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Star clusters stand at the crossroads between galaxies and single stars. Resolving the formation of star clusters in cosmological simulations represents an ambitious and challenging goal, since modelling their internal properties requires very high resolution. This paper is the third of a series within the SImulating the Environment where Globular clusters Emerged (SIEGE) project, where we conduct zoom-in cosmological simulations with sub-parsec resolution that include the feedback of individual stars, aimed to model the formation of star clusters in high-redshift proto-galaxies. We investigate the role of three fundamental quantities in shaping the intrinsic properties of star clusters, i. e., i) pre-supernova stellar feedback (continuous or instantaneous ejection of mass and energy through stellar winds); ii) star formation efficiency, defined as the fraction of gas converted into stars per freefall time, for which we test 2 different values (epsi_ff=0.1 and 1), and iii) stellar initial mass function (IMF, standard vs top-heavy). All our simulations are run down to z=10.5, which is sufficient for investigating some structural properties of the emerging clumps and clusters. [Abridged] The prescription for a continuous, low-intensity feedback, along with the adoption of epsi_ff=1, produces star clusters with maximum stellar density values up to 10^4 M_sun pc^(-2), in good agreement with the surface density-size relation observed in local young star clusters (YSCs). Therefore, a realistic stellar wind description and a high star formation effiency are the key ingredients that allow us to achieve realistic star clusters characterised by properties comparable to those of local YSCs. In contrast, the other models produce too diffuse clusters, in particular the one with a top-heavy IMF., Comment: 20 pages, 14 pages

New, deep HST photometry allowed us to identify and study eight compact and bright (M_V< -5.8) star clusters in the outskirts of the star-forming isolated dwarf galaxy NGC5238 (M_*= 10^8 M_sun). Five of these clusters are new discoveries, and six appear projected onto, and/or aligned with the tidal tails recently discovered around this galaxy. The clusters are partially resolved into stars and their colour magnitude diagrams reveal a well developed red giant branch, implying ages older than 1-2~Gyr. Their integrated luminosity and structural parameters are typical of classical globular clusters and one of them has M_V=-10.56 +/- 0.07, as bright as Omega Cen, the brightest globular cluster of the Milky Way. Since the properties of this cluster are in the range spanned by those of nuclear star clusters we suggest that it may be the nuclear remnant of the disrupted satellite of NGC5238 that produced the observed tidal tails., Comment: Accepted for publication by A&A Letters. Latex, 10 pages, 6 figures, 5 appendices

From deep imaging data obtained with the Large Binocular Telescope as part of the Smallest Scale of Hierarchy Survey (SSH), we have discovered low-surface brightness tidal features around NGC 5238 and UGC 8760, two nearby and relatively isolated dwarf galaxies with stellar masses of approximately $10^8 M_\odot$ and $2\times10^7 M_\odot$, respectively. In this study, we present detailed hydrodynamical $N$-body simulations that explain the observed faint substructures as the outcome of interactions between the dwarf galaxies and smaller satellite systems. We show that the asymmetric stellar distribution of NGC 5238 and the low-luminosity substructures observed to the northeast of UGC 8760 can be well attributed to recent interactions with smaller galaxies, each with a stellar mass roughly a few $10^5 M_\odot$, 50 times less massive than their respective hosts. In the simulations, these satellites have stellar and dark-matter masses consistent with the ones predicted by $\Lambda$CDM cosmology and share properties similar to those of local dwarf galaxies with similar stellar masses. The satellite-to-main galaxy mass ratio is approximately 1:10 in both cases. This satellite population aligns closely with predictions from cosmological simulations in terms of the number and mass relative to the host galaxy mass., Comment: Accepted for publication in A&A, 15 pages, 8 figures

Local gravitational instability (LGI) is considered crucial for regulating star formation and gas turbulence in galaxy discs, especially at high redshift. Instability criteria usually assume infinitesimally thin discs or rely on approximations to include the stabilising effect of the gas disc thickness. We test a new 3D instability criterion for rotating gas discs that are vertically stratified in an external potential. This criterion reads $Q_{\rm3D}<1$, where $Q_{\rm3D}$ is the 3D analogue of the Toomre parameter $Q$. The advantage of $Q_{\rm3D}$ is that it allows us to study LGI in and above the galaxy midplane in a rigorous and self-consistent way. We apply the criterion to a sample of 44 star-forming galaxies at $0\lesssim\mathrm{z}\lesssim5$ hosting rotating discs of cold gas. The sample is representative of galaxies on the main sequence at $\mathrm{z}\approx 0$ and includes massive star-forming and starburst galaxies at $1\lesssim\mathrm{z}\lesssim5$. For each galaxy, we first apply the Toomre criterion for infinitesimally thin discs, finding 10 unstable systems. We then obtain maps of $Q_{\rm 3D}$ from a 3D model of the gas disc derived in the combined potential of dark matter, stars and the gas itself. According to the 3D criterion, two galaxies with $Q<1$ show no evidence of instability and the unstable regions that are 20% smaller than those where $Q<1$. No unstable disc is found at $0\lesssim\mathrm{z}\lesssim 1$, while $\approx 60$% of the systems at $2\lesssim\mathrm{z}\lesssim5$ are locally unstable. In these latter, a relatively small fraction of the total gas ($\approx 30$%) is potentially affected by the instability. Our results disfavour LGI as the main regulator of star formation and turbulence in moderately star-forming galaxies in the present-day Universe. LGI likely becomes important at high redshift, but the input by other mechanisms seems required [abridged], Comment: 19 pages (6 figures, 2 tables) + appendixes, accepted by Astronomy & Astrophysics

It has been recently claimed that a surprisingly massive black hole (BH) is present in the core of the dwarf spheroidal galaxy (dSph) Leo I. Based on integral field spectroscopy, this finding challenges the typical expectation of dSphs hosting BHs of intermediate-mass, since such a BH would better be classified as supermassive. Indeed, the analysis points toward Leo I harboring a BH with a lower mass limit exceeding a few $10^6M_\odot$ at $1\sigma$, and the no BH case excluded at 95\% significance. Such a value, comparable to the entire stellar mass of the galaxy, makes Leo I a unique system that warrants further investigations. Using equilibrium models based on distribution functions (DFs) depending on actions $f({\boldsymbol J})$ coupled with the same integral field spectroscopy data and an extensive exploration of a very large parameter space, we demonstrate, within a comprehensive Bayesian framework of model-data comparison, that the posterior on the BH mass is flat towards the low-mass end and, thus, that the kinematics of the central galaxy region only imposes an upper limit on the BH mass of few $10^5M_\odot$ (at $3\sigma$). Such an upper limit brings back the putative BH of Leo I under the category of intermediate-mass BHs, and it is also in line with formation scenarios and expectations from scaling relations at the mass regime of dwarf galaxies., Comment: Accepted for publication in A&A Letters

