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

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4. Results

In this section we present all results related to the observations of stars surroundings of each GC. We discuss individually each cluster for the particular observational biases which could affect its results. Grillmair et al. (1995) found that the clusters in their sample with obvious tidal extensions showed a break in their surface density profiles, becoming pure power law at large radii. We try to link in a systematic way the shape of each observed tidal tail to the orbital phase of the corresponding cluster. For this we define [FORMULA] as the slope of the radial surface density between [FORMULA] and [FORMULA]. The slope of the radial surface density is computed when the tidal tails are not dominated by the noise which would lead to a flat slope. In practice, we choose to compute the three slopes [FORMULA], [FORMULA], and [FORMULA], and give in Table 3 their values only for clusters where the signal/noise ratio for these azimuth averaged parameters is sufficiently high. Practically, this means that we remove all clusters with [FORMULA] shallower than -0.5. Whenever possible, our surface density profiles 2 are extended inwards with the surface-brightness profiles from Trager et al. (1995), assuming a linear relation between light emission and stellar surface density through the globular cluster. Crowding and saturation problems in our plates/films make the inner parts of our density profiles highly unreliable. Consequently, the adjustment between Trager et al. 's profiles and ours is done, in the short radius range where both profiles are reliable, by adjusting a constant K in the following way:

[EQUATION]

where µ is the fitted surface brightness at r (see Trager et al. 1995). For Trager et al. (1995) profiles, only data outside the radius r=1´ are shown. We point out that differences between the two profiles in the very outer parts can partly be explained by mass segregation in the cluster, unveiled by different limiting magnitudes.


[TABLE]

Table 3. Slopes [FORMULA] of the radial surface density profiles for different ranges in radius for some the globular clusters in our sample (see text for explanations). We consider here only clusters with [FORMULA] smaller than -0.5. Note that the error bars do not include the uncertainties in the background determination.
Notes:
[FORMULA]) [FORMULA]
[FORMULA]) Fit between 10 et 20´
[FORMULA]) Statistical dispersion (NGC 5139 not included).


It is worth mentioning that the measured slope will be flattened at small radii since the closer to the cluster the larger the crowding and since a azimuthal averaged value is more sensitive to noise at large radii. For a power law dependence, with a slope [FORMULA], of the tidal tail surface density, the tail/noise surface density ratio scales as [FORMULA], where [FORMULA] is the background surface density. We choose the quantity [FORMULA] - the only one we are able to determine in a large enough number of GCs - as a quantitative estimator for comparing the outer structures of these clusters. Table 4 gives, for all GCs in our sample, the dynamical and structural parameters (from GO97 and references therein) which are representative of the internal and external dynamical evolution of these globular clusters; [FORMULA] is the relaxation time at the half-mass radius; [FORMULA] is the destruction rate due to evaporation; the ratio [FORMULA] of the total destruction rate to the destruction rate due to evaporation illustrates the importance of the galaxy-driven evolution suffered by the clusters; [FORMULA] is the concentration of the cluster, where [FORMULA] and [FORMULA] are the core and tidal radii, respectively; M is the cluster mass and [FORMULA] is the V magnitude of the horizontal branch stars. Given the low surface density and low S/N of some cluster tidal tails, the radial surface density profile is not shown for all the clusters.


[TABLE]

Table 4. Dynamical and structural parameters linked to the dynamical evolution of the globular clusters in our sample (from Gnedin & Ostriker 1997, GO97).
Notes:
The destruction rate [FORMULA] includes the total destruction rate due to disk and bulge shocks from the model by Bahcall et al. (1983). The structural properties of the GCs come from the following references: (1) Pryor & Meylan (1993), (2) Hesser et al. (1986), (3) Geisler et al. (1995), (4) Meylan & Mayor (1991), (5) Webbink (1981), (6) Schweitzer et al. (1993), (7) Armandroff & Da Costa (1991), and (8) Meylan et al. (1995). All [FORMULA] values are from Harris (1996).
[FORMULA]) These high ratio values are due to the gravitational shocks, stronger in the Bahcall et al. (1983) model than in the Caldwell & Ostriker (1983) model (see GO97).


4.1. NGC 104 [FORMULA] 47 Tucanae

NGC 104 is at a distance of 4.1 kpc from the sun, with its horizontal branch (HB) at V = 14.06 mag. It has a tidal radius of about 55 pc with a rather high concentration c = log ([FORMULA]) = 2.04 (see Table 4). It is one of the most massive and nearby GCs (Meylan & Mayor 1986; Meylan 1989). In their study, Odenkirchen et al. (1997) estimate that NGC 104 has experienced a disk crossing about 60 Myr ago and suffers frequent disk-crossing events with a period of about 160 Myr between each passages. The rotation of this cluster (Meylan & Mayor 1986) should enhance its mass-loss rate by a factor of about 1.5 (Longaretti & Lagoute 1996). Unfortunately the detection of extra-tidal material is made difficult by the strong pollution along the line of sight due to the Small Magellanic Cloud (SMC) background stars: in the CMD of NGC 104, the cluster sequences are superposed, with a vertical translation, with the sequences drawn by the stellar populations in the SMC. In order to discriminate efficiently between cluster and SMC stars, we compute the tail/background S/N function relative to the SMC by taking the background field for the s(i,j) function on the SMC (see Fig. 4. We fit a 3[FORMULA]3 bivariate surface in order to reproduce the SMC overdensity. A strong residual of the SMC is still present (see Fig. 7), fortunately located in the S-E corner. It represents a high surface density of stars of the SMC, well correlated with the dust emission seen in the IRAS 100-µm  map. About the globular cluster itself, tidal extensions towards the N-W and S-W directions are marginally present around NGC 104. The IRAS 100-µm  map does not exhibit any anticorrelation with these tidal extensions. No fit of the surface density profile of these tidal tails has been performed because of their poor statistical significance. A steep mass function must be present in the tidal tails because of the mass segregation observed in this cluster (Anderson & King 1996)

[FIGURE] Fig. 7a and b. NGC 104 [FORMULA] 47 Tuc. a : Surface density plot displaying tidal tails (in Log) around NGC 104 (47 Tuc). The different arrows indicate the directions of the cluster proper motion (dotted arrow), of the galactic center (dashed arrow), and of the direction perpendicular to the galactic plane (solid arrow). The dashed circle centered on the cluster indicates its tidal radius. The horizontal double arrow stands for 150 pc. b : IRAS 100-µm  chart overlaid with the above tidal-tail surface density contours. The strong emission in the S-E corner is coming from the Small Magellanic Cloud (SMC).

