We report on the optical identification of the neutron star burster EXO 1745-248 in Terzan 5. The identification was performed by exploiting HST/ACS images acquired in Director's Discretionary Time shortly after (approximately 1 month) the Swift detection of the X-ray burst. The comparison between these images and previous archival data revealed the presence of a star that currently brightened by ~3 magnitudes, consistent with expectations during an X-ray outburst. The centroid of this object well agrees with the position, in the archival images, of a star located in the Turn-Off/Sub Giant Branch region of Terzan 5. This supports the scenario that the companion should has recently filled its Roche Lobe. Such a system represents the pre-natal stage of a millisecond pulsar, an evolutionary phase during which heavy mass accretion on the compact object occurs, thus producing X-ray outbursts and re-accelerating the neutron star.

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.

By using XSHOOTER spectra acquired at the ESO Very Large Telescope, we have studied the surface chemical composition of the companion star to the binary millisecond pulsar PSR J1740-5340 in the globular cluster NGC 6397. The measured abundances of Fe, Mg, Al and Na confirm that the star belongs to the cluster. On the other hand, the measured surface abundance of nitrogen ([N/Fe]=+0.53 +- 0.15 dex) combined with the carbon upper limit ([C/Fe] <-2 dex) previously obtained from UVES spectra allow us to put severe constraints on its nature, strongly suggesting that the pulsar companion is a deeply peeled star. In fact, the comparison with theoretical stellar models indicates that the matter currently observed at the surface of this star has been processed by the hydrogen-burning CN-cycle at equilibrium. In turn, this evidence suggests that the pulsar companion is a low mass (~0.2 Msun) remnant star, descending from a ~0.8 Msun progenitor which lost ~70-80 % of its original material because of mass transfer activity onto the pulsar.

We report on the identification of the optical counterpart to the recently detected INTEGRAL transient IGR J18245-2452 in the Galactic globular cluster M28. From the analysis of a multi epoch HST dataset we have identified a strongly variable star positionally coincident with the radio and Chandra X-ray sources associated to the INTEGRAL transient. The star has been detected during both a quiescent and an outburst state. In the former case it appears as a faint, unperturbed main sequence star, while in the latter state it is about two magnitudes brighter and slightly bluer than main sequence stars. We also detected Halpha excess during the outburst state, suggestive of active accretion processes by the neutron star.

We present the identification of the companion star to the intermediate mass binary pulsar J1439-5501 obtained by means of ground-based deep images in the B, V and I bands, acquired with FORS2 mounted at the ESO-VLT. The companion is a massive white dwarf (WD) with B=23.57+-0.02, V=23.21+-0.01 and I=22.96+-0.01, located at only ~0.05" from the pulsar radio position. Comparing the WD location in the (B, B-V) and (V, V-I) Color-Magnitude diagrams with theoretical cooling sequences we derived a range of plausible combinations of companion masses (1<~Mcom<~1.3 Msun), distances (d<~1200 pc), radii (<~7.8 10^3 Rsun) and temperatures (T=31350^{+21500}_{-7400}). From the PSR mass function and the estimated mass range we also constrained the inclination angle i >~ 55 degrees and the pulsar mass (Mpsr <~2.2 Msun). The comparison between the WD cooling age and the spin down age suggests that the latter is overestimated by a factor of about ten.

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<2" and suggesting the presence of a black hole with a mass of 17,000 Msol (Lutzgendorf et al. 2011). We also found some evidence of systemic rotation with amplitude Arot ~8 km/s in the innermost 2" (0.13 pc), decreasing to Arot= 3.2 km/s at 18"<r<160".

We report the discovery in the Rossi X-Ray Timing Explorer data of GRS 1915+105 of a second quasi-periodic oscillation at 34 Hz, simultaneous with that observed at 68 Hz in the same observation. The data corresponded to those observations from 2003 where the 68-Hz oscillation was very strong. The significance of the detection is 4.2 sigma. These observations correspond to a very specific position in the colour-colour diagram for GRS 1915+105, corresponding to a harder spectrum compared to those where a 41 Hz oscillation was discovered. We discuss the possible implications of the new pair of frequencies comparing them with the existing theoretical models.

