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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 $\Lambda_{\rm max}$. 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 $\Lambda_{\rm max}$ 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 $\Lambda_{\rm max}$ could induce possibly misleading conclusions on the chaoticity of systems with small (and possibly large $N$., Comment: 9 pages, 8 figures. Submitted, comments welcome

The Fornax dwarf spheroidal galaxy (dSph) represents a challenge for some globular cluster (GC) formation models, because an exceptionally high fraction of its stellar mass is locked in its GC system. In order to shed light on our understanding of GC formation, we aim to constrain the amount of stellar mass that Fornax has lost via tidal interaction with the Milky Way (MW). Exploiting the flexibility of effective multi-component $N$-body simulations and relying on state-of-the-art estimates of Fornax's orbital parameters, we study the evolution of the mass distribution of the Fornax dSph in observationally justified orbits in the gravitational potential of the MW over 12 Gyr. We find that, though the dark-matter mass loss can be substantial, the fraction of stellar mass lost by Fornax to the MW is always negligible, even in the most eccentric orbit considered. We conclude that stellar-mass loss due to tidal stripping is not a plausible explanation for the unexpectedly high stellar mass of the GC system of the Fornax dSph and we discuss quantitatively the implications for GC formation scenarios., Comment: 15 pages, 12 figures. Version accepted in A&A

Aims. We explore the dynamical friction on a test mass in gravitational systems in the Quasi linear formulation of Modified Newtonian Dynamics (QuMOND). Methods. Exploiting the quasi linearity of QuMOND we derive a simple expression for the dynamical friction in akin to its Newtonian counterpart in the standard Chandrasekhar derivation. Moreover, adopting a mean field approach based on the Liouville equation we obtain a more rigorous (though in integral form) dynamical friction formula that can be evaluated numerically for a given choice of the QuMOND interpolation function. Results. Consistently with previous work, we observe that dynamical friction is stronger in MOND with respect to a baryon only Newtonian system with the same mass distribution. This amounts to a correction of the Coulomb logarithmic factor via extra terms proportional to the MOND radius of the system. Moreover, with the aid of simple numerical experiments we confirm our theoretical predictions and those of previous work on MOND., Comment: 12 pages, 3 Figures. Version accepted for publication in A&A

Future gravitational wave observatories can probe dark matter by detecting the dephasing in the waveform of binary black hole mergers induced by dark matter overdensities. Such a detection hinges on the accurate modelling of the dynamical friction, induced by dark matter on the secondary compact object in intermediate and extreme mass ratio inspirals. In this paper, we introduce NbodyIMRI, a new publicly available code designed for simulating binary systems within cold dark matter `spikes'. Leveraging higher particle counts and finer timesteps, we validate the applicability of the standard dynamical friction formalism and provide an accurate determination of the maximum impact parameter of particles which can effectively scatter with a compact object, across various mass ratios. We also show that in addition to feedback due to dynamical friction, the dark matter also evolves through a `stirring' effect driven by the time-dependent potential of the binary. We introduce a simple semi-analytical scheme to account for this effect and demonstrate that including stirring tends to slow the rate of dark matter depletion and therefore enhances the impact of dark matter on the dynamics of the binary., Comment: 11 pages, 9 figures + appendices. Companion paper to "Sharpening the dark matter signature in gravitational waveforms I: Accretion and eccentricity evolution" (arXiv:2402.13053). NbodyIMRI code available here: https://github.com/bradkav/NbodyIMRI