4.2. NGC 288

NGC 288 is at a distance of 8.1 kpc from the sun, with its horizontal branch (HB) at V = 15.38 mag. It has a tidal radius of about 32 pc (see Table 4). Its concentration is low, with c = log ([FORMULA]) = 0.96. It is located close to the South Galactic Pole, at 8 kpc from the Sun (Harris 1996), with a retrograde orbit (Dinescu et al. 1997). From GO97, NGC 288 is a cluster with a dynamical evolution strongly driven by the galactic tidal field (see Table 4). NGC 288 was already observed by Grillmair et al. (1995), who found tidal extensions on a field [FORMULA] smaller than ours, but with the same spatial resolution (16´). In Fig. 8, the wavelet decomposition clearly reveals some wide structures missed by Grillmair et al. (1995), especially towards the south. (The arrows indicating the direction of the Galactic center in Grillmair et al. (1995) for NGC 288, NGC 362, and NGC 1904 are in error - Grillmair, private communication). No dust emission from the IRAS 100-µm  survey is detected. NGC 288 is nearly free of observational biases, apart from some galaxy clusters. A few such clusters of galaxies are clearly detected (see Fig. 8). We suggest that the tidal radius determination could be overestimated because of the presence of the clusters Abell 118 and 122, as already pointed out by Scholz et al. (1998) for Pal 5.

[FIGURE] Fig. 8a-d. NGC 288. a : Surface density plot displaying tidal tails (in Log) around NGC 288. The different arrows indicate the directions of the cluster proper motion (dotted arrow), of the galactic center (dashed arrow), and of the direction perpendicular to the galactic plane (solid arrow). The dashed circle centered on the cluster indicates its tidal radius. The horizontal double arrow scale stands for 200 pc. b : tidal-tail density overlaid with the surface density contours of galaxies ([FORMULA]3-[FORMULA]) at the same resolution. c : Radial surface density profile with the power-law fit to our data in the external parts, while the inner surface density profile comes from the data (diamond) by Trager et al. (1995), shifted vertically to fit our star count data. The vertical arrow indicates the tidal radius. d : Overdensities of galaxy counts overlaid with the positions of the Abell clusters (triangle) known in the same field.

Tidal tails are well separated in two directions: first, towards the galactic center (dashed arrow), second, aligned with the orbit of the GC (dotted arrow). NGC 288 has recently undergone a gravitational shock (Odenkirchen 1998). It is very likely that the tidal tails visible in Fig. 8 a are the results, in projection on the plane sky, of both the disk shocking and the relics of the bulge shocking from the last passage close to the bulge (Dauphole et al. 1996). NGC 288 exhibits very important tidal tails, extending up to 350 pc from the cluster: this has to be related to its strong interaction with the Galaxy, as found by GO97 (see Table 4). We count about 1200 stars outside the tidal radius of the cluster but we did not attempt an estimate of the mass in the outer parts of the cluster because of the poor photometry. Further CCD observations with deep and precise photometry should provide very accurate mass loss rates. From its orbital motion, this cluster appears to be a very good candidate for tracing the local galactic potential (disk scale height and surface density).

4.3. NGC 1261

NGC 1261 is a remote cluster at a distance of 15.1 kpc from the sun, with its horizontal branch (HB) at V = 16.70 mag. It has a tidal radius of about 34 pc and a concentration c = log ([FORMULA]) = 1.27. Its evolution is probably driven by its internal dynamics (Zoccalli et al. 1998, GO97). Its field is not polluted by strong dust extinction (E([FORMULA]) = 0.02), but the main bias is coming from the extra-galactic object overdensities. Although no Abell cluster is present in the field, we detect the presence of galaxy clusters which are strongly correlated with some stellar extensions as visible in Fig. 9. We can conclude here that the N-E extension of the extra-tidal material, which is aligned with the direction of the galactic center (dashed arrow), is a real tidal feature of the GC, because there is no strong galaxy cluster at this location. The slope [FORMULA] (see Table 3) is probably highly contaminated by back- and foreground stars and not useful. Zoccali et al. (1998) find evidence for mass segregation in the cluster ([FORMULA]), segregation which should affect the tidal tails as discussed in Sect. 5.

[FIGURE] Fig. 9a-d. NGC 1261. a : Surface density plot displaying tidal tails (in Log) around NGC 1261. The different arrows indicate the direction of the galactic center (dashed arrow) and of the direction perpendicular to the galactic plane (solid arrow). The dashed circle centered on the cluster indicates its tidal radius. The horizontal double arrow scale stands for 100 pc. b : Tidal-tail density overlaid with the surface density contours of galaxies ([FORMULA]3-[FORMULA]) at the same resolution. c : Radial surface density profile with the power-law fit to our data in the external parts, while the inner surface density profile comes from the data (diamond) by Trager et al. (1995), shifted vertically to fit our star count data. The vertical arrow indicates the tidal radius. d : Overdensities of galaxy counts; there is no Abell galaxy cluster in this field.