Highly-collimated gas ejections are among the most dramatic structures in the Universe, observed to emerge from very different astrophysical systems - from active galactic nuclei down to young brown dwarf stars. Even with the huge span in spatial scales, there is convincing evidence that the physics at the origin of the phenomenon, namely the acceleration and collimation mechanisms, is the same in all classes of jets. Here we report on the discovery of a giant, highly-collimated jet from Sanduleak's star in the Large Magellanic Cloud (LMC). With a physical extent of 14 parsecs at the distance of the LMC, it represents the largest stellar jet ever discovered, and the first resolved stellar jet beyond the Milky Way. The kinematics and extreme chemical composition of the ejecta from Sanduleak's star bear strong resemblance with the low-velocity remnants of SN1987A and with the outer filaments of the most famous supernova progenitor candidate, i.e., eta Carinae. Moreover, the precise knowledge of the jet's distance implies that it will be possible to derive accurate estimates of most of its physical properties. Sanduleak's bipolar outflow will thus become a crucial test-bed for future theoretical modeling of astrophysical jets.

By means of chemical evolution models of different morphological types, we study the mass-metallicity (MZ) relation and its evolution with redshift. Our aim is to understand the role of galaxies of different morphological types in the MZ relation at various redshift. One major result is that at high redshift, the majority of the galaxies falling on the MZ plot are apparently proto-ellipticals. Finally, we show some preliminary results of a study of the MZ relation in a framework of hierarchical galaxy formation.

By means of chemical evolution models for ellipticals, spirals and irregular galaxies, we aim at investigating the physical meaning and the redshift evolution of the mass-metallicity relation as well as how this relation is connected with galaxy morphology. {abridged} We assume that galaxy morphologies do not change with cosmic time. We present a method to account for a spread in the epochs of galaxy formation and to refine the galactic mass grid. (abridged) We compare our predictions to observational results obtained for galaxies between redshifts 0.07 and 3.5. We reproduce the mass-metallicity (MZ) relation mainly by means of an increasing efficiency of star formation with mass in galaxies of all morphological types, without any need to invokegalactic outflows favoring the loss of metals in the less massive galaxies. Our predictions can help constraining the slope and the zero point of the observed local MZ relation, both affected by uncertainties related to the use of different metallicity calibrations. We show how, by considering the MZ, the O/H vs star formation rate (SFR), and the SFR vs galactic mass diagrams at various redshifts, it is possible to constrain the morphology of the galaxies producing these relations. Our results indicate that the galaxies observed at z=3.5 should be mainly proto-ellipticals, whereas at z=2.2 the observed galaxies consist of a morphological mix of proto-spirals and proto-ellipticals. At lower redshifts, the observed MZ relation is well reproduced by considering both spirals and irregulars. (abridged)

MASYS is the AKARI spectroscopic survey of Symbiotic Stars in the Magellanic Clouds, and one of the European Open Time Observing Programmes approved for the AKARI (Post-Helium) Phase-3. It is providing the first ever near-IR spectra of extragalactic symbiotic stars. The observations are scheduled to be completed in July 2009.

We have used a combination of ACS-HST high-resolution and wide-field SUBARU data in order to study the Blue Straggler Star (BSS) population over the entire extension of the remote Galactic globular cluster NGC 2419. The BSS population presented here is among the largest ever observed in any stellar system, with more than 230 BSS in the brightest portion of the sequence. The radial distribution of the selected BSS is essentially the same as that of the other cluster stars. In this sense the BSS radial distribution is similar to that of omega Centauri and unlike that of all Galactic globular clusters studied to date, which have highly centrally segregated distributions and, in most cases, a pronounced upturn in the external regions. As in the case of omega Centauri, this evidence indicates that NGC 2419 is not yet relaxed even in the central regions. This observational fact is in agreement with estimated half-mass relaxation time, which is of the order of the cluster age.