We use zoom-in, hydrodynamical, cosmological $N$-body simulations tracing the formation of the first stellar clumps from the SImulating the Environments where Globular clusters Emerged (SIEGE) project, to study key structural properties of dark matter haloes when the Universe was only $0.92$ Gyr old. The very high-resolution (maximum physical resolution 0.3 h$^{-1}$ pc at $z=6.14$, smallest dark-matter particle mass $164\,M_{\odot}$) allows us to reach the very low mass end of the stellar-to-halo mass relation ($M_{\rm vir}=10^{7.5-9.5}\,M_{\odot}$) to study the processes that mould dark matter haloes during the first stages of structure formation. We investigate the role of baryonic cooling and stellar feedback, modeled from individual stars, in shaping haloes, and of environmental effects as accretion of dark matter along cosmic filaments and mergers. We find that the onset of star formation (typically for $\log M_{\rm vir}/M_{\odot}\simeq7.6$) causes the inner cusp in the haloes density profile to flatten into a core with constant density and size proportionally to the halo virial mass. Even at these mass scales, we confirm that baryons make haloes that have formed stars rounder in the central regions than haloes that have not formed stars yet, with median minor-to-major $\langle q \rangle$ and intermediate-to-major $\langle s \rangle$ axes 0.66 and 0.84, respectively. Our morphological analysis shows that, at $z=6.14$, haloes are largely prolate in the outer parts, with the major axis aligned along filaments of the cosmic web or towards smaller sub-haloes, with the degree of elongation having no significant dependence on the halo mass., Comment: 20 pages, 11 figures. Accepted for publication in MNRAS

We developed self-consistent dynamical models of stellar systems in the framework of quasi-linear modified Newtonian dynamics (QUMOND). The models are constructed from the anisotropic distribution function of Gunn & Griffin (1979), combined with the modified Poisson equation defining this gravitation theory and take into account the external field effect. We have used these models, and their Newtonian analogues, to fit the projected density and the velocity dispersion profiles of a sample of 18 Galactic globular clusters, using the most updated datasets of radial velocities and Gaia proper motions. We have thus obtained, for each cluster, estimates of the dynamical mass-to-light ratio ($M/L$) for each theory of gravity. The selected clusters have accurate proper motions and a well sampled mass function down to the very low mass regime. This allows us to constrain the degree of anisotropy and to provide, from comparison with stellar evolution isochrones, a dynamics-independent estimate of the minimum mass-to-light ratio $(M/L)_{min}$. Comparing the best-fitting dynamical $M/L$ with $(M/L)_{min}$, we find that for none of the analyzed clusters the two gravity theories are significantly incompatible with the observational data, although for one of them (NGC 5024) the dynamical $M/L$ predicted by QUMOND lies at $2.8\sigma$ below $(M/L)_{min}$. Though the proposed approach suffers from some limitations (in particular the lack of a treatment of mass segregation), the obtained results suggest that the kinematics of globular clusters in a relatively weak external field can be a powerful tool to prove alternative theories of gravitation., Comment: Accepted for publication in MNRAS. Dedicated to the memory of Antonio Sollima, who conceived, developed and carried out most of this work

HI and CO observations indicate that the cold gas in galaxies is very turbulent. However, the turbulent energy is expected to be quickly dissipated, implying that some energy source is needed to explain the observations. The nature of such turbulence was long unclear, as even the main candidate, supernova (SN) feedback, seemed insufficient. Other mechanisms have been proposed, but without reaching a general consensus. The key novelty of our work is considering that the gas disc thickness and flaring increase the dissipation timescale of turbulence, thus reducing the energy injection rate required to sustain it. In excellent agreement with the theoretical expectations, we found that the fraction of the SN energy (a.k.a. SN coupling efficiency) needed to maintain the cold gas turbulence is $\sim 1$%, solving a long-standing conundrum., Comment: 3 pages, 1 figure, Proceedings IAU Symposium 373, accepted

Star formation laws are empirical relations between the cold gas (HI+H$_2$) content of a galaxy and its star formation rate (SFR), being crucial for any model of galaxy formation and evolution. A well known example of such laws is the Schmidt-Kennicutt law, which is based on the projected surface densities. However, it has been long unclear whether a more fundamental relation exists between the intrinsic volume densities. By assuming the vertical hydrostatic equilibrium, we infer radial profiles for the thickness of gaseous discs in a sample of 23 local galaxies, and use these measurements to convert the observed surface densities of the gas and the SFR into the de-projected volume densities. We find a tight correlation linking these quantities, that we call the volumetric star formation law. This relation and its properties have crucial implications for our understanding of the physics of star formation., Comment: 3 pages, 1 figure, Proceedings IAU Symposium 373, accepted

Using Large Binocular Telescope deep imaging data from the Smallest Scale of Hierarchy Survey (SSH) and archival Hubble Space Telescope data, we reveal the presence of two elongated stellar features contiguous to a bar-like stellar structure in the inner regions of the dwarf irregular galaxy NGC 3741. These structures are dominated by stars younger than a few hundred Myr and collectively are about twice as extended as the old stellar component. These properties are very unusual for dwarf galaxies in the nearby Universe and difficult to explain by hydro-dynamical simulations. From the analysis of archival 21-cm observations, we find that the young stellar "bar" coincides with an HI high-density region proposed by previous studies to be a purely gaseous bar; we furthermore confirm radial motions of a few km/s, compatible with an inflow/outflow, and derive a steeply-rising rotation curve and high HI surface density at the center, indicating a very concentrated mass distribution. We propose that the peculiar properties of the stellar and gaseous components of NGC 3741 may be explained by a recent merger or ongoing gas accretion from the intergalactic medium, which caused gas inflows towards the galaxy center and triggered star formation a few hundred Myr ago. This event may explain the young and extended stellar features, the bar-like structure, the very extended HI disc and the central HI spiral arms. The high central HI density and the steeply rising rotation curve suggest that NGC 3741 may be the progenitor or the descendant of a starburst dwarf., Comment: Accepted for publication in MNRAS. Corrected typo in the list of authors

