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Pierfrancesco Di Cintio

Publications and source records attributed to Pierfrancesco Di Cintio.

At least 37 records · Page 2Linked to original sources
arXiv2023

Dynamics of intermediate mass black holes in globular clusters. Wander radius and anisotropy profiles

We recently introduced a new method for simulating collisional gravitational N-body systems with approximately linear time scaling with $N$, based on the Multi-Particle Collision (MPC) scheme, previously applied in Plasma Physics. We simulate globular clusters with a realistic number of stellar particles (at least up to several times $10^6$) on a standard workstation. We simulate clusters hosting an intermediate mass black hole (IMBH), probing a broad range of BH-cluster and BH-average-star mass ratios, unrestricted by the computational constraints affecting direct N-body codes. We use either single mass models or models with a Salpeter mass function, with the IMBH initially sitting at the centre. The force exerted by and on the IMBH is evaluated with a direct scheme. We measure the evolution of the Lagrangian radii and core density and velocity dispersion over time. In addition, we study the evolution of the velocity anisotropy profiles. We find that models with an IMBH undergo core collapse at earlier times, the larger the IMBH mass the shallower, with an approximately constant central density at core collapse. The presence of an IMBH tends to lower the central velocity dispersion. These results hold independently of the mass function. For the models with Salpeter MF we observe that equipartition of kinetic energies is never achieved. Orbital anisotropy at large radii appears driven by energetic escapers on radial orbits. We measure the wander radius. Among the results we obtained, which mostly confirm or extend previously known trends that had been established over the range of parameters accessible to direct N-body simulations, we underline that the leptokurtic nature of the IMBH wander radius distribution might lead to IMBHs presenting as off-center more frequently than expected, with implications on observational IMBH detection.

astro-ph.GA↗
arXiv2023

Modified Thirring model beyond the excluded-volume approximation

Long-range interacting systems may exhibit ensemble inequivalence and can possibly attain equilibrium states under completely open conditions, for which energy, volume and number of particles simultaneously fluctuate. Here we consider a modified version of the Thirring model for self-gravitating systems with attractive and repulsive long-range interactions in which particles are treated as hard spheres in dimension d=1,2,3. Equilibrium states of the model are studied under completely open conditions, in the unconstrained ensemble, by means of both Monte Carlo simulations and analytical methods and are compared with the corresponding states at fixed number of particles, in the isothermal-isobaric ensemble. Our theoretical description is performed for an arbitrary local equation of state, which allows us to examine the system beyond the excluded-volume approximation. The simulations confirm the theoretical prediction of the possible occurrence of first-order phase transitions in the unconstrained ensemble. This work contributes to the understanding of long-range interacting systems exchanging heat, work and matter with the environment.

cond-mat.stat-mech↗
arXiv2022

Symplectic coarse graining approach to the dynamics of spherical self-gravitating systems

We investigate the evolution of the phase-space distribution function around slightly perturbed stationary states and the process of violent relaxation in the context of the dissipationless collapse of an isolated spherical self-gravitating system. By means of the recently introduced symplectic coarse graining technique, we obtain an effective evolution equation that allows us to compute the scaling of the frequencies around a stationary state, as well as the damping times of Fourier modes of the distribution function, with the magnitude of the Fourier $k-$vectors themselves. We compare our analytical results with $N$-body simulations.

astro-ph.GA↗
arXiv2021

Hierarchical generative models for star clusters from hydro-dynamical simulations

Star formation in molecular clouds is clumpy, hierarchically subclustered. Fractal structure also emerges in hydro-dynamical simulations of star-forming clouds. Simulating the formation of realistic star clusters with hydro-dynamical simulations is a computational challenge, considering that only the statistically averaged results of large batches of simulations are reliable, due to the chaotic nature of the gravitational N-body problem. While large sets of initial conditions for N-body runs can be produced by hydro-dynamical simulations of star formation, this is prohibitively expensive in terms of computational time. Here we address this issue by introducing a new technique for generating many sets of new initial conditions from a given set of star masses, positions and velocities from a hydro-dynamical simulation. We use hierarchical clustering in phase space to learn a tree representation of the spatial and kinematic relations between stars. This constitutes the basis for the random generation of new sets of stars which share the same clustering structure of the original ones but have individually different masses, positions, and velocities. We apply this method to the output of a number of hydro-dynamical star-formation simulations, comparing the generated initial conditions to the original ones through a series of quantitative tests, including comparing mass and velocity distributions and fractal dimension. Finally, we evolve both the original and the generated star clusters using a direct N-body code, obtaining a qualitatively similar evolution.