We study interstellar dust evolution in various environments by means of chemical evolution models for galaxies of different morphological types. We start from the formalism developed by Dwek (1998) to study dust evolution in the solar neighbourhood and extend it to ellipticals and dwarf irregular galaxies, showing how the evolution of the dust production rates and of the dust fractions depend on the galactic star formation history. The observed dust fractions observed in the solar neighbourhood can be reproduced by assuming that dust destruction depends the condensation temperatures T_c of the elements. In elliptical galaxies, type Ia SNe are the major dust factories in the last 10 Gyr. With our models, we successfully reproduce the dust masses observed in local ellipticals (~10^6 M_sun) by means of recent FIR and SCUBA observations. We show that dust is helpful in solving the iron discrepancy observed in the hot gaseous halos surrounding local ellipticals. In dwarf irregulars, we show how a precise determination of the dust depletion pattern could be useful to put solid constraints on the dust condensation efficiencies. Our results will be helpful to study the spectral properties of dust grains in local and distant galaxies.

We investigate the present-day photometric properties of the dwarf spheroidal galaxies in the Local Group. From the analysis of their integrated colours, we consider a possible link between dwarf spheroidals and giant ellipticals. From the analysis of the V vs (B-V) plot, we search for a possible evolutionary link between dwarf spheroidal galaxies (dSphs) and dwarf irregular galaxies (dIrrs). By means of chemical evolution models combined with a spectro-photometric model, we study the evolution of six Local Group dwarf spheroidal galaxies (Carina, Draco, Sagittarius, Sculptor, Sextans and Ursa Minor). The chemical evolution models, which adopt up-to-date nucleosynthesis from low and intermediate mass stars as well as nucleosynthesis and energetic feedback from supernovae type Ia and II, reproduce several observational constraints of these galaxies, such as abundance ratios versus metallicity and the metallicity distributions. The proposed scenario for the evolution of these galaxies is characterised by low star formation rates and high galactic wind efficiencies. Such a scenario allows us to predict integrated colours and magnitudes which agree with observations. Our results strongly suggest that the first few Gyrs of evolution, when the star formation is most active, are crucial to define the luminosities, colours, and other photometric properties as observed today. After the star formation epoch, the galactic wind sweeps away a large fraction of the gas of each galaxy, which then evolves passively. Our results indicate that it is likely that at a certain stage of their evolution, dSphs and dIrrs presented similar photometric properties. However, after that phase, they evolved along different paths, leading them to their currently disparate properties.

By combining high-resolution HST and wide-field ground based observations, in ultraviolet and optical bands, we study the Blue Straggler Star (BSS) population of the low density galactic globular cluster M55 (NGC 6809) over its entire radial extent. The BSS projected radial distribution is found to be bimodal, with a central peak, a broad minimum at intermediate radii, and an upturn at large radii. Similar bimodal distributions have been found in other globular clusters (M3, 47 Tucanae, NGC 6752, M5), but the external upturn in M55 is the largest found to date. This might indicate a large fraction of primordial binaries in the outer regions of M55, which seems somehow in contrast with the relatively low (\sim 10%) binary fraction recently measured in the core of this cluster.

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.

By combining high-resolution (HST-WFPC2) and wide-field ground based (2.2m ESO-WFI) and space (GALEX) observations, we have collected a multi-wavelength photometric data base (ranging from the far UV to the near infrared) of the galactic globular cluster NGC1904 (M79). The sample covers the entire cluster extension, from the very central regions up to the tidal radius. In the present paper such a data set is used to study the BSS population and its radial distribution. A total number of 39 bright ($m_{218}\le 19.5$) BSS has been detected, and they have been found to be highly segregated in the cluster core. No significant upturn in the BSS frequency has been observed in the outskirts of NGC 1904, in contrast to other clusters (M 3, 47 Tuc, NGC 6752, M 5) studied with the same technique. Such evidences, coupled with the large radius of avoidance estimated for NGC 1904 ($r_{avoid}\sim 30$ core radii), indicate that the vast majority of the cluster heavy stars (binaries) has already sunk to the core. Accordingly, extensive dynamical simulations suggest that BSS formed by mass transfer activity in primordial binaries evolving in isolation in the cluster outskirts represent only a negligible (0--10%) fraction of the overall population.

