Past and Present Research Interests

My research activity in Theoretical Astrophysics is mainly concerned with Stellar Dynamics applied to the study of the evolution of Globular Clusters (hereafter GCs) and Galactic Nuclei. In the following, the relevant aspects of this activity are briefly described.

AGN and galactic nuclei accretion

In the last part of my Ph.D. thesis ([1]), I have dealt with the problem of the fuelling and accretion of Active Galactic Nuclei and, in particular, I have been working on a model which could explain both the origin of the great amount of mass needed to sustain the huge observed AGN's luminosity (as well as to accrete and form the required massive black hole, see [2]) and the nature of the dynamical mechanisms which have allowed such a large mass to concentrate in the relatively small nuclear region.

In this accretion model (see, Tremaine et al., 1975, ApJ, 199, 407 and Capuzzo Dolcetta, 1993, ApJ, 415, 616) it is assumed that most of the mass feeding AGN belongs to a nuclear cluster which formed through the merging of GCs spiralled into the nuclear region because of dynamical friction. In this respect, an estimate of the gravitational waves emission rate from stellar remnants falling toward the central massive black hole was given ([3]), and several simulations were performed about the dynamical evolution of GCs orbiting across the very central region of a galaxy. This study produced interesting results thanks to the level of accuracy and of detailed modelling not achievable by means of pure analytical methods (see [1]).

Merging and tidal distruction of GCs

Another series of simulations have produced results that support the validity of the nuclear accretion model above outlined. The dynamical evolution of GCs moving within the nuclear region of a triaxial galaxy (represented by a Schwarzschild's model), and also experiencing dynamical friction, was studied. The most important conclusions are that:

  • sufficiently massive and compact clusters are able to survive the strong galactic tidal interaction so to end up into the galactic nucleus with a nearly intact structure (see [4]);
  • orbitally decayed clusters can merge in a relatively short time (tens of galactic core crossing times) so to form a massive nuclear star cluster having a central density comparable with the sum of the progenitors initial central density (see [5], [6]).
  • The following animations (.avi files) are related to the results of the mentioned simulations. In this animation two GCs are moving on quasi-radial orbits. The size of the orbits is about 2 Kpc and the time duration of the animation corresponds to 2 orbital periods of the clusters, during which they collide four times at the passage across the galactic centre. In the simulation the clusters were represented by half a million of particles each. This second animation is a zoom around the apogalacticon of one of the two clusters involved in the previous animation. Some sub-structures ("clumps" and "ripples") formed by the tidal interaction with the galactic potential. In this regard, I have been also involved in the study of the structure and formation of "tidal tails" around GCs as well as on the connection between their morphology and the orbital path of the cluster they originated from (see [7], [8]).
    As regards the final stage of the clusters merging process, this further animation shows a merging event among 4 GCs (in the same galactic model as above) occurring in less than 20 Myr. The size of the projected volume is about 400 pc.

    Besides galactic nuclei accretion and feeding, the study of the merging among GCs is an issue that has recently revealed interesting connections with the problem of the origin and formation history of those systems, generally called "Nuclear Clusters" (NCs), that reside at the photocenters of many galaxies along the entire Hubble sequence and that show properties that are intermediate between those of GCs and those of Dwarf Galaxies (see, e.g., Oh & Lin, 2000, ApJ, 543, 620; Fellhauer & Kroupa, 2002, MNRAS, 330, 642; Bekki, Couch & Drinkwater, 2004, ApJ, 610, L13; Hartmann et al., 2011, MNRAS, 418, 2697). See, about this subject, the talk I delivered at the MODEST-8 meeting (Bad Honnef, Germany). Interestingly enough, Andersen et al. (2008, ApJ, 688, 990) located NCs significantly far from both the photometric and kinematic centre of NGC 2139, in agreement with the prediction of the formation mechanism that my collaborators and I suggested and studied ([6]).