Using hydrodynamical $N$-body simulations, we show that the observed structure and kinematics of the extremely metal-poor, dwarf irregular galaxy DDO 68 is compatible with a merger event with at least two smaller satellite galaxies. We were able to obtain a self-consistent model that simultaneously reproduces several of its observed features, including: the very asymmetric and disturbed shape of the stellar component, the overall HI distribution and its velocity field, the arc-like stellar structure to the west, the low-surface brightness stellar stream to the north. The model implies the interaction of the main progenitor of DDO 68 with two systems with dynamical masses $7\times10^8\,M_{\odot}$ and almost $10^8\,M_{\odot}$ -- 1/20 and 1/150 times the dynamical mass of DDO 68, respectively. We show that the merger between DDO 68 and the most massive of its satellites offers a route to explain the large offset of DDO 68 from the mass-metallicity relation. Assuming that the interacting galaxies have metallicities prior to the merger compatible with those of galaxies with similar stellar masses, we provide quantitative evidence that gas mixing alone does not suffice at diluting the gas of the two components; according to our simulations, the HII regions observed along the Cometary Tail trace the low metallicity of the accreted satellite rather than that of DDO 68's main body. In this case, the mass corresponding to the low metallicity is that of the secondary body and DDO 68 becomes consistent with the mass-metallicity relation., Comment: Accepted for publication in MNRAS. 17 pages, 10 figures

The gravitational potentials of realistic galaxy models are in general non-integrable, in the sense that they admit orbits that do not have three independent isolating integrals of motion and are therefore chaotic. However, if chaotic orbits are a small minority in a stellar system, it is expected that they have negligible impact on the main dynamical properties of the system. In this paper we address the question of quantifying the importance of chaotic orbits in a stellar system, focusing, for simplicity, on axisymmetric systems. Chaotic orbits have been found in essentially all (non-St\"ackel) axisymmetric gravitational potentials in which they have been looked for. Based on the analysis of the surfaces of section, we add new examples to those in the literature, finding chaotic orbits, as well as resonantly trapped orbits among regular orbits, in Miyamoto-Nagai, flattened logarithmic and shifted Plummer axisymmetric potentials. We define the fractional contributions in mass of chaotic ($\xi_{\rm c}$) and resonantly trapped ($\xi_{\rm t}$) orbits to a stellar system of given distribution function, which are very useful quantities, for instance in the study of the dispersal of stellar streams of galaxy satellites. As a case study, we measure $\xi_{\rm c}$ and $\xi_{\rm t}$ in two axisymmetric stellar systems obtained by populating flattened logarithmic potentials with the Evans ergodic distribution function, finding $\xi_{\rm c}\sim 10^{-4}-10^{-3}$ and $\xi_{\rm t}\sim 10^{-2}-10^{-1}$., Comment: Accepted for publication in MNRAS. 15 pages, 11 figures

We present dynamical models of the star-forming galaxy NGC 5474 based on $N$-body hydrodynamical numerical simulations. We investigate the possible origin of the compact round stellar structure, generally interpreted as the bulge of the galaxy, but unusually off-set by $\simeq1$ kpc in projection from the visual and the kinematic centres of both the star and the gas discs. We argue that it is very unlikely that the putative bulge is in a co-planar orbit in the disc plane, showing that such a configuration would be hardly compatible with its smooth and regular spatial distribution, and, in case its mass is above $10^8\,M_{\odot}$, also with the regular HI velocity field of NGC 5474. Instead, if the putative bulge is in fact an early-type satellite galaxy orbiting around NGC 5474, not only the off-set can be easily produced by projection effects, but our simulations suggest that the gravitational interaction between the two systems can explain also the warped HI distribution of NGC 5474 and the formation of its loose spiral arms. As a by-product of the simulations, we find that the peculiar over-density of old stars detected in the south-west region of NGC 5474 may be explained with the interaction between NGC 5474 and a smaller stellar system, unrelated to the putative bulge, accreted in the disc plane., Comment: Accepted for publication on MNRAS. 22 pages, 19 figures. Comments are welcome

We present the first analysis of the stellar content of the structures and substructures identified in the peculiar star-forming galaxy NGC5474, based on Hubble Space Telescope resolved photometry from the LEGUS survey. NGC5474 is a satellite of the giant spiral M101, and is known to have a prominent bulge that is significantly off-set from the kinematic center of the underlying HI and stellar disc. The youngest stars (age~ 100 Myr) trace a flocculent spiral pattern extending out to ~8 kpc from the center of the galaxy. On the other hand intermediate-age (age > 500 Myr) and old (age > 2 Gyr) stars dominate the off-centred bulge and a large substructure residing in the South Western part of the disc and not correlated with the spiral arms (SW over-density). The old age of the stars in the SW over-density suggests that this may be another signature of the dynamical interaction/s that have shaped this anomalous galaxy. We suggest that a fly by with M101, generally invoked as the origin of the anomalies, may not be sufficient to explain all the observations. A more local and more recent interaction may help to put all the pieces of this galactic puzzle together., Comment: Accepted for publication on Astronomy & Astrophysics. Latex, 10 pages, 12 figures (colors)

The Smallest Scale of Hierarchy (SSH) survey is an ongoing strategic large program at the Large Binocular Telescope, aimed at the detection of faint stellar streams and satellites around 45 late-type dwarf galaxies located in the Local Universe within $\simeq$10 Mpc. SSH exploits the wide-field, deep photometry provided by the Large Binocular Cameras in the two wide filters $g$ and $r$. This paper describes the survey, its goals, and the observational and data reduction strategies. We present preliminary scientific results for five representative cases (UGC 12613, NGC 2366, UGC 685, NGC 5477 and UGC 4426) covering the whole distance range spanned by the SSH targets. We reach a surface brightness limit as faint as $\mu(r)\sim$ 31 mag arcsec$^{-2}$ both for targets closer than 4$-$5 Mpc, which are resolved into individual stars, and for more distant targets through the diffuse light. Our analysis reveals the presence of extended low surface brightness stellar envelopes around the dwarfs, reaching farther out than what traced by the integrated light, and as far out as, or even beyond, the observed HI disk. Stellar streams, arcs, and peculiar features are detected in some cases, indicating possible perturbation, accretion, or merging events. We also report on the discovery of an extreme case of Ultra Diffuse Galaxy ($\mu_g(0)=27.9$~mag/arcsec$^2$) in the background of one of our targets, to illustrate the power of the survey in revealing extremely low surface brightness systems., Comment: Accepted for publication in MNRAS

