arXiv subjects

David H. Weinberg

Publications and source records attributed to David H. Weinberg.

At least 37 records · Page 2Linked to original sources

arXiv2024

Modeling the Ages and Chemical Abundances of Elliptical Galaxies

Spectroscopic studies of elliptical galaxies show that their stellar population ages, mean metallicity, and $α$-enhancement traced by [Mg/Fe] all increase with galaxy stellar mass or velocity dispersion. We use one-zone galactic chemical evolution (GCE) models with a flexible star formation history (SFH) to model the age, [Mg/H], and [Mg/Fe] inferred from simple stellar population (SSP) fits to observed ellipticals at $z \sim 0$ and $z \sim 0.7$. We show that an SSP fit to the spectrum computed from a full GCE model gives ages and abundances close to the light-weighted, logarithmically averaged values of the composite stellar population, , <[Mg/H]>, and <[Mg/Fe]>. With supernova Mg and Fe yields fixed to values motivated by Milky Way stellar populations, we find that predicted <[Mg/H]>- and <[Mg/Fe]>- relations are surprisingly insensitive to SFH parameters: older galaxies have higher <[Mg/Fe]>, but the detailed form of the SFH has limited impact. The star formation efficiency and outflow efficiency affect the early and late evolution of <[Mg/H]>, respectively; explaining observed trends requires higher star formation efficiency and lower outflows in more massive galaxies. With core collapse supernova yields calibrated to the plateau [Mg/Fe]$_{\rm cc} \approx0.45$ observed in many Milky Way studies, our models underpredict the observed <[Mg/Fe]> ratios of ellipticals by 0.05-0.1 dex. Increasing the core collapse yield ratio to [Mg/Fe]$_{\rm cc} = 0.55$ improves the agreement, though the models still lie below the data. We discuss potential resolutions of this discrepancy, including the possibility that many ellipticals terminate their star formation with a self-enriching, terminating burst that reduces the light-weighted age and boosts <[Mg/Fe]>.

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arXiv2024

Chemical Cartography with APOGEE: Two-process Parameters and Residual Abundances for 288,789 Stars from Data Release 17

Stellar abundance measurements are subject to systematic errors that induce extra scatter and artificial correlations in elemental abundance patterns. We derive empirical calibration offsets to remove systematic trends with surface gravity $\log(g)$ in 17 elemental abundances of 288,789 evolved stars from the SDSS APOGEE survey. We fit these corrected abundances as the sum of a prompt process tracing core-collapse supernovae and a delayed process tracing Type Ia supernovae, thus recasting each star's measurements into the amplitudes $A_{\text{cc}}$ and $A_{\text{Ia}}$ and the element-by-element residuals from this two-parameter fit. As a first application of this catalog, which is $8\times$ larger than that of previous analyses that used a restricted $\log(g)$ range, we examine the median residual abundances of 14 open clusters, nine globular clusters, and four dwarf satellite galaxies. Relative to field Milky Way disk stars, the open clusters younger than 2 Gyr show $\approx 0.1-0.2$ dex enhancements of the neutron-capture element Ce, and the two clusters younger than 0.5 Gyr also show elevated levels of C+N, Na, S, and Cu. Globular clusters show elevated median abundances of C+N, Na, Al, and Ce, and correlated abundance residuals that follow previously known trends. The four dwarf satellites show similar residual abundance patterns despite their different star formation histories, with $\approx 0.2-0.3$ dex depletions in C+N, Na, and Al and $\approx 0.1$ dex depletions in Ni, V, Mn, and Co. We provide our catalog of corrected APOGEE abundances, two-process amplitudes, and residual abundances, which will be valuable for future studies of abundance patterns in different stellar populations and of additional enrichment processes that affect galactic chemical evolution.

