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Leandro Beraldo e Silva

Publications and source records attributed to Leandro Beraldo e Silva.

48 records · Page 3Linked to original sources

How stars formed in warps settle into (and contaminate) thick discs

In recent years star formation has been discovered in the Milky Way's warp. These stars formed in the warp (warp stars) must eventually settle into the plane of the disc. We use an $N$-body$+$smooth particle hydrodynamics model of a warped galaxy to study how warp stars settle into the disc. By following warp stars in angular momentum space, we show that they first tilt to partially align with the main disc in a time scale of $\sim1$ Gyr. Then, once differential precession halts this process, they phase mix into an axisymmetric distribution on a time scale of $\sim 6$ Gyr. The warp stars end up contaminating the geometric thick disc. Because the warp in our fiducial simulation is growing, the {\it warp stars} settle to a distribution with a negative vertical age gradient as younger stars settle further from the mid-plane. While vertically extended, warp star orbits are still nearly circular and they are therefore subject to radial migration, with a net movement inwards. As a result warp stars can be found throughout the disc. The density distribution of a given population of warp stars evolves from a torus to an increasingly centrally filled-in density distribution. Therefore we argue that, in the Milky Way, warp stars should be found in the Solar Neighbourhood. Moreover, settled warp stars may constitute part of the young flaring population seen in the Milky Way's outskirts.

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Tracing birth properties of stars with abundance clustering

To understand the formation and evolution of the Milky Way disk, we must connect its current properties to its past. We explore hydrodynamical cosmological simulations to investigate how the chemical abundances of stars might be linked to their origins. Using hierarchical clustering of abundance measurements in two Milky Way-like simulations with distributed and steady star formation histories, we find that abundance clusters of stars comprise different groups in birth place ($R_\text{birth}$) and time (age). Simulating observational abundance errors (0.05 dex), we find that to trace discrete groups of ($R_\text{birth}$, age) requires a large vector of abundances. Using 15-element abundances (Fe, O, Mg, S, Si, C, P, Mn, Ne, Al, N, V, Ba, Cr, Co), up to $\approx$ 10 clusters can be defined with $\approx$ 25% overlap in ($R_\text{birth}$, age). We build a simple model to show that it is possible to infer a star's age and $R_\text{birth}$ from abundances with precisions of $\pm$0.06 Gyr and $\pm$1.17 kpc respectively. We find that abundance clustering is ineffective for a third simulation, where low-$α$ stars form distributed in the disc and early high-$α$ stars form more rapidly in clumps that sink towards the galactic center as their constituent stars evolve to enrich the interstellar medium. However, this formation path leads to large age-dispersions across the [$α$/Fe]-[Fe/H] plane, which is inconsistent with the Milky Way's observed properties. We conclude that abundance clustering is a promising approach toward charting the history of our Galaxy.

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Recovering the origins of the lenticular galaxy NGC 3115 using multi-band imaging

A detailed study of the morphology of lenticular galaxies is an important way to understand how this type of galaxy formed and evolves over time. Decomposing a galaxy into its components (disc, bulge, bar, ...) allows recovering the colour gradients present in each system, its star formation history, and its assembly history. We use GALFITM to perform a multi-wavelength structural decomposition of the closest lenticular galaxy, NGC 3115, resulting in the description of its stellar light into several main components: a bulge, a thin disc, a thick disc and also evidence of a bar. We report the finding of central bluer stellar populations in the bulge, as compared to the colour of the galaxy outskirts, indicating either the presence of an Active Galactic Nucleus (AGN) and/or recent star formation activity. From the spectral energy distribution results, we show that the galaxy has a low luminosity AGN component, but even excluding the effect of the nuclear activity, the bulge is still bluer than the outer-regions of the galaxy, revealing a recent episode of star formation. Based on all of the derived properties, we propose a scenario for the formation of NGC 3115 consisting of an initial gas-rich merger, followed by accretions and feedback that quench the galaxy, until a recent encounter with the companion KK084 that reignited the star formation in the bulge, provoked a core displacement in NGC 3115 and generated spiral-like features. This result is consistent with the two-phase formation scenario, proposed in previous studies of this galaxy.