Several open questions on galaxy formation and evolution have their roots in the lack of a universal star formation law, that could univocally link the gas properties, e.g. its density, to the star formation rate (SFR) density. In a recent paper, we used a sample of nearby disc galaxies to infer the volumetric star formation (VSF) law, a tight correlation between the gas and the SFR volume densities derived under the assumption of hydrostatic equilibrium for the gas disc. However, due to the dearth of information about the vertical distribution of the SFR in these galaxies, we could not find a unique slope for the VSF law, but two alternative values. In this paper, we use the scale height of the SFR density distribution in our Galaxy adopting classical Cepheids (age$\lesssim 200$ Myr) as tracers of star formation. We show that this latter is fully compatible with the flaring scale height expected from gas in hydrostatic equilibrium. These scale heights allowed us to convert the observed surface densities of gas and SFR into the corresponding volume densities. Our results indicate that the VSF law $\rho_\mathrm{SFR} \propto \rho_\mathrm{gas}^\alpha$ with $\alpha \approx 2$ is valid in the Milky Way as well as in nearby disc galaxies., Comment: 9 pages, 4 figures, + 4 pages of Appendix, accepted by A&A

Dwarf spheroidal galaxies (dSphs) appear to be some of the most dark matter dominated objects in the Universe. Their dynamical masses are commonly derived using the kinematics of stars under the assumption of equilibrium. However, these objects are satellites of massive galaxies (e.g.\ the Milky Way) and thus can be influenced by their tidal fields. We investigate the implication of the assumption of equilibrium focusing on the Sculptor dSph by means of ad-hoc $N$-body simulations tuned to reproduce the observed properties of Sculptor following the evolution along some observationally motivated orbits in the Milky Way gravitational field. For this purpose, we used state-of-the-art spectroscopic and photometric samples of Sculptor's stars. We found that the stellar component of the simulated object is not directly influenced by the tidal field, while $\approx 30\%-60\%$ the mass of the more diffuse DM halo is stripped. We conclude that, considering the most recent estimate of the Sculptor proper motion, the system is not affected by the tides and the stellar kinematics represents a robust tracer of the internal dynamics. In the simulations that match the observed properties of Sculptor, the present-day dark-to-luminous mass ratio is $\approx 6$ within the stellar half-light radius ($\approx0.3$ kpc) and $>50$ within the maximum radius of the analysed dataset ($\approx1.5^\circ\approx2$ kpc)., Comment: 19 pages, 10 figures, accepted for publication in MNRAS. V3: updated after editor comments See our playlist for simulation videos: https://av.tib.eu/series/633/supplemental+videos+of+the+paper+the+effect+of+tides+on+the+sculptor+dwarf+spheroidal+galaxy

We present new Hubble Space Telescope (HST) imaging of a stream-like system associated with the dwarf galaxy DDO 68, located in the Lynx-Cancer Void at a distance of D$\sim$12.65 Mpc from us. The stream, previously identified in deep Large Binocular Telescope images as a diffuse low surface brightness structure, is resolved into individual stars in the F606W (broad V) and F814W ($\sim$I) images acquired with the Wide Field Camera 3. The resulting V, I color-magnitude diagram (CMD) of the resolved stars is dominated by old (age$\gtrsim$1-2 Gyr) red giant branch (RGB) stars. From the observed RGB tip, we conclude that the stream is at the same distance as DDO 68, confirming the physical association with it. A synthetic CMD analysis indicates that the large majority of the star formation activity in the stream occurred at epochs earlier than $\sim$1 Gyr ago, and that the star formation at epochs more recent than $\sim$500 Myr ago is compatible with zero. The total stellar mass of the stream is $\sim10^{6} M_{\odot}$, about 1/100 of that of DDO~68. This is a striking example of hierarchical merging in action at the dwarf galaxy scales., Comment: ApJ in press

We present chemical abundances and radial velocities of six HII regions in the extremely metal-poor star-forming dwarf galaxy DDO 68. They are derived from deep spectra in the wavelength range 3500 - 10,000 {\AA}, acquired with the Multi Object Double Spectrograph (MODS) at the Large Binocular Telescope (LBT). In the three regions where the [O III]$\lambda$4363 {\AA} line was detected, we inferred the abundance of He, N, O, Ne, Ar, and S through the "direct" method. We also derived the oxygen abundances of all the six regions adopting indirect method calibrations. We confirm that DDO 68 is an extremely metal-poor galaxy, and a strong outlier in the luminosity - metallicity relation defined by star-forming galaxies. With the direct-method we find indeed an oxygen abundance of 12+log(O/H)=7.14$\pm$0.07 in the northernmost region of the galaxy and, although with large uncertainties, an even lower 12+log(O/H)=6.96$\pm$0.09 in the "tail". This is, at face value, the most metal-poor direct abundance detection of any galaxy known. We derive a radial oxygen gradient of -0.06$\pm$0.03 dex/kpc (or -0.30 dex $R_{25}^{-1}$) with the direct method, and a steeper gradient of -0.12$\pm$0.03 dex/kpc (or -0.59 dex $R_{25}^{-1}$) from the indirect method. For the $\alpha$-element to oxygen ratios we obtain values in agreement with those found in other metal-poor star-forming dwarfs. For nitrogen, instead, we infer much higher values, leading to log(N/O)$\sim-1.4$, at variance with the suggested existence of a tight plateau at $-1.6$ in extremely metal poor dwarfs. The derived helium mass fraction ranges from Y=0.240$\pm$0.005 to Y=0.25$\pm$0.02, compatible with standard big bang nucleosynthesis. Finally, we measured HII region radial velocities in the range 479$-$522 km/s from the tail to the head of the "comet", consistent with the rotation derived in the HI., Comment: Accepted for publication in MNRAS

We exploit the first \gaia data release to study the properties of the Galactic stellar halo as traced by RR Lyrae. We demonstrate that it is possible to select a pure sample of RR Lyrae using only photometric information available in the Gaia+2MASS catalogue. The final sample contains about 21600 RR Lyrae covering an unprecedented fraction ($\sim60\%$) of the volume of the Galactic inner halo ($\text{R}<28$ kpc). We study the morphology of the stellar halo by analysing the RR Lyrae distribution with parametric and non-parametric techniques. Taking advantage of the uniform all-sky coverage, we test halo models more sophisticated than usually considered in the literature, such as those with varying flattening, tilt and/or offset of the halo with respect to the Galactic disc. A consistent picture emerges: the inner halo is well reproduced by a smooth distribution of stars settled on triaxial ellipsoids. The minor axis is perpendicular to the Milky Ways disc, while the major axis is misaligned by $\sim20^{\circ}$ from the Galactic Y axis. The elongation along the major axis is mild ($\text{p}=1.27$), and the vertical flattening is shown to evolve from a squashed state with $\text{q}\approx0.57$ in the centre to a more spherical $\text{q}\approx0.75$ at the outer edge of our dataset. The density slope is well approximated by a single power-law with exponent $\alpha=-2.96$. Within the range probed, we see no significant evidence for a change of the radial density slope, out of the plane tilt or an offset of the halo with respect to the Galaxy's centre., Comment: Accepted for publication in MNRAS

