arXiv subjects

Jennifer A. Johnson

Publications and source records attributed to Jennifer A. Johnson.

At least 55 records · Page 3Linked to original sources

arXiv2021

Final Targeting Strategy for the SDSS-IV APOGEE-2N Survey

APOGEE-2 is a dual-hemisphere, near-infrared (NIR), spectroscopic survey with the goal of producing a chemo-dynamical mapping of the Milky Way Galaxy. The targeting for APOGEE-2 is complex and has evolved with time. In this paper, we present the updates and additions to the initial targeting strategy for APOGEE-2N presented in Zasowski et al. (2017). These modifications come in two implementation modes: (i) "Ancillary Science Programs" competitively awarded to SDSS-IV PIs through proposal calls in 2015 and 2017 for the pursuit of new scientific avenues outside the main survey, and (ii) an effective 1.5-year expansion of the survey, known as the Bright Time Extension, made possible through accrued efficiency gains over the first years of the APOGEE-2N project. For the 23 distinct ancillary programs, we provide descriptions of the scientific aims, target selection, and how to identify these targets within the APOGEE-2 sample. The Bright Time Extension permitted changes to the main survey strategy, the inclusion of new programs in response to scientific discoveries or to exploit major new datasets not available at the outset of the survey design, and expansions of existing programs to enhance their scientific success and reach. After describing the motivations, implementation, and assessment of these programs, we also leave a summary of lessons learned from nearly a decade of APOGEE-1 and APOGEE-2 survey operations. A companion paper, Santana et al. (submitted), provides a complementary presentation of targeting modifications relevant to APOGEE-2 operations in the Southern Hemisphere.

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arXiv2021

Final Targeting Strategy for the SDSS-IV APOGEE-2S Survey

APOGEE is a high-resolution (R sim 22,000), near-infrared, multi-epoch, spectroscopic survey of the Milky Way. The second generation of the APOGEE project, APOGEE-2, includes an expansion of the survey to the Southern Hemisphere called APOGEE-2S. This expansion enabled APOGEE to perform a fully panoramic mapping of all the main regions of the Milky Way; in particular, by operating in the H-band, APOGEE is uniquely able to probe the dust-hidden inner regions of the Milky Way that are best accessed from the Southern Hemisphere. In this paper we present the targeting strategy of APOGEE-2S, with special attention to documenting modifications to the original, previously published plan. The motivation for these changes is explained as well as an assessment of their effectiveness in achieving their intended scientific objective. In anticipation of this being the last paper detailing APOGEE targeting, we present an accounting of all such information complete through the end of the APOGEE-2S project; this includes several main survey programs dedicated to exploration of major stellar populations and regions of the Milky Way, as well as a full list of programs contributing to the APOGEE database through allocations of observing time by the Chilean National Time Allocation Committee (CNTAC) and the Carnegie Institution for Science (CIS). This work was presented along with a companion article, R. Beaton et al. (submitted; AAS29028), presenting the final target selection strategy adopted for APOGEE-2 in the Northern Hemisphere.

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arXiv2021

Chemical Cartography with APOGEE: Mapping Disk Populations with a Two-Process Model and Residual Abundances

We apply a novel statistical analysis to measurements of 16 elemental abundances in 34,410 Milky Way disk stars from the final data release (DR17) of APOGEE-2. Building on recent work, we fit median abundance ratio trends [X/Mg] vs. [Mg/H] with a 2-process model, which decomposes abundance patterns into a "prompt" component tracing core collapse supernovae and a "delayed" component tracing Type Ia supernovae. For each sample star, we fit the amplitudes of these two components, then compute the residuals Δ[X/H] from this two-parameter fit. The rms residuals range from ~0.01-0.03 dex for the most precisely measured APOGEE abundances to ~0.1 dex for Na, V, and Ce. The correlations of residuals reveal a complex underlying structure, including a correlated element group comprised of Ca, Na, Al, K, Cr, and Ce and a separate group comprised of Ni, V, Mn, and Co. Selecting stars poorly fit by the 2-process model reveals a rich variety of physical outliers and sometimes subtle measurement errors. Residual abundances allow comparison of populations controlled for differences in metallicity and [α/Fe]. Relative to the main disk (R=3-13 kpc, |Z|<2 kpc), we find nearly identical abundance patterns in the outer disk (R=15-17 kpc), 0.05-0.2 dex depressions of multiple elements in LMC and Gaia Sausage/Enceladus stars, and wild deviations (0.4-1 dex) of multiple elements in ωCen. Residual abundance analysis opens new opportunities for discovering chemically distinctive stars and stellar populations, for empirically constraining nucleosynthetic yields, and for testing chemical evolution models that include stochasticity in the production and redistribution of elements.