4.4. NGC 1851

NGC 1851 is a remote cluster at a distance of 11.7 kpc from the sun, with its horizontal branch (HB) at V = 16.15 mag. It has a tidal radius of about 49 pc and a very high concentration c = log ([FORMULA]) = 2.24. The western part and the S-W part of NGC 1851 extension are contaminated by galaxy clusters (Abell 514 and anonymous) and by a bright star also observed by the IRAS 100-µm  map (see Fig. 10). The extinction is not important towards NGC 1851, with E([FORMULA]) = 0.02. Stars unbound from the cluster are likely tracing the orbital path, here these tails seem to have a preferential direction towards the galactic center (dashed arrow and S-E extension). The cluster position indicates that it is not suffering a strong shock, as confirmed by the ratio [FORMULA] from GO97, which indicates that the evolution of this cluster is mainly internally driven. Consequently, the surface density profile in the outer parts of the cluster is mainly shaped by evaporation and tidal stripping at its location in the Galaxy. Saviane et al. (1998) found a slight mass segregation in this cluster which affects the tidal tail detection by lowering the mean mass of the unbound stars (Sect. 5).

[FIGURE] Fig. 10a-e. NGC 1851. a : Surface density plot displaying tidal tails (in Log) around NGC 1851. The different arrows indicate the direction of the galactic center (dashed arrow), and of the direction perpendicular to the galactic plane (solid arrow). The dashed circle centered on the cluster indicates its tidal radius. The horizontal double arrow scale stands for 100 pc. b : Tidal-tail density overlaid with the surface density contours of galaxies ([FORMULA]3-[FORMULA]) at the same resolution. c : IRAS 100-µm  chart overlaid with the above tidal-tail surface density contours. d : Overdensities of galaxy counts overlaid with the Abell clusters (triangle) detected in the same field. e : Radial surface density profile with the power-law fit to our data in the external parts, while the inner surface density profile comes from the data (diamond) by Trager et al. (1995), shifted vertically to fit our star count data. The vertical arrow indicates the tidal radius.

4.5. NGC 1904 [FORMULA] M79

NGC 1904 is a remote cluster located at a distance of 12.2 kpc from the sun, with its horizontal branch (HB) at V = 16.15 mag. It has a tidal radius of about 32 pc and a concentration c = log ([FORMULA]) = 1.72. NGC 1904 is surrounded by a halo of unbound stars (see Fig. 11), as previously seen by Grillmair et al. (1995), on a wider field but with a lower spatial resolution (them with 16´, us with 6.5´) which blurred all the small structures we observe around the cluster. We do not find evidence for a large southern tidal extension as observed by Grillmair et al. (1995). The difference here could be accounted to the lower resolution used by them, one part of this large tail could be due to the southern galaxy clusters not well separated. We point out that in their and our work we select stars below the completeness limit ([FORMULA] mag), completeness fluctuation are another possibility to explain some differences, but not on such a large scale. The tail is oriented in the direction of the galactic center (dashed arrow). As in the case of NGC 288, the tidal radius determination may be overestimated because of the presence of galaxy clusters close to NGC 1904. Nevertheless, the tidal tails of this cluster do not appear to be correlated with the distribution of the extra-galactic objects. The dust extinction is low towards this cluster (E([FORMULA]) = 0.01) and the fluctuations of the dust emission are low as traced by the IRAS 100-µm  map. Because of the short relaxation time of NGC 1904 ([FORMULA] yr), the mass segregation should affect as well the stellar populations in the tidal tails. Since, following GO97, [FORMULA] is about 30% higher than [FORMULA], this may indicate a slight influence of the galaxy on this cluster.

[FIGURE] Fig. 11a-d. NGC 1904. a : Surface density plot displaying tidal tails (in Log) around NGC 1904. The different arrows indicate the direction of the galactic center (dashed arrow) and of the direction perpendicular to the galactic plane (solid arrow). The dashed circle centered on the cluster indicates its tidal radius. The horizontal double arrow scale stands for 100 pc. b : Tidal-tail density overlaid with the surface density contours of galaxies ([FORMULA]3-[FORMULA]) at the same resolution. c : Radial surface density profile with the power-law fit to our data in the external parts, while the inner surface density profile comes from the data (diamond) by Trager et al. (1995), shifted vertically to fit our star count data. The vertical arrow indicates the tidal radius. d : Overdensities of galaxy counts; there is no Abell galaxy cluster in this field.

4.6. NGC 2298

NGC 2298 is a remote cluster located at a distance of 10.4 kpc from the sun, with its horizontal branch (HB) at V = 16.11 mag. It has a tidal radius of about 19 pc and a concentration c = log ([FORMULA]) = 1.40. There are background fluctuations owing to the dust along the line of sight, as clearly traced by the IRAS 100-µm  map (see Fig. 12). We perform a quite high tail/background S/N CMD selection because of the high background density (see Fig. 4, but there is still a bias because of the dust extinction, as seen in Fig. 12. There is a southern extension towards the galactic center (dashed arrow) which is interrupted by dust absorption. Some parts of the Eastern extension located at (x = -50, y = -10) of the tidal tails may be questionable, because of the stronger dust presence, nevertheless the lower absorption can hardly explain all these overdensities, since their distribution does not follow the minimum IRAS 100-µm  emission map. Clearly, the overdensity at (x = 60, y = 60) is associated with a low IRAS emission area. Given the position and the distance of NGC 2298 from the galactic center (15.1 kpc), the southern extension is likely tracing its orbital path and not the result of gravitational shock, as indicated by the ratio [FORMULA] from GO97. The low value [FORMULA], likely due to the small extensions in the outer parts, is questionable.

[FIGURE] Fig. 12a and b. NGC 2298. a : Surface density plot displaying tidal tails (in Log) around NGC 2298. The different arrows indicate the direction of the galactic center (dashed arrow) and of the direction perpendicular to the galactic plane (solid arrow). The dashed circle centered on the cluster indicates its tidal radius. The horizontal double arrow scale stands for 100 pc. b : IRAS 100-µm  chart overlaid with the above tidal-tail surface density contours.

