arXiv subjects

Alessandro Alberto Trani

Publications and source records attributed to Alessandro Alberto Trani.

At least 19 recordsLinked to original sources

arXiv2026

Planar Three-Body Problem: theoretical predictions and simulation results

We investigate the statistical properties of the non-hierarchical planar three-body problem, relevant to astrophysical systems with nearly planar dynamics, including protoplanetary disks and AGN disks. Using the Flux-based statistical theory of the three-body problem, previously studied in three dimensions, we derive theoretical predictions for several statistical observables in the planar case. Focusing on ergodic disintegration outcomes, we compare these predictions directly with numerical simulations and contrast the results with the corresponding unconstrained three-dimensional case. Our analysis is based on one million simulations for each of eight distinct mass sets. We examine escape probabilities, properties of marginal escape events, eccentricity distributions, lifetime distributions, and relative prevalence of prograde and retrograde escapes. While several of the theoretical predictions are in good agreement with the simulations, others exhibit unexpected discrepancies. We discuss possible explanations for these deviations.

astro-ph.EP↗

arXiv2026

AGN-driven BBH mergers: Black hole populations and hierarchical growth across the AGN parameter space

Active galactic nuclei (AGNs) have been proposed as efficient environments for the formation of binary black holes (BBHs). We present an updated semi-analytical framework for BBH formation and evolution in AGN disks, following the capture, migration, pair-up, gas-driven hardening, binary--single encounters, and merger of stellar-origin black holes. We systematically explore the dependence of the resulting BBH merger population on the main AGN parameters, namely the supermassive black hole mass $M_\bullet$, the Eddington ratio $λ_\bullet$, and the disk viscosity parameter $α$, and construct an intrinsic BBH population by weighting the simulations according to observed low-redshift AGN properties. We find that AGN disks can produce repeated mergers and build a high-mass tail extending beyond the pair-instability mass gap and into the intermediate-mass range. Hierarchical growth is more efficient in lower-viscosity disks, with $α=0.01$, while higher-viscosity disks suppress the formation of massive remnants. The merger efficiency generally increases with $λ_\bullet$, but its dependence on $M_\bullet$ is non-trivial. The AGN-assisted BBH population is characterized by increasingly unequal mass ratios at high primary mass, a correlation between primary mass and $|χ_{\rm eff}|$, and an effective-spin distribution that depends strongly on the fraction of binaries born in prograde or retrograde configurations. We find that the AGN channel can reproduce systems broadly consistent with the massive BBH events GW190521 and GW231123. We test several variations of the physical model, including different formalisms for migration torques, gas hardening, and three-body encounters. The general properties of the population are robust across these variations, with the high-mass tail and spin signatures persisting in all cases except when gas hardening is switched off.

astro-ph.GA↗

arXiv2026

On an empirical method to build near-equilibrium axisymmetric and triaxial galaxy models

We introduce a numerical technique to implement $N-$body realizations of axisymmetric and triaxial self-gravitating system starting from a spherical self-consistent models for which a phase-space distribution is known. The method is an improvement of the so-called adiabatic squeezing technique and allows one to have a better control of the effective ellipticities of the particle distribution and produces virialized systems that can be used as non-spherical initial conditions for $N-$body simulations. Some numerical stability tests are presented and discussed.

astro-ph.GA↗

arXiv2026

Beyond the Largest Lyapunov Exponent: Entropy-Based Diagnostics of Chaos in Henon-Heiles and N-Body Dynamics

The largest Lyapunov exponent is widely used to diagnose chaos in gravitational dynamics, but in mixed phase spaces and finite-N systems it does not always provide a complete description of orbital complexity and phase-space transport. Entropy-based diagnostics may offer a complementary perspective. We investigate whether trajectory-based information entropy can provide a useful diagnostic of chaos in gravitational systems and how it relates to the largest Lyapunov exponent as a function of orbital energy and of the number of degrees of freedom. We computed the largest Lyapunov exponent and a coarse-grained Shannon entropy for ensembles of trajectories in the Henon-Heiles potential and for test-particle orbits in live N-body realizations of a Plummer model. We then compared the dependence of both quantities on orbital energy and, for the N-body case, on particle number. In the Henon-Heiles system, the Shannon entropy follows the transition from weak to widespread chaos and exhibits an energy dependence that closely mirrors that of the largest Lyapunov exponent. For test-particle orbits in live N-body potentials, both diagnostics indicate stronger chaos for more tightly bound trajectories. However, their dependence on N differs: the largest Lyapunov exponent remains nearly constant over the explored range of particle numbers, whereas the Shannon entropy decreases monotonically as N increases. These results show that the information entropy can complement the largest Lyapunov exponent and may better capture changes in global phase-space mixing, especially in systems where the leading Lyapunov exponent alone is not sufficiently informative. It therefore provides a promising alternative for diagnosing chaos when tangent-space dynamics is unavailable or computationally expensive, and it is naturally suited to systems with densely sampled trajectories, such as minor bodies in the Solar System.