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arXiv2024

Modeling the Galactic Chemical Evolution of Helium

We examine the galactic chemical evolution (GCE) of $^4$He in one-zone and multi-zone models, with particular attention to theoretical predictions and empirical constraints on IMF-averaged yields. Published models of massive star winds and core collapse supernovae span a factor of 2 -- 3 in the IMF-averaged $^4$He yield, $y\mathrm{_{He}^{CC}}$. Published models of intermediate mass, asymptotic giant branch (AGB) stars show better agreement on the IMF-averaged yield, $y\mathrm{_{He}^{AGB}}$, and they predict that more than half of this yield comes from stars with $M=4-8 M_\odot$, making AGB $^4$He enrichment rapid compared to Fe enrichment from Type Ia supernovae. Although our GCE models include many potentially complicating effects, the short enrichment time delay and mild metallicity dependence of the predicted yields makes the results quite simple: across a wide range of metallicity and age, the non-primordial $^4$He mass fraction $ΔY = Y-Y_{\mathrm{P}}$ is proportional to the abundance of promptly produced $α$-elements, like oxygen, with $ΔY/Z_{\mathrm{O}} \approx (y\mathrm{_{He}^{CC}}+y\mathrm{_{He}^{AGB}})/y\mathrm{_{O}^{CC}}$. Reproducing solar abundances with our fiducial choice of the oxygen yield $y\mathrm{_{O}^{CC}}=0.0071$ implies $y\mathrm{_{He}^{CC}}+y\mathrm{_{He}^{AGB}} \approx 0.022$, i.e., $0.022M_\odot$ of net $^4$He production per solar mass of star formation. Our GCE models with this yield normalization are consistent with most available observations, though the implied $y\mathrm{_{He}^{CC}}$ is low compared to most of the published massive star models. More precise measurements of $ΔY$ in stars and gas across a wide range of metallicity and [$α$/Fe] ratio could test our models more stringently, either confirming the simple picture suggested by our calculations or revealing surprises in the evolution of the second most abundant element.

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arXiv2024

Nature vs. Nurture: Distinguishing Effects from Stellar Processing and Chemical Evolution on Carbon and Nitrogen in Red Giant Stars

The surface [C/N] ratios of evolved giants are strongly affected by the first dredge-up (FDU) of nuclear-processed material from stellar cores. C and N also have distinct nucleosynthetic origins and serve as diagnostics of mixing and mass loss. We use subgiants to find strong trends in the birth [C/N] with [Fe/H], which differ between the low-$α$ and high-$α$ populations. We demonstrate that these birth trends have a strong impact on the surface abundances after the FDU. This effect is neglected in current stellar models, which use solar-scaled C and N. We map out the FDU as a function of evolutionary state, mass, and composition using a large and precisely measured asteroseismic dataset in first-ascent red giant branch (RGB) and core He-burning, or red clump (RC), stars. We describe the domains where [C/N] is a useful mass diagnostic and find that the RC complements the RGB and extends the range of validity to higher mass. We find evidence for extra mixing on the RGB below [Fe/H]= -0.4, matching literature results, for high-$α$ giants, but there is no clear evidence of mixing in the low-$α$ giants. The predicted signal of mass loss is weak and difficult to detect in our sample. We discuss implications for stellar physics and stellar population applications.

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arXiv2024

Deciphering baryonic feedback with galaxy clusters

Upcoming cosmic shear analyses will precisely measure the cosmic matter distribution at low redshifts. At these redshifts, the matter distribution is affected by galaxy formation physics, primarily baryonic feedback from star formation and active galactic nuclei. Employing measurements from the Magneticum and IllustrisTNG simulations and a dark matter + baryon (DMB) halo model, this paper demonstrates that Sunyaev-Zel'dovich (SZ) effect observations of galaxy clusters, whose masses have been calibrated using weak gravitational lensing, can constrain the baryonic impact on cosmic shear with statistical and systematic errors subdominant to the measurement errors of DES-Y3 and LSST-Y1. We further dissect the contributions from different scales and halos with different masses to cosmic shear, highlighting the dominant role of SZ clusters at scales critical for cosmic shear analyses. These findings suggest a promising avenue for future joint analyses of Cosmic Microwave Background (CMB) and lensing surveys.

