globular clusters emphasizes strongly the importance of the interactions of these stellar systems with the Galaxy. In the light of the possible biases present in the above observed fields, it is possible to give an estimate of the physical status of the clusters relative to the gravitational shocks they suffer in the Galaxy (see Table 5). In the case of a cluster experiencing disk-shocking only, it will be first compressed in the direction perpendicular to the galactic plane, during the short time of the crossing; then the tidally released stars form tails perpendicular to the galactic plane (see, e.g., NGC 5139). In the case of a cluster experiencing bulge-shocking only, i.e., not too far from the Galaxy center, the tails are elongated mainly along the galactic density gradient (spherical symmetry) and one can expect a correlation between the tidal tail direction and the galactic center. This is true also for the more general case of galaxy-shocking, when bulge- and disk-shocking are both at play, i.e., when the cluster is close to the galactic center. If the cluster has not experienced for a long time a gravitational shock, its tidal tails are on a large scale oriented along its orbit. However Grillmair (1992) showed using N-body simulations, without any disk potential, that strong "bars" orthogonal to the orbital path will develop naturally near the apogalactica of the cluster's orbit. In Table 5 we, tentatively, give the processes at play for creating the recent mass loss in the clusters: it is based on tidal tails shapes, but, as well, on their positions in the Galaxy and their orbit and proper motions, when they are available. It explains the discrepancy between some tidal tail orientation and the type of physical process. We point out that the projection effect must be important in some case (e.g NGC 288). It has to be noted that a combination of disk- and bulge-shocking are expected to confuse the above simplified scenario (e.g. NGC 6535).


[TABLE]

Table 5. Characteristics of the tails.
Notes:
We indicate a reliability level from 0 (reliable, no observational bias) to 5 (unreliable) for the observed overdensities (tidal tails) around these clusters. The position of the cluster in the galaxy is given through its distance to the sun ([FORMULA]), to the galactic center (RGC) and to the plane (Z). We give an indication of the alignment of the tidal tails perpendicular to the galactic plane (1), aligned with the galactic center (2) and with no correlation relative to any of these two directions (3). [FORMULA]) OP: Orbital path, DS: disk shocking, BS: bulge shocking (+ means both processes are probably at play; / means probably one of the two processes).


The case of NGC 5904 is interesting since its proper motion is known: the small tidal extension observed is perfectly aligned towards the galactic center and the direction perpendicular to the galactic plane and not with its motion along its orbit. Given its position in the Galaxy, this cluster is probably suffering a weak disk and bulge shocking.

In Fig. 27 we show the slope values [FORMULA] (between [FORMULA] and 3[FORMULA]) versus [FORMULA] (between 3[FORMULA] and 6[FORMULA]) for the few clusters where it is possible to measure these two parameters. We emphasize that these slope values are probably overestimated, especially for [FORMULA], because of central crowding. As found in dynamical simulations by Johnston et al. (1998) and in other observations by Grillmair et al. (1998) on different radius ranges, the mean slope value for [FORMULA] is [FORMULA]. The coefficient [FORMULA] presents a strong scatter (1.69) around its mean value equal to -1.0. Its determination is difficult because the stars no more bound to the cluster have a very low density in the outer parts where the noise dominates (see, e.g., NGC 2298). The quantity [FORMULA] must be a reliable indicator of the recent mass loss from the cluster, with a steep slope for the cluster suffering shocks. Then the diffusion of the heated stars will flatten the surface density profile.

[FIGURE] Fig. 27. The slope values [FORMULA] (between [FORMULA] and 3[FORMULA]) versus [FORMULA] (between 3[FORMULA] and 6[FORMULA]) in clusters with wide enough field. The dotted line stands for [FORMULA] = [FORMULA].

In Fig. 28, we present, from our N-body simulations (CLM99), the variation with time of the surface density slope fitted on a power law for two different ranges of radii. It is remarkable to note the strong variation of the slopes during the crossing of the galactic plane. Moreover there is a delay between the variation of the [FORMULA] slope and [FORMULA] slope. Here the dumping frequency of the simulations is too low to allow any estimate of the diffusion velocity of the bulk of stars stripped during the crossing. It appears nevertheless to be lower than the velocity dispersion of the simulated globular cluster ([FORMULA] 8 km s-1).

