arXiv subjects

Danny Horta

Publications and source records attributed to Danny Horta.

At least 37 records · Page 2Linked to original sources

arXiv2025

Chemical tagging with APOGEE, MUSE, and HST: constraints on the formation of $ω$ Centauri

A plethora of evidence suggests that $ω$ Centauri ($ω$ Cen) is the nuclear star cluster of a galaxy that merged with the Milky Way in early times. We use APOGEE, Gaia, MUSE, and HST data supplemented by galaxy chemical evolution models to place constraints on the assembly and chemical enrichment history of $ω$ Cen. The APOGEE data reveal three stellar populations occupying separate loci on canonical chemical planes. One population resembles metal-poor halo field stars (P1), a second shows light-element abundance anti-correlations typical of metal-poor globular clusters (IM), and a third population (P2) is characterised by an extreme "second-generation" abundance pattern. Both P1 and P2 populations cover a broad range of metallicity, consistent with extended histories of bursty star formation (SF), which is also evident from their light- and $α$-element abundance patterns. Conversely, the IM stars exhibit a narrow metallicity spread, combined with the Al-Mg, Na-O, and C-N anti-correlations common to metal-poor Galactic globular clusters. Moreover, these three populations alone seem to account for the distribution of $ω$ Cen stars in the chromosome map. We discuss these findings in context of a scenario according to which $ω$ Cen formed by a combination of in situ SF within the host galaxy (P1), followed by the spiralling in of gas-rich globular clusters (IM), leading to another burst of SF (P2). We perform a robust comparison of the chemical composition of $ω$ Cen with those of halo substructures well represented in APOGEE DR17, finding no chemical associations to a high confidence level.

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arXiv2025

Cosmological predictions for minor axis stellar density profiles in the inner regions of Milky Way-mass galaxies

$Λ$CDM cosmology predicts the hierarchical formation of galaxies which build up mass by merger events and accreting smaller systems. The stellar halo of the Milky Way has proven to be useful a tool for tracing this accretion history. However, most of this work has focused on the outer halo where dynamical times are large and the dynamical properties of accreted systems are preserved. In this work, we investigate the inner galaxy regime, where dynamical times are relatively small and systems are generally completely phase-mixed. Using the FIRE-2 and Auriga cosmological zoom-in simulation suites of Milky Way-mass galaxies, we find the stellar density profiles along the minor axis (perpendicular to the galactic disk) within the NFW scale radii (R$\approx$15 kpc) are best described as an exponential disk with scale height <0.3 kpc and a power law component with slope $α\approx$-4. The stellar density amplitude and slope for the power law component is not significantly correlated with metrics of the galaxy's accretion history. Instead, we find the stellar profiles strongly correlate with the dark matter profile. Across simulation suites, the galaxies studied in this work have a stellar to dark matter mass ratio that decreases as $1/r^2$ along the minor axis.

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arXiv2025

Modelling the density and mass of the Milky Way's proto-galaxy components with $APOGEE$-$Gaia$

Unravelling galaxy formation theory requires understanding galaxies both at high and low redshifts. A possible way to connect both realms is by studying the oldest stars in the Milky Way (i.e., the proto-Galaxy). We use the $APOGEE$-$Gaia$ surveys to perform a purely chemical dissection of Milky Way (MW) stellar populations, and identify samples of stars likely belonging to proto-Galactic fragments. The metallicity dependence of the distribution of old MW stars in the [Mg/Mn]-[Al/Fe] enables the distinction of at least two populations in terms of their star formation histories: a rapidly evolved population likely associated with the main progenitor system of the proto-MW; and populations characterised by less efficient, slower, star formation. In the Solar neighbourhood less efficient star forming populations are dominated by the $Gaia$-$Enceladus$/$Sausage$ accretion debris. In the inner Galaxy, they are largely associated with the $Heracles$ structure. We model the density of chemically defined proto-Galaxy populations, finding that they are well represented by a Plummer model with a scale radius of $a\sim3.5$ kpc, and an oblate ellipsoid with flattening parameters [$p\sim0.8$; $q\sim0.6$]; this finding indicates that the MW plausibly hosts a low-mass, metal-poor, bulge component. We integrate this density for $chemically$ $unevolved$ stars between $-2 < \mathrm{[Fe/H]} < -0.5$ to obtain a minimum stellar mass for the proto-Galaxy of $M_{*} (r<10~\mathrm{kpc}) = 9.1\pm0.2\times10^{8}$ M$_{\odot}$. Our results suggest the proto-Milky Way is at least comprised of two significant fragments: the main $in$ $situ$ progenitor and the $Heracles$ structure.

