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By exploiting two ACS/HST datasets separated by a temporal baseline of ~7 years, we have determined the relative stellar proper motions (providing membership) and the absolute proper motion of the Galactic globular cluster M71. The absolute proper motion has been used to reconstruct the cluster orbit within a Galactic, three-component, axisymmetric potential. M71 turns out to be in a low latitude disk-like orbit inside the Galactic disk, further supporting the scenario in which it lost a significant fraction of its initial mass. Since large differential reddening is known to affect this system, we took advantage of near-infrared, ground-based observations to re-determine the cluster center and density profile from direct star counts. The new structural parameters turn out to be significantly different from the ones quoted in the literature. In particular, M71 has a core and a half-mass radii almost 50% larger than previously thought. Finally we estimate that the initial mass of M71 was likely one order of magnitude larger than its current value, thus helping to solve the discrepancy with the observed number of X-ray sources., Accepted for publication in ApJ

We present the first evidence of multiple populations in the Galactic globular cluster NGC 6362. We used optical and near-UV Hubble Space Telescope and ground based photometry, finding that both the sub giant and red giant branches are split in two parallel sequences in all color magnitude diagrams where the F336W filter (or U band) is used. This cluster is one of the least massive globulars (M_tot~5x10^4 M_sun) where multiple populations have been detected so far. Even more interestingly and at odds with any previous finding, we observe that the two identified populations share the same radial distribution all over the cluster extension. NGC 6362 is the first system where stars from different populations are found to be completely spatially mixed. Based on N-body and hydrodynamical simulations of multiple stellar generations, we argue that, to reproduce these findings, NGC 6362 should have lost up to the 80% of its original mass, Comment: Accepted for publication by ApJ Letters; 6 pages, 5 figures

By exploiting two sets of high-resolution images obtained with HST ACS/WFC over a baseline of ~10 years we have measured relative proper motions of ~70,000 stars in the stellar system Terzan 5. The results confirm the membership of the three sub-populations with different iron abudances discovered in the system. The orbit of the system has been derived from a first estimate of its absolute proper motion, obtained by using bulge stars as reference. The results of the integration of this orbit within an axisymmetric Galactic model exclude any external accretion origin for this cluster. Terzan 5 is known to have chemistry similar to the Galactic bulge; our findings support a kinematic link between the cluster and the bulge, further strengthening the possibility that Terzan 5 is the fossil remnant of one of the pristine clumps that originated the bulge., 25 pages, 14 figures, accepted for publication by ApJ

We present the first evidence of clear signatures of tidal distortions in the density distribution of the fascinating open cluster NGC 6791. We used deep and wide-field data obtained with the Canada-France-Hawaii-Telescope covering a 2x2 square degrees area around the cluster. The two-dimensional density map obtained with the optimal matched filter technique shows a clear elongation and an irregular distribution starting from ~300" from the cluster center. At larger distances, two tails extending in opposite directions beyond the tidal radius are also visible. These features are aligned to both the absolute proper motion and to the Galactic center directions. Moreover, other overdensities appear to be stretched in a direction perpendicular to the Galactic plane. Accordingly to the behaviour observed in the density map, we find that both the surface brightness and the star count density profiles reveal a departure from a King model starting from ~600" from the center. These observational evidence suggest that NGC 6791 is currently experiencing mass loss likely due to gravitational shocking and interactions with the tidal field. We use this evidence to argue that NGC 6791 should have lost a significant fraction of its original mass. A larger initial mass would in fact explain why the cluster survived so long. Using available recipes based on analytic studies and N-body simulations, we derived the expected mass loss due to stellar evolution and tidal interactions and estimated the initial cluster mass to be M_ini=(1.5-4) x 10^5 M_sun., Comment: Accepted for publication in the MNRAS (9 pages, 8 Figures)