We present new photometry of the dwarf irregular galaxy DDO 68, one of the most metal-poor and least massive dwarfs, located in the Lynx-Cancer Void. The images were acquired with the Large Binocular Telescope in the g and r passbands, and show unequivocally that DDO 68 has previously unknown stellar streams related to the accretion of at least two smaller companions: a flea with smaller fleas biting it, to put it in Jonathan Swift's words. Our data provide direct observational evidence of multiple merging occurring at very low galactic mass scales. We present the results of an N-body simulation of the interaction of three dwarf galaxies which reproduces well the main morphological features of DDO 68., Comment: Accepted for publication on ApJL

Clusters of galaxies are embedded in halos of optically thin, gravitationally stratified, weakly magnetized plasma at the system's virial temperature. Due to radiative cooling and anisotropic heat conduction, such intracluster medium (ICM) is subject to local instabilities, which are combinations of the thermal, magnetothermal and heat-flux-driven buoyancy instabilities. If the ICM rotates significantly, its stability properties are substantially modified and, in particular, also the magnetorotational instability (MRI) can play an important role. We study simple models of rotating cool-core clusters and we demonstrate that the MRI can be the dominant instability over significant portions of the clusters, with possible implications for the dynamics and evolution of the cool cores. Our results give further motivation for measuring the rotation of the ICM with future X-ray missions such as ASTRO-H and ATHENA., Comment: 17 pages, 10 figures, accepted for publication in Journal of Plasma Physics, Special Issue "Complex Plasma Phenomena in the Laboratory and in the Universe"

The mass returned to the ambient medium by aging stellar populations over cosmological times sums up to a significant fraction (20% - 30% or more) of their initial mass. This continuous mass injection plays a fundamental role in phenomena such as galaxy formation and evolution, fueling of supermassive black holes in galaxies and the consequent (negative and positive) feedback phenomena, and the origin of multiple stellar populations in globular clusters. In numerical simulations the calculation of the mass return can be time consuming, since it requires at each time step the evaluation of a convolution integral over the whole star formation history, so the computational time increases quadratically with the number of time-steps. The situation can be especially critical in hydrodynamical simulations, where different grid points are characterized by different star formation histories, and the gas cooling and heating times are shorter by orders of magnitude than the characteristic stellar lifetimes. In this paper we present a fast and accurate method to compute the mass return from stellar populations undergoing arbitrarily complicated star formation histories. At each time-step the mass return is calculated from its value at the previous time, and the star formation rate over the last time-step only. Therefore in the new scheme there is no need to store the whole star formation history, and the computational time increases linearly with the number of time-steps., Comment: 8 pages, 4 figures, submitted, comments welcome

A few years ago we started an observational campaign aimed at the thorough study of the massive and remote globular cluster NGC2419. We have used the collected data, e.g., to test alternative theories of gravitation, to constrain the stellar M/L ratio by direct analysis of the observed luminosity function, and to search for Dark Matter within the cluster. Here we present some recent results about (a) the peculiar abundance pattern that we observed in a sample of cluster giants, and (b) newly found photometric evidence for the presence of multiple populations in the cluster. In particular, from new deep and accurate uVI LBT photometry, we find that the color spread on the Red Giant Branch is significantly larger than the observational errors both in V-I and u-V, and that the stars lying to the blue of the RGB ridge line are more concentrated toward the center of the cluster than those lying to the red of the ridge line., Comment: 4 pages, 3 figures, proceedings of the meeting "Reading the book of globular clusters with the lens of stellar evolution", Rome, Nov. 26-28, 2012, to be published in Memorie della Societa' Astronomica Italiana

We present the analysis of a large sample of early-type galaxies (ETGs) at 02 are removed from the sample, suggesting an accelerated increase of the typical sizes at z>2, especially for the ETGs with the largest masses. A pure dry merging LambdaCDM model is marginally consistent with the average size evolution at 02 progenitor ETGs. This opens the crucial question on what physical mechanism can explain the accelerated evolution at z>2, or whether an unclear observational bias is partly responsible for that., Comment: MNRAS (Letters), in press, 5 pages, 3 figures

Early-type galaxies (ETGs) are observed to be more compact at z>2 than in the local Universe. Remarkably, much of this size evolution appears to take place in a short (1.8 Gyr) time span between z=2.2 and z=1.3, which poses a serious challenge to hierarchical galaxy formation models where mergers occurring on a similar timescale are the main mechanism for galaxy growth. We compute the merger-driven redshift evolution of stellar mass Mstar\propto(1+z)^aM, half-mass radius Re\propto(1+z)^aR and velocity-dispersion sigma0\propto(1+z)^asigma predicted by concordance Lambda cold dark matter for a typical massive ETG in the redshift range z=1.3-2.2. Neglecting dissipative processes, and thus maximizing evolution in surface density, we find -1.52. Furthermore, we find that the scatter introduced in the size-mass correlation by the predicted merger-driven growth is difficult to reconcile with the tightness of the observed scaling law. We conclude that - barring unknown systematics or selection biases in the current measurements - minor and major mergers with spheroids are not sufficient to explain the observed size growth of ETGs within the standard model., Comment: 20 pages, 14 figures, matching version published in MNRAS. Corrected plots in Figs 6, 7 and 8 with respect to previous version

We present the results of a detailed analysis of the projected velocity dispersion of the globular cluster Palomar 14 performed using recent high-resolution spectroscopic data and extensive Monte Carlo simulations. The comparison between the data and a set of dynamical models (differing in fraction of binaries, degree of anisotropy, mass-to-light ratio M/L, cluster orbit and theory of gravity) shows that the observed velocity dispersion of this stellar system is well reproduced by Newtonian models with a fraction of binaries f_b<30% and a M/L compatible with the predictions of stellar evolution models. Instead, models computed with a large fraction of binaries systematically overestimate the cluster velocity dispersion. We also show that, across the parameter space sampled by our simulations, models based on the Modified Newtonian Dynamics theory can be reconciled with observations only assuming values of M/L lower than those predicted by stellar evolution models under standard assumptions., Comment: 13 pages, 13 figures, accepted for publication by ApJ