Aims. Recent observational studies suggest that feedback from active galactic nuclei (AGNs) may play an important role in the formation and evolution of low-mass dwarf galaxies, an issue that has received little attention from a theoretical perspective. Methods. We investigate this using two sets of 12 cosmological magneto-hydrodynamical simulations of the formation of dwarf galaxies: one set using a version of the AURIGA galaxy formation physics model including AGN feedback and a parallel set with AGN feedback turned off. Results. We show that the full-physics AGN runs satisfactorily reproduce several scaling relations, including the M_ BH-M_*, M_ BH-sigma_* and the baryonic Tully-Fisher relation. We find that the global star formation (SF) of galaxies run with AGN is reduced compared to the one in which AGN has been turned off, suggesting that this type of feedback is a viable way of suppressing SF in low-mass dwarfs, even though none of our galaxies is completely quenched by z=0. Furthermore, we found a tight correlation between the median SF rates and the black-hole-to-stellar mass ratio (M_BH/M_star) in our simulated dwarfs. SF is suppressed due to gas heating in the vicinity of the AGN: less HI gas is available in AGN runs, though the total amount of gas is preserved across the two settings within each galaxy. This indicates that the main effect of AGN feedback in our dwarfs is to heat up and push the gas away from the galaxy's centre rather than expelling it completely. Finally, we show that the two galaxies harbouring the largest BHs have suffered a considerable (up to 65%) reduction in their central dark matter density, pinpointing the role of AGNs in determining the final dark matter mass distribution within dwarf galaxies. This pilot paper highlights the importance of modelling AGN feedback at the lowest mass scales and the impact this can have on dwarf galaxy evolution., Comment: 13 pages, 10 figures and 2 tables Submitted to A&A

Prompted by the relevant problem of temperature inversion (i.e. gradient of density anti-correlated to the gradient of temperature) in astrophysics, we introduce a novel method to model a gravitationally confined multi-component collisionless plasma in contact with a fluctuating thermal boundary. We focus on systems with anti-correlated (inverted) density and temperature profiles, with applications to solar physics. The dynamics of the plasma is analytically described via the coupling of an appropriated coarse-grained distribution function and temporally coarse-grained Vlasov dynamics. We derive a stationary solution of the system and predict the inverted density and temperature profiles of the two-species for scenarios relevant for the corona. We validate our method by comparing the analytical results with kinetic numerical simulations of the plasma dynamics in the context of the two-species Hamiltonian mean-field model (HMF). Finally, we apply our theoretical framework to the problem of the temperature inversion in the solar corona obtaining density and temperature profiles in remarkably good agreement with the observations., Comment: 27 pages, 12 Figs. Version accepted for publication in JPP

Context. Deur (2014) and Winters et al. (2023) proposed an empirical relation between the dark to total mass ratio and ellipticity in elliptical galaxies from their observed total dynamical mass-to-light ratio data M/L = (14.1 +/- 5.4){\epsilon}. In other words, the larger is the content of dark matter in the galaxy, the more the stellar component would be flattened. Such observational claim, if true, appears to be in stark contrast with the common intuition of the formation of galaxies inside dark halos with reasonably spherical symmetry. Aims. Comparing the processes of dissipationless galaxy formation in different theories of gravity, and emergence of the galaxy scaling relations therein is an important frame where, in principle one could discriminate them. Methods. By means of collisionless N-body simulations in modified Newtonian dynamics (MOND) and Newtonian gravity with and without active dark matter halos, with both spherical and clumpy initial structure, I study the trends of intrinsic and projected ellipticities, S\'ersic index and anisotropy with the total dynamical to stellar mass ratio. Results. It is shown that, the end products of both cold spherical collapses and mergers of smaller clumps depart more and more from the spherical symmetry for increasing values of the total dynamical mass to stellar mass, at least in a range of halo masses. The equivalent Newtonian systems of the end products of MOND collapses show a similar behaviour. The M/L relation obtained from the numerical experiments in both gravities is however rather different from that reported by Deur and coauthors., Comment: 11 pages, 8 figures, 1 table. Version accepted in A&A