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arXiv2024

A slow spin to win -- the gradual evolution of the proto-Galaxy to the old disc

Observational studies are identifying stars thought to be remnants from the earliest stages of the hierarchical mass assembly of the Milky Way, referred to as the proto-Galaxy. We use red giant stars with kinematics and [$α$/M] and [M/H] estimates from Gaia DR3 data to investigate the relationship between azimuthal velocity and metallicity, aiming to understand the transition from a chaotic proto-Galaxy to a well-ordered, rotating (old) disc-like population. To analyse the structure of the data in [M/H]-v$_ϕ$ space for both high- and low-$α$ samples with carefully defined $α$-separation, we develop a model with two Gaussian components in v$_ϕ$: one representing a disc-like population and the other a halo-like population. This model is designed to capture the conditional distribution P(v$_ϕ$ $\mid$ [M/H]) with a 2-component Gaussian Mixture Model with fixed azimuthal velocities means and standard deviations. To quantify the spin-up of the high-$α$ disc population, we extend this two-component model by allowing the mean velocity and velocity dispersion to vary between the spline knots across the metallicity range used. We also compare our findings with existing literature using traditional Gaussian Mixture Modelling in bins of [M/H] and investigate using orbital circularity instead of azimuthal velocity. Our findings show that the metal-poor high-$α$ disc gradually spins up across [M/H] $\sim$ -1.7 to -1.0, while the low-$α$ sample exhibits a sharp transition at [M/H] $\sim$ -1.0. This latter result is due to the accreted debris dominating the metal-poor end, underscoring the critical role of [$α$/M] selection in studying the (old) disc evolution of the Milky Way. These results indicate that the proto-Galaxy underwent a slow, monotonic spin-up phase rather than a rapid, dramatic spin-up at [M/H] $\sim$ -1.0, as previously inferred.

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arXiv2024

[X/Fe] Marks the Spot: Mapping Chemical Azimuthal Variations in the Galactic Disk with APOGEE

Chemical cartography of the Galactic disk provides insights to its structure and assembly history over cosmic time. In this work, we use chemical cartography to explore chemical gradients and azimuthal substructure in the Milky Way disk with giant stars from APOGEE DR17. We confirm the existence of a radial metallicity gradient in the disk of $Δ$[Fe/H]/$Δ$R $\sim -0.066 \pm 0.0004$ dex/kpc and a vertical metallicity gradient of $Δ$[Fe/H]/$Δ$Z $\sim -0.164 \pm 0.001$ dex/kpc. We find azimuthal variations ($\pm0.1$ dex) on top of the radial metallicity gradient that have been previously established with other surveys. The APOGEE giants show strong correlations with stellar age and the intensity of azimuthal variations in iron; older stellar populations show the largest deviations from the radial metallicity gradient. Beyond iron, we show that other elements (e.g., Mg, O) display azimuthal variations at the $\pm0.05$ dex-level across the Galactic disk. We illustrate that moving into the orbit-space could help constrain the mechanisms producing these azimuthal metallicity variations. These results suggest that the spiral arms of the Galaxy are not solely responsible for azimuthal metallicity variations and other Galactic processes are at play.

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arXiv2024

Measuring Dwarf Galaxy Intrinsic Abundance Scatter with Mid-resolution Spectroscopic Surveys: Calibrating APOGEE Abundance Errors

The first generations of stars left their chemical fingerprints on metal-poor stars in the Milky Way and its surrounding dwarf galaxies. While instantaneous and homogeneous enrichment implies that groups of co-natal stars should have the same element abundances, small amplitudes of abundance scatter are seen at fixed [Fe/H]. Measurements of intrinsic abundance scatter have been made with small, high-resolution spectroscopic datasets where measurement uncertainty is small compared to this scatter. In this work, we present a method to use mid-resolution survey data, which has larger errors, to make this measurement. Using APOGEE DR17, we calculate the intrinsic scatter of Al, O, Mg, Si, Ti, Ni, and Mn relative to Fe for 333 metal-poor stars across 6 classical dwarf galaxies around the Milky Way, and 1604 stars across 19 globular clusters. We first calibrate the reported abundance errors in bins of signal-to-noise and [Fe/H] using a high-fidelity halo dataset. We then apply these calibrated errors to the APOGEE data, and find small amplitudes of average intrinsic abundance scatter in dwarf galaxies ranging from 0.032 - 0.14 dex with a median value of 0.043 dex. For the globular clusters, we find intrinsic scatters ranging from 0.018 - 0.21 dex, with particularly high scatter for Al and O. Our measurements of intrinsic abundance scatter place important upper limits on the intrinsic scatter in these systems, as well as constraints on their underlying star formation history and mixing, that we can look to simulations to interpret.