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arXiv2023

Forecasting the constraints on optical selection bias and projection effects of galaxy cluster lensing with multiwavelength data

Galaxy clusters identified with optical imaging tend to suffer from projection effects, which impact richness (the number of member galaxies in a cluster) and lensing coherently. Physically unassociated galaxies can be mistaken as cluster members due to the significant uncertainties in their line-of-sight distances, thereby changing the observed cluster richness; at the same time, projection effects alter the weak gravitational lensing signals of clusters, leading to a correlated scatter between richness and lensing at a given halo mass. As a result, the lensing signals for optically selected clusters tend to be biased high. This optical selection bias problem of cluster lensing is one of the key challenges in cluster cosmology. Fortunately, recently available multiwavelength observations of clusters provide a solution. We analyze a simulated data set mimicking the observed lensing of clusters identified by both optical photometry and gas properties, aiming to constrain this selection bias. Assuming a redMaPPer sample from the Dark Energy Survey with South Pole Telescope Sunyaev-Zeldovich effect observations, we find that an overlapping survey of 1300 square deg, 0.2 < z < 0.65, can constrain the average lensing bias to an accuracy of 5 percent. This provides an exciting opportunity for directly constraining optical selection bias from observations. We further show that our approach can remove the optical selection bias from the lensing signal, paving the way for future optical cluster cosmology analyses.

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arXiv2023

KPM: A Flexible and Data-Driven K-Process Model for Nucleosynthesis

The element abundance pattern found in Milky Way disk stars is close to two-dimensional, dominated by production from one prompt process and one delayed process. This simplicity is remarkable, since the elements are produced by a multitude of nucleosynthesis mechanisms operating in stars with a wide range of progenitor masses. We fit the abundances of 14 elements for 48,659 red-giant stars from APOGEE DR17 using a flexible, data-driven K-process model -- dubbed KPM. In our fiducial model, with $K=2$, each abundance in each star is described as the sum of a prompt and a delayed process contribution. We find that KPM with $K=2$ is able to explain the abundances well, recover the observed abundance bimodality, and detect the bimodality over a greater range in metallicity than previously has been possible. We compare to prior work by Weinberg et al. (2022), finding that KPM produces similar results, but that KPM better predicts stellar abundances, especially for elements C+N and Mn and for stars at super-solar metallicities. The model fixes the relative contribution of the prompt and delayed process to two elements to break degeneracies and improve interpretability; we find that some of the nucleosynthetic implications are dependent upon these detailed choices. We find that moving to four processes adds flexibility and improves the model's ability to predict the stellar abundances, but doesn't qualitatively change the story. The results of KPM will help us to interpret and constrain the formation of the Galaxy disk, the relationship between abundances and ages, and the physics of nucleosynthesis.

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arXiv2023

Realistic simulated galaxies form [$α$/Fe]-[Fe/H] knees due to a sustained decline in their star formation rates

We examine the stellar [$α$/Fe]-[Fe/H] distribution of $\simeq1000$ present-day galaxies in a high-resolution EAGLE simulation. A slight majority of galaxies exhibit the canonical distribution, characterised by a sequence of low-metallicity stars with high [$α$/Fe] that transitions at a "knee" to a sequence of declining [$α$/Fe] with increasing metallicity. This population yields a knee metallicity - galaxy-mass relation similar to that observed in Local Group galaxies, both in slope and scatter. However, many simulated galaxies lack a knee or exhibit more complicated distributions. Knees are found only in galaxies with star formation histories (SFHs) featuring a sustained decline from an early peak ($t\simeq7~{\rm Gyr}$), which enables enrichment by Type Ia supernovae to dominate that due to Type II supernovae (SN II), reducing [$α$/Fe] in the interstellar gas. The simulation thus indicates that, contrary to the common interpretation implied by analytic galactic chemical evolution (GCE) models, knee formation is not a consequence of the onset of enrichment by SN Ia. We use the SFH of a simulated galaxy exhibiting a knee as input to the VICE GCE model, finding it yields an $α$-rich plateau enriched only by SN II, but the plateau comprises little stellar mass and the galaxy forms few metal-poor ([Fe/H]$\lesssim - 1$) stars. This follows from the short, constant gas consumption timescale typically assumed by GCEs, which implies the presence of a readily-enriched, low-mass gas reservoir. When an initially longer, evolving consumption timescale is adopted, VICE reproduces the simulated galaxy's track through the [$α$/Fe]-[Fe/H] plane and its metallicity distribution function.

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arXiv2023

Dark Energy Survey Year 1 Clusters are Consistent with Planck

The recent Dark Energy Survey Year 1 (DES-Y1) analysis of galaxy cluster abundances and weak lensing produced $Ω_{\rm m}$ and $σ_8$ constraints in 5.6$σ$ tension with Planck. It is suggested in that work that this tension is driven by unmodelled systematics in optical cluster selection. We present a novel simulation-based forward modeling framework that explicitly incorporates cluster selection into its model predictions. Applying this framework to the DES-Y1 data we find consistency with Planck, resolving the tension found in the DES-Y1 analysis. An extension of this approach to the final DES data set will produce robust constraints on $Λ$CDM parameters and correspondingly strong tests of cosmological models.