astro-ph.GA↗
arXiv2021

Monte Carlo simulations in the unconstrained ensemble

The unconstrained ensemble describes completely open systems whose control parameters are chemical potential, pressure, and temperature. For macroscopic systems with short-range interactions, thermodynamics prevents the simultaneous use of these intensive variables as control parameters, because they are not independent and cannot account for the system size. When the range of the interactions is comparable with the size of the system, however, these variables are not truly intensive and may become independent, so equilibrium states defined by the values of these parameters may exist. Here, we derive a Monte Carlo algorithm for the unconstrained ensemble and show that simulations can be performed using chemical potential, pressure, and temperature as control parameters. We illustrate the algorithm by applying it to physical systems where either the system has long-range interactions or is confined by external conditions. The method opens up a new avenue for the simulation of completely open systems exchanging heat, work, and matter with the environment.

cond-mat.stat-mech↗
arXiv2021

Introducing a new multi-particle collision method for the evolution of dense stellar systems II. Core collapse

In a previous paper we introduced a new method for simulating collisional gravitational $N$-body systems with linear time scaling on $N$, based on the Multi-Particle Collision (MPC) approach. This allows us to simulate globular clusters with a realistic number of stellar particles in a matter of hours on a typical workstation. We evolve star clusters containing up to $10^6$ stars to core collapse and beyond. We quantify several aspects of core collapse over multiple realizations and different parameters, while always resolving the cluster core with a realistic number of particles. We run a large set of N-body simulations with our new code. The cluster mass function is a power-law with no stellar evolution, allowing us to clearly measure the effects of the mass spectrum. Leading up to core collapse, we find a power-law relation between the size of the core and the time left to core collapse. Our simulations thus confirm the theoretical self-similar contraction picture but with a dependence on the slope of the mass function. The time of core collapse has a non-monotonic dependence on the slope, which is well fit by a parabola. This holds also for the depth of core collapse and for the dynamical friction timescale of heavy particles. Cluster density profiles at core collapse show a broken power law structure, suggesting that central cusps are a genuine feature of collapsed cores. The core bounces back after collapse, and the inner density slope evolves to an asymptotic value. The presence of an intermediate-mass black hole inhibits core collapse. We confirm and expand on several predictions of star cluster evolution before, during, and after core collapse. Such predictions were based on theoretical calculations or small-size direct $N$-body simulations. Here we put them to the test on MPC simulations with a much larger number of particles, allowing us to resolve the collapsing core.

astro-ph.GA↗
arXiv2021

Kinetic and hydrodynamic regimes in multi-particle-collision dynamics of a one-dimensional fluid with thermal walls

We study the non-equilibrium steady-states of a one-dimensional ($1D1V$) fluid in a finite space region of length $L$. Particles interact among themselves by multi-particle collisions and are in contact with two thermal-wall heat reservoirs, located at the boundaries of the region. After an initial ballistic regime, we find a crossover from a normal (kinetic) transport regime to an anomalous (hydrodynamic) one, above a characteristic size $L_*$. We argue that $L_*$ is proportional to the cube of the collision time among particles. Motivated by the physics of emissive divertors in fusion plasma, we consider the more general case of thermal walls injecting particles with given average (non-thermal) velocity. For fast and relatively cold particles, short systems fail to establish local equilibrium and display non-Maxwellian distributions of velocities.

cond-mat.stat-mech↗
arXiv2020

Introducing a new multi-particle collision method for the evolution of dense stellar systems. Crash-test N-body simulations

Stellar systems are broadly divided into collisional and non-collisional. The latter are large-N systems with long relaxation timescales and can be simulated disregarding two-body interactions, while either computationally expensive direct N-body simulations or approximate schemes are required to properly model the former. Large globular clusters and nuclear star clusters, with relaxation timescales of the order of a Hubble time, are small enough to display some collisional behaviour and big enough to be impossible to simulate with direct $N$-body codes and current hardware. We introduce a new method to simulate collisional stellar systems, and validate it by comparison with direct $N$-body codes on small-$N$ simulations. The Multi-Particle collision for Dense stellar systems Code (MPCDSS) is a new code for evolving stellar systems with the Multi-Particle Collision method. Such method amounts to a stochastic collision rule that allows to conserve exactly the energy and momentum over a cluster of particles experiencing the collision. The code complexity scales with $N \log N$ in the number of particles. Unlike Monte-Carlo codes, MPCDSS can easily model asymmetric, non-homogeneous, unrelaxed and rotating systems, while allowing us to follow the orbits of individual stars. We evolve small ($N = 3.2 \times 10^4$) star clusters with MPCDSS and with the direct-summation code NBODY6, finding a similar evolution of key indicators. We then simulate different initial conditions in the $10^4 - 10^6$ star range. MPCDSS bridges the gap between small, collisional systems that can be simulated with direct $N$-body codes and large noncollisional systems. MPCDSS in principle allows us to simulate globular clusters such as Omega Cen and M54 and even the nuclear star cluster, beyond the limits of current direct N-body codes in terms of the number of particles.