Accretion of fresh gas at a rate of ~ 1 M_{sun} yr^{-1} is necessary in star-forming disc galaxies, such as the Milky Way, in order to sustain their star-formation rates. In this work we present the results of a new hydrodynamic simulation supporting the scenario in which the gas required for star formation is drawn from the hot corona that surrounds the star-forming disc. In particular, the cooling of this hot gas and its accretion on to the disc are caused by the passage of cold galactic fountain clouds through the corona., Comment: 2 pages, 1 figure. To appear in the proceedings of the conference "Assembling the Puzzle of the Milky Way", Le Grand-Bornand 17-22 April 2011, European Physical Journal, editors C. Reyl\'e, A. Robin and M. Schultheis

We present the analysis of a kinematic data set of stars in the globular cluster NGC 2419, taken with Keck/DEIMOS. Combined with a reanalysis of deep HST and Subaru imaging data, which provide an accurate luminosity profile of the cluster, we investigate the validity of a large set of dynamical models of the system, which are checked for stability via N-body simulations. We find that isotropic models in either Newtonian or Modified Newtonian Dynamics (MOND) are ruled out with extremely high confidence. However, a simple Michie model in Newtonian gravity with anisotropic velocity dispersion provides an excellent representation of the luminosity profile and kinematics. In contrast, with MOND we find that Michie models that reproduce the luminosity profile either over-predict the velocity dispersion on the outskirts of the cluster if the mass to light ratio is kept at astrophysically-motivated values, or else they under-predict the central velocity dispersion if the mass to light ratio is taken to be very small. We find that the best Michie model in MOND is a factor of 10000 less likely than the Newtonian model that best fits the system. A likelihood ratio of 350 is found when we investigate more general models by solving the Jeans equation with a Markov-Chain Monte Carlo scheme. We verified with N-body simulations that these results are not significantly different when the MOND external field effect is accounted for. If the assumptions that the cluster is in dynamical equilibrium, spherical, not on a peculiar orbit, and possesses a single dynamical tracer population of constant M/L are correct, we conclude that the present observations provide a very severe challenge for MOND. [abridged], Comment: 25 pages, 19 figures, accepted for publication in ApJ

In galaxies like the Milky Way, cold (~ 10^4 K) gas ejected from the disc by stellar activity (the so-called galactic-fountain gas) is expected to interact with the virial-temperature (~ 10^6 K) gas of the corona. The associated transfer of momentum between cold and hot gas has important consequences for the dynamics of both gas phases. We quantify the effects of such an interaction using hydrodynamical simulations of cold clouds travelling through a hot medium at different relative velocities. Our main finding is that there is a velocity threshold between clouds and corona, of about 75 km/s, below which the hot gas ceases to absorb momentum from the cold clouds. It follows that in a disc galaxy like the Milky Way a static corona would be rapidly accelerated: the corona is expected to rotate and to lag, in the inner regions, by ~ 80-120 km/s with respect to the cold disc. We also show how the existence of this velocity threshold can explain the observed kinematics of the cold extra-planar gas., Comment: 10 pages, 6 figures, 1 table. Accepted for publication in MNRAS. Several typos corrected

It is argued that galaxies like ours sustain their star formation by transferring gas from an extensive corona to the star-forming disc. The transfer is effected by the galactic fountain -- cool clouds that are shot up from the plane to kiloparsec heights above the plane. The Kelvin-Helmholtz instability strips gas from these clouds. If the pressure and the the metallicity of the corona are high enough, the stripped gas causes a similar mass of coronal gas to condense in the cloud's wake. Hydrodynamical simulations of cloud-corona interaction are presented. These confirm the existence of a critical ablation rate above which the corona is condensed, and imply that for the likely parameters of the Galactic corona this rate lies near the actual ablation rate of clouds. In external galaxies trails of HI behind individual clouds will not be detectable, although the integrated emission from all such trails should be significant. Parts of the trails of the clouds that make up the Galaxy's fountain should be observable and may account for features in targeted 21-cm observations of individual high-velocity clouds and surveys of Galactic HI emission. Taken in conjunction with the known decline in the availability of cold infall with increasing cosmic time and halo mass, the proposed mechanism offers a promising explanation of the division of galaxies between the blue cloud to the red sequence in the colour-luminosity plane., Comment: 12 pages, 8 figures, 1 table. Accepted for publication in MNRAS

Star-forming disc galaxies such as the Milky Way need to accrete $\gsim$ 1 $M_{\odot}$ of gas each year to sustain their star formation. This gas accretion is likely to come from the cooling of the hot corona, however it is still not clear how this process can take place. We present simulations supporting the idea that this cooling and the subsequent accretion are caused by the passage of cold galactic-fountain clouds through the hot corona. The Kelvin-Helmholtz instability strips gas from these clouds and the stripped gas causes coronal gas to condense in the cloud's wake. For likely parameters of the Galactic corona and of typical fountain clouds we obtain a global accretion rate of the order of that required to feed the star formation., Comment: 2 pages, 1 figure, to appear in "Hunting for the Dark: The Hidden Side of Galaxy Formation", Malta, 19-23 Oct. 2009, eds. V.P. Debattista & C.C. Popescu, AIP Conf. Ser

The characteristic size of early-type galaxies (ETGs) of given stellar mass is observed to increase significantly with cosmic time, from redshift z>2 to the present. A popular explanation for this size evolution is that ETGs grow through dissipationless ("dry") mergers, thus becoming less compact. Combining N-body simulations with up-to-date scaling relations of local ETGs, we show that such an explanation is problematic, because dry mergers do not decrease the galaxy stellar-mass surface-density enough to explain the observed size evolution, and also introduce substantial scatter in the scaling relations. Based on our set of simulations, we estimate that major and minor dry mergers increase half-light radius and projected velocity dispersion with stellar mass (M) as M^(1.09+/-0.29) and M^(0.07+/-0.11), respectively. This implies that: 1) if the high-z ETGs are indeed as dense as estimated, they cannot evolve into present-day ETGs via dry mergers; 2) present-day ETGs cannot have assembled more than ~45% of their stellar mass via dry mergers. Alternatively, dry mergers could be reconciled with the observations if there was extreme fine tuning between merger history and galaxy properties, at variance with our assumptions. Full cosmological simulations will be needed to evaluate whether this fine-tuned solution is acceptable., Comment: 5 pages, 2 figures. Accepted for publication in ApJ Letters