This work explores the mixing rate of metals in the interstellar medium (ISM), comparing observational constraints from our solar neighbourhood to high resolution cosmological hydrodynamical simulations of Milky Way (MW)-like galaxies. The mixing rate, described by the coefficient C, is varied in simulations between 0 and 0.05, with resultant simulated galaxies compared to observations of metallicity dispersion in young star clusters, HII regions and neutral gas in the disc of the MW. A value of C between 0.003125 and 0.0125 is found to self-consistently match a range of observables, with a best estimate of C=0.0064$\pm$0.0004. We demonstrate that the relationship between metal dispersion in young stars, HII regions and neutral gas, versus the coefficient C, can be described by a power law. These constrained mixing rates infer a comparatively well mixed ISM in the solar neighbourhood, at odds with some recent observations that have reported a highly inhomogeneous ISM. The degree of mixing suggested by this work is lower than what often employed in many hydrodynamical simulations. Our results have implications for studying the metallicity distribution of stars as well as of gas in the interstellar and circumgalactic media., Comment: 7 pages, 3 figures, accepted for publication in MNRAS

We investigate the core-cusp problem of the $\Lambda$ cold dark matter ($\Lambda$CDM) scenario in the context of Modified Newtonian Dynamics (MOND) paradigm exploiting the concept of equivalent Newtonian system (ENS). By means of particle-mesh $N-$body simulations in MOND we explore processes of galaxy formation via cold dissipationless collapse or merging of smaller substructures. From the end states of our simulations we recover the associated ENS and study the properties of their dark matter halos. We compare the simulation results with simple analytical estimates with a family of $\gamma-$models. We find that the dark matter density of ENSs of most spherical cold collapses ha a markedly cored structure, in particular for the lowest values of the initial virial ratios. End states of some simulations with clumpy initial conditions have more complex profiles and some of their ENSs exhibit a moderate cusp, with logarithmic density slope always shallower than 1. These results seem to point towards the fact that the absence in most observed galaxies of a central DM cusp, at variance with what one would expect from theoretical and numerical arguments in $\Lambda$CDM, would be totally consistent in a MONDian description., Comment: 10 pages, 8 figures 1 table. Matching the version accepted in A&A

An anti-correlation between the central density of the dark matter halo ($\rho_{150,\ {\rm DM}}$) and the pericentric distances ($r_{p}$) of the Milky Way's (MW's) dwarf spheroidal galaxies (dSphs) has been reported in the literature. The existence and origin of such anti-correlation is however controversial, one possibility being that only the densest dSphs can survive the tidal field towards the centre of our Galaxy. In this work, we place particular emphasis on quantifying the statistical significance of such anti-correlation, by using available literature data in order to explore its robustness under different assumptions on the MW gravitational potential, and for various derivations of $\rho_{150}$ and $r_{p}$. We consider models in which the MW is isolated and has a low ($8.8\times10^{11}\,M_{\odot}$) and high ($1.6\times10^{12}\, M_{\odot}$) halo mass, respectively, as well as configurations in which the MW's potential is perturbed by a Large Magellanic Cloud (LMC) infall. We find that, while data generally support models in which the dSphs' central DM density decreases as a function of their pericentric radius, this anti-correlation is statistically significant at $3\sigma$ level only in $\sim$12$\%$ of the combinations of $\rho_{150}$ and $r_{p}$ explored. Moreover, including the impact of the LMC's infall onto the MW weakens or even washes away this anti-correlation, with respect to models in which the MW is isolated. Our results suggest that the strength and existence of such anti-correlation is still debatable: exploring it with high-resolution simulations including baryonic physics and different DM flavours will help us to understand its emergence., Comment: 10 pages, 3 figures. Accepted for publication in MNRAS

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., Comment: 11 pages, 10 figures. Matching the version of the ms accepted in A&A