We present some results of numerical simulations of a globular cluster orbiting in the central region of a triaxial galaxy on a set of 'loop' orbits. Tails start forming after about a quarter of the globular cluster orbital period and develop, in most cases, along the cluster orbit, showing clumpy substructures as observed, for example, in Palomar 5. If completely detectable, clumps can contain about 7,000 solar masses each, i.e. about 10% of the cluster mass at that epoch. The morphology of tails and clumps and the kinematical properties of stars in the tails are studied and compared with available observational data. Our finding is that the stellar velocity dispersion tends to level off at large radii, in agreement to that found for M15 and Omega Centauri., Comment: LaTeX 2e, uses AASTeX v5.x, 40 pages with 18 figures. Submitted to The Astronomical Journal

Globular star clusters that formed at the same cosmic time may have evolved rather differently from a dynamical point of view (because that evolution depends on the internal environment) through a variety of processes that tend progressively to segregate stars more massive than the average towards the cluster centre. Therefore clusters with the same chronological age may have reached quite different stages of their dynamical history (that is, they may have different dynamical ages). Blue straggler stars have masses greater than those at the turn-off point on the main sequence and therefore must be the result of either a collision or a mass-transfer event. Because they are among the most massive and luminous objects in old clusters, they can be used as test particles with which to probe dynamical evolution. Here we report that globular clusters can be grouped into a few distinct families on the basis of the radial distribution of blue stragglers. This grouping corresponds well to an effective ranking of the dynamical stage reached by stellar systems, thereby permitting a direct measure of the cluster dynamical age purely from observed properties., Comment: Published on the 20 December 2012 issue of Nature

We present the results of a set of N-body simulations aimed at exploring how the process of mass segregation (as traced by the spatial distribution of blue straggler stars, BSSs) is affected by the presence of a population of heavy dark remnants (as neutron stars and black holes). To this end, clusters characterized by different initial concentrations and different fractions of dark remnants have been modeled. We find that an increasing fraction of stellar-mass black holes significantly delays the mass segregation of BSSs and the visible stellar component. In order to trace the evolution of BSS segregation, we introduce a new parameter ($A^+$) that can be easily measured when the cumulative radial distribution of these stars and a reference population are available. Our simulations show that $A^+$ might also be used as an approximate indicator of the time remaining to the core collapse of the visible component., ApJ accepted

We present a detailed investigation of the radial distribution of blue straggler star and binary populations in the Galactic globular cluster NGC 5466, over the entire extension of the system. We used a combination of data acquired with the ACS on board the Hubble Space Telescope, the LBC-blue mounted on the Large Binocular Telescope, and MEGACAM on the Canadian-France-Hawaii Telescope. Blue straggler stars show a bimodal distribution with a mild central peak and a quite internal minimum. This feature is interpreted in terms of a relatively young dynamical age in the framework of the "dynamical clock" concept proposed by Ferraro et al. (2012). The estimated fraction of binaries is 6-7% in the central region (r200". Quite interestingly, the comparison with the results of Milone et al. (2012) suggests that also binary systems may display a bimodal radial distribution, with the position of the minimum consistent with that of blue straggler stars. If confirmed, this feature would give additional support to the scenario where the radial distribution of objects more massive than the average cluster stars is primarily shaped by the effect of dynamical friction. Moreover, this would also be consistent with the idea that the unperturbed evolution of primordial binaries could be the dominant BSS formation process in low-density environments., Accepted for publication on ApJ

By combining high spatial resolution and wide-field spectroscopy performed, respectively, with SINFONI and FLAMES at the ESO/VLT we measured the radial velocities of more than 600 stars in the direction of NGC 6388, a Galactic globular cluster which is suspected to host an intermediate-mass black hole. Approximately 55% of the observed targets turned out to be cluster members. The cluster velocity dispersion has been derived from the radial velocity of individual stars: 52 measurements in the innermost 2", and 276 stars located between 18" and 600". The velocity dispersion profile shows a central value of ~13 km/s, a flat behavior out to ~60" and a decreasing trend outwards. The comparison with spherical and isotropic models shows that the observed density and velocity dispersion profiles are inconsistent with the presence of a central black hole more massive than ~2000 Msol. These findings are at odds with recent results obtained from integrated light spectra, showing a velocity dispersion profile with a steep central cusp of 23-25 km/s at r, Comment: Accepted for publication by ApJ; 38 pages, 3 tables, 15 figures