astro-ph.GA↗
arXiv2020

Taking apart the dynamical clock. Fat-tailed dynamical kicks shape the blue-straggler star bimodality

In globular clusters, blue straggler stars are heavier than the average star, so dynamical friction strongly affects them. The radial distribution of BSS, normalized to a reference population, appears bimodal in a fraction of Galactic GCs, with a density peak in the core, a prominent zone of avoidance at intermediate radii, and again higher density in the outskirts. The zone of avoidance appears to be located at larger radii the more relaxed the host cluster, acting as a sort of dynamical clock. We use a new method to compute the evolution of the BSS radial distribution under dynamical friction and diffusion. We evolve our BSS in the mean cluster potential under dynamical friction plus a random fluctuating force, solving the Langevin equation with the Mannella quasi symplectic scheme. This amounts to a new simulation method which is much faster and simpler than direct N-body codes but retains their main feature: diffusion powered by strong, if infrequent, kicks. We compute the radial distribution of initially unsegregated BSS normalized to a reference population as a function of time. We trace the evolution of its minimum, corresponding to the zone of avoidance. We compare the evolution under kicks extracted from a Gaussian distribution to that obtained using a Holtsmark distribution. The latter is a fat tailed distribution which correctly models the effects of close gravitational encounters. We find that the zone of avoidance moves outwards over time, as expected based on observations, only when using the Holtsmark distribution. Thus the correct representation of near encounters is crucial to reproduce the dynamics of the system. We confirm and extend earlier results that showed how the dynamical clock indicator depends both on dynamical friction and effective diffusion powered by dynamical encounters.

astro-ph.GA↗
arXiv2020

Discreteness effects, $N-$body chaos and the onset of radial-orbit instability

We study the stability of a family of spherical equilibrium models of self-gravitating systems, the so-called $γ-$models with Osipkov-Merritt velocity anisotropy, by means of $N-$body simulations. In particular, we analyze the effect of self-consistent $N-$body chaos on the onset of radial-orbit instability (ROI). We find that degree of chaoticity of the system associated to its largest Lyapunov exponent $Λ_{\rm max}$ has no appreciable relation with the stability of the model for fixed density profile and different values of radial velocity anisotropy. However, by studying the distribution of the Lyapunov exponents $λ_{\rm m}$ of the individual particles in the single-particle phase space, we find that more anisotropic systems have a larger fraction of orbits with larger $λ_{\rm m}$.

astro-ph.GA↗
arXiv2019

$N$-body chaos and the continuum limit in numerical simulations of self-gravitating systems, revisited

We revisit the rôle of discreteness and chaos in the dynamics of self-gravitating systems by means of $N$-body simulations with active and frozen potentials, starting from spherically symmetric stationary states and considering the orbits of single particles in a frozen $N$-body potential as well as the orbits of the system in the full $6N$-dimensional phase space. We also consider the intermediate case where a test particle moves in the field generated by $N$ non-interacting particles, which in turn move in a static smooth potential. We investigate the dependence on $N$ and on the softening length of the largest Lyapunov exponent both of single particle orbits and of the full $N$-body system. For single orbits we also study the dependence on the angular momentum and on the energy. Our results confirm the expectation that orbital properties of single orbits in finite-$N$ systems approach those of orbits in smooth potentials in the continuum limit $N \to \infty$ and that the largest Lyapunov exponent of the full $N$-body system does decrease with $N$, for sufficiently large systems with finite softening length. However, single orbits in frozen models and active self-consistent models have different largest Lyapunov exponents and the $N$-dependence of the values in non-trivial, so that the use of frozen $N$-body potentials to gain information on large-$N$ systems or on the continuum limit may be misleading in certain cases.