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arXiv2023

The Scale of Stellar Yields: Implications of the Measured Mean Iron Yield of Core Collapse Supernovae

The scale of alpha-element yields is difficult to predict from theory because of uncertainties in massive star evolution, supernova physics, and black hole formation, and it is difficult to constrain empirically because the impact of higher yields can be compensated by greater metal loss in galactic winds. We use a recent measurement of the mean iron yield of core collapse supernovae (CCSN) by Rodriguez et al. (RMN23), $\bar{y}_{\rm Fe}^{\rm cc} =0.058 \pm 0.007 M_\odot$, to infer the scale of alpha-element yields by assuming that the plateau of [alpha/Fe] abundance ratios observed in low metallicity stars represents the yield ratio of CCSN. For a Kroupa IMF and a plateau at [alpha/Fe]=0.45, we find that the population-averaged yields of O and Mg per unit mass of star formation are about equal to the mass fractions of these elements in the sun. The inferred O and Fe yields agree with predictions of the Sukhbold et al. (2016) CCSN models assuming their Z9.6+N20 neutrino-driven engine, a scenario in which many progenitors with $M<40M_\odot$ implode to black holes rather than exploding. The yields are lower than assumed in some models of galactic chemical evolution (GCE) and the galaxy mass-metallicity relation, reducing the level of outflows needed to match observed abundances. For straightforward assumptions, we find that one-zone GCE models with mass-loading factor $η\approx 0.6$ evolve to solar metallicity at late times. By requiring that models reach [alpha/Fe]=0 at late times, and assuming a mean Fe yield of $0.7M_\odot$ per Type Ia supernova, we infer a Hubble-time integrated SNIa rate of $1.1\times 10^{-3} M_\odot^{-1}$, compatible with estimates from supernova surveys. The RMN23 measurement provides one of the few empirical anchors for the absolute scale of nucleosynthetic yields, with wide-ranging implications for stellar and galactic astrophysics.

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arXiv2023

Strong Outflows and Inefficient Star Formation in the Reionization-era Ultra-faint Dwarf Galaxy Eridanus II

We present novel constraints on the underlying galaxy formation physics (e.g., mass loading factor, star formation history, metal retention) at $z\gtrsim7$ for the low-mass ($M_*\sim10^5$ M$_\odot$) Local Group ultra-faint dwarf galaxy (UFD) Eridanus {\sc II} (Eri II). Using a hierarchical Bayesian framework, we apply a one-zone chemical evolution model to Eri II's CaHK-based photometric metallicity distribution function (MDF; [Fe/H]) and find that the evolution of Eri II is well-characterized by a short, exponentially declining star-formation history ($τ_\text{SFH}=0.39\pm_{0.13}^{0.18}$ Gyr), a low star-formation efficiency ($τ_\text{SFE}=27.56\pm_{12.92}^{25.14}$ Gyr), and a large mass-loading factor ($η=194.53\pm_{42.67}^{33.37}$). Our results are consistent with Eri II forming the majority of its stars before the end of reionization. The large mass-loading factor implies strong outflows in the early history of Eri II and is in good agreement with theoretical predictions for the mass-scaling of galactic winds. It also results in the ejection of $>$90\% of the metals produced in Eri II. We make predictions for the distribution of [Mg/Fe]-[Fe/H] in Eri II as well as the prevalence of ultra metal-poor stars, both of which can be tested by future chemical abundance measurements. Spectroscopic follow-up of the highest metallicity stars in Eri II ($\text{[Fe/H]} > -2$) will greatly improve model constraints. Our new framework can readily be applied to all UFDs throughout the Local Group, providing new insights into the underlying physics governing the evolution of the faintest galaxies in the reionization era.