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arXiv2021

Searching For Transiting Planets Around Halo Stars. I. Sample Selection and Validation

By measuring the elemental abundances of a star, we can gain insight into the composition of its initial gas cloud -- the formation site of the star and its planets. Planet formation requires metals, the availability of which is determined by the elemental abundance. In the case where metals are extremely deficient, planet formation can be stifled. To investigate such a scenario requires a large sample of metal-poor stars and a search for planets therein. This paper focuses on the selection and validation of a halo star sample. We select ~17,000 metal-poor halo stars based on their Galactic kinematics, and confirm their low metallicities ([Fe/H] < -0.5), using spectroscopy from the literature. Furthermore, we perform high-resolution spectroscopic observations using LBT/PEPSI and conduct detailed metallicity ([Fe/H]) analyses on a sample of 13 previously known halo stars that also have hot kinematics. We can use the halo star sample presented here to measure the frequency of planets and to test planet formation in extremely metal-poor environments. The result of the planet search and its implications will be presented and discussed in a companion paper by Boley et al.

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arXiv2021

CNO dredge-up in a sample of APOGEE/Kepler red giants: Tests of stellar models and Galactic evolutionary trends of N/O and C/N

Surface abundances of C, N, and O in red giants are affected by processed material mixed into the stars' convective envelopes. Using a sample of $\sim 5100$ stars with elemental abundances from APOGEE and asteroseismic masses from {\it Kepler}, we test theoretical stellar models that predict this mixing, then apply these models to derive birth C, N, and O abundances for these stars. Our models with standard mixing can reproduce the observed trends to within plausible uncertainties in the birth abundances. Some models with ''extra'' mixing processes fail, predicting trends with surface gravity or evolutionary state that are not observed. Applying mixing corrections to the APOGEE abundances removes the observed age-dependence of log(N/O) and log(C/N), but it leaves trends of log(N/O) and log(C/N) with metallicity, as expected based on nucleosynthesis models. The stellar N/O trend agrees well with Dopita et al.'s calibration of gas phase log(N/O) with metallicity, and with gas phase trends in the MaNGA integral field survey of nearby galaxies. We also find a substantial separation in birth [N/Mg] ratios between high-[$α$/Fe] (''thick disc'') stars and low-[$α$/Fe] (''thin disc'') stars. We find a smaller but still clear separation for [C/Mg]. The trends of birth C and N abundances with [Fe/H] and [$α$/Fe] could affect spectroscopic age estimates for red giants that rely on the observed C/N ratio as a diagnostic of stellar mass.

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arXiv2021

An Intermediate-age Alpha-rich Galactic Population in K2

We explore the relationships between the chemistry, ages, and locations of stars in the Galaxy using asteroseismic data from the K2 mission and spectroscopic data from the Apache Point Galactic Evolution Experiment survey. Previous studies have used giant stars in the Kepler field to map the relationship between the chemical composition and the ages of stars at the solar circle. Consistent with prior work, we find that stars with high [Alpha/Fe] have distinct, older ages in comparison to stars with low [Alpha/Fe]. We provide age estimates for red giant branch (RGB) stars in the Kepler field, which support and build upon previous age estimates by taking into account the effect of alpha-enrichment on opacity. Including this effect for [Alpha/Fe]-rich stars results in up to 10% older ages for low-mass stars relative to corrected solar mixture calculations. This is a significant effect that Galactic archaeology studies should take into account. Looking beyond the Kepler field, we estimate ages for 735 red giant branch stars from the K2 mission, mapping age trends as a function of the line of sight. We find that the age distributions for low- and high-[Alpha/Fe] stars converge with increasing distance from the Galactic plane, in agreement with suggestions from earlier work. We find that K2 stars with high [Alpha/Fe] appear to be younger than their counterparts in the Kepler field, overlapping more significantly with a similarly aged low-[Alpha/Fe] population. This observation may suggest that star formation or radial migration proceeds unevenly in the Galaxy.

