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Charlie Conroy

Publications and source records attributed to Charlie Conroy.

At least 127 records · Page 7Linked to original sources

A Diffuse Metal-Poor Component of the Sagittarius Stream Revealed by the H3 Survey

The tidal disruption of the Sagittarius dwarf galaxy has generated a spectacular stream of stars wrapping around the entire Galaxy. We use data from $Gaia$ and the H3 Stellar Spectroscopic Survey to identify 823 high-quality Sagittarius members based on their angular momenta. The H3 Survey is largely unbiased in metallicity, and so our sample of Sagittarius members is similarly unbiased. Stream stars span a wide range in [Fe/H] from $-0.2$ to $\approx -3.0$, with a mean overall metallicity of $\langle$[Fe/H]$\rangle=-0.99$. We identify a strong metallicity-dependence to the kinematics of the stream members. At [Fe/H]$\gt -0.8$ nearly all members belong to the well-known cold ($σ_v \lt 20$ km/s) leading and trailing arms. At intermediate metallicities ($-1.9 \lt$[Fe/H]$\lt -0.8$) a significant population (24$\%$) emerges of stars that are kinematically offset from the cold arms. These stars also appear to have hotter kinematics. At the lowest metallicities ([Fe/H]$\lesssim-2$), the majority of stars (69$\%$) belong to this kinematically-offset diffuse population. Comparison to simulations suggests that the diffuse component was stripped from the Sagittarius progenitor at earlier epochs, and therefore resided at larger radius on average, compared to the colder metal-rich component. We speculate that this kinematically diffuse, low metallicity, population is the stellar halo of the Sagittarius progenitor system.

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Spatial and Kinematic Clustering of Stars in the Galactic Disk

The Galactic disk is expected to be spatially, kinematically, and chemically clustered on many scales due to both star formation and non-axisymmetries in the Galactic potential. In this work we calculate the spatial and kinematic two-point correlation functions using a sample of $1.7 \times 10^6$ stars within 1 kpc of the Sun with 6D phase space information available from \textit{Gaia} DR2. Clustering is detected on spatial scales of 1-300 pc and velocity scales of at least 15 km s$^{-1}$. With bound structures included, the data have a power-law index ($ξ(Δr) \propto Δr^γ$) of $γ\approx-2$ at most spatial scales, which is in line with theoretical predictions. After removing bound structures, the data have a power-law index of $γ\approx-1$ for $<100$ pc and $γ\lesssim -1.5$ for $>100$ pc. We interpret these results with the aid of a novel star-by-star simulation of the Galaxy in which stars are born in clusters orbiting in a realistic potential that includes spiral arms, a bar, and GMCs. We find that the simulation largely agrees with the observations (within a factor of 2-3) at all spatial and kinematic scales. In detail, the correlation function in the simulation is shallower than the data at $< 20$ pc scales, and steeper than the data at $> 30$ pc scales. We also find a persistent clustering signal in the kinematic correlation function for the data at large $Δv$ ($>5$ km s$^{-1}$) not present in the simulations. We speculate that this mismatch between observations and simulations may be due to two processes not included in the simulation: hierarchical star formation and transient spiral arms. We also use the simulations to predict the clustering signal as a function of pair-wise metallicity and age separations. Ages and metallicities measured with a precision of $50\%$ and $0.05$ dex are required in order to enhance the clustering signal.

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Brackett-$γ$ as a Gold-standard Test of Star Formation Rates Derived from SED Fitting

Using a local reference sample of 21 galaxies, we compare observations of the $λ$2.16 $μ$m Brackett-$γ$ (Br$γ$) hydrogen recombination line with predictions from the Prospector Bayesian inference framework, which was used to fit the broadband photometry of these systems. This is a clean test of the spectral-energy-distribution-derived star formation rates (SFRs), as dust is expected to be optically thin at this wavelength in nearly all galaxies; thus, the internal conversion of SFR to predicted line luminosity does not depend strongly on the adopted dust model and posterior dust parameters, as is the case for shorter-wavelength lines such as H$α$. We find that Prospector predicts Br$γ$ luminosities and equivalent widths with small offsets ($\sim$0.05 dex), and scatter ($\sim$0.2 dex), consistent with measurement uncertainties, though we caution that the derived offset is dependent on the choice of stellar isochrones. We demonstrate that even when the Prospector-derived dust attenuation does not well describe, e.g., H$α$ line properties or observed reddening between H$α$ and Br$γ$, the underlying SFRs are accurate, as verified by the dust-free Br$γ$ comparison. Finally, we discuss in what ways Br$γ$ might be able to help constrain model parameters when treated as an input to the model, and comment on its potential as an accurate monochromatic SFR indicator in the era of JWST multiobject near-IR spectroscopy.

