Search

The Southern Photometric Local Universe Survey (S-PLUS) is a project to map $\sim9300$ sq deg of the sky using twelve bands (seven narrow and five broadbands). Observations are performed with the T80-South telescope, a robotic telescope located at the Cerro Tololo Observatory in Chile. The survey footprint consists of several large contiguous areas, including fields at high and low galactic latitudes, and towards the Magellanic Clouds. S-PLUS uses fixed exposure times to reach point source depths of about $21$ mag in the $griz$ and $20$ mag in the $u$ and the narrow filters. This paper describes the S-PLUS Data Release 4 (DR4), which includes calibrated images and derived catalogues for over 3000 sq deg, covering the aforementioned area. The catalogues provide multi-band photometry performed with the tools \texttt{DoPHOT} and \texttt{SExtractor} -- point spread function (\PSF) and aperture photometry, respectively. In addition to the characterization, we also present the scientific potential of the data. We use statistical tools to present and compare the photometry obtained through different methods. Overall we find good agreement between the different methods, with a slight systematic offset of 0.05\,mag between our \PSF and aperture photometry. We show that the astrometry accuracy is equivalent to that obtained in previous S-PLUS data releases, even in very crowded fields where photometric extraction is challenging. The depths of main survey (MS) photometry for a minimum signal-to-noise ratio $S/N = 3$ reach from $\sim19.5$ for the bluer bands to $\sim21.5$ mag on the red. The range of magnitudes over which accurate \PSF photometry is obtained is shallower, reaching $\sim19$ to $\sim20.5$ mag depending on the filter. Based on these photometric data, we provide star-galaxy-quasar classification and photometric redshift for millions of objects., Comment: 26 pages, 17 figures, 14 tables, accepted for A&A

A tracer sample in a gravitational potential, starting from a generic initial condition, phase-mixes towards a stationary state. This evolution is accompanied by an entropy increase, and the final state is characterized by a distribution function (DF) that depends only on integrals of motion (Jeans theorem). In terms of angle-action variables, the final state is uniform in angles (high entropy) and maximally clustered in actions (low entropy). We present a method exploring this fact to constrain a gravitational potential using a sample that is stationary in it. We estimate the entropy in the action space of trial potentials and recover the true potential by minimizing this entropy. This method avoids assuming a known DF, and may be applicable to other sets of integrals. We provide expressions for the entropy of DFs depending on energy, $f(E)$, energy and angular momentum, $f(E,L)$, or three actions, $f(\vec{J})$, and investigate the bias and fluctuations in their estimates. We show that the method correctly recovers the potential parameters for spherical and axisymmetric potentials. We also present a methodology to characterize the posterior probability distribution of the parameters with an Approximate Bayesian Computation, and indicate a pathway for application to observational data. Using $N=10^4$ tracers with $20\%$-uncertainties in the 6D coordinates, we recover the flattening parameter $q$ of an axisymmetric potential with $\sigma_q/q\sim 10\%$., Comment: 17 pages + appendix + references, 13 figs. Comments are very welcome!

We present ~ 126 new spectroscopically identified members of the GD-1 tidal stream obtained with the 5000-fiber Dark Energy Spectroscopic Instrument (DESI). We confirm the existence of a ``cocoon'' which is broad (FWHM~2.932deg~460pc) and kinematically hot (velocity dispersion, sigma~5-8km/s) component that surrounds a narrower (FWHM~0.353deg~55pc) and colder (sigma~ 2.2-2.6km/s) thin stream component (based on a median per star velocity precision of 2.7km/s). The cocoon extends over at least a ~ 20deg segment of the stream observed by DESI. The thin and cocoon components have similar mean values of [Fe/H]: -2.54+/- 0.04dex and -2.45+/-0.06dex suggestive of a common origin. The data are consistent with the following scenarios for the origin of the cocoon. The progenitor of the GD-1 stream was an accreted globular cluster (GC) and: (a) the cocoon was produced by pre-accretion tidal stripping of the GC while it was still inside its parent dwarf galaxy; (b) the cocoon is debris from the parent dwarf galaxy; (c) an initially thin GC tidal stream was heated by impacts from dark subhalos in the Milky Way; (d) an initially thin GC stream was heated by a massive Sagittarius dwarf galaxy; or a combination of some these. In the first two cases the velocity dispersion and mean metallicity are consistent with the parent dwarf galaxy having a halo mass of ~0^9\msun. Future DESI spectroscopy and detailed modeling may enable us to distinguish between these possible origins., Comment: Submitted to ApJ, 23 pages, 13 figures 4 tables