    Internal GC dynamics

    During the last few years of my activity, I have dealt with the problem of the construction of self-consistent realistic models of GCs. In particular, I generated multimass King-Michie parametric models (with velocity anisotropy) that implement exact kinetic energy equipartition at the centre of the cluster; then, I checked the consequences that the "isothermal approximation", usually adopted to impose central equipartition in models constructed in the standard way (see e.g. Gunn & Griffin, 1979, AJ, 84, 752), has in the estimate of the various structural parameters. I found that the adoption of the approximated equipartition produces substantial changes in such parameters, e.g. in the remnant abundances and in the total mass (see [9] for details).

    As regards the actual (still debated) presence of equipartition at the centre of a real clusters, which would be a direct consequence of mass segregation, the availability of very accurate (collisional) N-body numerical codes will be crucial to ascertain whether 2-body (and higher order) collisions lead eventually to such equipartition or not (see e.g., Watters et al., 2000, ApJ, 539, 331). Moreover, only an accurate modelling of collisional dynamics could give insight to many important issues in the comprehension of the GCs evolution, formation and structure, such as: the global and the radial behaviour of the mass-to-light ratio (Boily et al., 2005, ApJ, 620, L27), the evolution of the stellar mass function (Baumgardt & Makino, 2003, MNRAS, 340, 227), the formation of central Intermediate-mass Black Holes (IMBHs) through "runaway" stellar merging (Portegies Zwart et al., 2004, Nature, 428, 724), etc.

    Thus, in relation to the existence of IMBHs in GCs, I have extended the above mentioned multimass model to incorporate self-consistently the presence of a central IMBH through the inclusion of the Bachall & Wolf (1976, ApJ, 209, 214) distribution function. Then, I investigated the influence this object exerts on the morphological and physical properties of GCs and found - in agreement with accurate numerical studies (Baumgardt et al, 2005, ApJ, 620, 238; Trenti et al, 2007, MNRAS, 374, 857; Umbreit et al., 2009) - that a cluster hosting an IMBH shows, outside the region of gravitational influence of the black hole, a core-like profile resembling that of a medium concentration cluster, although with a slightly steeper behaviour in the core region. A particular relation between the IMBH mass and the slope of the GC core profile (as well as its concentration) is deduced by generating a wide range of models. When applying this relation to a set of 39 GCs, I found that NGC 2808, NGC 6388, M80, M13, M62, M54 and G1 (in M31) probably host an IMBH.
    An important result of this analysis is that a strong correlation emerges between the presence of an extreme blue horizontal-branch (EHB) and the presence of an IMBH. In particular, the presence of a central IMBH in M13 and NGC 6388 could explain why these clusters possess EHB stars, in contrast to their &lquot;second parameter&rquot; counterparts M3 and 47 Tuc (see [14] for details).
    Recently, this model has been applied to individual parametric fits of the stellar count profile of various clusters, inferring the presence of a 6 × 103 solar masses IMBH in the centre of NGC 6388 (see [15]), of 104 solar masses in M54 ([16]) and 2 × 104 solar masses in ω Centauri ([17]).

    The study of the internal clusters dynamics is also of crucial importance to shed light on the nature and origin of Blue Struggles Stars (BSS). In this regard, I have been involved in the conduction and interpretation of N-body simulations whose aim is the analysis of the role and time-scales of the mass segregation driven by the dynamical friction, following an approach that is more self-consistent in respect with the less detailed methods used so far (e.g. Montecarlo codes, see Mapelli et al. 2006, MNRAS, 373, 361). The intention is to explain the causes of the bi-modal behaviour observed in the radial distribution of BSS (see [18] and [19]) and far from being fully understood. The preliminary results (Pasquato et al. in preparation) are encouraging, since they seem to reproduce this peculiar behaviour. Recently, I have been collaborating in a work in which the presence and location of some features of this behaviour have been proposed as a sort of “dynamical clock” able to measure the dynamical age of a cluster ([19]).

    Computational techniques

    Since my graduation thesis I have been working on the implementation and development of various numerical algorithms for the simulation of self-gravitating N-body systems, with or without a gaseous component. See the talk (in Italian) I gave at the Astronomical Observatory of "Collurania" (Teramo, Italy), for a review on numerical N-body methods.