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The relative efficiencies of bars and clumps in driving disc stars to retrograde motion

The presence of stars on retrograde orbits in disc galaxies is usually attributed to accretion events, both via direct accretion, as well as through the heating of the disc stars. Recent studies have shown that retrograde orbits can also be produced via scattering by dense clumps, which are often present in the early stages of a galaxy's evolution. However, so far it has been unclear whether other internally-driven mechanisms, such as bars, are also capable of driving retrograde motion. Therefore, in this paper, we investigate the efficiencies with which bars and clumps produce retrograde orbits in disc galaxies. We do this by comparing the retrograde fractions and the spatial distributions of the retrograde populations in four $N$-body$+$smooth particle hydrodynamics (SPH) simulations of isolated disc galaxies spanning a range of evolutionary behaviours. We find that both bars and clumps are capable of generating significant retrograde populations of order $\sim 10\%$ of all stars. We also find that while clump-driven retrograde stars may be found at large galactocentric radii, bar-driven retrograde stars remain in the vicinity of the bar, even if the bar dissolves. Consequently, we find that retrograde stars in the Solar Neighbourhood in the clumpy models are exclusively clump-driven, but this is a trace population, constituting $0.01-0.04\%$ of the total stellar population in this region. Finally, we find that neither bars (including dissolving ones) nor clumps in the models are able to produce rotationally supported counter-rotating discs.

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Co-formation of the thin and thick discs revealed by APOGEE-DR16 and Gaia-DR2

Since thin disc stars are younger than thick disc stars on average, the thin disc is predicted by some models to start forming after the thick disc had formed, around 10 Gyr ago. Accordingly, no significant old thin disc population should exist. Using 6-D coordinates from Gaia-DR2 and age estimates from Sanders & Das (2018), we select $\sim 24000$ old stars (${τ> 10}$ Gyr, with uncertainties $\lesssim 15\%$) within 2 kpc from the Sun (full sample). A cross-match with APOGEE-DR16 ($\sim 1000$ stars) reveals comparable fractions of old chemically defined thin/thick disc stars. We show that the full sample pericenter radius ($r_\mathrm{per}$) distribution has three peaks, one associated with the stellar halo and the other two having contributions from the thin/thick discs. Using a high-resolution $N$-body+Smooth Particle Hydrodynamics simulation, we demonstrate that one peak, at $r_\mathrm{per}\approx 7.1$ kpc, is produced by stars from both discs which were born in the inner Galaxy and migrated to the Solar Neighbourhood. In the Solar Neighbourhood, $\sim 1/2$ ($\sim 1/3$) of the old thin (thick) disc stars are classified as migrators. Our results suggest that thin/thick discs are affected differently by radial migration inasmuch as they have different eccentricity distributions, regardless of vertical scale heights. We interpret the existence of a significant old thin disc population as evidence for an early co-formation of thin/thick discs, arguing that clump instabilities in the early disc offer a compelling explanation for the observed trends.

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The Splash without a merger

The Milky Way's progenitor experienced several merger events which left their imprints on the stellar halo, including the Gaia-Sausage/Enceladus. Recently, it has been proposed that this event perturbed the proto-disk and gave rise to a metal rich ([Fe/H] $>-1$) low angular momentum ($v_ϕ < 100$ km/s) stellar population. These stars have dynamical and chemical properties different from the accreted stellar halo, but are continuous with the canonical thick disk. In this letter, we use a hydrodynamical simulation of an isolated galaxy which develops clumps that produce a bimodal thin$+$thick disk chemistry to explore whether it forms such a population. We demonstrate clump scattering forms a metal-rich, low angular momentum population, without the need for a major merger. We show that, in the simulation, these stars have chemistry, kinematics and density distribution in good agreement with those in the Milky Way.