This paper presents the first public data release of the S-PLUS Ultra-Short Survey (USS), a photometric survey with short exposure times, covering approximately 9300 deg$^{2}$ of the Southern sky. The USS utilizes the Javalambre 12-band magnitude system, including narrow and medium-band and broad-band filters targeting prominent stellar spectral features. The primary objective of the USS is to identify bright, extremely metal-poor (EMP; [Fe/H] $\leq -3$) and ultra metal-poor (UMP; [Fe/H] $\leq -4$) stars for further analysis using medium- and high-resolution spectroscopy.}{This paper provides an overview of the survey observations, calibration method, data quality, and data products. Additionally, it presents the selection of EMP and UMP candidates.}{The data from the USS were reduced and calibrated using the same methods as presented in the S-PLUS DR2. An additional step was introduced, accounting for the offset between the observed magnitudes off the USS and the predicted magnitudes from the very low-resolution Gaia XP spectra.}{This first release contains data for 163 observed fields totaling $\sim$324 deg$^{2}$ along the Celestial Equator. The magnitudes obtained from the USS are well-calibrated, showing a difference of $\sim 15$ mmag compared to the predicted magnitudes by the GaiaXPy toolkit. By combining colors and magnitudes, 140 candidates for EMP or UMP have been identified for follow-up studies.}{The S-PLUS USS DR1 is an important milestone in the search for bright metal-poor stars, with magnitudes in the range 10 $ < r \leq 14$. The USS is an ongoing survey; in the near future, it will provide many more bright metal-poor candidate stars for spectroscopic follow-up., Comment: Accepted for publication in A&A. 17 pages 6 figures. Long table at the end of the paper

We study azimuthal variations in the mean stellar metallicity, <[Fe/H]>, in a self-consistent, isolated simulation in which all stars form out of gas. We find <[Fe/H]> variations comparable to those observed in the Milky Way and which are coincident with the spiral density waves. The azimuthal variations are present in young and old stars and therefore are not a result of recently formed stars. Similar variations are present in the mean age and alpha-abundance. We measure the pattern speeds of the <[Fe/H]>-variations and find that they match those of the spirals, indicating that they are at the origin of the metallicity patterns. Because younger stellar populations are not just more [Fe/H]-rich and alpha-poor but also dynamically cooler, we expect them to more strongly support spirals, which is indeed the case in the simulation. However, if we measure the radial action, J_R, using the Stackel axisymmetric approximation, we find that the spiral ridges are traced by regions of high J_R, contrary to expectations. Assuming that the passage of stars through the spirals leads to unphysical variations in the measured J_R, we obtain an improved estimate of J_R by averaging over a 1 Gyr time interval. This time-averaged J_R is a much better tracer of the spiral structure, with minima at the spiral ridges. We conclude that the errors incurred by the axisymmetric approximation introduce correlated deviations large enough to render the instantaneous radial action inadequate for tracing spirals., Comment: 21 pages. Submitted to MNRAS. Comments welcomed