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arXiv2024

The imprint of dark matter on the Galactic acceleration field

Measurements of the accelerations of stars enabled by time-series extreme-precision spectroscopic observations, from pulsar timing, and from eclipsing binary stars in the Solar Neighborhood offer insights into the mass distribution of the Milky Way that do not rely on traditional equilibrium modeling. Given the measured accelerations, we can determine a total mass density, and from this, by accounting for the mass in stars, gas, and dust, we can infer the amount of dark matter. Leveraging the FIRE-2 simulations of Milky Way-mass galaxies, we compare vertical acceleration profiles between cold dark matter (CDM) and self-interacting dark matter (SIDM) with constant cross-section of 1 cm$^2$ g$^{-1}$ across three halos with diverse assembly histories. Notably, significant asymmetries in vertical acceleration profiles near the midplane at fixed radii are observed in both CDM and SIDM, particularly in halos recently affected by mergers with satellites of Sagittarius/SMC-like masses or greater. These asymmetries offer a unique window into exploring the merger history of a galaxy. We show that SIDM halos consistently exhibit higher local stellar and dark matter densities and steeper vertical acceleration gradients, up to 30% steeper near the Solar Neighborhood. SIDM halos also manifest a more oblate halo shape in the Solar Neighborhood. Furthermore, enhanced precision in acceleration measurements and larger datasets promise to provide better constraints on the local dark matter density, complementing our understanding from kinematic analysis of their distribution within galaxies.

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arXiv2024

Evidence of Truly Young high-$α$ Dwarf Stars

The existence of high-$α$ stars with inferred ages < 6 Gyr has been confirmed recently with large spectroscopic and photometric surveys. However, stellar mergers or binary interactions can induce properties associated with young ages, such as high mass, rapid rotation, or high activity, even in old populations. Literature studies have confirmed that at least some of these apparently young stars are old merger products. However, none have ruled out the possibility of genuinely young high-$α$ stars. Because cool GKM dwarfs spin down, rapid rotation can be used to indicate youth. In this paper, we provide strong evidence that truly young high-$α$ stars exist by studying high-$α$ rotators in the Kepler and K2 field with abundance measurements from GALAH and APOGEE. After excluding close binaries using radial velocity (RV) measurements from Gaia DR3 and multi-epoch RVs from APOGEE, we find a total of 70 high-$α$ rapid rotators with periods ~10-30 days, 29 of which have lithium measurements from GALAH, indicating that they have not gone through past mass transfer or stellar merger events. We identify 10 young high-$α$ candidates with no signs of merger-induced mixing or close companions. One clear example is a G dwarf with a measurable rotation and an age of 1.98$^{+0.12}_{-0.28}$ Gyr that is likely a single star with multiple RV measurements from APOGEE, has significant lithium detection from GALAH (A(Li) = 1.79), and has no signs of planet engulfment.

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arXiv2024

2-process Model and Residual Abundance Analysis of the Milky Way Massive Satellites

The ``2-process Model'' is a promising technique for interpreting stellar chemical abundance data from large-scale surveys (e.g., SDSS-IV/V, GALAH), enabling more quantitative empirical studies of differences in chemical enrichment history between galaxies without relying on detailed yield and evolution models. In this work, we fit 2-process model parameters to (1) a luminous giant Milky Way (MW) sample and (2) stars comprising the Sagittarius Dwarf Galaxy (Sgr). We then use these two sets of model parameters to predict the abundances of 14 elements of stars belonging to the MW and in five of its massive satellite galaxies, analyzing the residuals between the predicted and observed abundances. We find that the model fit to (1) results in large residuals (0.1-0.3 dex) for most metallicity-dependent elements in the metal-rich ([Mg/H] $>$ -0.8) stars of the satellite galaxies. However, the model fit to (2) results in small or no residuals for all elements across all satellite galaxies. Therefore, despite the wide variation in [X/Mg]-[Mg/H] abundance patterns of the satellite galaxies, the 2-process framework provides an accurate characterization of their abundance patterns across many elements, but these multi-element patterns are systematically different between the dwarf galaxy satellites and the MW disks. We consider a variety of scenarios for the origin of this difference, highlighting the possibility that a large inflow of pristine gas to the MW disk diluted the metallicity of star-forming gas without changing abundance ratios.