We used ultra-deep $J$ and $K_s$ images secured with the near-infrared GSAOI camera assisted by the multi-conjugate adaptive optics system GeMS at the GEMINI South Telescope in Chile, to obtain a ($K_s$, $J-K_s$) color-magnitude diagram (CMD) for the bulge globular cluster NGC 6624. We obtained the deepest and most accurate near-infrared CMD from the ground for this cluster, by reaching $K_s$ $\sim$ 21.5, approximately 8 magnitudes below the horizontal branch level. The entire extension of the Main Sequence (MS) is nicely sampled and at $K_s$ $\sim$ 20 we detected the so-called MS "knee" in a purely near-infrared CMD. By taking advantage of the exquisite quality of the data, we estimated the absolute age of NGC 6624 ($t_{age}$ = 12.0 $\pm$ 0.5 Gyr), which turns out to be in good agreement with previous studies in the literature. We also analyzed the luminosity and mass functions of MS stars down to M $\sim$ 0.45 M$_{\odot}$ finding evidence of a significant increase of low-mass stars at increasing distances from the cluster center. This is a clear signature of mass segregation, confirming that NGC 6624 is in an advanced stage of dynamical evolution., Comment: Accepted for publication by ApJ. 39 pages, 19 figures, 1 table

Recently, both stellar mass-segregation and binary-fractions were uniformly measured on relatively large samples of Galactic Globular Clusters (GCs). Simulations show that both sizeable binary-star populations and Intermediate-Mass Black Holes (IMBHs) quench mass-segregation in relaxed GCs. Thus mass-segregation in GCs with a reliable binary-fraction measurement is a valuable probe to constrain IMBHs. In this paper we combine mass-segregation and binary-fraction measurements from the literature to build a sample of 33 GCs (with measured core-binary fractions), and a sample of 43 GCs (with a binary fraction measurement in the area between the core radius and the half-mass radius). Within both samples we try to identify IMBH-host candidates. These should have relatively low mass-segregation, a low binary fraction (< 5%), and short (< 1 Gyr) relaxation time. Considering the core binary fraction sample, no suitable candidates emerge. If the binary fraction between the core and the half-mass radius is considered, two candidates are found, but this is likely due to statistical fluctuations. We also consider a larger sample of 54 GCs where we obtained an estimate of the core binary fraction using a predictive relation based on metallicity and integrated absolute magnitude. Also in this case no suitable candidates are found. Finally, we consider the GC core- to half-mass radius ratio, that is expected to be larger for GCs containing either an IMBH or binaries. We find that GCs with large core- to half-mass radius ratios are less mass-segregated (and show a larger binary fraction), confirming the theoretical expectation that the energy sources responsible for the large core are also quenching mass-segregation, 5 pages, 7 figures, ApJ accepted

Context. The problem of the existence of intermediate-mass black holes (IMBHs) at the centre of globular clusters is a hot and controversial topic in current astrophysical research with important implications in stellar and galaxy formation. Aims. In this paper, we aim at giving further support to the presence of an IMBH in omega Centauri and at providing an independent estimate of its mass. Methods. We employed a self-consistent spherical model with anisotropic velocity distribution. It consists in a generalisation of the King model by including the Bahcall-Wolf distribution function in the IMBH vicinity. Results. By the parametric fitting of the model to recent HST/ACS data for the surface brightness profile, we found an IMBH to cluster total mass ratio of M_BH/M = 5.8(+0.9-1.2) x 10^(-3). It is also found that the model yields a fit of the line-of-sight velocity dispersion profile that is better without mass segregation than in the segregated case. This confirms the current thought of a non-relaxed status for this peculiar cluster. The best fit model to the kinematic data leads, moreover, to a cluster total mass estimate of M = (3.1 +/- 0.3) x 10^6 Msol, thus giving an IMBH mass in the range 13,000 < M_BH < 23,000 Msol (at 1-sigma confidence level). A slight degree of radial velocity anisotropy in the outer region (r > 12') is required to match the outer surface brightness profile., LateX, 5 pages, 5 figures. Accepted for publication by Astronomy & Astrophysics