[FIGURE] Fig. 28. Evolution in N-body simulations of the surface density slope for a power law between a radius of 30 and 40 pc (solid line) and 40 and 50 pc (dash-dotted line) for a globular cluster on polar orbit (CLM99). The disk crossing occur at t = 10, 70, 150, 240, 310, and 380 Myr. The crossing at t = 10, 150, 240 and 380 are clearly visible on the variations of [FORMULA] and [FORMULA].

We may link the case of NGC 6254 (see Fig. 20) to the surface density profile computed from our N-body simulations (CLM99) before and after the crossing and displayed in Fig. 29). Clearly the second break, at a radius [FORMULA], in the observed cluster density profile ([FORMULA]) and simulated cluster density profile ([FORMULA]) indicates that disk shocking is currently at play on NGC 6254 and the halo of unbound stars has not yet diffused outwards. Even if other mechanisms could produce such break (e.g. "bars" at the apogalactica radius) we note that this NGC 6254 is currently just 1.6 kpc above the galactic plane.

[FIGURE] Fig. 29. Surface density profiles (Log) from N-body simulations (CLM99) at t=230 Myr (solid line) and t=275 Myr (dash-dotted line). The disk crossing occurs at 240 Myr.

The variations of the [FORMULA] coefficient between clusters with a strong galaxy-driven evolution are expected to be important as observed in the simulations. Nevertheless this coefficient is, as well, dependent on the orbital phase as shown by Grillmair (1992).

From our N-body simulations (CLM99), using multi-mass King-Michie models, we show that the tidal tails are populated mainly by the lighter stars of the pruned globular cluster, because of its mass segregation. In Fig. 30, we present the evolution of the mass function slope (assumed to be a power-law) for a simulation with a globular cluster on polar orbit (CLM99). The duration of this simulation is too short to observe strong changes in the mass spectrum through the cluster itself, nevertheless it can be seen that the radius of constant mass function slope is slightly expanding during the 800 Myr of the simulation. This is especially true in the inner parts of the cluster (see e.g. the isocontour [FORMULA] on Fig. 30).

[FIGURE] Fig. 30. Variations with time of the slope of the mass function fitted by a power-law (-2.35 for a Salpeter law). The simulation is from CLM99.

Let us compare the amount of tidally stripped stars obtained in our simulations and observations. Because of the magnitude limitation of the plates and films, it is likely that we underestimate the observed tidal tails. The mass of the tidal tails in the case of NGC 5139 has been computed for a Salpeter law: if we assume a steep slope [FORMULA]= -2.8 for the mass function in the tidal tails, we get a tail mass equal to about 1% of the total mass of the cluster, equal to 5.1 106 [FORMULA]. In spite of the great uncertainty on the star counts of the tidal tails, such a large mass is an upper limit for the tidal tail mass from the simulations (CLM99). It confirms both that NGC 5139 has a genuinely large total mass (Meylan et al. 1995) and that the spectrum mass is likely less steep than [FORMULA] in the outer part. All these considerations point toward a mass for the tidal tails between 0.6 and 1.0% of the total mass of NGC 5139. From N-body simulation performed by Moore (1996) we can note that the presence of tidal tails is the indication of low dark matter content in globular clusters.

NGC 7492 and Pal 12 provide an interesting comparison because of their similar characteristics: low masses (6 and 2 [FORMULA] [FORMULA] [FORMULA], respectively), low concentrations (1.0 and 0.9, respectively), and large distances from the galactic center (23.5 and 14.7 kpc, respectively). They are also both strongly influenced by the Galaxy: GO97 compute [FORMULA] = 77.8 and 17.9, respectively. Nevertheless, their tidal tails appear strongly different, with a very extended structure for Pal 12 and very tiny one for NGC 7492. The last gravitational shock suffered by NGC 7492, if any, has to have occured much before the last one for Pal 12. The long time since the last gravitational shock suffered NGC 7492 has allowed the surface density of the unbound stars to fade along the cluster orbit. We estimate the last tidal shock suffered by Pal 12 to be about 350 Myr.

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Online publication: July 13, 2000
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