astro-ph.EP↗

arXiv2026

The long-term evolution of Ultra Faint Dwarf Galaxies and observational implications

Context. In the Local Group, dwarf spheroidal galaxies (dSphs) and ultra-faint dwarf galaxies (UFDs) exhibit large velocity dispersions. These values are generally attributed to the presence of substantial amounts of dark matter (DM), in line with the predictions of the standard model of galaxy formation. However, alternative, more conservative explanations exist, such as non-virialized dynamical states induced by tidal interactions, the presence of stellar streams, and artificial inflation of the velocity dispersion caused by binary-star orbital motion. Aims. We study the dynamical evolution of UFDs using purely stellar ("dry") dynamics, without invoking DM. We dynamically evolve our systems up to a Hubble time and compare our results with observational studies and previous theoretical work. Methods. We employ direct high precision NBODY simulations performed with the NBODY6++GPU code. We explore the role of binaries in inflating the velocity dispersion of low-mass host galaxies. We also present both the stellar and dynamical evolution of the stellar population, which is necessary to properly interpret our results. Results. We find that, in all our models, the UFD remains globally quasi-stationary for approximately 3000 Myr. Subsequently, the system undergoes mass segregation and experiences a phase resembling core collapse. Red giants and white dwarfs (WD) are found to play significant, but distinct, roles. Red giants provide the dominant contribution to the luminosity, whereas WDs constitute the largest fraction of the non-luminous component, accounting for approximately 13% of the total stellar population. Finally, if not taken into account properly, velocity dispersion measurements can be strongly biased by the presence of a significant binary population, which can lead to substantial overestimates of velocity dispersion in UFDs

astro-ph.GA↗

arXiv2025

Turbulent drag on stellar mass black holes embedded in disks of active galactic nuclei

We investigate how AGN disk turbulence affects the orbital dynamics of a stellar-mass black hole (BH) initially located at a migration trap, focusing on the long-term behavior of eccentricity and inclination in the quasi-embedded regime. We develop a semi-analytical framework in which turbulence is modeled as a stochastic velocity field acting through a modified drag force. We integrate the resulting stochastic differential equations both in Cartesian coordinates and in orbital elements using a linearized perturbative approach, and compare these results with full numerical simulations. Eccentricity and inclination evolve toward steady-state Rayleigh distributions, with variances determined by the local disk properties and the ratio of the gas damping rate to the orbital frequency. The analytical predictions agree well with the numerical simulations. We provide closed-form expressions for the variances in both the fast and slow damping regimes. These results are directly applicable to Monte Carlo population models and can serve as physically motivated initial conditions for hydrodynamical simulations. Turbulent forcing prevents full circularization and alignment of BH orbits in AGN disks, even in the presence of strong gas drag. This has important implications for BH merger and binary formation rates, which are sensitive to the residual eccentricity and inclination. Our results highlight the need to account for turbulence-induced stochastic heating when modeling the dynamical evolution of compact objects in AGN environments.

astro-ph.HE↗

arXiv2025

Chaos in violent relaxation dynamics. Disentangling micro- and macro-chaos in numerical experiments of dissipationless collapse