Stars in globular clusters are generally believed to have all formed at the same time, early in the Galaxy's history. 'Blue stragglers' are stars massive enough that they should have evolved into white dwarfs long ago. Two possible mechanisms have been proposed for their formation: mass transfer between binary companions and stellar mergers resulting from direct collisions between two stars. Recently, the binary explanation was claimed to be dominant. Here we report that there are two distinct parallel sequences of blue stragglers in M30. This globular cluster is thought to have undergone 'core collapse', during which both the collision rate and the mass transfer activity in binary systems would have been enhanced. We suggest that the two observed sequences arise from the cluster core collapse, with the bluer population arising from direct stellar collisions and the redder one arising from the evolution of close binaries that are probably still experiencing an active phase of mass transfer., Published on the 24th December 2009 issue of Nature

We report the detection of a stellar density cusp and a velocity dispersion increase in the center of the globular cluster M54, located at the center of the Sagittarius dwarf galaxy (Sgr). The central line of sight velocity dispersion is 20.2 +/- 0.7 km/s, decreasing to 16.4 +/- 0.4 km/s at 2.5" (0.3 pc). Modeling the kinematics and surface density profiles as the sum of a King model and a point-mass yields a black hole (BH) mass of ~ 9400 M_sun. However, the observations can alternatively be explained if the cusp stars possess moderate radial anisotropy. A Jeans analysis of the Sgr nucleus reveals a strong tangential anisotropy, probably a relic from the formation of the system., Accepted for publication by The Astrophysical Journal (Letters). Latex. 5 pages, 4 color figures, 2 with reduced resolution, one in greyscale. A full-resolution color version of the paper can be retrieved from http://www.bo.astro.it/SGR/Sgr_BH.pdf

In the last decade, observational studies have shown the existence of tidal streams in the outer part of many galactic globular clusters. The most striking examples of clusters with well defined tidal tails are represented by Palomar 5 and NGC 5466 (both observed in the framework of the Sloan Digital Sky Survey), which show structures elongated for 4 kpc and 1 kpc in length, respectively. Unfortunately, most of the observational studies about globular clusters (GCs) do not cover such a large field of the sky as the SDSS does. In this framework, by mean of a parallel, adaptive tree-code, we performed detailed N-body simulations of GCs moving in a realistic three-components (bulge, disk and halo) Milky Way potential, in order to clarify whether and to what extent tails in the clusters outer regions (few tidal radii) are tracers of the local orbits and, also, if some kind of correlation exists among the cluster orbital phase and the orientation of such streams., LaTeX, 2 pages, 1 figure. Contribution to "Globular Clusters: Guides to Galaxies", March 6th-10th, 2006

We present results of fully self-consistent N-body simulations of the motion of four globular clusters moving in the inner region of their parent galaxy. With regard to previous simplified simulations, we confirm merging and formation of an almost steady nuclear cluster, in a slightly shorter time. The projected surface density profile shows strong similarity to that of resolved galactic nuclei. This similarity reflects also in the velocity dispersion profile which exhibits a central colder component as observed in many nucleated galaxies., Comment: 5 pages, 6 figures, submitted to MNRAS letters