Ultra-diffuse galaxies (UDGs) are attractive candidates to probe cosmological models and test theories of galaxy formation at low masses; however, they are difficult to detect because of their low surface brightness. In the Local Group a handful of UDGs have been found to date, most of which are satellites of the Milky Way and M31, and only two are isolated galaxies. It is unclear whether so few UDGs are expected. We address this by studying the population of UDGs formed in hydrodynamic constrained simulations of the Local Group from the HESTIA suite. For a Local Group with a total enclosed mass $M_{\rm LG}\!\left(< 2.5\, {\rm Mpc}\right)=8\times10^{12}\, {\rm M_\odot}$, we predict that there are $12\pm3$ isolated UDGs (68% confidence) with stellar masses $10^6 \leq M_\ast\, /\, {\rm M_\odot} < 10^9,$ and effective radii $R_{\rm e} \geq 1.5\, {\rm kpc}$, within 2.5 Mpc of the Local Group, of which $2^{+2}_{-1}$ (68% confidence) are detectable in the footprint of the Sloan Digital Sky Survey (SDSS). Accounting for survey incompleteness, we find that almost the entire population of UDGs in the Local Group field would be observable in a future all-sky survey with a depth similar to the SDSS, the Dark Energy Survey, or the Legacy Survey of Space and Time. Our results suggest that there is a population of UDGs in the Local Group awaiting discovery., Comment: 9 pages including acknowledgements and references. Contains 5 figures and two tables. A repository of reduced data and scripts to reproduce the results in this manuscript is available at https://github.com/Musical-Neutron/lg_field_udgs and archived at https://doi.org/10.5281/zenodo.7757685 . Accepted by ApJL

Numerical simulations within a cold dark matter (DM) cosmology form halos whose density profiles have a steep inner slope (`cusp'), yet observations of galaxies often point towards a flat central `core'. We develop a convolutional mixture density neural network model to derive a probability density function (PDF) of the inner density slopes of DM halos. We train the network on simulated dwarf galaxies from the NIHAO and AURIGA projects, which include both DM cusps and cores: line-of-sight velocities and 2D spatial distributions of their stars are used as inputs to obtain a PDF representing the probability of predicting a specific inner slope. The model recovers accurately the expected DM profiles: $\sim$82$\%$ of the galaxies have a derived inner slope within $\pm$0.1 of their true value, while $\sim$98$\%$ within $\pm$0.3. We apply our model to four Local Group dwarf spheroidal galaxies and find results consistent with those obtained with the Jeans modelling based code GravSphere: the Fornax dSph has a strong indication of possessing a central DM core, Carina and Sextans have cusps (although the latter with large uncertainties), while Sculptor shows a double peaked PDF indicating that a cusp is preferred, but a core can not be ruled out. Our results show that simulation-based inference with neural networks provide a innovative and complementary method for the determination of the inner matter density profiles in galaxies, which in turn can help constrain the properties of the elusive DM., Comment: 14 pages, 11 figures, submitted to MNRAS. comments welcome

We extend the classical formulation of the dynamical friction effect on a test star by Chandrasekhar to the case of relativistic velocities and velocity distributions also accounting for post-Newtonian corrections to the gravitational force. The original kinetic framework is revised and used to construct a special-relativistic dynamical friction formula where the relative velocities changes in subsequent encounters are added up with Lorentz transformation and the velocity distribution of the field stars accounts for relativistic velocities. Furthermore, a simple expression is obtained for systems where the post-Newtonian correction on the gravitational forces become relevant even at non-relativistic particle velocities. Finally, using a linearized Lagrangian we derive another expression for the dynamical friction expression in a more compact form than that of Lee (1969). Comparing our formulation with the classical one, we observe that a given test particle suffers a slightly stronger drag when moving through a distribution of field stars with relativistic velocity distribution. Vice versa, a purely classical treatment of a system where post-Newtonian (PN) corrections should be included, over estimates the effect of dynamical friction at low test particle velocity, regardless of the form of velocity distribution. Finally, a first order PN dynamical friction covariant formulation is less strong than its classical counterpart at small velocities but much higher for large velocities over a broad range of mass ratios, Comment: 15 pages, 3 figures. Version accepted in A&A