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arXiv2024

Stellar Mergers or Truly Young? Intermediate-Age Stars on Highly-Radial Orbits in the Milky Way's Stellar Halo

Reconstructing the mass assembly history of the Milky Way relies on obtaining detailed measurements of the properties of many stars in the Galaxy, especially in the stellar halo. One of the most constraining quantities is stellar age, as it can shed light on the accretion time and quenching of star formation in merging satellites. However, obtaining reliable age estimates for large samples of halo stars is difficult. We report published ages of 120 subgiant halo stars with highly-radial orbits that likely belong to the debris of the \textsl{Gaia-Enceladus/Sausage}~(GES) galaxy. The majority of these halo stars are old, with an age distribution characterized by a median of 11.6~Gyr and 16$^{\rm th}$(84$^{\rm th}$) percentile of 10.5~(12.7)~Gyr. However, the distribution is skewed, with a tail of younger stars that span ages down to $\sim6$--$9$ Gyr. All highly-radial halo stars have chemical and kinematic/orbital quantities that associate them with the GES debris. Initial results suggest that these intermediate-age stars are not a product of mass transfer and/or stellar mergers, which can bias their age determination low. If this conclusion is upheld by upcoming spectro-photometric studies, then the presence of these stars will pose an important challenge for constraining the properties of the GES merger and the accretion history of the Galaxy.

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arXiv2024

The Extremely Metal Rich Knot of Stars at the Heart of the Galaxy

We show with Gaia XP spectroscopy that extremely metal-rich stars in the Milky Way (EMR; $[M/H]_{XP} > 0.5$) - but only those - are largely confined to a tight "knot" at the center of the Galaxy. This EMR knot is round in projection, has a fairly abrupt edge near $\sim 1.5$kpc, and is a dynamically hot system. This central knot also contains very metal-rich (VMR; $+0.2\le [M/H]_{XP} \le +0.4$) stars. However, in contrast to EMR stars, the bulk of VMR stars form an extended, highly flattened distribution in the inner Galaxy ($R_{\mathrm{GC}}\lesssim 5$ kpc). We draw on TNG50 simulations of Milky Way analogs for context and find that compact, metal-rich knots confined to $<1.5$kpc are a universal feature. In typical simulated analogs, the top 5-10% most metal-rich stars are confined to a central knot; however, in our Milky Way data this fraction is only 0.1%. Dust-penetrating wide-area near-infrared spectroscopy, such as SDSS-V, will be needed for a rigorous estimate of the fraction of stars in the Galactic EMR knot. Why in our Milky Way only EMR giants are confined to such a central knot remains to be explained. Remarkably, the central few kiloparsecs of the Milky Way harbor both the highest concentration of metal-poor stars (the `poor old heart') and almost all EMR stars. This highlights the stellar population diversity at the bottom of galactic potential wells.

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arXiv2024

The Debris of the "Last Major Merger" is Dynamically Young

The Milky Way's (MW) inner stellar halo contains an [Fe/H]-rich component with highly eccentric orbits, often referred to as the "last major merger." Hypotheses for the origin of this component include Gaia-Sausage/Enceladus (GSE), where the progenitor collided with the MW proto-disk 8-11 Gyr ago, and the Virgo Radial Merger (VRM), where the progenitor collided with the MW disk within the last 3 Gyr. These two scenarios make different predictions about observable structure in local phase space, because the morphology of debris depends on how long it has had to phase mix. The recently-identified phase-space folds in Gaia DR3 have positive caustic velocities, making them fundamentally different than the phase-mixed chevrons found in simulations at late times. Roughly 20\% of the stars in the prograde local stellar halo are associated with the observed caustics. Based on a simple phase-mixing model, the observed number of caustics are consistent with a merger that occurred 1--2 Gyr ago. We also compare the observed phase-space distribution to FIRE-2 Latte simulations of GSE-like mergers, using a quantitative measurement of phase mixing (2D causticality). The observed local phase-space distribution best matches the simulated data 1--2 Gyr after collision, and certainly not later than 3 Gyr. This is further evidence that the progenitor of the "last major merger" did not collide with the MW proto-disk at early times, as is thought for the GSE, but instead collided with the MW disk within the last few Gyr, consistent with the body of work surrounding the VRM.