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arXiv2021

Analytic Estimates of the Achievable Precision on the Physical Properties of Transiting Planets Using Purely Empirical Measurements

We present analytic estimates of the fractional uncertainties on the mass, radius, surface gravity, and density of a transiting planet, using only empirical or semi-empirical measurements. We first express these parameters in terms of transit photometry and radial velocity (RV) observables, as well as the stellar radius $R_{\star}$, if required. In agreement with previous results, we find that, assuming a circular orbit, the surface gravity of the planet ($g_p$) depends only on empirical transit and RV parameters; namely, the planet period $P$, the transit depth $δ$, the RV semi-amplitude $K_{\star}$, the transit duration $T$, and the ingress/egress duration $τ$. However, the planet mass and density depend on all these quantities, plus $R_{\star}$. Thus, an inference about the planet mass, radius, and density must rely upon an external constraint such as the stellar radius. For bright stars, stellar radii can now be measured nearly empirically by using measurements of the stellar bolometric flux, the effective temperature, and the distance to the star via its parallax, with the extinction $A_V$ being the only free parameter. For any given system, there is a hierarchy of achievable precisions on the planetary parameters, such that the planetary surface gravity is more accurately measured than the density, which in turn is more accurately measured than the mass. We find that surface gravity provides a strong constraint on the core mass fraction of terrestrial planets. This is useful, given that the surface gravity may be one of the best measured properties of a terrestrial planet.

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arXiv2020

The K2 Galactic Archaeology Program Data Release 2: Asteroseismic results from campaigns 4, 6, & 7

Studies of Galactic structure and evolution have benefitted enormously from Gaia kinematic information, though additional, intrinsic stellar parameters like age are required to best constrain Galactic models. Asteroseismology is the most precise method of providing such information for field star populations $\textit{en masse}$, but existing samples for the most part have been limited to a few narrow fields of view by the CoRoT and Kepler missions. In an effort to provide well-characterized stellar parameters across a wide range in Galactic position, we present the second data release of red giant asteroseismic parameters for the K2 Galactic Archaeology Program (GAP). We provide $ν_{\mathrm{max}}$ and $Δν$ based on six independent pipeline analyses; first-ascent red giant branch (RGB) and red clump (RC) evolutionary state classifications from machine learning; and ready-to-use radius & mass coefficients, $κ_R$ & $κ_M$, which, when appropriately multiplied by a solar-scaled effective temperature factor, yield physical stellar radii and masses. In total, we report 4395 radius and mass coefficients, with typical uncertainties of $3.3\% \mathrm{\ (stat.)} \pm 1\% \mathrm{\ (syst.)}$ for $κ_R$ and $7.7\% \mathrm{\ (stat.)} \pm 2\% \mathrm{\ (syst.)}$ for $κ_M$ among RGB stars, and $5.0\% \mathrm{\ (stat.)} \pm 1\% \mathrm{\ (syst.)}$ for $κ_R$ and $10.5\% \mathrm{\ (stat.)} \pm 2\% \mathrm{\ (syst.)}$ for $κ_M$ among RC stars. We verify that the sample is nearly complete -- except for a dearth of stars with $ν_{\mathrm{max}} \lesssim 10-20μ$Hz -- by comparing to Galactic models and visual inspection. Our asteroseismic radii agree with radii derived from Gaia Data Release 2 parallaxes to within $2.2 \pm 0.3\%$ for RGB stars and $2.0 \pm 0.6\%$ for RC stars.

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arXiv2020

Response to Comment on "A Non-Interacting Low-Mass Black Hole -- Giant Star Binary System"

van den Heuvel & Tauris argue that if the red giant star in the system 2MASS J05215658+4359220 has a mass of 1 solar mass (M$_\odot$), then its unseen companion could be a binary composed of two 0.9 M$_\odot$ stars, making a triple system. We contend that the existing data are most consistent with a giant of mass $3.2^{+1.0}_{-1.0}$ M$_\odot$, implying a black hole companion of $3.3^{+2.8}_{-0.7}$ M$_\odot$.