4.7. NGC 4372

NGC 4372 is a nearby globular cluster located at a distance of 4.6 kpc from the sun, with its horizontal branch (HB) at V = 15.30 mag. It has a tidal radius of about 52 pc and a concentration c = log ([FORMULA]) = 1.30. The presentation of the detection of the overdensities around this cluster illustrates the dramatic influence of varying dust extinction (see Fig. 13). Strangely enough, the very elongated dust filament observed in the IRAS 100-µm  map ends very close to the cluster: this may suggest an interaction of the cluster with the interstellar medium currently at play. Following GO97 (see Table 4), this cluster has an evolution strongly driven by the galaxy ([FORMULA]).

[FIGURE] Fig. 13. NGC 4372. IRAS 100-µm  map overlaid with the contours of the overdensities in star-counts, which are completely disturbed by the dust extinction, particularly along the elongated dust filament. The different arrows indicate the direction of the galactic center (dashed arrow) and of the direction perpendicular to the galactic plane (solid arrow). The dashed circle centered on the cluster indicates its tidal radius. The horizontal double arrow scale stands for 100 pc.

4.8. NGC 5139, [FORMULA] Cen

NGC 5139, the most massive galactic globular cluster (Meylan 1987; Meylan et al. 1995; Merritt et al. 1997), currently crossing the disk plane, is a nearby globular cluster located at a distance of 5.0 kpc from the sun, with its horizontal branch (HB) at V = 14.53 mag. It has a tidal radius of about 65 pc and a concentration c = log ([FORMULA]) = 1.24. Its relative proximity allows to reach the main sequence for the star count selection.

Given the very good tail/background S/N ratio, we perform an absolute calibration of the photometry using the data from Cannon & Stobie (1973) and Alcaino & Liller (1987) with an error which is still about [FORMULA] = 0.2 mag. Although obvious biases by dust absorption affect the star counts, as seen, e.g., at the positions (x = 50, y = -25) and (x = -50, y = -70) on the IRAS 100-µm  map (Fig. 14), there are two large and significant tidal tails: NGC 5139 is releasing currently some large amounts of stars. The tidal tail extensions are perpendicular to the galactic plane (see Fig. 14), which is a clear sign of disk-shocking, as observed in our numerical simulations (CLM99). By considering star-counts with magnitude [FORMULA] (the completeness limit), we found about 7000 [FORMULA] stars outside one tidal radius, in the [FORMULA] field. This magnitude corresponds to a 0.63 [FORMULA] star at a distance of 5 kpc. Assuming the same mass function in the cluster and in the tidal extensions, because of its large relaxation time, we estimate a total of 1.9 [FORMULA] [FORMULA] for the escaped stars, with the assumption of a Salpeter law ([FORMULA] = -2.35) mass function for the stars down to 0.1 [FORMULA]. Thus the tidal tails represent about 0.6% of the cluster mass for total cluster mass of about 5.1 106 [FORMULA]. This is consistent with the numerical simulations (CLM99, Johnston et al. 1998) given the high uncertainties on the mass function, the photometric calibration, the mass-luminosity relation used (see e.g., Saviane et al. 1998), and the possible steeper mass function in the tidal tails, as discussed in Sect. 5 for a slope [FORMULA]= -2.8. We point out that a steeper mass function has been observed in the halo of NGC 5139 (Anderson 1998)

[FIGURE] Fig. 14a-c. NGC 5139 [FORMULA] [FORMULA] Centauri. a : Surface density plot displaying tidal tails (in Log) around NGC 5139. The different arrows indicate the directions of the cluster proper motion (dotted arrow), of the galactic center (dashed arrow), and of the direction perpendicular to the galactic plane (solid arrow). The dashed circle centered on the cluster indicates its tidal radius. The horizontal double arrow stands for 100 pc. b : IRAS 100-µm  chart overlaid with the above tidal-tail surface density contours. c : Radial surface density profile with the power-law fit to our data in the external parts, while the inner surface density profile comes from the data (diamond) by Trager et al. (1995), shifted vertically to fit our star count data. The vertical arrow indicates the tidal radius.

The [FORMULA] parameter value and the position of the cluster in the galaxy indicate that NGC 5139 is presently experiencing a disk shocking, with an important mass loss of stars, whose presence is clearly observed in the immediate neighborhood of the cluster. The observed proper motion of NGC 5139 indicates that this cluster is in the early phases of its disk crossing. This confirms the high value of the ratio [FORMULA] estimated by GO97. In the case of NGC 5139, the disk-shocking consequences are combined with the bulge-shocking ones, since the cluster orbit goes as close as 1.8 kpc from the galactic center (Dauphole et al. 1996).

We choose to present here the same wavelet planes that those for the other clusters, but given the high density - significance - of NGC 5139 tidal tails, we illustrate, in Fig. 6, the different spatial resolutions for [FORMULA] Cen after filtering of the background noise. It is worth mentioning that, because of the internal rotation of this cluster (Meylan & Mayor 1986; Merritt et al. 1997), the global mass loss rate is enhanced by a factor of 2 with respect to the N-body simulations (CLM99) and Fokker-Planck estimates (Longaretti & Lagoute 1996). In the discussion we consider the effect of the mass segregation on the mass loss derivation.