    The fundamental aim of an N-body code is to evaluate as fast as possible the gravitational interactions among a very large number of particles, preserving a sufficiently good accuracy. To achieve this, I implemented and optimized a tree-code and a Fast Multipole Method, whose performances have been deeply compared for typical astrophysical particle distributions, see [10] and this presentation (delivered during a short visiting period at the Dept. of Astronomy of the Washington University in Seattle, USA). Moreover, for the simulation of the hydrodynamics of self-gravitating gaseous components, these algorithms have been used coupled with suitable particle methods like the Smooth Particle Hydrodynamics, which I have implemented and tested as well. Some of these methods was successfully parallelized using PGHPF/CRAFT directives, as well as, more recently, following the and OpenMP and MPI paradigms. They have run on different high performance platforms such as: Cray T3E, SUN 4500, SGI Origin, IBM SP4-5-6, etc. In this regard, a new parallelization method was proposed for the tree-code; see the talk given at the "AG2000" meeting (Bremen, Germany) and the paper [11].

    I have collaborated with S. Mikkola (Tuorla Observ., Pikkio, Finland), in a project aiming at implementing specific routines for the regularization of close encounters between stars within the short-range force computation part of the tree-code. This will give powerful tools capable to handle large number of particles (thanks to the tree-code velocity in evaluating long-range gravitational interactions) with a high level of accuracy even in very collisional contexts (exploiting advanced regularization approach, e.g. Mikkola & Tanikawa, 1999, CeMDA, 74, 287; Mikkola & Aarseth, 2002, CeMDA, 84, 343).

    One of the applications of these techniques, has been the study of the statistical and “thermodynamic” properties of gravitational clustering in Cosmology, see [13] for details.

    Finally, I have made available to the scientific community the bhking website where the user can generate and download the density and line of sight velocity dispersion profiles of self-consistent models of globular clusters (in both King and Wilson variant). In addition, these models can include a central IMBH.

    Teaching experiences

    During my activity, I have also delivered several lectures on "Gravitation" and "Stellar Dynamics" to undergraduate students at the Department of Mathematics of the University of Rome "La Sapienza" (URLS). Moreover, I have been Assistant Lecturer on "Mathematical Method for Astronomy" for the students of the Bachelor of "Physics and Astrophysics" at the URLS, being also a member of the Examination Committee. Finally, I was engaged by a private school to teach Physics and Mathematics to undergraduate students (see my CV). As far as popular science is concerned, I have given several talks on Cosmology, Astrophysics and Relativity in various cultural and educational Institutions and I have collaborated with the editorial board of the on-line newspaper Cassiopea concerning popular Astronomy.

    Future Plans

    One of the scientific activity I plan to accomplish is the investigation of the existence of IMBHs in the centre of GCs, to be pursued by a careful study of the influence it would exert on stellar populations features. As above-discussed, the link between the presence of an IMBH and that of a significant population of EHB stars was suggested by [14] on simple statistical grounds —the frequency of GCs with EHB stars among the clusters thought to host an IMBH, is much higher than that it would be in an equal number of randomly chosen clusters— and was physically justified by a (rough) estimate of the rate of close encounters between an IMBH and a giant star, sufficiently close to give rise to 'tidal stripping' events on the giant, which would lead to the formation of an EHB star. This rate turned out to be just that required to produce the far-UV excess in GC emission of some (even metal-rich) clusters (e.g. NGC6388), as well as the observed EHB stars abundances.

    My intention is to study in detail these IMBH-giant collisions by means of self-consistent hydrodynamical simulations, so as to model accurately the tidal disruption of the giant outer layers and to estimate in more detail the actual cross section of the process.

    In this context, it will be also important to verify certain assumptions on the basis of the self-consistent model constructed in [14] and including the central IMBH, mostly in the more realistic multi-mass case. It is, indeed, still controversial if, and up to what extent, the presence of this object allows stars of different masses to reach energy equipartition in the central region (Gill et al., 2008, ApJ, 686, 303). Moreover, the real extension of the gravitational influence region around the IMBH is still rather uncertain. These important points must be investigated by a careful analysis of devoted N-body simulation, including the IMBH.