Violent relaxation (VR) is often regarded as the mechanism leading stellar systems to collisionless meta equilibrium via rapid changes in the collective potential. We investigate the role of chaotic instabilities on single particle orbits in leading to nearly-invariant phase-space distributions, aiming at disentangling it from the chaos induced by collective oscillations in the self-consistent potential. We explore as function of the systems size (i.e. number of particles $N$) the chaoticity in terms of the largest Lyapunov exponent of test trajectories in a simplified model of gravitational cold collapse, mimicking a $N-$body calculation via a time dependent smooth potential and a noise-friction process accounting for the discreteness effects. A new numerical method to evaluate effective Lyapunov exponents for stochastic models is presented and tested. We find that the evolution of the phase-space of independent trajectories reproduces rather well what observed in self-consistent $N-$body simulations of dissipationless collapses. The chaoticity of test orbits rapidly decreases with $N$ for particles that remain weakly bounded in the model potential, while it decreases with different power laws for more bound orbits, consistently with what observed in previous self-consistent $N$-body simulations. The largest Lyapunov exponents of ensembles of orbits starting from initial conditions uniformly sampling the accessible phase-space are somewhat constant for $N\lesssim 10^9$, while decreases towards the continuum limit with a power-law trend. Moreover, our numerical results appear to confirm the trend of a specific formulation of dynamical entropy and its relation with Lyapunov time scales.

astro-ph.GA↗

arXiv2024

Partial suppression of chaos in relativistic three-body problems

Recent numerical results seem to suggest that in certain regimes of typical particle velocities the gravitational $N-$body problem (for $3\leq N\lesssim 10^3$) is intrinsically less chaotic when the post-Newtonian (PN) force terms are included, with respect to its classical counterpart that exhibits a slightly larger maximal Lyapunov exponent $Λ_{\rm max}$. In this work we explore the dynamics of wildly chaotic, regular and nearly regular configurations of the 3-body problem with and without the PN corrective terms aiming at shedding some light on the behaviour of the Lyapunov spectra under the effect of said corrections. Because the interaction of the tangent-space dynamics in gravitating systems, needed to evaluate the Lyapunov exponents, becomes rapidly computationally heavy due to the complexity of the higher order force derivatives involving multiple powers of $v/c$, we introduce a technique to compute a proxy of the Lyapunov spectrum based on the time-dependent diagonalization of the inertia tensor of a cluster of trajectories in phase-space. We find that, for a broad range of orbital configurations, the relativistic 3-body problem has a smaller $Λ_{\rm max}$ than its classical counterpart starting with the exact same initial condition. However, the rest of the Lyapunov spectrum can be either lower or larger in the classical case, suggesting that the relativistic precession effectively reduces chaos only along one (or few) directions in phase-space. As a general trend, the dynamical entropy of the relativistic simulations as function of the rescaled speed of light always has a regime in which falls below the classical value.} We observe that, the sole analysis of $Λ_{\rm max}$ could induce possibly misleading conclusions on the chaoticity of systems with small (and possibly large $N$.

astro-ph.GA↗

arXiv2024

Isles of regularity in a sea of chaos amid the gravitational three-body problem

The three-body problem (3BP) poses a longstanding challenge in physics and celestial mechanics. Despite the impossibility of obtaining general analytical solutions, statistical theories have been developed based on the ergodic principle. This assumption is justified by chaos, which is expected to fully mix the accessible phase space of the 3BP. This study probes the presence of regular (i.e. non chaotic) trajectories within the 3BP and assesses their impact on statistical escape theories. Using numerical simulations, we establish criteria for identifying regular trajectories and analyse their impact on statistical outcomes. Our analysis reveals that regular trajectories occupy up to 32% of the phase space, and their outcomes defy the predictions of statistical escape theories. The coexistence of regular and chaotic regions at all scales is characterized by a multi-fractal behaviour. Integration errors manifest as numerical chaos, artificially enhancing the mixing of the phase space and affecting the reliability of individual simulations, yet preserving the statistical correctness of an ensemble of realizations. Our findings underscore the challenges in applying statistical escape theories to astrophysical problems, as they may bias results by excluding the outcome of regular trajectories. This is particularly important in the context of formation scenarios of gravitational wave mergers, where biased estimates of binary eccentricity can significantly impact estimates of coalescence efficiency and detectable eccentricity.