By means of a multimass isotropic and spherical model that includes the self-consistent treatment of a central intermediate-mass black hole (IMBH), the influence of this black hole on the morphological and physical properties of globular clusters is investigated. In agreement with recent numerical studies, it is found that a cluster (with mass M) hosting an IMBH (with mass M_BH) shows, outside the region of gravitational influence of the black hole, a core-like profile resembling a King profile with concentration c < 2, although with a slightly steeper behaviour in the core region. In particular, the core logarithmic slope is s < 0.25 for reasonably low IMBH masses (M_BH < M/100), and c decreases monotonically with M_BH. Completely power-law density profiles (similar to, for example, those of collapsed clusters) are admitted only in the presence of a black hole with an unrealistic M_BH > M. The mass range estimate 12s - 4.8 < log (M_BH/M)< -1.1c - 0.69, depending on the morphological parameters, is deduced by considering a wide range of models. Applying this estimate to a set of 39 globular clusters, it is found that NGC 2808, NGC 6388, M80, M13, M62, M54 and G1 (in M31) probably host an IMBH. For them, the scaling laws M_BH ~ 0.09(M/M_sol)^{0.7} M_sol and M_BH ~ 50[sigma/ (km s^-1)]^{1.2} M_sol are identified from weighted least-squares fits. An important result of this 'collective' study is that a strong correlation exists between the presence of an extreme blue horizontal branch and the presence of an IMBH. In particular, the presence of a central IMBH in M13 and NGC 6388 could explain why these clusters possess extreme horizontal-branch stars, in contrast to their 'second parameter' counterparts M3 and 47 Tuc., LaTeX, 15 pages, 8 figures, 4 tables included. Final version with new G1 data. Accepted for publication on MNRAS. The definitive version is available at www.blackwell-synergy.com

10 pages, 8 figures, 3 tables, 1 appendix.-- See also http://www.sdss.org., We present the results of detailed N-body simulations of clusters moving in a realistic Milky Way (MW) potential. The strong interaction with the bulge and the disk of the Galaxy leads to the formation of tidal tails, emanating from opposite sides of the cluster. Some characteristic features in the morphology and orientation of these streams are recognized and interpreted. The tails have a complex morphology, particularly when the cluster approaches its apogalacticon, showing multiple "arms" in remarkable similarity to the structures observed around NGC 288 and Willman 1. Actually, the tails are generally good tracers of the cluster path quite far from the cluster center (>7-8 tidal radii), while on the smaller scale they are mainly pointing in the direction of the Galaxy center. In particular, the orientation of the inner part of the tails is highly correlated with the cluster orbital phase and the local orbital angular acceleration. This implies that, in general, the orbital path cannot be estimated directly from the orientation of the tails, unless a sufficient large field around the cluster is available

We have used a combination of high resolution (HST ACS-HRC, ACS-WFC, and WFPC2) and wide-field (ESO-WFI) observations of the galactic globular cluster NGC 6388 to derive its center of gravity, projected density profile, and central surface brightness profile. While the overall projected profiles are well fit by a King model with intermediate concentration (c=1.8) and sizable core radius (rc=7"), a significant power law (with slope \alpha=-0.2) deviation from a flat core behavior has been detected within the inner 1 arcsecond. These properties suggest the presence of a central intermediate mass black hole. The observed profiles are well reproduced by a multi-mass isotropic, spherical model including a black hole with a mass of ~5.7x10^3 Msol., Comment: ApJ Letter in press

By exploiting the exceptional high-resolution capabilities of the near-IR camera GSAOI combined with the multi-conjugate adaptive optics system GeMS at the GEMINI South Telescope, we investigated the structural and physical properties of the heavily obscured globular cluster Liller 1 in the Galactic bulge. We have obtained the deepest and most accurate color-magnitude diagram published so far for this cluster, reaching Ks ~ 19 (below the main sequence turn-off level). We used these data to re-determine the center of gravity of the system, finding that it is located about 2.2" south-east from the literature value. We also built new star density and surface brightness profiles for the cluster, and re-derived its main structural and physical parameters (scale radii, concentration parameter, central mass density, total mass). We find that Liller 1 is significantly less concentrated (concentration parameter c=1.74) and less extended (tidal radius r_t=298" and core radius r_c=5.39") than previously thought. By using these newly determined structural parameters we estimated the mass of Liller 1 M_tot = 2.3 x 10^6 Msun (Mtot = 1.5 x 10^6 Msun for a Kroupa IMF), which is comparable to that of the most massive clusters in the Galaxy (omega Centauri and Terzan 5). Also Liller 1 has the second highest collision rate (after Terzan 5) among all star clusters in the Galaxy, thus confirming that it is an ideal environment for the formation of collisional objects (such as millisecond pulsars)., Comment: Accepted for publication by ApJ. 32 pages, 8 figures, 1 table

