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Astron. Astrophys. 327, 1004-1016 (1997)

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5. Radial density profile from star counts

The CMD allows a unique way to obtain a reliable measure of the radial density profiles of GCs. In fact, the CMD allows us to sort out the stars belonging to the cluster, limiting the problems generated by the presence of the field stars. This also permits to extract radial profiles for distinct stellar masses.

We have first created a profile as in King et al. (1968), in order to compare our results with the existing data in the literature. The comparison has been done with the radial density profile of M 55 published by Pryor et al. (1991) which includes the visual star counts of King et al.. We could not compare our data with Irwin & Trinble (1984) because they have not published their observations in tabular form.

5.1. Density profile for stars above the TO

Fig. 9 shows the radial density profile for the TO plus SGB stars extracted from the CMD of M 55 (from 1 magnitude below the TO to the brightest limit of our photometry). We have selected the stars within [FORMULA] from the fiducial line of the CMD plus the contribution coming from the BS and HB stars; star counts has been limited at the magnitude [FORMULA]. This relatively bright limit corresponds approximately to the limit of the visual star counts by King et al. (1968) on the plate ED-2134 (in order to make the comparison easier we used the same radial bins of King). Our counts have been transformed to surface brightness and adjusted in zero point to fit the Pryor et al. (1991) profile of M 55.

The agreement with the data presented by Pryor is good everywhere but in the outer parts where our CCD star counts are clearly above those of King et al. (1968). This difference is probably due to our better estimate of the background star contamination. In the plot we have shown also the raw star counts (crosses) prior to the background star subtraction: it can be clearly seen that our star counts go well beyond the tidal radius, [FORMULA], published by Trager et al. (1995). This allow us to estimate in a better way than in the past the stellar background contribution. The background star counts show a small radial gradient: we will discuss this point in greater detail in the next section. Here, the minimum value has been taken as an estimate of the background level.

We point out that the differences present in the central zones of the cluster could be in part due to some residual incompleteness of our star counts, to the absence in the starcounts of the brightest saturated stars, and to the difficulties in finding the center of the cluster. We searched for the center using a variant of the mirror autocorrelation technique developed by Djorgovski (1988). In the case of M 55 we encountered some problems due to a surface density which is almost constant inside a radius of [FORMULA].

In order to evaluate the structural parameters of M 55, we have fitted the profile Fig. 9 with a multi-mass isotropic King (1966) model as described in the previous section. In the following table we show the parameters of the best fitting model and we compare them with the results of Trager et al. (1995), Pryor et al. (1991), and Irwin & Trimble (1984):

[TABLE]

The concentration parameter of M 55 is one of the smallest known for a globular cluster. Such a small concentration implies strong dynamical evolution and indicates that the cluster is probably in a state of high disgregation (Aguilar et al. 1988; Gnedin & Ostriker 1997).

Our value of the tidal radius is well in agreement with that of Trager et al. (1995) who used a similar method to fit the data. Pryor et al. (1991) give a value of [FORMULA] 10% smaller than ours. We note that Pryor and Trager used the same observational data set. The difference with Irwin & Trimble (1984) is probably due to the fact that the authors have not fitted their data directly but made only a comparison with a plot of King models.

5.2. The density profile for different stellar masses

Having verified the compatibility of our density profile with previously published ones, we have extracted surface density profiles for different magnitude ranges corresponding to different stellar masses. The adopted magnitude intervals have been chosen to have a significant number of stars in each bin. We used logarithmic radial binning that allows a better sampling of the stars in the outer part of the cluster. In order to lower the noise in the outer part of the profile, we have smoothed the profiles with a median static filter of fixed width of 3 points. We verified that the filtering procedure did not introduce spurious radial gradients in the density profiles. The mean masses in each magnitude bin adopted for the profiles, as obtained from the isochrone by VandenBerg & Bell (1985) (cf. also Sect.  4.1), are:

[TABLE]

The relative profiles, without subtraction of the background stars, are shown in Fig. 10 and 11. The arrows in both figures indicate [FORMULA], [FORMULA] and [FORMULA].

[FIGURE] Fig. 10. Radial density profile of M 55 for different magnitude intervals. All the profiles has been smoothed in the external parts. In the graph the positions of [FORMULA], 2 [FORMULA] and [FORMULA] are shown. The profiles have been normalized in the radial range [FORMULA].

The profiles plotted in Fig. 10 are clearly different from each other: this is as expected from the mass segregation effects. To better compare the profiles, in Fig. 10 they have been normalized in the radial interval [FORMULA] (where the profiles have a similar gradient) to the profile of the TO stars. This operation is possible because in this radial range the effects of mass segregation are small (cf. Fig. 7); they are more evident within one core radius. The density profiles are consistent with the mass segregation effects that we have already seen in the mass function of the cluster.

The more interesting aspect of the profiles in Fig. 10 is the clear presence of a stellar radial gradient in the star counts of the background field stars. In Fig. 11, we show the radial profiles of the extra cluster stars after normalization of the profiles outside [FORMULA]. The 4 profiles are not exactly coincident outside [FORMULA]. Let us discuss various possible explanations for this observation:

[FIGURE] Fig. 11. Radial density profile of M 55 for different magnitude intervals. An arrow marks the position of [FORMULA]. The profiles are normalized in the radial range [FORMULA] to better compare the extra-tidal profiles. We show also the power law interpolation of the profiles.
[FIGURE] Fig. 12. Surface density map of M 55 with contour levels.

