On the relation between the mass of Compact Massive Objects and their host galaxies

Supermassive black holes and/or very dense stellar clusters are found in the central regions of galaxies. Nuclear star clusters are present mainly in faint galaxies while upermassive black holes are common in galaxies with masses $\geq 10^{10}$ M$_\odot$. In the intermediate galactic mass range both types of central massive objects (CMOs) are found. Here we present our collection of a huge set of nuclear star cluster and massive black hole data that enlarges significantly already existing data bases useful to investigate for correlations of their absolute magnitudes, velocity dispersions and masses with structural parameters of their host galaxies. In particular, we directed our attention to some differences between the correlations of nuclear star clusters and massive black holes as subsets of CMOs with hosting galaxies. In this context, the mass-velocity dispersion relation plays a relevant role because it seems the one that shows a clearer difference between the supermassive black holes and nuclear star clusters. The $M_{MBH}-{\sigma}$ has a slope of $5.19\pm 0.28$ while $M_{NSC}-{\sigma}$ has the much smaller slope of $1.84\pm 0.64$. The slopes of the CMO mass- host galaxy B magnitude of the two types of CMOs are indistinguishable within the errors while that of the NSC mass-host galaxy mass relation is significantly smaller than for supermassive black holes. Another important result is the clear depauperation of the NSC population in bright galaxy hosts, which reflects also in a clear flattening of the NSC mass vs host galaxy mass at high host masses.Comment: 12 pages, 22 figures, 2 tables, accepted for publication in MNRA

Evolution of globular cluster systems in three galaxies of the Fornax cluster

We studied and compared the radial profiles of globular clusters and of the stellar bulge component in three galaxies of the Fornax cluster observed with the WFPC2 of the HST. A careful comparative analysis of these distributions confirms that stars are more concentrated toward the galactic centres than globular clusters, in agreement with what was observed in many other galaxies. If the observed difference is the result of evolution of the globular cluster system sstarting from initial profiles similar to those of the halo--bulge stellar components, a relevant fraction of their mass (74%, 47%, 52% for NGC 1379, NGC 1399 and NGC 1404, respectively) is disappeared in the inner regions, likely contributing to the nuclear field population, local dynamics and high energy phenomena in the primeval life of the galaxy. An indication in favour of the evolutionary interpretation of the difference between the globular cluster system and stellar bulge radial profiles is given by the positive correlation we found between the value of the mass lost from the GCS and the central galactic black hole mass in the set of seven galaxies for which these data are available.Comment: paper submitted to MNRAS; 8 pages, including 4 figures and 1 tabl

Formation and evolution of clumpy tidal tails around globular clusters

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 Journa

ON THE MAXIMUM PRINCIPLE FOR VISCOSITY SOLUTIONS OF FULLY NONLINEAR ELLIPTIC EQUATIONS IN GENERAL DOMAINS

We analyze the validity of the Maximum Principle for viscosity solutions of fully nonlinear second order elliptic equations in general unbounded domains under suitable structure conditions on the equation allowing notably quadratic growth in the gradient terms.We analyze the validity of the Maximum Principle for viscosity solutions of fully nonlinear second order elliptic equations in general unbounded domains under suitable structure conditions on the equation allowing notably quadratic growth in the gradient terms

The max-plus finite element method for solving deterministic optimal control problems: basic properties and convergence analysis

We introduce a max-plus analogue of the Petrov-Galerkin finite element method to solve finite horizon deterministic optimal control problems. The method relies on a max-plus variational formulation. We show that the error in the sup norm can be bounded from the difference between the value function and its projections on max-plus and min-plus semimodules, when the max-plus analogue of the stiffness matrix is exactly known. In general, the stiffness matrix must be approximated: this requires approximating the operation of the Lax-Oleinik semigroup on finite elements. We consider two approximations relying on the Hamiltonian. We derive a convergence result, in arbitrary dimension, showing that for a class of problems, the error estimate is of order $\delta+\Delta x(\delta)^{-1}$ or $\sqrt{\delta}+\Delta x(\delta)^{-1}$, depending on the choice of the approximation, where $\delta$ and $\Delta x$ are respectively the time and space discretization steps. We compare our method with another max-plus based discretization method previously introduced by Fleming and McEneaney. We give numerical examples in dimension 1 and 2.Comment: 31 pages, 11 figure

Merging of globular clusters within inner galactic regions. I. Do they survive the tidal interaction?

The main topic of this paper is the investigation of the modes of interaction of globular clusters (GCs) moving in the inner part of a galaxy. This is tackled by means of high-resolution N-body simulations, whose first results are presented in this article. Our simulations dealt with primordial very massive (order of 10^7 solar masses) GCs that were able to decay, because of dynamical friction, into the inner regions of triaxial galaxies on a time much shorter than their internal relaxation time. To check the disruptive role of both tidal forces and GC-GC collisions, we maximised the tidal interaction considering GCs on quasi-radial orbits. The available CPU resources allowed us to follow 8 oscillations of the GCs along their orbits and the main findings are: i) clusters with an initial high enough King concentration parameter (c>=1.2), preserve up to 50% of their initial mass; ii) the inner density distribution of the survived clusters keep a King model profile; iii) GC-GC collisions have a negligible effect with respect to that caused by the passage through the galactic center; iv) the orbital energy dissipation due to the tidal interaction is of the same order of that caused by dynamical friction; v) complex sub-structures like "ripples" and "clumps" formed, as observed around real clusters. These findings support the validity of the hypothesis of merging of GCs in the galactic central region, with modes that deserve further careful investigations.Comment: LaTeX 2e, AASTeX v5.x, 23 pages with 14 figures. Accepted for publication on the Astrophysical Journal. Final version with major change