We present semi-analytical models and simplified $N$-body simulations with $10^4$ and $10^5$ particles aimed at probing the role of dynamical friction (DF) in determining the radial distribution of Blue Straggler Stars (BSSs) in globular clusters. The semi-analytical models show that DF (which is the only evolutionary mechanism at work) is responsible for the formation of a bimodal distribution with a dip progressively moving toward the external regions of the cluster. However, these models fail to reproduce the formation of the long-lived central peak observed in all dynamically evolved clusters. The results of $N$-body simulations confirm the formation of a sharp central peak, which remains as a stable feature over the time regardless of the initial concentration of the system. In spite of a noisy behavior, a bimodal distribution forms in many cases, with the size of the dip increasing as a function of time. In the most advanced stages the distribution becomes monotonic. These results are in agreement with the observations. Also the shape of the peak and the location of the minimum (which in most of the cases is within 10 core radii) turn out to be consistent with observational results. For a more detailed and close comparison with observations, including a proper calibration of the timescales of the dynamical processes driving the evolution of the BSS spatial distribution, more realistic simulations will be necessary., Accepted for publication by ApJ; 11 pages, 11 figures

The decay of globular clusters to the center of their mother galaxy corresponds to carrying a quantity of mass sufficient to sustain the gravitational activity of a small pre-existing nucleus and to accrete it in a significant way. This is due to both dynamical friction of field stars and tidal disruption by the compact nucleus. The results of the simplified model presented here show that the active galactic nuclei luminosity and lifetime depend on the characteristics of the globular cluster system and are quite insensitive to the nucleus' initial mass., Comment: 8 pages Latex + 1 eps figure, memsait.sty and epsf.sty included; to be published on PASS special issue on Cel. Mechanics

We present the results of detailed N-body simulations regarding the interaction of four massive globular clusters in the central region of a triaxial galaxy. The systems undergo a full merging event, producing a sort of 'Super Star Cluster' (SSC) whose features are close to those of a superposition of the individual initial mergers. In contrast with other similar simulations, the resulting SSC structural parameters are located along the observed scaling relations of globular clusters. These findings seem to support the idea that a massive SSC may have formed in early phases of the mother galaxy evolution and contributed to the growth of a massive nucleus., Comment: LaTeX, 4 pages, contribution to "Globular Clusters: Guides to Galaxies", March 6th-10th, 2006

In the construction of multi-mass King-Michie models of globular clusters, an approximated central energy equipartition between stars of different masses is usually imposed by scaling the velocity parameter of each mass class inversely with the stellar mass, as if the distribution function were isothermal. In this paper, this 'isothermal approximation' (IA) has been checked and its consequences on the model parameters studied by a comparison with models including central energy equipartition correctly. It is found that, under the IA, the 'temperatures' of a pair of components can differ to a non-negligible amount for low concentration distributions. It is also found that, in general, this approximation leads to a significantly reduced mass segregation in comparison with that given under the exact energy equipartition at the centre. As a representative example, an isotropic 3-component model fitting a given projected surface brightness and line-of-sight velocity dispersion profiles is discussed. In this example, the IA gives a cluster envelope much more concentrated (central dimensionless potential W=3.3) than under the true equipartition (W=0.059), as well as a higher logarithmic mass function slope. As a consequence, the inferred total mass (and then the global mass-to-light ratio) results a factor 1.4 times lower than the correct value and the amount of mass in heavy dark remnants is 3.3 times smaller. Under energy equipartition, the fate of stars having a mass below a certain limit is to escape from the system. This limit is derived as a function of the mass and W of the giants and turn-off stars component., Comment: LaTeX 2e, 9 pages with 7 figures. Accepted for publication in MNRAS