  • Errors in the completeness correction or errors in the star counts. We repeated the extensive tests on the data made to assess the validity of the mass segregation seen in the LFs. We checked that the variation in the completeness limit of the various EMMI fields does not introduce spurious trends. In a different test, we divided the cluster in two slices along a line at [FORMULA] from the center of the cluster up to the field 19 (cf. Fig. 1), and built the radial profiles for each of the 4 magnitude bins: in all cases there were no significant differences. The radial profile of the stars in the magnitude range [FORMULA] ([FORMULA] in Fig. 5) has the lowest contamination of background stars, as shown by its LF in Fig. 5.
  • A non-uniform distribution of the field stars around M 55. It is possible that the field stars around M 55 are distributed in a non-uniform way. In the work by (Grillmair et al. 1995) it clearly appears that the field stars of some GCs present a non-uniform distribution around the clusters. The gradients are significant and the authors used bidimensional interpolation to the surface density of the field stars to subtract their contribution to the star counts of the clusters. In the present case, field star gradients could be a real possibility, but we cannot test it because we do not have [FORMULA] coverage of the cluster: our coverage of M 55 is only a little more than a quadrant. The Galactic position of M 55 ([FORMULA], [FORMULA]) can give some possibility to this option. At this angular distance from the Galactic center the bulge and halo stars probably have a detectable radial gradient. However it remains difficult to explain the existence of the gradient also for the stars in the magnitude range [FORMULA]: for them (cf. Sect.  4), as stated before, we have the lowest contamination from the field stars.

    We have created a surface density map of the starcounts of M 55. The map was constructed using all the stars of the [FORMULA] -selected sample of our photometry (excluding fields 25 and 35), counting stars in square areas of approximately [FORMULA] and then smoothing the resulting map with a gaussian filter. The starcounts are not corrected for crowding but we stopped at [FORMULA]. The map is presented in Fig. 12. The map has the same orientation as Fig. 1. We have also overplotted contour levels to help in reading the map. Fig. 12 clearly shows that well outside the tidal radius of M 55 (located approximately at the center of the map) there is a visible gradient in the star counts.

  • A gradient generated by the presence of the dwarf spheroidal in Sagittarius (Ibata et al. 1995). Between the Galaxy center and M 55 there is the dwarf spheroidal galaxy called Sagittarius (Ibata et al. 1995). Sagittarius is interacting strongly with the Galaxy and probably is in the last phases of a tidal destruction by the Galactic bulge. The distance between the supposed tidal limit of this galaxy (using the contour map of Ibata et al. 1995) and M 55 is [FORMULA]. In the recent work by Mandashev et al. (1996) the giant sequence of the Sagittarius appears clearly overlapped with the sequence of M 55. This happens only in the magnitude range [FORMULA] where our star counts end. Fahlman et al. (1996) showed that the SGB sequence of the Sagittarius crosses the main sequence of M 55 at [FORMULA], and at a corresponding color of [FORMULA]. Similar results were found by Mateo et al. (1996). This is due to the different distances of these two systems from us: [FORMULA]  kpc for M 55 and [FORMULA]  kpc for Sagittarius. This implies that out star counts can be influenced by the stars of the dwarf spheroidal only in our last magnitude bin, [FORMULA]. Our selection of stars along the CMD of M 55 limits the Sagittarius stars to those effectively crossing the main sequence. In conclusion, if effectively the Sagittarius stars are present as background stars we should see them only in one of the 4 profiles, but the coincidence of the 4 profiles excludes this ipothesis.
  • A halo of stars escaping from the clusters. This possibility is more suggestive. The stellar gradient could be a possible extra-tidal extension of the cluster, similar to what Grillmair et al. (1995) found in their sample of 12 clusters. The tidal extension could be caused by the tidal-shocks to which the cluster has been exposed during its perigalactic passages, through the Galactic disk. Another possibility is the creation of the stellar halo by stellar dynamical evaporation from the inner part of the cluster. Such mechanisms work independently of stellar mass (Aguilar et al. 1988) and so the stellar halo should have a similar gradient for all the stellar masses as in the present case. Such halos are very similar to the theoretical results obtained by Oh & Lin (1992) and Grillmair et al. (1995), who have obtained tidal tails for globular clusters N-bodies simulations.

We believe that the probable explanation for the phenomenon shown in Figs. 10 and 11 is in the presence of an extra-tidal stellar halo or tidal tail. Doubt resides in the unknown gradient of the background field stars. To resolve this we need to map the whole cluster and a large area surrounding the cluster. This would also allow us to find the exact level of field stars. Our star counts stop at 33´ ([FORMULA]), from the center of M 55 while the tidal tails of Grillmair et al. (1995) stop at [FORMULA]. Consequently, we cannot correctly subtract the contribution of the field stars from our star counts. We can give only an estimate of the exponent of the power law, [FORMULA], fitting the profiles at [FORMULA]. Without subtracting any background counts [FORMULA], while subtracting different levels of background stars the slope varies in the interval [FORMULA]: the highest value comes out after subtracting the outermost value of the density profiles. When it will be available a better estimate of the background/foreground level of the sky it will be possible to assign a value to the slope of the gradient of stars: actually our range, [FORMULA], is in accordance with those found theoretically by Oh & Lin (1992) and observationally by Grillmair et al. (1995).

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© European Southern Observatory (ESO) 1997

Online publication: April 6, 1998
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