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arXiv2024

On the mass assembly history of the Milky Way: clues from its stellar halo

Stellar halos of galaxies retain crucial clues to their mass assembly history. It is in these galactic components that the remains of cannibalised galactic building blocks are deposited. For the case of the Milky Way, the opportunity to analyse the stellar halo's structure on a star-by-star basis in a multi-faceted approach provides a basis from which to infer its past and assembly history in unrivalled detail. Moreover, the insights that can be gained about the formation of the Galaxy not only help constrain the evolution of our Milky Way, but may also help place constraints on the formation of other disc galaxies in the Universe. This paper includes a summary of work undertaken during a PhD thesis aiming to make progress toward answering the most fundamental question in the field of Galactic archaeology: "How did the Milky Way form?" Through the effort to answer this question, we summarise new insights into aspects of the history of assembly and evolution of our Galaxy and measurements of the structure of various of its Galactic components.

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arXiv2024

Disentangling the Galaxy's Gordian knot: evidence from $APOGEE-Gaia$ for a knotted and slower bar in the Milky Way

The inner $\sim5$ kiloparsec (kpc) region of the Milky Way is complex. Unravelling the evolution of the Galaxy requires precise understanding of the formation of this region. We report a study focused on disentangling the inner Galaxy ($r < 5$ kpc) using the measured positions, velocities, and element abundance ratios of red giant stars from the $APOGEE-Gaia$ surveys. After removing the stellar halo, inner Galaxy populations can be grouped into three main components based on their angular momentum: bar, disc, and a previously unreported ``knot'' component. The knot has a spheroidal shape, is concentrated in the inner $\sim1.5$ kpc, is comprised of stars on nearly-radial orbits, and contains stars with super-solar [Fe/H] element abundances. The chemical compositions of the knot are qualitatively similar to the Galactic bar and inner disc, suggestive that these three populations share a common genesis; the chemical/dynamic properties of the knot suggest it could constitute a classical bulge formed via secular evolution. Moreover, our results show that the bar is more slowly rotating than previously thought, with a pattern speed of $Ω_{\mathrm{bar}}=24\pm3$ km s$^{-1}$ kpc$^{-1}$. This new estimate suggests that the influence of the bar extends beyond the solar radius, with $R_{\mathrm{CR}}\sim9.4-9.8$ kpc, depending on the adopted Milky Way rotation curve; it also suggests a ratio of corotation to bar length of $\mathcal{R}\sim1.8-2$. Our findings help place constraints on the formation and evolution of inner Galaxy populations, and directly constrain dynamical studies of the Milky Way bar and stars in the solar neighbourhood.

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arXiv2024

Radial phase spirals in the Solar neighbourhood

The second data release of ESA's $Gaia$ mission revealed numerous signatures of disequilibrium in the Milky Way's disc. These signatures are seen in the planar kinematics of stars, which manifest as ridges and ripples in $R-v_ϕ$, and in vertical kinematics, where a prominent spiral is seen in the $z-v_z$ phase space. In this work, we show an equivalent $ΔR-v_{\mathrm{R}}$ phase spiral forms following a perturbation to the disc. We demonstrate the behaviour of the $ΔR-v_{\mathrm{R}}$ phase spirals in both a toy model and a high resolution $N$-body simulation of a satellite interaction. We then confront these models with the data, where we find partial $ΔR-v_{\mathrm{R}}$ phase spirals in the Solar neighborhood using the most recent data from $Gaia$ DR3. This structure indicates ongoing radial phase mixing in the Galactic disc, suggesting a history of recent perturbations, either through internal or external (e.g., satellite) processes. Future work modelling the $z-v_z$ and $ΔR-v_{\mathrm{R}}$ phase spirals in tandem may help break degeneracy's between possible origins of the perturbation.