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arXiv2023

A Tale of Two Disks: Mapping the Milky Way with the Final Data Release of APOGEE

We present new maps of the Milky Way disk showing the distribution of metallicity ([Fe/H]), $α$-element abundances ([Mg/Fe]), and stellar age, using a sample of 66,496 red giant stars from the final data release (DR17) of the Apache Point Observatory Galactic Evolution Experiment (APOGEE) survey. We measure radial and vertical gradients, quantify the distribution functions for age and metallicity, and explore chemical clock relations across the Milky Way for the low-$α$ disk, high-$α$ disk, and total population independently. The low-$α$ disk exhibits a negative radial metallicity gradient of $-0.06 \pm 0.001$ dex kpc$^{-1}$, which flattens with distance from the midplane. The high-$α$ disk shows a flat radial gradient in metallicity and age across nearly all locations of the disk. The age and metallicity distribution functions shift from negatively skewed in the inner Galaxy to positively skewed at large radius. Significant bimodality in the [Mg/Fe]-[Fe/H] plane and in the [Mg/Fe]-age relation persist across the entire disk. The age estimates have typical uncertainties of $\sim0.15$ in $\log$(age) and may be subject to additional systematic errors, which impose limitations on conclusions drawn from this sample. Nevertheless, these results act as critical constraints on galactic evolution models, constraining which physical processes played a dominant role in the formation of the Milky Way disk. We discuss how radial migration predicts many of the observed trends near the solar neighborhood and in the outer disk, but an additional more dramatic evolution history, such as the multi-infall model or a merger event, is needed to explain the chemical and age bimodality elsewhere in the Galaxy.

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arXiv2023

New Dimensions of Galactic Chemical Evolution

Dramatic recent progress in understanding galactic chemical evolution (GCE) has been driven partly by direct observations of the distant past with HST and JWST of stellar abundances from giant high-resolution spectroscopic surveys (APOGEE, GALAH) and the complementary power of Gaia astrometry and photometry. Focusing on archaeology, I give a rapid-fire, and I hope synthesizing, review of work my collaborators and I have done on theoretical modeling and observational interpretation. I discuss (1) the interleaved but distinguishable roles of stellar scale astrophysics and galactic scale astrophysics in governing GCE, (2) the use of abundance ratio trends to empirically infer nucleosynthetic yields, (3) the uncertainty in the overall scale of yields and its degeneracy with the importance of galactic outflows, (4) the emergence of equilibrium in GCE, (5) the dimensionality of the stellar distribution in chemical abundance space, and (6) insights from chemical abundances on the early history of the Milky Way, including measurements of the intrinsic scatter of abundance ratios in metal-poor stars (-2 < [Fe/H] < -1), suggesting that a typical halo star at this metallicity is enriched by the products of $N \sim 50$ supernovae mixed over $\sim 10^5 M_\odot$ of star-forming gas.

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arXiv2023

A framework to measure the properties of intergalactic metal systems with two-point flux statistics

The abundance, temperature, and clustering of metals in the intergalactic medium are important parameters for understanding their cosmic evolution and quantifying their impact on cosmological analysis with the Ly $α$ forest. The properties of these systems are typically measured from individual quasar spectra redward of the quasar's Ly $α$ emission line, yet that approach may provide biased results due to selection effects. We present an alternative approach to measure these properties in an unbiased manner with the two-point statistics commonly employed to quantify large-scale structure. Our model treats the observed flux of a large sample of quasar spectra as a continuous field and describes the one-dimensional, two-point statistics of this field with three parameters per ion: the abundance (column density distribution), temperature (Doppler parameter) and clustering (cloud-cloud correlation function). We demonstrate this approach on multiple ions (e.g., C IV, Si IV, Mg II) with early data from the Dark Energy Spectroscopic Instrument (DESI) and high-resolution spectra from the literature. Our initial results show some evidence that the C IV abundance is higher than previous measurements and evidence for abundance evolution over time. The first full year of DESI observations will have over an order of magnitude more quasar spectra than this study. In a future paper we will use those data to measure the growth of clustering and its impact on the Ly $α$ forest, as well as test other DESI analysis infrastructure such as the pipeline noise estimates and the resolution matrix.