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The Universe at z>10: Predictions for JWST from the UniverseMachine DR1

The James Webb Space Telescope (JWST) is expected to observe galaxies at $z>10$ that are presently inaccessible. Here, we use a self-consistent empirical model, the UniverseMachine, to generate mock galaxy catalogues and lightcones over the redshift range $z=0-15$. These data include realistic galaxy properties (stellar masses, star formation rates, and UV luminosities), galaxy-halo relationships, and galaxy-galaxy clustering. Mock observables are also provided for different model parameters spanning observational uncertainties at $z<10$. We predict that Cycle 1 JWST surveys will very likely detect galaxies with $M_*>10^7 M_\odot$ and/or $M_{1500}<-17$ out to at least $z\sim 13.5$. Number density uncertainties at $z>12$ expand dramatically, so efforts to detect $z>12$ galaxies will provide the most valuable constraints on galaxy formation models. The faint-end slopes of the stellar mass/luminosity functions at a given mass/luminosity threshold steepen as redshift increases. This is because observable galaxies are hosted by haloes in the exponentially falling regime of the halo mass function at high redshifts. Hence, these faint-end slopes are robustly predicted to become shallower below current observable limits ($M_\ast < 10^7M_\odot$ or $M_\mathrm{1500}>-17$). For reionization models, extrapolating luminosity functions with a constant faint-end slope from $M_{1500}=-17$ down to $M_{1500}=-12$ gives the most reasonable upper limit for the total UV luminosity and cosmic star formation rate up to $z\sim 12$. We compare to three other empirical models and one semi-analytic model, showing that the range of predicted observables from our approach encompasses predictions from other techniques. Public catalogues and lightcones for common fields are available online.

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MINESweeper: Spectrophotometric Modeling of Stars in the Gaia Era

We present MINESweeper, a tool to measure stellar parameters by jointly fitting observed spectra and broadband photometry to model isochrones and spectral libraries. This approach enables the measurement of spectrophotometric distances, in addition to stellar parameters such as Teff, log(g), [Fe/H], [a/Fe], and radial velocity. MINESweeper employs a Bayesian framework and can easily incorporate a variety of priors, including Gaia parallaxes. Mock data are fit in order to demonstrate how the precision of derived parameters depends on evolutionary phase and SNR. We then fit a selection of data in order to validate the model outputs. Fits to a variety of benchmark stars including Procyon, Arcturus, and the Sun result in derived stellar parameters that are in good agreement with the literature. We then fit combined spectra and photometry of stars in the open and globular clusters M92, M13, M3, M107, M71, and M67. Derived distances, [Fe/H], [a/Fe], and log(g)-Teff, relations are in overall good agreement with literature values, although there are trends between metallicity and log(g), within clusters that point to systematic uncertainties at the ~0.1 dex level. Finally, we fit a large sample of stars from the H3 Spectroscopic Survey in which high quality Gaia parallaxes are also available. These stars are fit without the Gaia parallaxes so that the geometric parallaxes can serve as an independent test of the spectrophotometric distances. Comparison between the two reveals good agreement within their formal uncertainties after accounting for the Gaia zero point uncertainties.

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Powderday: Dust Radiative Transfer for Galaxy Simulations

We present Powderday, a flexible, fast, open-source dust radiative transfer package designed to interface with galaxy formation simulations. Powderday builds on FSPS population synthesis models, Hyperion dust radiative transfer, and employs yt to interface between different software packages. We include our stellar population synthesis modeling on the fly, which allows for significant run-time flexibility in the assumed stellar physics. We include a model for nebular line emission that can employ either precomputed Cloudy lookup tables (for efficiency), or direct photoionization calculations for all young stars (for flexibility). The dust content follows either observationally-motivated prescriptions, direct modeling from galaxy formation simulations, or a novel approach that includes the dust content via learning-based algorithms from the SIMBA cosmological galaxy formation simulation. AGN can additionally be included via a range of prescriptions. The output of these models are broadband SEDs, as well as filter-convolved images. Powderday is designed to eliminate last-mile efforts by researchers that employ different hydrodynamic galaxy formation models, and seamlessly interfaces with GIZMO, AREPO, GASOLINE, CHANGA, and ENZO. We demonstrate the capabilities of the code via three applications: a model for the star formation rate (SFR) - infrared luminosity relation in galaxies (including the impact of AGN); the impact of circumstellar dust around AGB stars on the mid-infrared emission from galaxy SEDs; and the impact of galaxy inclination angle on dust attenuation laws.