The Milky Way stellar disk has both a thin and a thick component. The thin disk is composed mostly of younger stars ($\lesssim$8 Gyr) with a lower abundance of $\alpha$ elements, while the thick disk contains predominantly older stars ($\gtrsim$8--12 Gyr) with a higher $\alpha$ abundance, giving rise to an $\alpha$-bimodality most prominent at intermediate metallicities. A proposed explanation for the bimodality is an episode of clumpy star formation, where high-$\alpha$ stars form in massive clumps that appear in the first few Gyrs of the Milky Way's evolution, while low-$\alpha$ stars form throughout the disk and over a longer time span. To better understand the evolution of clumps, we track them and their constituent stars in two clumpy Milky Way simulations that reproduce the $\alpha$-abundance bimodality, one with 10% and the other with 20% supernova feedback efficiency. We investigate the paths that these clumps take in the chemical space ([O/Fe]--[Fe/H]) as well as their mass, star formation rate (SFR), formation location, lifetime, and merger history. The clumps in the simulation with lower feedback last longer on average, with several lasting hundreds of Myr. Some of the clumps do not reach high-$\alpha$, but the ones that do on average had a higher SFR, longer lifetime, greater mass, and form closer to the galactic center than the ones that do not. Most clumps that reach high-$\alpha$ merge with others and eventually spiral into the galactic center, but shed stars along the way to form most of the thick disk component., Comment: 14 pages, 14 figures, accepted for publication in ApJ

As our nearest large neighbor, the Andromeda Galaxy provides a unique laboratory for investigating galaxy formation and the distribution and substructure properties of dark matter in a Milky Way-like galaxy. Here, we propose an initial 2-epoch ($\Delta t\approx 5$yr), 2-band Roman survey of the entire halo of Andromeda, covering 500 square degrees, which will detect nearly every red giant star in the halo (10$\sigma$ detection in F146, F062 of 26.5, 26.1AB mag respectively) and yield proper motions to $\sim$25 microarcsec/year (i.e., $\sim$90 km/s) for all stars brighter than F146 $\approx 23.6$ AB mag (i.e., reaching the red clump stars in the Andromeda halo). This survey will yield (through averaging) high-fidelity proper motions for all satellites and compact substructures in the Andromeda halo and will enable statistical searches for clusters in chemo-dynamical space. Adding a third epoch during the extended mission will improve these proper motions by $\sim t^{-1.5}$, to $\approx 11$ km/s, but this requires obtaining the first epoch in Year 1 of Roman operations. In combination with ongoing and imminent spectroscopic campaigns with ground-based telescopes, this Roman survey has the potential to yield full 3-d space motions of $>$100,000 stars in the Andromeda halo, including (by combining individual measurements) robust space motions of its entire globular cluster and most of its dwarf galaxy satellite populations. It will also identify high-velocity stars in Andromeda, providing unique information on the processes that create this population. These data offer a unique opportunity to study the immigration history, halo formation, and underlying dark matter scaffolding of a galaxy other than our own., Comment: Submitted in response to the call for Roman Space Telescope Core Community Survey white papers

Using N-body simulations we explore the effects of growing a supermassive black hole (SMBH) prior to or during the formation of a stellar bar. Keeping the final mass and growth rate of the SMBH fixed, we show that if it is introduced before or while the bar is still growing, the SMBH does not cause a decrease in bar amplitude. Rather, in most cases, it is strengthened. In addition early growing SMBHs always either decreases the buckling amplitude, delay buckling, or both. This weakening of buckling is caused by an increase in the disk vertical velocity dispersion at radii well beyond the nominal black hole sphere-of-influence. While we find considerable stochasticity and sensitivity to initial conditions, the only case where the SMBH causes a decrease in bar amplitude is when it is introduced after the bar has attained a steady state. In this case we confirm previous findings that the decrease in bar strength is a result of scattering of bar-supporting orbits with small pericenter radii. By heating the inner disk both radially and vertically, an early growing SMBH increases the fraction of stars that can be captured by the Inner Lindblad Resonance (ILR) and the vertical ILR, thereby strengthening both the bar and the boxy peanut shaped bulge. Using orbital frequency analysis of star particles, we show that when an SMBH is introduced early and the bar forms around it, the bar is populated by different families of regular bar-supporting orbits than when the bar forms without an SMBH., Comment: 26 pages, 15 figures. Updated figures and some arguments in Sec. 5.3,5.4, Results Unchanged. Updates reflect format and style of final published version