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arXiv2020

Stellar Characterization of M-dwarfs from the APOGEE Survey: A Calibrator Sample for the M-dwarf Metallicities

We present spectroscopic determinations of the effective temperatures, surface gravities and metallicities for 21 M-dwarfs observed at high-resolution (R $\sim$ 22,500) in the \textit{H}-band as part of the SDSS-IV APOGEE survey. The atmospheric parameters and metallicities are derived from spectral syntheses with 1-D LTE plane parallel MARCS models and the APOGEE atomic/molecular line list, together with up-to-date H$_{2}$O and FeH molecular line lists. Our sample range in $T_{\rm eff}$ from $\sim$ 3200 to 3800K, where eleven stars are in binary systems with a warmer (FGK) primary, while the other 10 M-dwarfs have interferometric radii in the literature. We define an $M_{K_{S}}$--Radius calibration based on our M-dwarf radii derived from the detailed analysis of APOGEE spectra and Gaia DR2 distances, as well as a mass-radius relation using the spectroscopically-derived surface gravities. A comparison of the derived radii with interferometric values from the literature finds that the spectroscopic radii are slightly offset towards smaller values, with $Δ$ = -0.01 $\pm$ 0.02 $R{\star}$/$R_{\odot}$. In addition, the derived M-dwarf masses based upon the radii and surface gravities tend to be slightly smaller (by $\sim$5-10\%) than masses derived for M-dwarf members of eclipsing binary systems for a given stellar radius. The metallicities derived for the 11 M-dwarfs in binary systems, compared to metallicities obtained for their hotter FGK main-sequence primary stars from the literature, shows excellent agreement, with a mean difference of [Fe/H](M-dwarf - FGK primary) = +0.04 $\pm$ 0.18 dex, confirming the APOGEE metallicity scale derived here for M-dwarfs.

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arXiv2019

Abundance ratios in GALAH DR2 and their implications for nucleosynthesis

Using a sample of 70 924 stars from the second data release of the GALAH optical spectroscopic survey, we construct median sequences of [X/Mg] vs. [Mg/H] for 21 elements, separating the high-$α$/``low-Ia'' and low-$α$/``high-Ia'' stellar populations through cuts in [Mg/Fe]. Previous work with the near-IR APOGEE survey has shown that such sequences are nearly independent of location in the Galactic disk, implying that they are determined by stellar nucleosynthesis yields with little sensitivity to other chemical evolution aspects. The separation between the two [X/Mg] sequences indicates the relative importance of prompt and delayed enrichment mechanisms, while the sequences' slopes indicate metallicity dependence of the yields. GALAH and APOGEE measurements agree for some of their common elements, but differ in sequence separation or metallicity trends for others. GALAH offers access to nine new elements. We infer that about $75\%$ of solar C comes from core collapse supernovae and $25\%$ from delayed mechanisms. We find core collapse fractions of $60-80\%$ for the Fe-peak elements Sc, Ti, Cu, and Zn, with strong metallicity dependence of the core collapse Cu yield. For the neutron capture elements Y, Ba, and La, we infer large delayed contributions with non-monotonic metallicity dependence. The separation of the [Eu/Mg] sequences implies that at least $\sim30\%$ of Eu enrichment is delayed with respect to star formation. We compare our results to predictions of several supernova and AGB yield models; C, Na, K, Mn, and Ca all show discrepancies with models that could make them useful diagnostics of nucleosynthesis physics.

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arXiv2019

Insights from the APOKASC Determination of the Evolutionary State of Red-Giant Stars by consolidation of different methods

The internal working of low-mass stars is of great significance to both the study of stellar structure and the history of the Milky Way. Asteroseismology has the power to directly sense the internal structure of stars and allows for the determination of the evolutionary state -- i.e. has helium burning commenced or is the energy generated only by the fusion in the hydrogen-burning shell? We use observational data from red-giant stars in a combination (known as APOKASC) of asteroseismology (from the \textit{Kepler} mission) and spectroscopy (from SDSS/APOGEE). The new feature of the analysis is that the APOKASC evolutionary state determination is based on the comparison of diverse approaches to the investigation of the frequency-power spectrum. The high level of agreement between the methods is a strong validation of the approaches. Stars for which there is not a consensus view are readily identified. The comparison also facilitates the identification of unusual stars including those that show evidence for very strong coupling between p and g cavities. The comparison between the classification based on the spectroscopic data and asteroseismic data have led to a new value for the statistical uncertainty in APOGEE temperatures. These consensus evolutionary states will be used as an input for methods that derive masses and ages for these stars based on comparison of observables with stellar evolutionary models (`grid-based modeling') and as a training set for machine-learning and other data-driven methods of evolutionary state determination