The study of the Fe abundance in the intra cluster medium (ICM) provides strong constraints on the integrated star formation history and supernova rate of the cluster galaxies, as well as on the ICM enrichment mechanisms. In this Letter, using chemical evolution models for galaxies of different morphological types, we study the evolution of the Fe content of clusters of galaxies. We assume that the ICM Fe enrichment occurs by means of galactic winds arising from elliptical galaxies and from gas stripped from the progenitors of S0 galaxies via external mechanisms, due to the interaction of the inter stellar medium with the ICM. The Fe-rich gas ejected by ellipticals accounts for the X_Fe,ICM values observed at z > 0.5, whereas the gas stripped from the progenitors of the S0 galaxies accounts for the increase of X_Fe,ICM observed at z<0.5. We tested two different scenarios for Type Ia supernova (SN) progenitors and we model the Type Ia SN rate observed in clusters, finding a good agreement between our predictions and the available observations.

The first substellar companion of possibly planetary mass around a normal star, GQ Lup, has been directly imaged (Neuhaeuser et al., 2005). Besides the unknown formation history, the mass of such an object is a criterion to decide about its true nature. We aim to determine the physical properties of the GQ Lup companion - effective temperate and surface gravity, and thus its mass independently from evolutionary models. We use the adaptive optics integral-field spectrograph SINFONI at the VLT for near-infrared spectroscopy from 1.1 to 2.5 um with a resolution of R = 2500--4000. We compare these spectra with synthetic atmospheric models (GAIA v2.0 cond). From the complete set of spectra we find a consistent effective temperature of Teff = 2600 +/- 100 K and surface gravity of log{g} = 3.7 +/- 0.5. Combined with a slightly revised luminosity of log(L/L_(\sun)) = -2.25 +/- 0.24 for the companion, we determine a radius of R = 3.50 (+1.50/-1.03) Jupiterradii and thus a mass of ~ 25 Jupitermasses. Due to the large uncertainty of the surface gravity, the mass could range from 4 to 155 Jupitermasses. By comparing the paramaters of the companion of GQ Lup to the ones of 2MASS J05352184-0546085, published by Stassun et al. (2006), we conclude that the companion to GQ Lup A has a mass lower than 36 Jupitermasses.

As part of the "All Wavelength Extended Groth Strip International Survey" (AEGIS), we describe the panchromatic characterization of an X-ray luminous active galactic nucleus (AGN) in a merging galaxy at z=1.15. This object is detected at infrared (8mic, 24mic, 70mic, 160mic), submillimeter (850mic) and radio wavelengths, from which we derive a bolometric luminosity L_bol ~ 9x10^12 Lsol. We find that the AGN clearly dominates the hot dust emission below 40mic but its total energetic power inferred from the hard X-rays is substantially less than the bolometric output of the system. About 50% of the infrared luminosity is indeed produced by a cold dust component that probably originates from enshrouded star formation in the host galaxy. In the context of a coeval growth of stellar bulges and massive black holes, this source might represent a ``transition'' object sharing properties with both quasars and luminous starbursts. Study of such composite galaxies will help address how the star formation and disk-accretion phenomena may have regulated each other at high redshift and how this coordination may have participated to the build-up of the relationship observed locally between the masses of black holes and stellar spheroids.