Metal-poor stars are key to our understanding of the early stages of chemical evolution in the Universe. New multi-filter surveys, such as the Southern Photometric Local Universe Survey (S-PLUS), are greatly advancing our ability to select low-metallicity stars. In this work, we analyse the chemodynamical properties and ages of 522 metal-poor candidates selected from the S-PLUS data release 3. About 92% of these stars were confirmed to be metal-poor ([Fe/H] $\leq -1$) based on previous medium-resolution spectroscopy. We calculated the dynamical properties of a subsample containing 241 stars, using the astrometry from Gaia Data Release 3. Stellar ages are estimated by a Bayesian isochronal method formalized in this work. We analyse the metallicity distribution of these metal-poor candidates separated into different subgroups of total velocity, dynamical properties, and ages. Our results are used to propose further restrictions to optimize the selection of metal-poor candidates in S-PLUS. The proposed astrometric selection ($\mathrm{parallax}>0.85$ mas) is the one that returns the highest fraction of extremely metal-poor stars (16.3% have [Fe/H] $\leq -3$); the combined selection provides the highest fraction of very metal-poor stars (91.0% have [Fe/H] $\leq -2$), whereas the dynamical selection (eccentricity > 0.35 and diskness < 0.75) is better for targetting metal-poor (99.5% have [Fe/H] $\leq -1$). Using only S-PLUS photometric selections, it is possible to achieve selection fractions of 15.6%, 88.5% and 98.3% for metallicities below $-$3, $-$2 and $-$1, respectively. We also show that it is possible to use S-PLUS to target metal-poor stars in halo substructures such as Gaia-Sausage/Enceladus, Sequoia, Thamnos and the Helmi stream., Comment: 18 pages, 13 figures. To be published in MNRAS main journal (accepted 15-may-2023)

In Paper I we showed that clumps in high-redshift galaxies, having a high star formation rate density (\Sigma_SFR), produce disks with two tracks in the [Fe/H]-[\alpha/Fe] chemical space, similar to that of the Milky Way's (MW's) thin + thick disks. Here we investigate the effect of clumps on the bulge's chemistry. The chemistry of the MW's bulge is comprised of a single track with two density peaks separated by a trough. We show that the bulge chemistry of an N-body + smoothed particle hydrodynamics clumpy simulation also has a single track. Star formation within the bulge is itself in the high-\Sigma_SFR clumpy mode, which ensures that the bulge's chemical track follows that of the thick disk at low [Fe/H] and then extends to high [Fe/H], where it peaks. The peak at low metallicity instead is comprised of a mixture of in-situ stars and stars accreted via clumps. As a result, the trough between the peaks occurs at the end of the thick disk track. We find that the high-metallicity peak dominates near the mid-plane and declines in relative importance with height, as in the MW. The bulge is already rapidly rotating by the end of the clump epoch, with higher rotation at low [\alpha/Fe]. Thus clumpy star formation is able to simultaneously explain the chemodynamic trends of the MW's bulge, thin + thick disks and the Splash., Comment: 25 pages, in press at ApJ