Supernovae feedback driven expansion has proven to be a viable mechanism to explain the average properties of Ultra Diffuse Galaxies (UDGs) such as the sizes, colors, mass and internal kinematics. Here, we explore the origin of stellar metallicity gradients in feedback driven simulated UDGs from the NIHAO project and compare them with the observed distribution of metallicity gradients of both Local Group dwarfs as well as of the recently observed UDG DF44. Simulated UDGs display a large variety of metallicity profiles, showing flat to negative gradients, similarly to what is observed in LG dwarfs, while DF44 data suggest a flat to positive gradient. The variety of metallicity gradients in simulations is set by the interplay between the radius at which star formation occurs and the subsequent supernovae feedback driven stellar redistribution: rotation supported systems tend to have flat metallicity profiles while dispersion supported galaxies show negative and steep profiles. Our results suggest that UDGs are not peculiar in what regards their metallicity gradients, when compared to regular dwarfs. Desirably, a larger observational sample of UDGs' gradients shall be available in the future, in order to test our predictions., Comment: 13 pages, 6+3 figures

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., Comment: 26 pages, 8 figures

We summarize a series of numerical experiments of collisional dynamics in dense stellar systems such as globular clusters (GCs) and in weakly collisional plasmas using a novel simulation technique, the so-called Multi-particle collision (MPC) method, alternative to Fokker-Planck and Monte Carlo approaches. MPC is related to particle-mesh approaches for the computation of self consistent long-range fields, ensuring that simulation time scales with $N\log N$ in the number of particles, as opposed to $N^2$ for direct $N$-body. The collisional relaxation effects are modelled by computing particle interactions based on a collision operator approach that ensures rigorous conservation of energy and momenta and depends only on particles velocities and cell-based integrated quantities., Comment: 7 pages, 2 figures. To appear in the proceedings of the 362 IAU symposium "Predictive Power of Computational Astrophysics as a Discovery Tool". Chamonix, France 8-12 Nov. 2021

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., Comment: 17 pages 7 figures. Version accepted for publication in MNRAS

By means of numerical simulations we study the radial-orbit instability in anisotropic self-gravitating $N-$body systems under the effect of noise. We find that the presence of additive or multiplicative noise has a different effect on the onset of the instability, depending on the initial value of the orbital anisotropy., Comment: 6 pages, 3 figures. To appear in the proceedings of the 364 IAU symposium, "Multi-scale (time and mass) Dynamics of Space Objects" 18-22 October 2021, Iasi Roumania

A central question regarding Ultra Diffuse Galaxies (UDGs) is whether they are a separate category to Low Surface Brightness (LSB) galaxies, or just their natural continuation towards low stellar masses. In this letter, we show that the rotation curve of the gas rich UDG AGC 242019 is well fit by a dark matter halo with inner slope that asymptotes to -0.54, and that such fit provides a concentration parameter that matches theoretical expectations. This finding, together with previously works in which shallow inner profiles are derived for UDGs, shows that the structural properties of these galaxies are like other observed LSBs. UDGs show slowly rising rotation curves and this favours formation scenarios in which internal processes, such as SNae driven gas outflows, are acting to modify UDGs profiles., Comment: Accepted for publication in ApJL

During the last decades, scientific community has been investigating both biological and hydrographic processes that affect fisheries. Such an interdisciplinary and synergic approach is nowadays giving a fundamental contribution, in particular, in connecting the dots between hydrographic phenomena and biomass variability and distribution of small pelagic fish. Here we estimate impacts of hydrographic fluctuations on small pelagic fishery, focusing on the inter-annual variability that characterizes connectivity between spawning and recruiting areas for the European anchovy (Engraulis encrasicolus, Linnaues 1758), in the Northern side of the Sicily Channel (Mediterranean Sea). Results show that coastal transport dynamics of a specific year largely affect the biomass recorded the following year. Our work, moreover, quantifies the specific monetary impacts on landings of European anchovy fishery due to hydrodynamics variability, connecting biomass fluctuations with fishery economics in a highly dynamic and exploited marine environment as the Sicily Channel. In particular, we build a model that attributes a monetary value to the hydrographic phenomena (i.e., cross-shore vs. alongshore eggs and larvae transport), registered in the FAO Geographical Sub-Area (GSA) 16 (Southern Sicily). This allows us to provide a monetary estimation of catches, derived from different transport dynamics. Our results highlight the paramount importance that hydrographic phenomena can have over the socio-economic performance of a fishery.