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arXiv2024

Data-driven Dynamics with Orbital Torus Imaging: A Flexible Model of the Vertical Phase Space of the Galaxy

The vertical kinematics of stars near the Sun can be used to measure the total mass distribution near the Galactic disk and to study out-of-equilibrium dynamics. With contemporary stellar surveys, the tracers of vertical dynamics are so numerous and so well measured that the shapes of underlying orbits are almost directly visible in the data through element abundances or even stellar density. These orbits can be used to infer a mass model for the Milky Way, enabling constraints on the dark matter distribution in the inner galaxy. Here we present a flexible model for foliating the vertical position-velocity phase space with orbits, for use in data-driven studies of dynamics. The vertical acceleration profile in the vicinity of the disk, along with the orbital actions, angles, and frequencies for individual stars, can all be derived from that orbit foliation. We show that this framework - "Orbital Torus Imaging" (OTI) - is rigorously justified in the context of dynamical theory, and does a good job of fitting orbits to simulated stellar abundance data with varying degrees of realism. OTI (1) does not require a global model for the Milky Way mass distribution, and (2) does not require detailed modeling of the selection function of the input survey data. We discuss the approximations and limitations of the OTI framework, which currently trades dynamical interpretability for flexibility in representing the data in some regimes, and which also presently separates the vertical and radial dynamics. We release an open-source tool, torusimaging, to accompany this article.

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arXiv2024

Spectacular nucleosynthesis from early massive stars

Stars formed with initial mass over 50 Msun are very rare today, but they are thought to be more common in the early universe. The fates of those early, metal-poor, massive stars are highly uncertain. Most are expected to directly collapse to black holes, while some may explode as a result of rotationally powered engines or the pair-creation instability. We present the chemical abundances of J0931+0038, a nearby low-mass star identified in early followup of SDSS-V Milky Way Mapper, which preserves the signature of unusual nucleosynthesis from a massive star in the early universe. J0931+0038 has relatively high metallicity ([Fe/H] = -1.76 +/- 0.13) but an extreme odd-even abundance pattern, with some of the lowest known abundance ratios of [N/Fe], [Na/Fe], [K/Fe], [Sc/Fe], and [Ba/Fe]. The implication is that a majority of its metals originated in a single extremely metal-poor nucleosynthetic source. An extensive search through nucleosynthesis predictions finds a clear preference for progenitors with initial mass > 50 Msun, making J0931+0038 one of the first observational constraints on nucleosynthesis in this mass range. However the full abundance pattern is not matched by any models in the literature. J0931+0038 thus presents a challenge for the next generation of nucleosynthesis models and motivates study of high-mass progenitor stars impacted by convection, rotation, jets, and/or binary companions. Though rare, more examples of unusual early nucleosynthesis in metal-poor stars should be found in upcoming large spectroscopic surveys.

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arXiv2023

Orbital Torus Imaging: Acceleration, density, and dark matter in the Galactic disk measured with element abundance gradients

Under the assumption of a simple and time-invariant gravitational potential, many Galactic dynamics techniques infer the Milky Way's mass and dark matter distribution from stellar kinematic observations. These methods typically rely on parameterized potential models of the Galaxy and must take into account non-trivial survey selection effects, because they make use of the density of stars in phase space. Large-scale spectroscopic surveys now supply information beyond kinematics in the form of precise stellar label measurements (especially element abundances). These element abundances are known to correlate with orbital actions or other dynamical invariants. Here, we use the Orbital Torus Imaging (OTI) framework that uses abundance gradients in phase space to map orbits. In many cases these gradients can be measured without detailed knowledge of the selection function. We use stellar surface abundances from the APOGEE survey combined with kinematic data from the Gaia mission. Our method reveals the vertical ($z$-direction) orbit structure in the Galaxy and enables empirical measurements of the vertical acceleration field and orbital frequencies in the disk. From these measurements, we infer the total surface mass density, $Σ$, and midplane volume density, $ρ_0$, as a function of Galactocentric radius and height. Around the Sun, we find $Σ_{\odot}(z=1.1$ kpc)$=72^{+6}_{-9}$M$_{\odot}$pc$^{-2}$ and $ρ_{\odot}(z=0)=0.081^{+0.015}_{-0.009}$ M$_{\odot}$pc$^{-3}$ using the most constraining abundance ratio, [Mg/Fe]. This corresponds to a dark matter contribution in surface density of $Σ_{\odot,\mathrm{DM}}(z=1.1$ kpc)$=24\pm4$ M$_{\odot}$pc$^{-2}$, and in total volume mass density of $ρ_{\odot,\mathrm{DM}}(z=0)=0.011\pm0.002$ M$_{\odot}$pc$^{-3}$. Moreover, using these mass density values we estimate the scale length of the low-$α$ disc to be $h_R=2.24\pm0.06$kpc.

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