Many barred galaxies exhibit upturns (shoulders) in their bar major-axis density profile. Simulation studies have suggested that shoulders are supported by looped $x_1$ orbits, occur in growing bars, and can appear after bar-buckling. We investigate the orbital support and evolution of shoulders via frequency analyses of orbits in simulations. We confirm that looped orbits are shoulder-supporting, and can remain so, to a lesser extent, after being vertically thickened. We show that looped orbits appear at the resonance $(\Omega_\varphi - \Omega_\mathrm{P})/\Omega_R=1/2$ (analogous to the classical Inner Lindblad Resonance, and here called ILR) with vertical-to-radial frequency ratios $1 \lesssim\Omega_z/\Omega_R \lesssim 3/2$ (vertically warm orbits). Cool orbits at the ILR (those with $\Omega_z/\Omega_R > 3/2$) are vertically thin and have no loops, contributing negligibly to shoulders. As bars slow and thicken, either secularly or by buckling, they populate warm orbits at the ILR. Further thickening carries these orbits towards crossing the vertical ILR [vILR, $(\Omega_\varphi - \Omega_\mathrm{P})/\Omega_z=1/2$], where they convert in-plane to vertical motion, become chaotic, kinematically hotter and less shoulder-supporting. Hence, persistent shoulders require bars to trap new stars, consistent with the need for a growing bar. Since buckling speeds up trapping on warm orbits at the ILR, it can be followed by shoulder formation, as seen in simulations. This sequence supports the recent observational finding that shoulders likely precede the emergence of BP-bulges. The python module for the frequency analysis, naif, is made available., Comment: Published in ApJ; A few additional figures in response to referee's request. Conclusions unchanged

We measure and compare the pattern speeds of vertical breathing, vertical bending, and spiral density waves in two isolated N-body+SPH simulations, using windowed Fourier transforms over 1 Gyr time intervals. We show that the pattern speeds of the breathing waves match those of the spirals but are different from those of the bending waves. We also observe matching pattern speeds between the bar and breathing waves. Our results not only strengthen the case that, throughout the disc, breathing motions are driven by spirals but indeed that the breathing motions are part and parcel of the spirals., Comment: 5 pages, 4 figures, published in MNRAS Letters

We describe the Milky Way Survey (MWS) that will be undertaken with the Dark Energy Spectroscopic Instrument (DESI) on the Mayall 4m telescope at the Kitt Peak National Observatory. Over the next 5 yr DESI MWS will observe approximately seven million stars at Galactic latitudes |b|>20 degrees, with an inclusive target selection scheme focused on the thick disk and stellar halo. MWS will also include several high-completeness samples of rare stellar types, including white dwarfs, low-mass stars within 100pc of the Sun, and horizontal branch stars. We summarize the potential of DESI to advance understanding of Galactic structure and stellar evolution. We introduce the final definitions of the main MWS target classes and estimate the number of stars in each class that will be observed. We describe our pipelines for deriving radial velocities, atmospheric parameters, and chemical abundances. We use ~500,000 spectra of unique stellar targets from the DESI Survey Validation program (SV) to demonstrate that our pipelines can measure radial velocities to ~1 km/s and [Fe/H] accurate to ~0.2 dex for typical stars in our main sample. We find the stellar parameter distributions from ~100 sq. deg of SV observations with >90% completeness on our main sample are in good agreement with expectations from mock catalogs and previous surveys., Comment: Accepted for publication in ApJ, 44 pages, 25 figures, 4 tables, one of a suite of 8 papers detailing targeting for DESI; v2 added links to data shown in figures, added citations to other DESI papers, corrected author list and minor typos; v3 fixed minor errors in Fig. 6 and clarified associated text; v4 updated to include minor changes in response to review

The major-axis density profiles of bars are known to be either exponential or 'flat'. We develop an automated non-parametric algorithm to detect flat profiles and apply it to a suite of simulations (with and without gas). We demonstrate that flat profiles are a manifestation of a bar's secular growth, producing a 'shoulder' region (an overdensity above an exponential) in its outskirts. Shoulders are not present when bars form, but develop as the bar grows. If the bar does not grow, shoulders do not form. Shoulders are often accompanied by box/peanut bulges, but develop separately from them and are independent tracers of a bar's growth. They can be observed at a wide range of viewing orientations with only their slope varying significantly with inclination. We present evidence that shoulders are produced by looped x1 orbits. Since the growth rate of the bar moderately correlates with the growth rate of the shoulder strength, these orbits are probably recently trapped. Shoulders therefore are evidence of bar growth. The properties of the shoulders do not, however, establish the age of a bar, because secondary buckling or strong spirals may destroy shoulders, and also because shoulders do not form if the bar does not grow much. In particular, our results show that an exponential profile is not necessarily an indication of a young bar., Comment: 20 pages, 23 figures, 2 tables. Published in MNRAS