Stellar prolate rotation in dwarf galaxies is rather uncommon, with only two known galaxies in the Local Group showing such feature (Phoenix and And II). Cosmological simulations show that in massive early-type galaxies prolate rotation likely arises from major mergers. However, the origin of such kinematics in the dwarf galaxies regime has only been explored using idealized simulations. Here we made use of hydrodynamical cosmological simulations of dwarfs galaxies with stellar mass between $3\times10^5$ and $5\times10^8$ M$_{\odot}$ to explore the formation of prolate rotators. Out of $27$ dwarfs, only one system showed clear rotation around the major axis, whose culprit is a major merger at $z=1.64$, which caused the transition from an oblate to a prolate configuration. Interestingly, this galaxy displays a steep metallicity gradient, reminiscent of the one measured in Phoenix and And II: this is the outcome of the merger event that dynamically heats old, metal-poor stars, and of the centrally concentrated residual star formation. Major mergers in dwarf galaxies offer a viable explanation for the formation of such peculiar systems, characterized by steep metallicity gradients and prolate rotation., Comment: 5 pages, 3 figures

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., Comment: Updated version of the manuscript: "Seeing the forest for the trees: hierarchical generative models for star clusters from hydro-dynamical simulations". 15 pages, 15 figures, 2 tables. Comments welcome

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., Comment: 7 pages, 3 figures

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., Comment: 8 pages, 9 figs., 1 tab. Version accepted for publication in A&A

Local Group satellite galaxies show a wide diversity of star formation histories (SFHs) whose origin is yet to be fully understood. Using hydrodynamical simulations from the Constrained Local UniversE project, we study the SFHs of satellites of Milky Way-like galaxies in a cosmological context: while in the majority of the cases the accretion onto their host galaxy causes the satellites to lose their gas, with a subsequent suppression in SF, in about 25$\%$ of our sample we observe a clear enhancement of SF after infall. Peaks in SF clearly correlate with the satellite pericentric passage around its host and, in one case, with a satellite-satellite interaction. We identify two key ingredients that result in enhanced SF after infall: galaxies must enter the host's virial radius with a reservoir of cold gas $M_{\rm gas,inf}/M_{\rm vir,inf}\gtrsim 10^{-2}$ and with a minimum pericentric distance $\gtrsim$10 kpc (mean distance $\sim$50 kpc for the full sample), in order to form new stars due to compression of cold gas at pericentric passage. On the other hand, satellites that infall with little gas or whose pericentric distance is too small, have their gas ram-pressure stripped and subsequent SF quenched. The pericentric passage of satellites likewise correlates with SF peaks in their hosts, suggesting that this mechanism induces bursts of SF in satellites and central galaxies alike, in agreement with recent studies of our Galaxy's SFH. Our findings can explain the recently reported multiple stellar populations observed in dwarf galaxies such as Carina and Fornax, and should be taken into account in semi-analytic models of galaxy formation and satellite quenching., Comment: 15 pages, 12 figures, matches accepted MNRAS version. Expanded sec 3.2. New figures 2 and 3 show comparison between simulated and observed SFHs of satellites and isolated dwarfs

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., Comment: Accepted for publication in Physical Review Research

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., Comment: 12 pages, 13 figures. Matching the version accepted for publication in A&A