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arXiv2023

Buzzard to Cardinal: Improved Mock Catalogs for Large Galaxy Surveys

We present the Cardinal mock galaxy catalogs, a new version of the Buzzard simulation that has been updated to support ongoing and future cosmological surveys, including DES, DESI, and LSST. These catalogs are based on a one-quarter sky simulation populated with galaxies out to a redshift of $z=2.35$ to a depth of $m_{\rm{r}}=27$. Compared to the Buzzard mocks, the Cardinal mocks include an updated subhalo abundance matching (SHAM) model that considers orphan galaxies and includes mass-dependent scatter between galaxy luminosity and halo properties. This model can simultaneously fit galaxy clustering and group--galaxy cross-correlations measured in three different luminosity threshold samples. The Cardinal mocks also feature a new color assignment model that can simultaneously fit color-dependent galaxy clustering in three different luminosity bins. We have developed an algorithm that uses photometric data to improve the color assignment model further and have also developed a novel method to improve small-scale lensing below the ray-tracing resolution. These improvements enable the Cardinal mocks to accurately reproduce the abundance of galaxy clusters and the properties of lens galaxies in the Dark Energy Survey data. As such, these simulations will be a valuable tool for future cosmological analyses based on large sky surveys. The cardinal mock will be released upon publication at https://chunhaoto.com/cardinalsim.

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arXiv2023

Overview of the DESI Milky Way Survey

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.

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arXiv2022

The chemical characterisation of halo substructure in the Milky Way based on APOGEE

Galactic haloes in a $Λ$-CDM universe are predicted to host today a swarm of debris resulting from cannibalised dwarf galaxies. The chemo-dynamical information recorded in their stellar populations helps elucidate their nature, constraining the assembly history of the Galaxy. Using data from APOGEE and \textit{Gaia}, we examine the chemical properties of various halo substructures, considering elements that sample various nucleosynthetic pathways. The systems studied are Heracles, \textit{Gaia}-Enceladus/Sausage (GES), the Helmi stream, Sequoia, Thamnos, Aleph, LMS-1, Arjuna, I'itoi, Nyx, Icarus, and Pontus. Abundance patterns of all substructures are cross-compared in a statistically robust fashion. Our main findings include: {\it i)} the chemical properties of most substructures studied match qualitatively those of dwarf Milky Way satellites, such as the Sagittarius dSph. Exceptions are Nyx and Aleph, which are chemically similar to disc stars, implying that these substructures were likely formed \textit{in situ}; {\it ii)} Heracles differs chemically from {\it in situ} populations such as Aurora and its inner halo counterparts in a statistically significant way. The differences suggest that the star formation rate was lower in Heracles than in the early Milky Way; {\it iii)} the chemistry of Arjuna, LMS-1, and I'itoi is indistinguishable from that of GES, suggesting a possible common origin; {\it iv)} all three Sequoia samples studied are qualitatively similar. However, only two of those samples present chemistry that is consistent with GES in a statistically significant fashion; {\it v)} the abundance patterns of the Helmi stream and Thamnos are different from all other halo substructures.

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arXiv2022

Untangling the Sources of Abundance Dispersion in Low-Metallicity Stars

We measure abundances of 12 elements (Na, Mg, Si, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni) in a sample of 86 metal-poor ($-2 \lesssim \text{[Fe/H]} \lesssim -1$) subgiant stars in the solar neighborhood. Abundances are derived from high-resolution spectra taken with the Potsdam Echelle Polarimetric and Spectroscopic Instrument on the Large Binocular Telescope, modeled using iSpec and MOOG. By carefully quantifying the impact of photon-noise ($< 0.05$ dex for all elements) we robustly measure the intrinsic scatter of abundance ratios. At fixed [Fe/H] the RMS intrinsic scatter in [X/Fe] ranges from 0.04 dex (Cr) to 0.16 dex (Na), with a median of 0.08 dex. Scatter in [X/Mg] is similar, and accounting for [$α$/Fe] only reduces the overall scatter moderately. We consider several possible origins of the intrinsic scatter with particular attention to fluctuations in the relative enrichment by core-collapse supernovae (CCSN) and Type Ia supernovae (SNIa) and stochastic sampling of the CCSN progenitor mass distribution. The stochastic sampling scenario provides a good quantitative explanation of our data if the effective number of CCSN contributing to the enrichment of a typical sample star is $N \sim 50$. At the median metallicity of our sample, this interpretation implies that the CCSN ejecta are mixed over a gas mass $\sim 10^5 M_{\odot}$ before forming stars. The scatter of elemental abundance ratios is a powerful diagnostic test for simulations of star formation, feedback, and gas mixing in the early phases of the Galaxy.

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