The Milky Way stellar halo contains relics of ancient mergers that tell the story of our Galaxy's formation. Some of them are identified due to their similarity in energy, actions and chemistry, referred to as the "chemodynamical space", and are often attributed to distinct merger events. It is also known that our Galaxy went through a significant merger event that shaped the local stellar halo during its first Gyr. Previous studies using $N$-body only and cosmological hydrodynamical simulations have shown that such single massive merger can produce several "signatures" in the chemodynamical space, which can potentially be misinterpreted as distinct merger events. Motivated by these, in this work we use a subset of the GASTRO, library which consists of several SPH+$N$-body models of single accretion event in a Milky Way-like galaxy. Here, we study models with orbital properties similar to the main merger event of our Galaxy and explore the implications to known stellar halo substructures. We find that: $i.$ supernova feedback efficiency influences the satellite's structure and orbital evolution, resulting in distinct chemodynamical features for models with the same initial conditions, $ii.$ very retrograde high energy stars are the most metal-poor of the accreted dwarf galaxy and could be misinterpreted as a distinct merger $iii.$ the most bound stars are more metal-rich in our models, the opposite of what is observed in the Milky Way, suggesting a secondary massive merger, and finally $iv.$ our models can reconcile other known substructures to an unique progenitor., Comment: Published in ApJ

Despite efforts over several decades, direct-detection experiments have not yet led to the discovery of the dark matter (DM) particle. This has led to increasing interest in alternatives to the Lambda CDM (LCDM) paradigm and alternative DM scenarios (including fuzzy DM, warm DM, self-interacting DM, etc.). In many of these scenarios, DM particles cannot be detected directly and constraints on their properties can ONLY be arrived at using astrophysical observations. The Dark Energy Spectroscopic Instrument (DESI) is currently one of the most powerful instruments for wide-field surveys. The synergy of DESI with ESA's Gaia satellite and future observing facilities will yield datasets of unprecedented size and coverage that will enable constraints on DM over a wide range of physical and mass scales and across redshifts. DESI will obtain spectra of the Lyman-alpha forest out to z~5 by detecting about 1 million QSO spectra that will put constraints on clustering of the low-density intergalactic gas and DM halos at high redshift. DESI will obtain radial velocities of 10 million stars in the Milky Way (MW) and Local Group satellites enabling us to constrain their global DM distributions, as well as the DM distribution on smaller scales. The paradigm of cosmological structure formation has been extensively tested with simulations. However, the majority of simulations to date have focused on collisionless CDM. Simulations with alternatives to CDM have recently been gaining ground but are still in their infancy. While there are numerous publicly available large-box and zoom-in simulations in the LCDM framework, there are no comparable publicly available WDM, SIDM, FDM simulations. DOE support for a public simulation suite will enable a more cohesive community effort to compare observations from DESI (and other surveys) with numerical predictions and will greatly impact DM science., Comment: Contributed white paper to Snowmass 2021, CF03; minor revisions

Gaia has revealed clear evidence of bending waves in the vertical kinematics of stars in the Solar Neighbourhood. We study bending waves in two simulations, one warped, with the warp due to misaligned gas inflow, and the other unwarped. We find slow, retrograde bending waves in both models, with the ones in the warped model having larger amplitudes. We also find fast, prograde bending waves. Prograde bending waves in the unwarped model are very weak, in agreement with the expectation that these waves should decay on short, ~ crossing, timescales, due to strong winding. However, prograde bending waves are much stronger for the duration of the warped model, pointing to irregular gas inflow along the warp as a continuous source of excitation. We demonstrate that large amplitude bending waves that propagate through the Solar Neighbourhood give rise to a correlation between the mean vertical velocity and the angular momentum, with a slope consistent with that found by Gaia. The bending waves affect populations of all ages, but the sharpest features are found in the young populations, hinting that short wavelength waves are not supported by the older, kinematically hotter, populations. Our results demonstrate the importance of misaligned gas accretion as a recurrent source of vertical perturbations of disc galaxies, including in the Milky Way., Comment: 21 pages, 20 figures; Published on MNRAS