The kinematics of the extra-planar neutral and ionised gas in disc galaxies shows a systematic decline of the rotational velocity with height from the plane (vertical gradient). This feature is not expected for a barotropic gas, whilst it is well reproduced by baroclinic fluid homogeneous models. The problem with the latter is that they require gas temperatures (above $10^5$ K) much higher than the temperatures of the cold and warm components of the extra-planar gas layer. In this paper, we attempt to overcome this problem by describing the extra-planar gas as a system of gas clouds obeying the Jeans equations. In particular, we consider models having the observed extra-planar gas distribution and gravitational potential of the disc galaxy NGC 891: for each model we construct pseudo-data cubes and we compare them with the HI data cube of NGC 891. In all cases the rotational velocity gradients are in qualitative agreement with the observations, but the synthetic and the observed data cubes of NGC 891 show systematic differences that cannot be accommodated by any of the explored models. We conclude that the extra-planar gas in disc galaxies cannot be satisfactorily described by a stationary Jeans-like system of gas clouds., Comment: 14 pages, 7 figures, accepted for pubblication in MNRAS

We test the modified Newtonian dynamics (MOND) theory with the velocity-dispersion profiles of Galactic globular clusters populating the outermost region of the Milky Way halo, where the Galactic acceleration is lower than the characteristic MOND acceleration a_0. For this purpose, we constructed self-consistent, spherical models of stellar systems in MOND, which are the analogues of the Newtonian King models. The models are spatially limited, reproduce well the surface-brightness profiles of globular clusters, and have velocity-dispersion profiles that differ remarkably in shape from the corresponding Newtonian models. We present dynamical models of six globular clusters, which can be used to efficiently test MOND with the available observing facilities. A comparison with recent spectroscopic data obtained for NGC2419 suggests that the kinematics of this cluster might be hard to explain in MOND., Comment: 13 pages, 9 figures, accepted for publication by MNRAS

We examine the proposal that the HI "high-velocity" clouds (HVCs) surrounding the Milky Way and other disc galaxies form by condensation of the hot galactic corona via thermal instability. Under the assumption that the galactic corona is well represented by a non-rotating, stratified atmosphere, we find that for this formation mechanism to work the corona must have an almost perfectly flat entropy profile. In all other cases the growth of thermal perturbations is suppressed by a combination of buoyancy and thermal conduction. Even if the entropy profile were nearly flat, cold clouds with sizes smaller than 10 kpc could form in the corona of the Milky Way only at radii larger than 100 kpc, in contradiction with the determined distances of the largest HVC complexes. Clouds with sizes of a few kpc can form in the inner halo only in low-mass systems. We conclude that unless even slow rotation qualitatively changes the dynamics of a corona, thermal instability is unlikely to be a viable mechanism for formation of cold clouds around disc galaxies., Comment: MNRAS, accepted. 13 pages, 8 figures. Added discussion with respect to submitted version

Whereas considerable effort has been afforded in understanding the properties of galaxies, a full physical picture, connecting their baryonic and dark-matter content, super-massive black holes, and (metric) theories of gravity, is still ill-defined. Strong gravitational lensing furnishes a powerful method to probe gravity in the central regions of galaxies. It can (1) provide a unique detection-channel of dark-matter substructure beyond the local galaxy group, (2) constrain dark-matter physics, complementary to direct-detection experiments, as well as metric theories of gravity, (3) probe central super-massive black holes, and (4) provide crucial insight into galaxy formation processes from the dark matter point of view, independently of the nature and state of dark matter. To seriously address the above questions, a considerable increase in the number of strong gravitational-lens systems is required. In the timeframe 2010-2020, a staged approach with radio (e.g. EVLA, e-MERLIN, LOFAR, SKA phase-I) and optical (e.g. LSST and JDEM) instruments can provide 10^(2-4) new lenses, and up to 10^(4-6) new lens systems from SKA/LSST/JDEM all-sky surveys around ~2020. Follow-up imaging of (radio) lenses is necessary with moderate ground/space-based optical-IR telescopes and with 30-50m telescopes for spectroscopy (e.g. TMT, GMT, ELT). To answer these fundamental questions through strong gravitational lensing, a strong investment in large radio and optical-IR facilities is therefore critical in the coming decade. In particular, only large-scale radio lens surveys (e.g. with SKA) provide the large numbers of high-resolution and high-fidelity images of lenses needed for SMBH and flux-ratio anomaly studies., Comment: White paper submitted to the 2010 Astronomy & Astrophysics Decadal Survey

Massive early-type galaxies are observed to lie on the Mass Plane (MP), a two-dimensional manifold in the space of effective radius R_e, projected mass M_p (measured via strong gravitational lensing) and projected velocity dispersion sigma within R_e/2. The MP is less `tilted' than the Fundamental Plane, and the two have comparable associated scatter. This means that c_e2=2*G*M_p/(R_e*sigma^2) is a nearly universal constant in the range sigma=175-400 km/s. This finding can be used to constrain the mass distribution and internal dynamics of early-type galaxies. We find that a relatively wide class of spherical galaxy models has values of c_e2 in the observed range, because c_e2 is not very strongly sensitive to the mass distribution and orbital anisotropy. If the total mass distribution is isothermal, a broad range of stellar luminosity profile and anisotropy is consistent with the observations, while NFW dark-matter halos require more fine tuning of the stellar mass fraction, luminosity profile and anisotropy. If future data can cover a broader range of masses, the MP could be seen to be tilted and the value of any such tilt would provide a discriminant between models for the total mass-density profile of the galaxies. [Abridged], Comment: MNRAS in press, 15 pages, 9 figures. Revised Section 4, Fig. 9 and discussion. Added references

We have tested a previous analytical estimate of the dynamical friction timescale in Modified Newtonian Dynamics (MOND) with fully non-linear N-body simulations. The simulations confirm that the dynamical friction timescale is significantly shorter in MOND than in equivalent Newtonian systems, i.e. systems with the same phase-space distribution of baryons and additional dark matter. An apparent conflict between this result and the long timescales determined for bars to slow and mergers to be completed in previous N-body simulations of MOND systems is explained. The confirmation of the short dynamical-friction timescale in MOND underlines the challenge that the Fornax dwarf spheroidal poses to the viability of MOND., Comment: Accepted for publication in MNRAS. 6 pages, 3 figures. Corrected typo in eq. (8), added panel to Fig. 1, added references and discussion. Results unchanged