We report the detection of HCO+(1-0) emission towards the Cloverleaf quasar (z=2.56) through observations with the Very Large Array. This is the first detection of ionized molecular gas emission at high redshift (z>2). HCO+ emission is a star formation indicator similar to HCN, tracing dense molecular hydrogen gas (n(H_2) ~= 10^5 cm^{-3}) within star-forming molecular clouds. We derive a lensing-corrected HCO+ line luminosity of L'(HCO+) = 3.5 x 10^9 K km/s pc^2. Combining our new results with CO and HCN measurements from the literature, we find a HCO+/CO luminosity ratio of 0.08 and a HCO+/HCN luminosity ratio of 0.8. These ratios fall within the scatter of the same relationships found for low-z star-forming galaxies. However, a HCO+/HCN luminosity ratio close to unity would not be expected for the Cloverleaf if the recently suggested relation between this ratio and the far-infrared luminosity were to hold. We conclude that a ratio between HCO+ and HCN luminosity close to 1 is likely due to the fact that the emission from both lines is optically thick and thermalized and emerges from dense regions of similar volumes. The CO, HCN and HCO+ luminosities suggest that the Cloverleaf is a composite AGN--starburst system, in agreement with the previous finding that about 20% of the total infrared luminosity in this system results from dust heated by star formation rather than heating by the AGN. We conclude that HCO+ is potentially a good tracer for dense molecular gas at high redshift.

A giant flare from the Soft Gamma-ray Repeater SGR 1806-20 has been detected by several satellites on 2004 December 27. This tremendous outburst, the first one observed from this source, was a hundred times more powerful than the two previous giant flares from SGR 0525-66 and SGR 1900+14. We report the results obtained for this event with the Anticoincidence Shield of the SPI spectrometer on board the INTEGRAL satellite, which provides a high-statistics light curve at E>~80 keV. The flare started with a very strong pulse, which saturated the detector for ~0.7 s, and whose backscattered radiation from the Moon was detected 2.8 s later. This was followed by a ~400 s long tail modulated at the neutron star rotation period of 7.56 s. The tail fluence corresponds to an energy in photons above 3 keV of 1.6x10^44 (d/15 kpc)^2 erg. This is of the same order of the energy emitted in the pulsating tails of the two giant flares seen from other soft repeaters, despite the hundredfold larger overall emitted energy of the SGR 1806-20 giant flare. Long lasting (~1 hour) hard X-ray emission, decaying in time as t^-0.85, and likely associated to the SGR 1806-20 giant flare afterglow has also been detected.

The low energy (<10 keV) X-ray emission of the Soft Gamma-ray Repeater SGR1806-20 has been studied by means of four XMM-Newton observations carried out in the last two years, the latter performed in response to a strong sequence of hard X-ray bursts observed on 2004 October 5. The source was caught in different states of activity: over the 2003-2004 period the 2-10 keV flux doubled with respect to the historical level observed previously. The long term raise in luminosity was accompanied by a gradual hardening of the spectrum, with the power law photon index decreasing from 2.2 to 1.5, and by a growth of the bursting activity. The pulse period measurements obtained in the four observations are consistent with an average spin-down rate of 5.5x10e-10 s/s, higher than the values observed in the previous years. The long-term behavior of SGR1806-20 exhibits the correlation between spectral hardness and spin-down rate previously found only by comparing the properties of different sources (both SGRs and Anomalous X-ray Pulsars). The best quality spectrum (obtained on 6 September 2004) cannot be fitted by a single power law, but it requires an additional blackbody component (kT=0.79 keV, R_BB = 1.9 (d/15 kpc)^2 km), similar to the spectra observed in other SGRs and in Anomalous X-ray Pulsars. No spectral lines were found in the persistent emission, with equivalent width upper limits in the range 30-110 eV. Marginal evidence for an absorption feature at 4.2 keV is present in the cumulative spectrum of 69 bursts detected in September-October 2004.