astro-ph.GA↗
arXiv2019

Brownian motion of supermassive black holes in galaxy cores

We investigate the dynamics of supermassive black holes (SMBHs) in galactic cores by means of a semi-analytic model based on the Langevin equation, including dynamical friction and stochastic noise accounting for the gravitational interactions with stars. The model is validated against direct $N$-body simulations of intermediate-mass black holes in stellar clusters where a realistic number of particles is accessible. For the galactic case, we find that the SMBH experiences a Brownian-like motion with a typical displacement from the geometric center of the Galaxy of a few parsecs, for system parameters compatible with M87. \keywords{stellar dynamics, black hole physics, methods: n-body simulations, methods: statistical.

astro-ph.GA↗
arXiv2019

$N$-body chaos, phase-space transport and relaxation in numerical simulations

Using direct $N$-body simulations of self-gravitating systems we study the dependence of dynamical chaos on the system size $N$. We find that the $N$-body chaos quantified in terms of the largest Lyapunov exponent $Λ_{\rm max}$ decreases with $N$. The values of its inverse (the so-called Lyapunov time $t_λ$) are found to be smaller than the two-body collisional relaxation time but larger than the typical violent relaxation time, thus suggesting the existence of another collective time scale connected to many-body chaos.

astro-ph.GA↗
arXiv2019

Equilibrium time-correlation functions of the long-range interacting Fermi-Pasta-Ulam model

We present a numerical study of dynamical correlations (structure factors) of the long-range generalization of the Fermi-Pasta-Ulam oscillator chain, where the strength of the interaction between two lattice sites decays as a power $α$ of the inverse of their distance. The structure factors at finite energy density display distinct peaks, corresponding to long-wavelength propagating modes, whose dispersion relation is compatible with the predictions of the linear theory. We demonstrate that dynamical scaling holds, with a dynamical exponent $z$ that depends weakly on $α$ in the range $1<α<3$. The lineshapes have a non-trivial functional form and appear somehow independent of $α$. Within the accessible time and size ranges, we also find that the short-range limit is hardly attained even for relatively large values of $α$.

cond-mat.stat-mech↗
arXiv2018

Transport in perturbed classical integrable systems: the pinned Toda chain

Nonequilibrium and thermal transport properties of the Toda chain, a prototype of classically integrable system, subject to additional (nonintegrable) terms are considered. In particular, we study via equilibrium and nonequilibrium simulations, the Toda lattice with a power-law pinning potential, recently analyzed by Lebowitz and Scaramazza [ArXiv:1801.07153]. We show that, according to general expectations, even the case with quadratic pinning is genuinely non-integrable, as demonstrated by computing the Lyapunov exponents, and displays normal (diffusive) conductivity for very long chains. However, the model has unexpected dynamical features and displays strong finite-size effects and slow decay of correlations to be traced back to the propagation of soliton-like excitations, weakly affected by the harmonic pinning potential. Some novel results on current correlations for the standard integrable Toda model are also reported.

physics.plasm-ph↗
arXiv2018

Fluid and kinetic modelling for non-local heat transport in magnetic fusion devices

In order to improve the presently used ad hoc flux limiter treatment of parallel heat flux transport in edge plasma fluid codes we consider here a generalized version of the Fourier law implementing a non-local kernel for the heat flux computation. The Bohm boundary condition at the wall is recovered introducing a volumetric loss term representing the contribution of suprathermal particles to the energy out flux. As expected, this contribution is negligible in the strongly collisional regime while it becomes more and more dominant for marginally and low collisional regimes. In the second part of the paper, we consider a kinetic approach where collisions are considered using the Multi-Particle-Collision (MPC) algorithm. Kinetic simulation results at medium and low collisionality are also reported.

physics.plasm-ph↗
arXiv2018

Collisional relaxation and dynamical scaling in multiparticle collisions dynamics

We present the Multi-Particle-Collision (MPC) dynamics approach to simulate properties of low-dimensional systems. In particular, we illustrate the method for a simple model: a one-dimensional gas of point particles interacting through stochastic collisions and admitting three conservation laws (density, momentum and energy). Motivated from problems in fusion plasma physics, we consider an energy-dependent collision rate that accounts for the lower collisionality of high-energy particles. We study two problems: (i) the collisional relaxation to equilibrium starting from an off-equilibrium state and (ii) the anomalous dynamical scaling of equilibrium time-dependent correlation functions. For problem (i), we demonstrate the existence of long-lived population of suprathermal particles that propagate ballistically over a quasi-thermalized background. For (ii) we compare simulations with the predictions of nonlinear fluctuating hydrodynamics for the structure factors of density fluctuations. Scaling analysis confirms the prediction that such model belong to the Kardar-Parisi-Zhang universality class.

physics.plasm-ph↗