4.9. NGC 5272 [FORMULA] M3

NGC 5272 is a globular cluster located at a distance of 9.7 kpc from the sun, with its horizontal branch (HB) at V = 15.65 mag. It has a tidal radius of about 105 pc and a concentration c = log ([FORMULA]) = 1.85. The cluster is near the edge of the plate, preventing the study of its Eastern side (see Fig. 15). The field is polluted only by 2 small galaxy clusters, viz. Abell 1781 and Abell 1769, the former being detected only at 2.5-[FORMULA] level. Unfortunately, a defect on the plate E131 (POSS) have blurred the extra-galactic object detection (peak at x = 120, y = -20). We emphasize that point-source detection with SExtractor is less affected by this defect. There is no anticorrelation at all between the tidal tails and the dust emission, as we checked with the IRAS 100-µm  map, which is at a low level (E([FORMULA]) = 0.01). The extension at (x = -30, y = -50), towards the galactic center (dashed arrow), is the more reliable. Thus from the low value of the slope [FORMULA], we can infer that the field pollution bias must be quite strong, providing a rather constant radial surface density. The comparison with the data from Trager et al. (1995), which obtained star-count values smaller than our data near the tidal radius, confirms this point. The long relaxation time of NGC 5272, viz. [FORMULA] yr, implies that the mass segregation should not affect strongly the mass function of the unbound stars. Gunn & Griffin (1979) found some weak rotation in this globular cluster which should slightly enhance the mass loss rate by a factor 1.1-1.2 (Longaretti & Lagoute 1996). There is no apparent correlation between the tidal tail direction and the proper motion of the cluster (dotted arrow).

[FIGURE] Fig. 15a-d. NGC 5272. a : Surface density plot displaying tidal tails (in Log) around NGC 5272. The different arrows indicate the directions of the cluster proper motion (dotted arrow), of the galactic center (dashed arrow), and of the direction perpendicular to the galactic plane (solid arrow). The dashed circle centered on the cluster indicates its tidal radius. The horizontal double arrow scale stands for 200 pc. b : Above tidal-tail density overlaid with the surface density contours of galaxies ([FORMULA]3-[FORMULA]) at the same resolution. c : Radial surface density profile with the power-law fit to our data in the external parts, while the inner surface density profile comes from the data (diamond) by Trager et al. (1995), shifted vertically to fit our star count data. The vertical arrow indicates the tidal radius. d : Overdensities of galaxy counts overlaid with the Abell clusters (triangle) detected in the same field. The extended structure is due to spurious detections because of a defect on the plate (see text).

4.10. NGC 5694

NGC 5694 is a very remote globular cluster located at a distance of 33 kpc from the sun, with its horizontal branch (HB) at V = 18.50 mag, which is a strong limitation for star counts. Given its large distance from the galactic center, namely 27.5 kpc, this cluster is not expected to suffer strong gravitational shocks ([FORMULA] = 1.0, GO97). It has a tidal radius of about 41 pc and a concentration c = log ([FORMULA]) = 1.84. We select the stars on the giant branch only, with a higher tail/background S/N ratio in order to avoid as much as possible the galaxies which are the strongest bias in this field (see Fig. 16). The lower dust extinction, mapped through IRAS 100-µm  emission, could induce an artificial extension in the S-W part of the cluster, at the position (x = 20, y = -15). But the huge extension in the S-E part can be attributed to extra-tidal material, with high confidence since it is correlated with higher dust extinction and there is only one small galaxy cluster at the position (x = -20, y = -3). It must be stars tidally stripped from the cluster, material which is now trailing/leading along the orbit of the cluster. As in the other clusters, it is aligned towards the galactic center direction (dashed arrow), but it might also be a projection effect of its orbital plane with the galactic center direction. The size of this extension is about 300 pc in the sky and is probably even much larger because of the shallow photometry available on this distant cluster.

[FIGURE] Fig. 16a-d. NGC 5694. a : Surface density plot displaying tidal tails (in Log) around NGC 5694. The different arrows indicate the direction of the galactic center (dashed arrow) and of the direction perpendicular to the galactic plane (solid arrow). The dashed circle centered on the cluster indicates its tidal radius. The horizontal double arrow scale stands for 200 pc. b : Tidal-tail density overlaid with the surface density contours of galaxies ([FORMULA]3-[FORMULA]) at the same resolution. c : IRAS 100-µm  chart overlaid with the above tidal-tail surface density contours. d : Overdensities of galaxy counts; there is no Abell galaxy cluster in this field.

4.11. NGC 5824

NGC 5824 is a very remote globular cluster located at a distance of 32.2 kpc from the sun, with its horizontal branch (HB) at V = 18.60 mag, which is a strong limitation for star counts. At a large distance from the galactic center, namely 26 kpc, this cluster is not expected to suffer strong gravitational shocks ([FORMULA] = 1.6, GO97). It has a tidal radius of about 147 pc and a concentration c = log ([FORMULA]) = 2.45. Because of a low tail/background S/N ratio, a consequence of the faint [FORMULA] magnitude, the overdensity map around NGC 5824 appears to be very noisy (Fig. 17). Grillmair et al. (1995) find around this cluster more extended structures, aligned with the N-S direction, than we do in the same field: this may be partly due to our rather shallow photographic films. There are some strong biases due to dust extinction as it can be seen on Fig. 17 at the position (x = -20, y = -20) and due also to some galaxies spread mainly over the Southern part. GO97 indicate that NGC 5824 should experience important interactions with the tidal galactic field, a prediction we are not able to confirm because of the tangled observational biases. But it appears that a preferential direction of the cluster extension could be perpendicular to the galactic plane (solid arrow), either due to a disk shocking or tracing the orbital motion of the cluster. Nevertheless a bulge shocking effect cannot be ruled out in the case of a very eccentric orbit.

[FIGURE] Fig. 17a-d. NGC 5824. a : Surface density plot displaying tidal tails (in Log) around NGC 5824. The different arrows indicate the direction of the galactic center (dashed arrow) and of the direction perpendicular to the galactic plane (solid arrow). The dashed circle centered on the cluster indicates its tidal radius. The horizontal double arrow scale stands for 400 pc. b : Tidal-tail density overlaid with the surface density contours of galaxies ([FORMULA]3-[FORMULA]) at the same resolution. c : IRAS 100-µm  chart overlaid with the above tidal-tail surface density contours. d : Overdensities of galaxy counts overlaid with the Abell cluster (triangle) detected in the same field.