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arXiv2019

The Origin of Elements Across Cosmic Time: Astro2020 Science White Paper

The problem of the origin of the elements is a fundamental one in astronomy and one that has many open questions. Prominent examples include (1) the nature of Type Ia supernovae and the timescale of their contributions; (2) the observational identification of elements such as titanium and potassium with the $α$-elements in conflict with core-collapse supernova predictions; (3) the number and relative importance of r-process sites; (4) the origin of carbon and nitrogen and the influence of mixing and mass loss in winds; and (5) the origin of the intermediate elements, such as Cu, Ge, As, and Se, that bridge the region between charged-particle and neutron-capture reactions. The next decade will bring to maturity many of the new tools that have recently made their mark, such as large-scale chemical cartography of the Milky Way and its satellites, the addition of astrometric and asteroseismic information, the detection and characterization of gravitational wave events, 3-D simulations of convection and model atmospheres, and improved laboratory measurements for transition probabilities and nuclear masses. All of these areas are key for continued improvement, and such improvement will benefit many areas of astrophysics.

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arXiv2019

Origin of $α$-rich young stars: clues from C, N and O

A small set of chemically old stars that appear young by their independently derived masses has been detected. These are so-called $α$-rich young stars. For a sample of 51 red-giant stars, for which spectra are available from SDSS/APOGEE and masses are available from asteroseismic measures based on \textit{Kepler} lightcurves, we derive the C, N and O abundances through an independent analysis. These stars span a wide range of N/C surface number density ratios. We interpret the high-mass stars with low N/C as being products of mergers or mass transfer during or after first dredge up, because the dredge-up features are the same as for low-mass stars. The $α$-rich young stars with high N/C follow the expected trend of N/C for their mass, and could be either genuine young stars (leaving their high [$α$/Fe] unexplained) or the results of mergers on the main sequence.

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arXiv2019

Discovery of a Candidate Black Hole - Giant Star Binary System in the Galactic Field

We report the discovery of the first likely black hole in a non-interacting binary system with a field red giant. By combining radial velocity measurements from the Apache Point Observatory Galactic Evolution Experiment (APOGEE) with photometric variability data from the All-Sky Automated Survey for Supernovae (ASAS-SN), we identified the bright rapidly-rotating giant 2MASS J05215658+4359220 as a binary system with a massive unseen companion. Subsequent radial velocity measurements reveal a system with an orbital period of 83 days and near-zero eccentricity. The photometric variability period of the giant is consistent with the orbital period, indicative of star spots and tidal synchronization. Constraints on the giant's mass and radius from its luminosity, surface gravity, and temperature imply an unseen companion with mass of $3.3^{+2.8}_{-0.7}$ M$_\odot$, indicating a low-mass black hole or an exceedingly massive neutron star. Measurement of the astrometric binary motion by {\it Gaia} will further characterize the system. This discovery demonstrates the potential of massive spectroscopic surveys like APOGEE and all-sky, high-cadence photometric surveys like ASAS-SN to revolutionize our understanding of the compact object mass function, and to test theories of binary star evolution and the supernova mechanism.

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arXiv2019

Constraining Metallicity-dependent Mixing and Extra Mixing using [C/N] in Alpha-Rich Field Giants

Internal mixing on the giant branch is an important process which affects the evolution of stars and the chemical evolution of the galaxy. While several mechanisms have been proposed to explain this mixing, better empirical constraints are necessary. Here, we use [C/N] abundances in 26097 evolved stars from the SDSS-IV/APOGEE-2 Data Release 14 to trace mixing and extra mixing in old field giants with -1.7< [Fe/H] < 0.1. We show that the APOGEE [C/N] ratios before any dredge-up occurs are metallicity dependent, but that the change in [C/N] at the first dredge-up is metallicity independent for stars above [Fe/H] ~ -1. We identify the position of the red giant branch (RGB) bump as a function of metallicity, note that a metallicity-dependent extra mixing episode takes place for low-metallicity stars ([Fe/H] <-0.4) 0.14 dex in log g above the bump, and confirm that this extra mixing is stronger at low metallicity, reaching $Δ$ [C/N] = 0.58 dex at [Fe/H] = -1.4. We show evidence for further extra mixing on the upper giant branch, well above the bump, among the stars with [Fe/H] < -1.0. This upper giant branch mixing is stronger in the more metal-poor stars, reaching 0.38 dex in [C/N] for each 1.0 dex in log g. The APOGEE [C/N] ratios for red clump (RC) stars are significantly higher than for stars at the tip of the RGB, suggesting additional mixing processes occur during the helium flash or that unknown abundance zero points for C and N may exist among the red clump RC sample. Finally, because of extra mixing, we note that current empirical calibrations between [C/N] ratios and ages cannot be naively extrapolated for use in low-metallicity stars specifically for those above the bump in the luminosity function.