The catalogue of the Johnson-Cousins B,V and I light curves obtained for 162 variable stars (135 RR Lyrae, 4 candidate Anomalous Cepheids, 11 Classical Cepheids, 11 eclipsing binaries and 1 delta Scuti star) in two areas close to the bar of the Large Magellanic Cloud is presented along with coordinates, finding charts, periods, epochs, amplitudes, and mean quantities (intensity- and magnitude-averaged luminosities) of the variables with full coverage of the light variations. A star by star comparison is made with MACHO and OGLE II photometries based on both variable and constant stars in common, and the transformation relationships to our photometry are provided. The pulsation properties of the RR Lyrae stars in the sample are discussed in detail. Parameters of the Fourier decomposition of the light curves are derived for the fundamental mode RR Lyrae stars with complete and regular curves (29 stars). They are used to estimate metallicities, absolute magnitudes, intrinsic (B-V)o colours, and temperatures of the variable stars, according to Jurcsik and Kovacs (1996), and Kovacs and Walker (2001) method. Quantities derived from the Fourier parameters are compared with the corresponding observed quantities. In particular, the "photometric" metallicities are compared with the spectroscopic metal abundances derived by Gratton et al. (2004) from low resolution spectra obtained with FORS at the Very Large Telescope.

Metallicities ([Fe/H]) from low resolution spectroscopy obtained with the Very Large Telescope (VLT) are presented for 98 RR Lyrae and 3 short period Cepheids in the bar of the Large Magellanic Cloud. Our metal abundances have typical errors of +/-0.17 dex. The average metallicity of the RR Lyrae stars is [Fe/H]=-1.48 +/- 0.03 +/- 0.06 on the scale of Harris (1996). The star-to-star scatter (0.29 dex) is larger than the observational errors, indicating a real spread in metal abundances. The derived metallicities cover the range -2.12 < [Fe/H] <-0.27, but there are only a few stars having [Fe/H] > -1. For the ab-type variables we compared our spectroscopic abundances with those obtained from the Fourier decomposition of the light curves. We find good agreement between the two techniques, once the systematic offset of 0.2 dex between the metallicity scales used in the two methods is taken into account. The spectroscopic metallicities were combined with the dereddened apparent magnitudes of the variables to derive the slope of the luminosity-metallicity relation for the LMC RR Lyrae stars: the resulting value is 0.214 +/- 0.047 mag/dex. Finally, the 3 short period Cepheids have [Fe/H] values in the range -2.0 < [Fe/H] <-1.5 . They are more metal-poor than typical LMC RR Lyrae stars, thus they are more likely to be Anomalous Cepheids rather than the short period Classical Cepheids that are being found in a number of dwarf Irregular galaxies.

N-body algorithms for long-range unscreened interactions like gravity belong to a class of highly irregular problems whose optimal solution is a challenging task for present-day massively parallel computers. In this paper we describe a strategy for optimal memory and work distribution which we have applied to our parallel implementation of the Barnes & Hut (1986) recursive tree scheme on a Cray T3D using the CRAFT programming environment. We have performed a series of tests to find an " optimal data distribution " in the T3D memory, and to identify a strategy for the " Dynamic Load Balance " in order to obtain good performances when running large simulations (more than 10 million particles). The results of tests show that the step duration depends on two main factors: the data locality and the T3D network contention. Increasing data locality we are able to minimize the step duration if the closest bodies (direct interaction) tend to be located in the same PE local memory (contiguous block subdivison, high granularity), whereas the tree properties have a fine grain distribution. In a very large simulation, due to network contention, an unbalanced load arises. To remedy this we have devised an automatic work redistribution mechanism which provided a good Dynamic Load Balance at the price of an insignificant overhead.

By means of numerical methods, we solve the equations of motion for the collapse of a shell of baryonic matter, made of galaxies and substructure falling into the central regions of a cluster of galaxies, taking into account the effect of the dynamical friction. The parameters on which the dynamical friction mainly depends are: the peaks' height, the number of peaks inside a protocluster multiplied by the correlation function evaluated at the origin, the filtering radius and the nucleus radius of the protocluster of galaxies. We show how the collapse time (Tau) of the shell depends on these parameters. We give a formula that links the dynamical friction coefficient (Eta) o the parameters mentioned above and an analytic relation between the collapse time and (Eta). Finally, we obtain an analytical relation between (Tau) and the mean overdensity (mean Delta) within the shell. All the analytical relations that we find are in excellent agreement with the numerical integration.