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., Comment: 8 pages, 6 figures. Version accepted in Astronomy & Astrophysics

In recent years a new window on galaxy evolution opened, thanks to the increasing discovery of galaxies with a low surface brightness, such as Ultra Diffuse Galaxies (UDGs). The formation mechanism of these systems is still a much debated question, and so are their kinematical properties. In this work, we address this topic by analyzing the stellar kinematics of isolated UDGs formed in the hydrodynamical simulation suite NIHAO. We construct projected line-of-sight velocity and velocity dispersion maps to compute the projected specific angular momentum, $\lambda_{\rm R}$, to characterize the kinematical support of the stars in these galaxies. We found that UDGs cover a broad distribution, ranging from dispersion to rotation supported galaxies, with similar abundances in both regimes. The degree of rotation support of simulated UDGs correlates with several properties such as galaxy morphology, higher HI fractions and larger effective radii with respect to the dispersion supported group, while the dark matter halo spin and mass accretion history are similar amongst the two populations. We demonstrate that the alignment of the infalling baryons into the protogalaxy at early $z$ is the principal driver of the $z$=0 stellar kinematic state: pressure supported isolated UDGs form via mis-aligned gas accretion while rotation supported ones build-up their baryons in an ordered manner. Accounting for random inclination effects, we predict that a comprehensive survey will find nearly half of field UDGs to have rotationally supported stellar disks.

Using cosmological hydrodynamic simulations with physically motivated models of super-massive black hole (SMBH) formation and growth, we compare the assembly of Milky Way-mass ( $M_{\mathrm{vir}} \approx 7 \times 10^{11}$ $M_{\odot}$ at $z = 0$) galaxies in cold dark matter (CDM) and self-interacting dark matter (SIDM) models. Our SIDM model adopts a constant cross-section of 1 cm$^2$/g. We find that SMBH formation is suppressed in the early universe due to SIDM coring. SMBH-SMBH mergers are also suppressed in SIDM as a consequence of the lower number of SMBHs formed. Lack of initial merger-driven SMBH growth in turn delays SMBH growth by billions of years in SIDM compared to CDM. Further, we find that this delayed growth suppresses SMBH accretion in the largest progenitors of the main SIDM galaxies during the first 5 Gyrs of their evolution. Nonetheless, by $z = 0.8$ the CDM and SIDM SMBH masses differ only by around 0.2 dex, so that both remain compatible with the $M_{BH}-M_{*}$ relation. We show that the reduced accretion causes the SIDM SMBHs to less aggressively regulate star formation in their host galaxies than their CDM counterparts, resulting in a factor of 3 or more stars being produced over the lifetime of the SIDM galaxies compared to the CDM galaxies. Our results highlight a new way in which SIDM can affect the growth and merger history of SMBHs and ultimately give rise to very different galaxy evolution compared to the classic CDM model.

We use Gaia DR2 systemic proper motions of 45 satellite galaxies to constrain the mass of the Milky Way using the scale free mass estimator of Watkins et al. (2010). We first determine the anisotropy parameter $\beta$, and the tracer satellites' radial density index $\gamma$ to be $\beta$=$-0.67^{+0.45}_{-0.62}$ and $\gamma=2.11\pm0.23$. When we exclude possible former satellites of the Large Magellanic Cloud, the anisotropy changes to $\beta$=$-0.21^{+0.37}_{-0.51}$. We find that the index of the Milky Way's gravitational potential $\alpha$, which is dependent on the mass itself, is the parameter with the largest impact on the mass determination. Via comparison with cosmological simulations of Milky Way-like galaxies, we carried out a detailed analysis of the estimation of the observational uncertainties and their impact on the mass estimator. We found that the mass estimator is biased when applied naively to the satellites of simulated Milky Way halos. Correcting for this bias, we obtain for our Galaxy a mass of $0.58^{+0.15}_{-0.14}\times10^{12}$M$_\odot$ within 64 kpc, as computed from the inner half of our observational sample, and $1.43^{+0.35}_{-0.32}\times10^{12}$M$_\odot$ within 273 kpc, from the full sample; this latter value extrapolates to a virial mass of $M_\mathrm{vir\,\Delta=97}$=$1.51^{+0.45}_{-0.40} \times 10^{12}M_{\odot}$ corresponding to a virial radius of R$_\mathrm{vir}$=$308\pm29$ kpc. This value of the Milky Way mass lies in-between other mass estimates reported in the literature, from various different methods., Comment: 17 pages, 10 figures, 2 tables. Accepted for publication in MNRAS