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Geometric properties of galactic discs with clumpy episodes

A scenario for the formation of the bi-modality in the chemical space [$α$/Fe] vs [Fe/H] of the Milky Way was recently proposed in which $α$-enhanced stars are produced early and quickly in clumps. Besides accelerating the enrichment of the medium with $α$-elements, these clumps scatter the old stars, converting in-plane to vertical motion, forming a geometric thick disc. In this paper, by means of a detailed analysis of the data from smooth particle hydrodynamical simulations, we investigate the geometric properties (in particular of the chemical thick disc) produced in this scenario. For mono-age populations we show that the surface radial density profiles of high-[$α$/Fe] stars are well described by single exponentials, while that of low-[$α$/Fe] stars require broken exponentials. This break is sharp for young populations and broadens for older ones. The position of the break does not depend significantly on age. The vertical density profiles of mono-age populations are characterized by single exponentials, which flare significantly for low-[$α$/Fe] stars but only weakly (or not at all) for high-[$α$/Fe] stars. For low-[$α$/Fe] stars, the flaring level decreases with age, while for high-[$α$/Fe] stars it weakly increases with age (although with large uncertainties). All these properties are in agreement with observational results recently reported for the Milky Way, making this a plausible scenario for the formation of the Galactic thick disc.

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Box/peanut-shaped bulges in action space

We introduce the study of box/peanut (B/P) bulges in the action space of the initial axisymmetric system. We explore where populations with different actions end up once a bar forms and a B/P bulge develops. We find that the density bimodality due to the B/P bulge (the X-shape) is better traced by populations with low radial, JR,0, or vertical, Jz,0, actions, or high azimuthal action, Jϕ,0. Generally populations separated by JR,0 have a greater variation in bar strength and vertical heating than those separated by Jz,0. While the bar substantially weakens the initial vertical gradient of Jz,0, it also drives a strikingly monotonic vertical profile of JR,0. We then use these results to guide us in assigning metallicity to star particles in a pure N-body model. Because stellar metallicity in unbarred galaxies depends on age as well as radial and vertical positions, the initial actions are particularly well suited for assigning metallicities. We argue that assigning metallicities based on single actions, or on positions, results in metallicity distributions inconsistent with those observed in real galaxies. We therefore use all three actions to assign metallicity to an N-body model by comparing with the actions of a star-forming, unbarred simulation. The resulting metallicity distribution is pinched on the vertical axis, has a realistic vertical gradient and has a stronger X-shape in metal-rich populations, as found in real galaxies.

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The discreteness-driven relaxation of collisionless gravitating systems: entropy evolution in external potentials, N-dependence and the role of chaos

We investigate the old problem of the fast relaxation of collisionless $N$-body systems which are collapsing or perturbed, emphasizing the importance of (non-collisional) discreteness effects. We integrate orbit ensembles in fixed external potentials, estimating the entropy of the ensemble to analyze the time evolution of the distribution function. We show that these estimates capture the correct physical behavior expected from the 2nd Law of Thermodynamics, without any spurious entropy production. For self-consistent (i.e. stationary) samples, the entropy is conserved, while for non-self-consistent samples, it increases within a few dynamical times up to a maximum where it stabilizes (even in integrable potentials). Our results shed light on the main ingredients for this fast collisionless relaxation. The fundamental ingredient is the discreteness (finite $N$) of gravitational systems in any potential. Additionally, in non-integrable potentials, the presence of chaotic orbits accelerates the entropy production. Contrary to the traditional violent relaxation scenario, our results indicate that a time-dependent potential is not necessary for this fast relaxation. For the first time, in connection with the Nyquist-Shannon theorem we determine the $N$-dependence of this discreteness-driven relaxation, deriving a typical relaxation time $T/τ_{cr}\approx 0.1 N^{1/6}$, with slightly weaker $N$-dependencies for non-integrable potentials with substantial fractions of chaotic orbits. This timescale is much smaller than the collisional timescale even for small-$N$ systems such as open clusters and represents an upper limit for real collisionless $N$-body systems. Additionally, our results reinforce the conclusion draw in Beraldo e Silva et al. (2017) that the Vlasov equation does not provide an adequate kinetic description of the fast relaxation of collapsing collisionless $N$-body systems.