4.12. NGC 5904 [FORMULA] M5

NGC 5904 is a globular cluster located at a distance of 7 kpc from the sun, with its horizontal branch (HB) at V = 15.06 mag. It has a tidal radius of about 66 pc and a concentration c = log ([FORMULA]) = 1.87. We present only the S-E part of the tidal extensions (Fig. 18) because of its position on the plate. No bias due to dust is reported towards this field (E([FORMULA]) = 0.03). The presence on a galaxy cluster close to the tidal radius of the cluster enhances artificially and locally the tidal tail pointing towards the galactic center (dashed arrow) and the direction perpendicular to the galactic plane (solid arrow). Nevertheless, it is obvious that an extension is present towards this direction, since the galaxy cluster size is significantly smaller than the size of the globular cluster extension, as shown on Fig. 18b with the same resolution used for the star and galaxy surface densities. Lehmann & Scholz (1996) found already indication of tidal tail around this cluster from its surface brightness profile which departs from a King profile; this may be explained as well by the galaxy cluster near the tidal radius. From Odenkirchen et al. (1997), NGC 5904 is just beginning its crossing through the disk and towards the galactic center. Consequently, we could observe the first effect of the gravitational shocking on this cluster, with the tail aligned towards the tidal directions (see CLM99) after being compressed during the crossing. Indeed the momentum transfer to the cluster stars is in the Z direction during the disk shocking. From GO97, NGC 5904 suffers strong interactions with the galaxy, with [FORMULA] = 26, a high value due to the use of the Bahcall et al. (1983) galactic model which enhances the gravitational shocks because of its nuclear component and the form of the disk potential which does not vanishes at the center as it is the case for the model from Ostriker & Caldwell (1983).

[FIGURE] Fig. 18a-c. NGC 5904 [FORMULA] M5. a : Surface density plot displaying tidal tails (in Log) around NGC 5904. The different arrows indicate the directions of the cluster proper motion (dotted arrow), of the galactic center (dashed arrow), and of the direction perpendicular to the galactic plane (solid arrow). The dashed circle centered on the cluster indicates its tidal radius. The horizontal double arrow scale stands for 100 pc. b : Tidal-tail density overlaid with the surface density contours of galaxies ([FORMULA]3-[FORMULA]) at the same resolution. c : Overdensities of galaxy counts overlaid with the Abell cluster (triangle) detected in the same field.

4.13. NGC 6205 [FORMULA] M13

NGC 6205 is a globular cluster located at a distance of 6.8 kpc from the sun, with its horizontal branch (HB) at V = 14.90 mag. It has a tidal radius of about 56 pc and a concentration c = log ([FORMULA]) = 1.49. The bias towards NGC 6205 are not strong as shown by the weak IRAS 100-µm  flux and the relatively high tail/background S/N ratio in the CMD. Given the position of the cluster on the survey plates, we extract a field of 90´ in size. There is no strong bulk of tidal stars (see Fig. 19) due to any shock and the field is too small to detect any large scale structure corresponding to the orbital path. An extension can be seen towards the galactic center (dashed arrow) at the position (x = -10, y = -25), although located inside the tidal radius, which highlights the limitation of an azimuthally averaged radial surface density. This extension is not correlated with the proper motion. We note that an extended default on the plate center worsens the cluster/background star separation.

[FIGURE] Fig. 19. NGC6205. Surface density plot displaying tidal tails (in Log) around NGC 6205. The different arrows indicate the directions of the cluster proper motion (dotted arrow), of the galactic center (dashed arrow), and of the direction perpendicular to the galactic plane (solid arrow). The dashed circle centered on the cluster indicates its tidal radius. The horizontal double arrow scale stands for 100 pc.

4.14. NGC 6254 [FORMULA] M10

NGC 6254 is a nearby globular cluster located at a distance of 4.1 kpc from the sun, with its horizontal branch (HB) at V = 14.65 mag. It has a tidal radius of about 26 pc and a concentration c = log ([FORMULA]) = 1.40. This cluster is a striking case because of a strong gradient in the dust extinction as seen on Fig. 20 with the IRAS 100-µm  map. The southern extension anticorrelates quite well with the dust emission which is the sign of a possible bias. An obvious decrease of the stellar surface density is correlated with the dust emission at the position (x = -40, y = -30). Nevertheless the inner NE-SW and the northern extensions are not anticorrelated with the dust emission. The second break at [FORMULA], apart from the one around the tidal radius, in the radial density profile (see Fig. 20c) must correspond to a very recent disk-shocking, with the diffusing stars (cf. CLM99) still close to the cluster. This conclusion is strengthenedd by the proper motion of the cluster whose direction (dotted arrow) is opposite to the disk direction (solid arrow): Odenkirchen et al. (1998) indicate that NGC 6254 suffered its last disk crossing about 20 Myr ago. Considering the northern extension as a genuine tidal tail made of stars from NGC 6254, we can give a lower limit for the diffusion velocity, which is a projected expansion velocity of the tidal material in the cluster reference frame: at a distance of 4.1 kpc, for a projected distance of 150 pc, we obtain about 7 km s-1 as a lower limit of the diffusion velocity. We note that the velocity dispersion of stars in NGC 6254 is similar, with [FORMULA] = 6.6 km s-1 (Pryor & Meylan 1993). This velocity diffusion probes the differential diffusion of stars released in the Galaxy along with the global dynamical friction of the cluster which is not felt by the unbound stars. Actually this diffusion velocity is surprisingly high compared to the dispersion velocity, where we would expect low velocity dispersion for the unbound stars: a misclassification of these clumps as genuine cluster stars or an underestimation of the last crossing time cannot be ruled out. Given the quite short relaxation time [FORMULA] yr, the mass segregation must be present in this cluster, even though Hurley et al. (1989) did not find any evidence. Such a mass segregation must lead to a steep mass function in the tidal tails.