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., Comment: 21 pages, 25 figures; Published on MNRAS

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$1.17 kpc respectively. We find that abundance clustering is ineffective for a third simulation, where low-$\alpha$ stars form distributed in the disc and early high-$\alpha$ 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 [$\alpha$/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., Comment: Submitted to ApJ

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., Comment: Accepted for publication in MNRAS: 22 pages, 15 figures, 7 tables, 1 appendix

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.

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 (${\tau > 10}$ 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., Comment: 12+2 pages, 10 figures, minor changes to match published version

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 ($v_{\phi} < 100$ 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., Comment: Accepted for publication in ApJL

A scenario for the formation of the bi-modality in the chemical space [$\alpha$/Fe] vs [Fe/H] of the Milky Way was recently proposed in which $\alpha$-enhanced stars are produced early and quickly in clumps. Besides accelerating the enrichment of the medium with $\alpha$-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-[$\alpha$/Fe] stars are well described by single exponentials, while that of low-[$\alpha$/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-[$\alpha$/Fe] stars but only weakly (or not at all) for high-[$\alpha$/Fe] stars. For low-[$\alpha$/Fe] stars, the flaring level decreases with age, while for high-[$\alpha$/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., Comment: 11 pages, 12 figures; Updated to published (MNRAS) version - inclusion of extra references and minor changes suggested by the referee

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, J{\phi},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., Comment: Submitted to MNRAS. Comments welcome. The appendix of figures for the simulation suite will be available, until journal publication, at http://www.star.uclan.ac.uk/~vpd/appendix.pdf (Caution: 57Mb)

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., Comment: Accepted for publication in ApJ

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 $T/\tau_{cr}\approx 0.1 N^{1/6}$, 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., Comment: Accepted for publication in ApJ

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., Comment: 26 pages, 15 figures - Significant changes in the Fokker-Planck description of the long-term evolution - Accepted by ApJ

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., Comment: Minor changes; Published in PRD

The velocity distribution function (VDF) of dark matter (DM) halos in $\Lambda$CDM dissipationless cosmological simulations, which must be non-separable in its radial and tangential components, is still poorly known. We present the first single-parameter, non-separable, anisotropic model for the VDF in $\Lambda$CDM halos, built from an isotropic $q$-Gaussian (Tsallis) VDF of the isotropic set of dimensionless spherical velocity components (after subtraction of streaming motions), normalized by the respective velocity dispersions. We test our VDF on 90 cluster-mass halos of a dissipationless cosmological simulation. Beyond the virial radius, $r_{\rm vir}$, our model VDF adequately reproduces that measured in the simulated halos, but no $q$-Gaussian model can adequately represent the VDF within $r_{\rm vir}$, as the speed distribution function is then flatter-topped than any $q$-Gaussian can allow. Nevertheless, our VDF fits significantly better the simulations than the commonly used Maxwellian (Gaussian) distribution, at virtually all radii within $5\,r_{\rm vir}$. Within 0.4 (1) $r_{\rm vir}$, the non-Gaussianity index $q$ is (roughly) linearly related to the slope of the density profile and also to the velocity anisotropy profile. We provide a parametrization of the modulation of $q$ with radius for both the median fits and the fit of the stacked halo. At radii of a few percent of $r_{\rm vir}$, corresponding to the Solar position in the Milky Way, our best-fit VDF, although fitting better the simulations than the Gaussian one, overproduces significantly the fraction of high velocity objects, indicating that one should not blindly use these $q$-Gaussian fits to make predictions on the direct detection rate of DM particles., Comment: This version consolidates the published version and the Erratum (changes in red)