We study the stability of a family of spherical equilibrium models of self-gravitating systems, the so-called $\gamma-$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 $\Lambda_{\rm max}$ 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 $\lambda_{\rm m}$ of the individual particles in the single-particle phase space, we find that more anisotropic systems have a larger fraction of orbits with larger $\lambda_{\rm m}$., Comment: 9 pages, 7 figures. Matching the version accepted for publication in MNRAS

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., Comment: 4 pages 2 figures. To appear in the Proceedings of the 351 IAU Symposium "Star Clusters: From the Milky Way to the Early Universe"

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 $\Lambda_{\rm max}$ decreases with $N$. The values of its inverse (the so-called Lyapunov time $t_\lambda$) 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., Comment: 4 pages, 2 figures. To appear in the proceedings of the 351 IAU Symposium "Star Clusters: from the Milky Way to the Early Universe"

We revisit the r\^{o}le 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., Comment: 13 pages 16 figures. Version accepted in MNRAS

The existence of galaxies with a surface brightness $\mu$ lower than the night sky has been known since three decades. Yet, their formation mechanism and emergence within a $\rm\Lambda CDM$ universe has remained largely undetermined. For the first time, we investigated the origin of Low Surface Brightness (LSB) galaxies with M$_{\star}$$\sim$10$^{9.5-10}$M$_{\odot}$, which we are able to reproduce within hydrodynamical cosmological simulations from the NIHAO suite. The simulated and observed LSBs share similar properties, having large HI reservoir, extended star formation histories and effective radii, low S\'{e}rsic index and slowly rising rotation curves. The formation mechanism of these objects is explored: simulated LSBs form as a result of co-planar co-rotating mergers and aligned accretion of gas at early times, while perpendicular mergers and mis-aligned gas accretion result in higher $\mu$ galaxies by $z$=0. The larger the merger, the stronger the correlation between merger orbital configuration and final $\mu$. While the halo spin parameter is consistently high in simulated LSB galaxies, the impact of halo concentration, feedback-driven gas outflows and merger time only plays a minor-to-no role in determining $\mu$. Interestingly, the formation scenario of such `classical' LSBs differs from the one of less massive, M$_{\star}$$\sim$10$^{7-9}$M$_{\odot}$, Ultra-Diffuse Galaxies, the latter resulting from the effects of SNae driven gas outflows: a M$_{\star}$ of $\sim$10$^9$M$_{\odot}$ thus represents the transition regime between a feedback-dominated to an angular momentum-dominated formation scenario in the LSB realm. Observational predictions are offered regarding spatially resolved star formation rates through LSB discs: these, together with upcoming surveys, can be used to verify the proposed emergence scenario of LSB galaxies., Comment: MNRAS Accepted 2019 April 02; in original form 2019 January 24. 15 pages,17 figures. main results in Fig 12 and 14. Added appendix A

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 $\alpha$ 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 $\alpha$ in the range $1<\alpha<3$. The lineshapes have a non-trivial functional form and appear somehow independent of $\alpha$. Within the accessible time and size ranges, we also find that the short-range limit is hardly attained even for relatively large values of $\alpha$., Comment: 14 Pages 9 Figures. Accepted the special issue of JPA, "Long-range Interactions and Synchronization"