[FIGURE] Fig. 20a-c. NGC 6254. a : Surface density plot displaying tidal tails (in Log) around NGC 6254. The different arrows indicate the directions of the cluster proper motion (dotted arrow), of the galactic center (dashed arrow), and of the direction perpendicular to the galactic plane (solid arrow). The dashed circle centered on the cluster indicates its tidal radius. The horizontal double arrow scale stands for 100 pc. b : IRAS 100-µm  chart overlaid with the above tidal-tail surface density contours. Lower-right panel c : Radial surface density profile with the power-law fit to our data in the external parts, while the inner surface density profile comes from the data (diamond) by Trager et al. (1995), shifted vertically to fit our star count data. The vertical arrow indicates the tidal radius.

4.15. NGC 6397

NGC 6397 is a very nearby globular cluster located at a distance of 2.2 kpc from the sun, with its horizontal branch (HB) at V = 12.87 mag. It has a tidal radius of about 66 pc and a concentration c = log ([FORMULA]) = 2.50. It is the only post core-collapsed cluster in our sample, although NGC 1851 and NGC 5824 have also rather large concentrations. This is the second example, with NGC 4372, of overdensities strongly biased by dust extinction fluctuation as it can be seen in Fig. 21. All the overdensities found in the northern and eastern parts cannot be disentangled from dust extinction. Only the S-E extension, at the position (x = -100, y = -100), could be a genuine tidal tail, but with a somewhat low confidence in spite of the fact that these star counts are more than 3 [FORMULA] above the background because the dust extinction fluctuations in this field are quite high ([FORMULA] MJy/sr for the IRAS-100µm  flux). Nevertheless, we emphasize that this extension is perpendicular to the plane (solid arrow) as expected for disk shocking (CLM99), thanks to the momentum transfer in the Z direction. During the disk crossing the gained acceleration for the cluster stars is directed towards the cluster equatorial plane parallel to the galactic plane. Then the energy gained is released in this direction, perpendicular to the galactic plane. The mass segregation found by Mould et al. (1996) in this cluster will affect the mass function of the tidal tails. A weak rotation of NGC 6397 has been found (Meylan & Mayor 1991) which should enhance the mass loss rate by about 20%, using Fig. 7 of Longaretti & Lagoute (1996).

[FIGURE] Fig. 21a and b. NGC 6397. a : Surface density plot displaying tidal tails (in Log) around NGC 6397. The different arrows indicate the directions of the cluster proper motion (dotted arrow), of the galactic center (dashed arrow), and of the direction perpendicular to the galactic plane (solid arrow). The dashed circle centered on the cluster indicates its tidal radius. The horizontal double arrow scale stands for 50 pc. b : IRAS 100-µm  chart overlaid with the above tidal-tail surface density contours.

4.16. NGC 6535

NGC 6535 is a globular cluster located at a distance of 6.6 kpc from the sun, with its horizontal branch (HB) at V = 15.73 mag. It has a tidal radius of about 17 pc and a concentration c = log ([FORMULA]) = 1.30. In spite of the high tail/background S/N color selection on the CMD in order to avoid the high background density, the cluster density remains lower than the background (see Fig. 22). The dust extinction induces a strong bias towards this field (E([FORMULA]) = 0.32) as seen in the IRAS 100-µm  map on Fig. 22. Part of the northern extension could be artificially enhanced by the local lower dust extinction. It is likely that the Southern extension is lowered by local higher dust extinction at the position (x = 0, y = -20). As indicated by GO97, the evolution of this cluster is influenced by the galactic potential ([FORMULA] = 1.4). Currently, NGC 6535 is experiencing a strong bulge shocking and disk shocking as indicated by the correlation of the tail with the disk/bulge direction (solid and dashed arrows, respectively) and confirmed by its location in the galaxy, viz. 1.2 kpc above the plane and 4 kpc from the galactic center (Harris 1996).

[FIGURE] Fig. 22a-c. NGC 6535. a : Surface density plot displaying tidal tails (in Log) around NGC 6535. The different arrows indicate the direction of the galactic center (dashed arrow) and of the direction perpendicular to the galactic plane (solid arrow). The dashed circle centered on the cluster indicates its tidal radius. The horizontal double arrow scale stands for 50 pc. b : IRAS 100-µm  chart overlaid with the above tidal-tail surface density contours. c : Radial surface density profile with the power-law fit to our data in the external parts, while the inner surface density profile comes from the data (diamond) by Trager et al. (1995), shifted vertically to fit our star count data. The vertical arrow indicates the tidal radius.

4.17. NGC 6809 [FORMULA] M55

NGC 6809 is a globular cluster located at a distance of 5.1 kpc from the sun, with its horizontal branch (HB) at V = 14.40 mag. It has a tidal radius of about 23 pc and a concentration c = log ([FORMULA]) = 0.76. The overdensities (see Fig. 23) are strongly anticorrelated with the dust emission traced by the IRAS 100-µm  map, e.g. at the position (x = -50, y = -50), where the dust extinction is probably disturbing the tail surface density. It may also be possible that the Western extension (x = 90, y = 0) towards the galactic center (dashed arrow) could be associated with the cluster, because it is not anticorrelated with the dust emission; the same remark applies for the extension at (x = -30, y = -30). The study of such a cluster should greatly benefit from the better transparency to the dust absorption offered in J and K bands. In a previous study in V and I bands, Zaggia et al. (1997) found already evidence for cluster stars in the halo of this object.

[FIGURE] Fig. 23a-c. NGC 6809 [FORMULA] M55. a : Surface density plot displaying tidal tails (in Log) around NGC 6809. The different arrows indicate the direction of the galactic center (dashed arrow) and of the direction perpendicular to the galactic plane (solid arrow). The dashed circle centered on the cluster indicates its tidal radius. The horizontal double arrow scale stands for 100 pc. b : IRAS 100-µm  chart overlaid with the above tidal-tail surface density contours. c : Radial surface density profile with the power-law fit to our data in the external parts, while the inner surface density profile comes from the data (diamond) by Trager et al. (1995), shifted vertically to fit our star count data. The vertical arrow indicates the tidal radius.