    In order to tackle these kinds of problems with sufficiently reliable numerical methods, I would like to continue my activity in constructing and improving numerical tools. My challenging goal is to carry out a 'hybrid' N-body code capable to handle the collisional dynamics of a GC by representing it with a realistic number of “particles”, that is as close as possible to the millions of stars of the real system, with no need of special purpose computers. This can be feasible, on one side, by implementing the most accurate regularization algorithms for the integration of short-range interactions and multiple close encounters (e.g., Mikkola & Tanikawa, 1999, CeMDA, 74, 287; Mikkola & Aarseth, 2002, CeMDA, 84, 343) within the tree-code, and, on the other side, by exploiting the enormous computing power achievable by the low-cost and flexible General Purpose Graphic Processing Units, that are being successfully employed in Numerical Astrophysics (e.g. Belleman et al., 2008, New Ast., 13, 103; Capuzzo-Dolcetta & Spera, 2013, arXiv:1304.1966).

    References

    [1] "Dynamical evolution of globular clusters and its influence on the galactic nuclei activity", Miocchi P., 1998, PhD thesis, Univ. of Rome "La Sapienza".

    [2] " Galactic nuclei activity sustained by globular cluster mass accretion", Capuzzo Dolcetta R., Miocchi P., 1998, Plan. & Space Sc., 46, 1579.

    [3] "Gravitational waves generated by globular cluster systems collapse", Capuzzo Dolcetta R., Miocchi P., 1998, IAU Symp. 184 (ed.: Y. Sofue), p.481.

    [4] "Merging of globular clusters within inner galactic regions. I. Do they survive the tidal interaction?", Miocchi P., Capuzzo Dolcetta R., Di Matteo P., Vicari, A. 2006 ApJ, 644, 940.

    [5] "Merging of globular clusters within inner galactic regions. II. The Nuclear Star Cluster formation ", Capuzzo-Dolcetta R., Miocchi P., 2008, ApJ, 681, 1136.

    [6] "Self-consistent simulations of Nuclear Cluster formation through Globular Cluster orbital decay and merging " Capuzzo-Dolcetta R., Miocchi P., 2008, MNRAS, 388, 69.

    [7] "Formation and evolution of clumpy tidal tails around globular clusters", Capuzzo Dolcetta R., Di Matteo P., Miocchi P., 2005, AJ, 129, 1906.

    [8] " Tidal tails around globular clusters. Are they a good tracer of cluster orbits?", Montuori M., Capuzzo Dolcetta R., Di Matteo P., Lepinette A., Miocchi P., 2007, ApJ, 659, 1212.

    [9] "Central energy equipartition in multi-mass models of globular clusters", Miocchi P., 2006, MNRAS, 366, 227.

    [10] "A comparison between the Fast Multipole Method and the Tree-Code to evaluate gravitational forces in 3-D", Capuzzo Dolcetta R., Miocchi P., 1998, Journ. of Comp. Phys., 143, 29.

    [11] "An efficient parallel tree-code for the simulation of self-gravitating systems", Miocchi P., Capuzzo Dolcetta, R., 2002, A&A, 382, 758.

    [12] " Astrocomp: web technologies for high performance computing on a network of supercomputers", Costa A. et al., 2005, Comp. Phys. Comm., 166, 17.

    [13] "Clustering in gravitating N-body systems", Bottaccio M. et al., 2002, Europhys. Lett., 57, 315.

    [14] "The presence of intermediate-mass black holes in globular clusters and its connection with extreme horizontal branch stars", Miocchi P., 2007, MNRAS, 381, 103.

    [15] " The surface density profile of NGC 6388: a good candidate for harboring an intermediate-mass black hole", Lanzoni B. et al., 2007, ApJ, 668, 139

    [16] " Density and Kinematic Cusps in M54 at the Heart of the Sagittarius Dwarf Galaxy: Evidence for A 104 Msun Black Hole?" Ibata R. et al., 2009, ApJ Lett, 699, 169

    [17] " A mass estimate of an intermediate-mass black hole in ω Centauri" Miocchi P., 2010, A&A, 514, A52

    [18] " Two distinct sequences of blue straggler stars in the globular cluster M30" Ferraro F.R. et al., 2010, Nature, 462, 1028

    [19] " Dynamical age differences among coeval star clusters as revealed by blue stragglers" Ferraro F.R. et al., 2012, Nature, 492, 393