astro-ph.EP↗

arXiv2024

pAGN: the one-stop solution for AGN disc modeling

Models of accretion discs surrounding active galactic nuclei (AGNs) find vast applications in high-energy astrophysics. The broad strategy is to parametrize some of the key disc properties such as gas density and temperature as a function of the radial coordinate from a given set of assumptions on the underlying physics. Two of the most popular approaches in this context were presented by Sirko & Goodman (2003) and Thompson et al. (2005). We present a critical reanalysis of these widely used models, detailing their assumptions and clarifying some steps in their derivation that were previously left unsaid. Our findings are implemented in the pAGN module for the Python programming language, which is the first public implementation of these accretion-disc models. We further apply pAGN to the evolution of stellar-mass black holes embedded in AGN discs, addressing the potential occurrence of migration traps.

astro-ph.HE↗

arXiv2024

Three-body encounters in black hole discs around a supermassive black hole: The disc velocity dispersion and the Keplerian tidal field determine the eccentricity and spin-orbit alignment of gravitational wave mergers

Dynamical encounters of stellar-mass black holes (BHs) in a disc of compact objects around a supermassive BH (SMBH) can accelerate the formation and coalescence of BH binaries. It has been proposed that binary-single encounters among BHs in such discs can lead to an excess of highly-eccentric BH mergers. However, previous studies have neglected how the disc velocity dispersion and the SMBH's tidal field affect the 3-body dynamics. We investigate the outcomes of binary-single encounters considering different values of the disc velocity dispersion, and examine the role of the SMBH's tidal field. We then demonstrate how their inclusion affects the properties of merging BH binaries. We perform simulations of 4-body encounters (i.e. with the SMBH as fourth particle) using the highly-accurate, regularized code TSUNAMI, which includes post-Newtonian corrections up to order 3.5PN. The disc velocity dispersion controls how orbits in the disc are aligned and circular, and determines the relative velocity of the binary-single pair before the encounter. As the velocity dispersion decreases, the eccentricity of post-encounter binaries transitions from thermal to superthermal, and binaries experience enhanced hardening. The transition between these two regimes happens at disc eccentricities and inclinations of order e ~ i ~ 10^-4. These distinct regimes correspond to a disc dominated by random motions, and one dominated by the Keplerian shear. The inclusion of the SMBH's tidal field and the disc velocity dispersion can significantly affect the number of GW mergers, and especially the number of highly-eccentric inspirals. These can be up to ~2 times higher at low velocity dispersion, and ~12 times lower at high velocity dispersions. The spin-orbit alignment is influenced by the tidal field exclusively at high velocity dispersions, effectively inhibiting the formation of anti-aligned binary BHs.

astro-ph.HE↗

arXiv2023

Active learning meets fractal decision boundaries: a cautionary tale from the Sitnikov three-body problem

Chaotic systems such as the gravitational N-body problem are ubiquitous in astronomy. Machine learning (ML) is increasingly deployed to predict the evolution of such systems, e.g. with the goal of speeding up simulations. Strategies such as active Learning (AL) are a natural choice to optimize ML training. Here we showcase an AL failure when predicting the stability of the Sitnikov three-body problem, the simplest case of N-body problem displaying chaotic behavior. We link this failure to the fractal nature of our classification problem's decision boundary. This is a potential pitfall in optimizing large sets of N-body simulations via AL in the context of star cluster physics, galactic dynamics, or cosmology.

astro-ph.GA↗

arXiv2023

The search for the lost attractor

N-body systems characterized by inverse square attractive forces may display a self similar collapse known as the gravo-thermal catastrophe. In star clusters, collapse is halted by binary stars, and a large fraction of Milky Way clusters may have already reached this phase. It has been speculated -- with guidance from simulations -- that macroscopic variables such as central density and velocity dispersion are governed post-collapse by an effective, low-dimensional system of ODEs. It is still hard to distinguish chaotic, low dimensional motion, from high dimensional stochastic noise. Here we apply three machine learning tools to state-of-the-art dynamical simulations to constrain the post collapse dynamics: topological data analysis (TDA) on a lag embedding of the relevant time series, Sparse Identification of Nonlinear Dynamics (SINDY), and Tests of Accuracy with Random Points (TARP).

astro-ph.GA↗

arXiv2023

Measurement of three-body chaotic absorptivity predicts chaotic outcome distribution