Dissipationless collapses in Modified Newtonian Dynamics (MOND) have been studied by using our MOND particle-mesh N-body code, finding that the projected density profiles of the final virialized systems are well described by Sersic profiles with index m<4 (down to m~2 for a deep-MOND collapse). The simulations provided also strong evidence that phase mixing is much less effective in MOND than in Newtonian gravity. Here we describe "ad hoc" numerical simulations with the force angular components frozen to zero, thus producing radial collapses. Our previous findings are confirmed, indicating that possible differences in radial orbit instability under Newtonian and MOND gravity are not relevant in the present context., Comment: 10 pages, 3 figures. To appear in the Proceedings of the International Workshop "Collective Phenomena in Macroscopic Systems", G. Bertin, R. Pozzoli, M. Rome, and K.R. Sreenivasan, eds., World Scientific, Singapore

Dissipationless collapses in Modified Newtonian Dynamics (MOND) are studied by using a new particle-mesh N-body code based on our numerical MOND potential solver. We found that low surface-density end-products have shallower inner density profile, flatter radial velocity-dispersion profile, and more radially anisotropic orbital distribution than high surface-density end-products. The projected density profiles of the final virialized systems are well described by Sersic profiles with index m~4, down to m~2 for a deep-MOND collapse. Consistently with observations of elliptical galaxies, the MOND end-products, if interpreted in the context of Newtonian gravity, would appear to have little or no dark matter within the effective radius. However, we found impossible (under the assumption of constant mass-to-light ratio) to simultaneously place the resulting systems on the observed Kormendy, Faber-Jackson and Fundamental Plane relations of elliptical galaxies. Finally, the simulations provide strong evidence that phase mixing is less effective in MOND than in Newtonian gravity., Comment: 15 pages, 6 figures, Accepted for publication in ApJ

By means of high-resolution N-body simulations we revisited the dissipationless collapse scenario for galaxy formation. We considered both single-component collapses and collapses of a cold stellar distribution in a live dark matter halo. Single-component collapses lead to stellar systems whose projected profiles are fitted very well by the Sersic R^(1/m) law with 3.6 < m < 8. The stellar end-products of collapses in a dark matter halo are still well described by the R^(1/m) law, but with 1.9 < m < 12, where the lowest m values are obtained when the halo is dominant. In all the explored cases the profiles at small radii deviate from their global best-fit R^(1/m) model, being significantly flatter. The break-radius values are comparable with those measured in `core' elliptical galaxies, and are directly related to the coldness of the initial conditions. The dissipationless collapse of initially cold stellar distributions in pre-existing dark matter haloes may thus have a role in determining the observed weak homology of elliptical galaxies., Comment: Accepted for publication in MNRAS (11 pages, 10 figures)

We present a simple method, based on the deformation of spherically symmetric potentials, to construct explicit axisymmetric and triaxial MOND density-potential pairs. General guidelines to the choice of suitable deformations, so that the resulting density distribution is nowhere negative, are presented. This flexible method offers for the first time the possibility to study the MOND gravitational field for sufficiently general and realistic density distributions without resorting to sophisticated numerical codes. The technique is illustrated by constructing the MOND density-potential pair for a triaxial galaxy model that, in the absence of deformation, reduces to the Hernquist sphere. Such analytical solutions are also relevant to test and validate numerical codes. Here we present a new numerical potential solver designed to solve the MOND field equation for arbitrary density distributions: the code is tested with excellent results against the analytic MOND triaxial Hernquist model and the MOND razor-thin Kuzmin disk, and a simple application is finally presented., Comment: 21 pages, 5 figures. Accepted for publication in the Astrophysical Journal

The X-ray cluster C0337-2522 at redshift $z=0.59$ hosts in its core a group of five elliptical galaxies. Using N-body simulations we show that a multiple merging event among the five galaxies is expected to take place in the next few Gyrs, forming a central brightest cluster galaxy. We also find indications that dynamical friction heating associated with this event is likely to modify the central slope of the cluster dark matter density profile., Comment: 2 pages, 1 fig., in press on the Proceedings of the ESO-USM-MPE Workshop "Multiwavelength mapping of galaxy formation and evolution", ESO Astrophysics Symposia, R. Bender and A. Renzini eds

According to the galactic cannibalism model, cD galaxies are formed in the center of galaxy clusters by merging of massive galaxies and accretion of smaller stellar systems: however, observational examples of the initial phases of this process are lacking. We have identified a strong candidate for this early stage of cD galaxy formation: a group of five elliptical galaxies in the core of the X-ray cluster C0337-2522 at redshift z=0.59. With the aid of numerical simulations, in which the galaxies are represented by N-body systems, we study their dynamical evolution up to z=0; the cluster dark matter distribution is also described as a N-body system. We find that a multiple merging event in the considered group of galaxies will take place before z=0 and that the merger remnant preserves the Fundamental Plane and the Faber-Jackson relations, while its behavior with respect to the Mbh-sigma relation is quite sensitive to the details of black hole merging [abridged]., Comment: 30 pages, 7 figures, MNRAS (accepted)

We explore the effects of dissipationless merging on the Fundamental Plane of elliptical galaxies by using a N-body code based on a new, high performance numerical scheme (Dehnen 2002). We investigate the extreme cases of galaxy growth by equal mass merging and accretion of small stellar systems; in a subset of simulations we also consider the presence of dark matter halos around the merging galaxies. Curiously, we found that the Fundamental Plane is preserved by major merging, while in the accretion scenario its edge--on thickness is only marginally reproduced, with substantial thickening in the case of merging with low angular momentum. We also found that both the Faber-Jackson and Kormendy relations are not reproduced by the simulations. Finally, we discuss the implications of our results for the origin of the Mbh-sigma and Magorrian relations. We found that dissipationless merging is unable to reproduce the Mbh-sigma relation, if Mbhs add linearly (while the Magorrian relation is nicely reproduced); on the contrary a black hole merging with substantial emission of gravitational waves reproduces the Mbh-sigma relation but fails at reproducing the Magorrian relation. [Abridged], Comment: 14 pages, 6 figures, MNRAS accepted

A new, momentum preserving fast Poisson solver for N-body systems sharing effective O(N) computational complexity, has been recently developed by Dehnen (2000, 2002). We have implemented the proposed algorithms in a Fortran-90 code, and parallelized it by a domain decomposition using the MPI routines. The code has been applied to intensive numerical investigations of galaxy mergers, in particular focusing on the possible origin of some of the observed scaling relations of elliptical galaxies. We found that the Fundamental Plane is preserved by an equal mass merging hierarchy, while it is not in a scenario where galaxies grow by accretion of smaller stellar systems. In addition, both the Faber-Jackson and Kormendy relations are not reproduced by our simulations., Comment: 9 pages, 7 figures, in "Computational astrophysics in Italy: methods and tools'', Proceedings of the workshop, Bologna, July 4-5, 2002, R. Capuzzo Dolcetta ed., SAIt Proc. on line, in press