4.18. NGC 7492

NGC 7492 is a remote globular cluster located at a distance of 24.3 kpc from the sun, with its horizontal branch (HB) at V = 17.63 mag. It has a tidal radius of about 62 pc and a concentration c = log ([FORMULA]) = 1.0. There is no dust emission towards this field and the background galaxy clusters are located far from the cluster, as indicated in Fig. 24. Obviously, the overdensity at the position (x = 18, y = 25) is associated with the galaxy cluster Abell 2533. Because of the low mass of this cluster, GO97 find a fast evolution in the Galaxy field, with [FORMULA], compared to its intrinsic evolution. Clearly, a tiny extension is visible, pointing towards the galactic center (dashed arrow). This lack of tidal extension is not in contradiction with the conclusion drawn by GO97, given its current location far from the center of the Galaxy (23.5 kpc). A higher tail/background S/N ratio selection, using high-quality CCD data, may allow the detection of very low surface density extension related to tidal tails extending away from NGC 7492.

[FIGURE] Fig. 24a-c. NGC7492. a : Surface density plot displaying tidal tails (in Log) around NGC 7492. The different arrows indicate the direction of the galactic center (dashed arrow) and of the direction perpendicular to the galactic plane (solid arrow). The dashed circle centered on the cluster indicates its tidal radius. The horizontal double arrow scale stands for 100 pc. b : Tidal-tail density overlaid with the surface density contours of galaxies ([FORMULA]3-[FORMULA]) at the same resolution. c : Overdensities of galaxy counts overlaid with the Abell cluster (triangle) detected in the same field.

4.19. Palomar 5

Palomar 5 is a remote globular cluster located at a distance of 21.8 kpc from the sun, with its horizontal branch (HB) at V = 17.63 mag. It has a tidal radius of about 107 pc and a concentration c = log ([FORMULA]) = 0.74. It is one of the most remote cluster with measured proper motions (Schweitzer et al. 1993; Scholz et al. 1998). The tidal radius could be lower than previously measured, down to 7´, in agreement with its orbit (Scholz et al. 1998). In Fig. 25 we present the overdensities, which are strongly biased by the background galaxy clusters present in the field. Because of the unreliable star/galaxy separation above [FORMULA], the confusion is quite strong for this remote and faint cluster. As pointed out already by Scholz et al. (1998), the galaxy cluster Abell 2050 could be responsible for the previous (commonly adopted) overestimate of the tidal radius. The dust extinction is very weak in this field (E([FORMULA]) = 0.03), and do not exhibit any anticorrelation with the overdensities, as checked on the IRAS 100-µm  map. The background galaxy distribution and the large distance to this cluster make difficult any conclusion on the genuine location, if any, of stars stripped from the cluster.

[FIGURE] Fig. 25a-c. Palomar 5. a : Surface density plot displaying tidal tails (in Log) around Pal 5. The different arrows indicate the directions of the cluster proper motion (dotted arrow), of the galactic center (dashed arrow), and of the direction perpendicular to the galactic plane (solid arrow). Here, the direction of the galactic center is similar, in projection, to the direction perpendicular to the galactic plane. The dashed circle centered on the cluster indicates its tidal radius. The horizontal double arrow scale stands for 200 pc. b : Tidal-tail density overlaid with the surface density contours of galaxies (3-[FORMULA]) at the same resolution. c : Overdensities of galaxy counts overlaid with the Abell clusters (triangle) detected in the same field.

4.20. Palomar 12

Palomar 12 is a remote globular cluster located at a distance of 17.8 kpc from the sun, with its horizontal branch (HB) at V = 17.13 mag. It has a tidal radius of about 49 pc and a concentration c = log ([FORMULA]) = 0.90. The dust extinction is very low (E([FORMULA]) = 0.02), but the contamination by background galaxy clusters is very important (see Fig. 26), although only two Abell galaxy clusters are reported in this field. The N-S oriented very long tail is contaminated by some galaxies as shown at position (x = 15, y = 30) in Fig. 26. Nevertheless this tail is a genuine feature made of stars tidally stripped, as shown by the distribution of the galaxies as the same resolution. The western and eastern overdensities are related mainly to galaxies. A higher tail/background S/N CMD selection confirmed the Pal 12 membership of the top and bottom clumps at positions (x = 0, y = [FORMULA]60). To get an estimate of the time of the last, if any, gravitational shock on this cluster, we assume that these two latter star clumps are remains of the last shock. Adopting a diffusion velocity for the tidal stars equal to 1 km s-1, similar to the velocity dispersion (Djorgovski & Meylan 1994) of such a low mass cluster ([FORMULA]) and assuming the distance in projection between the clumps and the cluster to be 350 pc, we estimate 350 Myr as the time since the last shock. This is a lower limit because of the projection effect and the limited field. Contrary to most other tidal tail directions, the extension is perpendicular to the galactic center direction (dashed arrow) and is in a plane parallel to the galactic disk.

[FIGURE] Fig. 26a-c. Palomar 12. a : Surface density plot displaying tidal tails (in Log) around Pal 12. The different arrows indicate the direction of the galactic center (dashed arrow) and of the direction perpendicular to the galactic plane (solid arrow). The dashed circle centered on the cluster indicates its tidal radius. The horizontal double arrow scale stands for 200 pc. b : Tidal-tail density overlaid with the surface density contours of galaxies ([FORMULA]3-[FORMULA]) at the same resolution. c : Overdensities of galaxy counts overlaid with the Abell clusters (triangle) detected in the same field

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Online publication: July 13, 2000
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