The flux-based statistical theory of the non-hierarchical three-body system predicts that the chaotic outcome distribution reduces to the chaotic emissivity function times a known function, the asymptotic flux. Here, we measure the chaotic emissivity function (or equivalently, the absorptivity) through simulations. More precisely, we follow millions of scattering events only up to the point when it can be decided whether the scattering is regular or chaotic. In this way, we measure a tri-variate absorptivity function. Using it, we determine the flux-based prediction for the chaotic outcome distribution over both binary binding energy and angular momentum, and we find good agreement with the measured distribution. This constitutes a detailed confirmation of the flux-based theory, and demonstrates a considerable reduction in computation to determine the chaotic outcome distribution.

math.DS↗

arXiv2022

Predicting the Stability of Hierarchical Triple Systems with Convolutional Neural Networks

Understanding the long-term evolution of hierarchical triple systems is challenging due to its inherent chaotic nature, and it requires computationally expensive simulations. Here we propose a convolutional neural network model to predict the stability of hierarchical triples by looking at their evolution during the first $5 \times 10^5$ inner binary orbits. We employ the regularized few-body code TSUNAMI to simulate $5\times 10^6$ hierarchical triples, from which we generate a large training and test dataset. We develop twelve different network configurations that use different combinations of the triples' orbital elements and compare their performances. Our best model uses 6 time-series, namely, the semimajor axes ratio, the inner and outer eccentricities, the mutual inclination and the arguments of pericenter. This model achieves an area under the curve of over $95\%$ and informs of the relevant parameters to study triple systems stability. All trained models are made publicly available, allowing to predict the stability of hierarchical triple systems $200$ times faster than pure $N$-body methods.

astro-ph.SR↗

arXiv2022

Revisiting Common Envelope Evolution -- A New Semi-Analytic Model for N-body and Population Synthesis Codes

We present a novel way of modeling common envelope evolution in binary and few-body systems. We consider the common envelope inspiral as driven by a drag force with a power-law dependence in relative distance and velocity. The orbital motion is resolved either by direct N-body integration or by solving the set of differential equations for the orbital elements as derived using perturbation theory. Our formalism can model the eccentricity during the common envelope inspiral, and it gives results consistent with smoothed particles hydrodynamical simulations. We apply our formalism to common envelope events from binary population synthesis models and find that the final eccentricity distribution resembles the observed distribution of post-common-envelope binaries. Our model can be used for time-resolved common-envelope evolution in population synthesis calculations or as part of binary interactions in direct N-body simulations of star clusters.

astro-ph.SR↗

arXiv2022

Compact Binary Coalescences: Astrophysical Processes and Lessons Learned

On 11 February 2016, the LIGO and Virgo scientific collaborations announced the first direct detection of gravitational waves, a signal caught by the LIGO interferometers on 14 September 2015, and produced by the coalescence of two stellar-mass black holes. The discovery represented the beginning of an entirely new way to investigate the Universe. The latest gravitational-wave catalog by LIGO, Virgo and KAGRA brings the total number of gravitational-wave events to 90, and the count is expected to significantly increase in the next years, when additional ground-based and space-born interferometers will be operational. From the theoretical point of view, we have only fuzzy ideas about where the detected events came from, and the answers to most of the five Ws and How for the astrophysics of compact binary coalescences are still unknown. In this work, we review our current knowledge and uncertainties on the astrophysical processes behind merging compact-object binaries. Furthermore, we discuss the astrophysical lessons learned through the latest gravitational-wave detections, paying specific attention to the theoretical challenges coming from exceptional events (e.g., GW190521 and GW190814).

astro-ph.HE↗

arXiv2022

Modeling gravitational few-body problems with TSUNAMI and OKINAMI

In recent years, an increasing amount of attention is being paid to the gravitational few-body problem and its applications to astrophysical scenarios. Among the main reasons for this renewed interest there is large number of newly discovered exoplanets and the detection of gravitational waves. Here, we present two numerical codes to model three- and few-body systems, called TSUNAMI and OKINAMI. The TSUNAMI code is a direct few-body code with algorithmic regularization, tidal forces and post-Newtonian corrections. OKINAMI is a secular, double-averaged code for stable hierarchical triples. We describe the main methods implemented in our codes, and review our recent results and applications to gravitational-wave astronomy, planetary science and statistical escape theories.

astro-ph.HE↗