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arXiv2018

APOGEE [C/N] Abundances Across the Galaxy: Migration and Infall from Red Giant Ages

We present [C/N]-[Fe/H] abundance trends from the SDSS-IV Apache Point Observatory Galactic Evolution Experiment (APOGEE) survey, Data Release 14 (DR14), for red giant branch stars across the Milky Way Galaxy (MW, 3 kpc $<$ R $<$ 15 kpc). The carbon-to-nitrogen ratio (often expressed as [C/N]) can indicate the mass of a red giant star, from which an age can be inferred. Using masses and ages derived by Martig et al., we demonstrate that we are able to interpret the DR14 [C/N]-[Fe/H] abundance distributions as trends in age-[Fe/H] space. Our results show that an anti-correlation between age and metallicity, which is predicted by simple chemical evolution models, is not present at any Galactic zone. Stars far from the plane ($|$Z$|$ $>$ 1 kpc) exhibit a radial gradient in [C/N] ($\sim$ $-$0.04 dex/kpc). The [C/N] dispersion increases toward the plane ($σ_{[C/N]}$ = 0.13 at $|$Z$|$ $>$ 1 kpc to $σ_{[C/N]}$ = 0.18 dex at $|$Z$|$ $<$ 0.5 kpc). We measure a disk metallicity gradient for the youngest stars (age $<$ 2.5 Gyr) of $-$0.060 dex/kpc from 6 kpc to 12 kpc, which is in agreement with the gradient found using young CoRoGEE stars by Anders et al. Older stars exhibit a flatter gradient ($-$0.016 dex/kpc), which is predicted by simulations in which stars migrate from their birth radii. We also find that radial migration is a plausible explanation for the observed upturn of the [C/N]-[Fe/H] abundance trends in the outer Galaxy, where the metal-rich stars are relatively enhanced in [C/N].

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arXiv2018

The origin of accreted stellar halo populations in the Milky Way using APOGEE, $\textit{Gaia}$, and the EAGLE simulations

Recent work indicates that the nearby Galactic halo is dominated by the debris from a major accretion event. We confirm that result from an analysis of APOGEE-DR14 element abundances and $\textit{Gaia}$-DR2 kinematics of halo stars. We show that $\sim$2/3 of nearby halo stars have high orbital eccentricities ($e \gtrsim 0.8$), and abundance patterns typical of massive Milky Way dwarf galaxy satellites today, characterised by relatively low [Fe/H], [Mg/Fe], [Al/Fe], and [Ni/Fe]. The trend followed by high $e$ stars in the [Mg/Fe]-[Fe/H] plane shows a change of slope at [Fe/H]$\sim-1.3$, which is also typical of stellar populations from relatively massive dwarf galaxies. Low $e$ stars exhibit no such change of slope within the observed [Fe/H] range and show slightly higher abundances of Mg, Al and Ni. Unlike their low $e$ counterparts, high $e$ stars show slightly retrograde motion, make higher vertical excursions and reach larger apocentre radii. By comparing the position in [Mg/Fe]-[Fe/H] space of high $e$ stars with those of accreted galaxies from the EAGLE suite of cosmological simulations we constrain the mass of the accreted satellite to be in the range $10^{8.5}\lesssim M_*\lesssim 10^{9}\mathrm{M_\odot}$. We show that the median orbital eccentricities of debris are largely unchanged since merger time, implying that this accretion event likely happened at $z\lesssim1.5$. The exact nature of the low $e$ population is unclear, but we hypothesise that it is a combination of $\textit{in situ}$ star formation, high $|z|$ disc stars, lower mass accretion events, and contamination by the low $e$ tail of the high $e$ population. Finally, our results imply that the accretion history of the Milky Way was quite unusual.

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