We use the Chandrasekhar formalism and direct N-body simulations to study the effect of dynamical friction on a test object only slightly more massive than the field stars, orbiting a spherically symmetric background of particles with a mass spectrum. The main goal is to verify whether the dynamical friction time (t_DF) develops a non-monotonic radial-dependence that could explain the bimodality of the Blue Straggler radial distributions observed in globular clusters. In these systems, in fact, relaxation effects lead to a mass and velocity radial segregation of the different mass components, so that mass-spectrum effects on t_DF are expected to be dependent on radius. We find that, in spite of the presence of different masses, t_DF is always a monotonic function of radius, at all evolutionary times and independently of the initial concentration of the simulated cluster. This because the radial dependence of t_DF is largely dominated by the total mass density profile of the background stars (which is monotonically decreasing with radius). Hence, a progressive temporal erosion of the BSS population at larger and larger distances from the cluster center remains the simplest and the most likely explanation of the shape of the observed BSS radial distributions, as suggested in previous works. We also confirm the theoretical expectation that approximating a multi-mass globular cluster as made of (averaged) equal-mass stars can lead to significant overestimates of t_DF within the half-mass radius., Comment: In press on ApJ

In this talk we discuss some of the main theoretical problems in the understanding of the statistical properties of gravity. By means of N-body simulations we approach the problem of understanding the r\^ole of gravity in the clustering of a finite set of N-interacting particles which samples a portion of an infinite system. Through the use of the conditional average density, we study the evolution of the clustering for the system putting in evidence some interesting and not yet understood features of the process., Comment: 5 pages, 1 figure

We describe a parallel version of our tree-code for the simulation of self-gravitating systems in Astrophysics. It is based on a dynamic and adaptive method for the domain decomposition, which exploits the hierarchical data arrangement used by the tree-code. It shows low computational costs for the parallelization overhead -- less than 4% of the total CPU-time in the tests done -- because the domain decomposition is performed 'on the fly' during the tree setting and the portion of the tree that is local to each processor 'enriches' itself of remote data only when they are actually needed. The performances of an implementation of the parallel code on a Cray T3E are presented and discussed. They exhibit a very good behaviour of the speedup (=15 with 16 processors and 10^5 particles) and a rather low load unbalancing (< 10% using up to 16 processors), achieving a high computation speed in the forces evaluation (>10^4 particles/sec with 8 processors)., 10 pages, 8 figures, LaTeX2e, A&A class file needed (included), submitted to A&A; corrected abstract word wrapping

We present preliminary results on the parallelization of a Tree-Code for evaluating gravitational forces in N-body astrophysical systems. Our HPF/CRAFT implementation on a CRAY T3E machine attained an encouraging speed-up behavior, reaching a value of 75 with 128 processor elements (PEs). The speed-up tests regard the evaluation of the forces among N = 130,369 particles distributed scaling the actual distribution of a sample of galaxies of the Leda catalog., Latex, 3 pages, 2 ps figures; presented at the 1998 Conference on Computational Physics, Granada (Spain), sept. 2-5, 1998, in press in Comp. Phys. Comm. (Elsevier pub.)

We present tests of comparison between our versions of the Fast Multipole Algorithm (FMA) and ``classic'' tree-code to evaluate gravitational forces in particle systems. We have optimized the Greengard's original version of FMA allowing for a more efficient criterion of well-separation between boxes, to improve the adaptivity of the method (which is very important in highly inhomogeneous situations) and to permit the smoothing of gravitational interactions. The results of our tests indicate that the tree-code is almost three times faster than FMA for both a homogeneous and a clumped distribution, at least in the interval of N (N< 10^5) here investigated and at the same level of accuracy (error ~ 10^{-3)). This order of accuracy is generally considered as the best compromise between CPU-time consumption and precision for astrophysical simulation. Moreover, the claimed linear dependence on N of the CPU-time of FMA is not confirmed and we give a ``theoretical'' explanation for that., 24 pages, 3 eps figures, aaspp4.sty and epsf.sty included; submitted to Journ. Comp. Phys