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The discreteness-driven relaxation of collisionless gravitating systems: entropy evolution and the Nyquist-Shannon theorem

The time irreversibility and fast relaxation of collapsing $N$-body gravitating systems (as opposed to the time reversibility of the equations of motion for individual stars or particles) are traditionally attributed to information loss due to coarse-graining in the observation. We show that this subjective element is not necessary once one takes into consideration the fundamental fact that these systems are discrete, i.e. composed of a finite number $N$ of stars or particles. We show that a connection can be made between entropy estimates for discrete systems and the Nyquist-Shannon sampling criterion. Specifically, given a sample with $N$ points in a space of $d$ dimensions, the Nyquist-Shannon criterion constrains the size of the smallest structures defined by a function in the continuum that can be uniquely associated with the discrete sample. When applied to an $N$-body system, this theorem sets a lower limit to the size of phase-space structures (in the continuum) that can be resolved in the discrete data. As a consequence, the finite $N$ system tends to a uniform distribution after a relaxation time that typically scales as $N^{1/d}$. This provides an explanation for the fast achievement of a stationary state in collapsing $N$-body gravitating systems such as galaxies and star clusters, without the need to advocate for the subjective effect of coarse-graining.

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The Arrow of Time in the collapse of collisionless self-gravitating systems: non-validity of the Vlasov-Poisson equation during violent relaxation

The collapse of a collisionless self-gravitating system, with the fast achievement of a quasi-stationary state, is driven by violent relaxation, with a typical particle interacting with the time-changing collective potential. It is traditionally assumed that this evolution is governed by the Vlasov-Poisson equation, in which case entropy must be conserved. We run N-body simulations of isolated self-gravitating systems, using three simulation codes: NBODY-6 (direct summation without softening), NBODY-2 (direct summation with softening) and GADGET-2 (tree code with softening), for different numbers of particles and initial conditions. At each snapshot, we estimate the Shannon entropy of the distribution function with three different techniques: Kernel, Nearest Neighbor and EnBiD. For all simulation codes and estimators, the entropy evolution converges to the same limit as N increases. During violent relaxation, the entropy has a fast increase followed by damping oscillations, indicating that violent relaxation must be described by a kinetic equation other than the Vlasov-Poisson, even for N as large as that of astronomical structures. This indicates that violent relaxation cannot be described by a time-reversible equation, shedding some light on the so-called "fundamental paradox of stellar dynamics". The long-term evolution is well described by the orbit-averaged Fokker-Planck model, with Coulomb logarithm values in the expected range 10-12. By means of NBODY-2, we also study the dependence of the 2-body relaxation time-scale on the softening length. The approach presented in the current work can potentially provide a general method for testing any kinetic equation intended to describe the macroscopic evolution of N-body systems.

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Statistical mechanics of self-gravitating systems: mixing as a criterion for indistinguishability

We propose an association between the phase-space mixing level of a self-gravitating system and the indistinguishability of its constituents (stars or dark matter particles). This represents a refinement in the study of systems exhibiting incomplete violent relaxation. Within a combinatorial analysis similar to that of Lynden-Bell, we make use of this association to obtain a distribution function that deviates from the Maxwell-Boltzmann distribution, increasing its slope for high energies. Considering the smallness of the occupation numbers for large distances from the center of the system, we apply a correction to Stirling's approximation which increases the distribution slope also for low energies. The distribution function thus obtained presents some resemblance to the "S" shape of distributions associated with cuspy density profiles (as compared to the distribution function obtained from the Einasto profile), although it is not quite able to produce sharp cusps. We also argue how the association between mixing level and indistinguishability can provide a physical meaning to the assumption of particle-permutation symmetry in the N-particle distribution function, when it is used to derive the one-particle Vlasov equation, which raises doubts about the validity of this equation during violent relaxation.

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