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Evidence from the H3 Survey that the Stellar Halo is Entirely Comprised of Substructure

In the $Λ$CDM paradigm the Galactic stellar halo is predicted to harbor the accreted debris of smaller systems. To identify these systems, the H3 Spectroscopic Survey, combined with $Gaia$, is gathering 6D phase-space and chemical information in the distant Galaxy. Here we present a comprehensive inventory of structure within 50 kpc from the Galactic center using a sample of 5684 giants at $|b|>40^{\circ}$ and $|Z|>2$ kpc. We identify known structures including the high-$α$ disk, the in-situ halo (disk stars heated to eccentric orbits), Sagittarius (Sgr), $Gaia$-Sausage-Enceladus (GSE), the Helmi Streams, Sequoia, and Thamnos. Additionally, we identify the following new structures: (i) Aleph ([Fe/H]$=-0.5$), a low eccentricity structure that rises a surprising 10 kpc off the plane, (ii, iii) Arjuna ([Fe/H]$=-1.2$) and I'itoi ([Fe/H]$<-2$), which comprise the high-energy retrograde halo along with Sequoia, and (iv) Wukong ([Fe/H]$=-1.6$), a prograde phase-space overdensity chemically distinct from GSE. For each structure we provide [Fe/H], [$α$/Fe], and orbital parameters. Stars born within the Galaxy are a major component at $|Z|\sim$2 kpc ($\approx$60$\%$), but their relative fraction declines sharply to $\lesssim$5$\%$ past 15 kpc. Beyond 15 kpc, $>$80$\%$ of the halo is built by two massive ($M_{\star}\sim10^{8}-10^{9}M_{\odot}$) accreted dwarfs: GSE ([Fe/H]$=-1.2$) within 25 kpc, and Sgr ([Fe/H]$=-1.0$) beyond 25 kpc. This explains the relatively high overall metallicity of the halo ([Fe/H]$\approx-1.2$). We attribute $\gtrsim$95$\%$ of the sample to one of the listed structures, pointing to a halo built entirely from accreted dwarfs and heating of the disk.

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A Tip of the Red Giant Branch Distance to the Dark Matter Deficient Galaxy NGC1052-DF4 from Deep Hubble Space Telescope Data

Previous studies have shown that the large, diffuse galaxies NGC1052-DF2 and NGC1052-DF4 both have populations of unusually luminous globular clusters as well as a very low dark matter content. Here we present newly-obtained deep Hubble Space Telescope (HST) Advanced Camera for Surveys (ACS) imaging of one of these galaxies, NGC1052-DF4. We use these data to measure the distance of the galaxy from the location of the tip of the red giant branch (TRGB). We find a rapid increase in the number of detected stars fainter than $m_{F814W} \sim 27.3$, which we identify as the onset of the red giant branch. Using a forward modeling approach that takes the photometric uncertainties into account, we find a TRGB magnitude of $m_{F814W,\rm TRGB}=27.47 \pm 0.16$. The inferred distance, including the uncertainty in the absolute calibration, is $D_{\rm TRGB}=20.0 \pm 1.6$ Mpc. The TRGB distance of NGC1052-DF4 is consistent with the previously-determined surface brightness fluctuation distance of $D_{\rm SBF}=18.7\pm 1.7$ Mpc to NGC1052-DF2 and is consistent with the distance of the bright elliptical galaxy NGC1052. We conclude that the unusual properties of these galaxies cannot be explained by distance errors.

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Timing the Early Assembly of the Milky Way with the H3 Survey

The archaeological record of stars in the Milky Way opens a uniquely detailed window into the early formation and assembly of galaxies. Here we use 11,000 main-sequence turn-off stars with well-measured ages, [Fe/H], [$α$/Fe], and orbits from the H3 Survey and Gaia to time the major events in the early Galaxy. Located beyond the Galactic plane, $1\lesssim |Z|/\rm kpc \lesssim4$, this sample contains three chemically distinct groups: a low metallicity population, and low-$α$ and high-$α$ groups at higher metallicity. The age and orbit distributions of these populations show that: 1) the high-$α$ group, which includes both disk stars and the in-situ halo, has a star-formation history independent of eccentricity that abruptly truncated $8.3\pm0.1$ Gyr ago ($z\simeq1$); 2) the low metallicity population, which we identify as the accreted stellar halo, is on eccentric orbits and its star formation truncated $10.2.^{+0.2}_{-0.1}$ Gyr ago ($z\simeq2$); 3) the low-$α$ population is primarily on low eccentricity orbits and the bulk of its stars formed less than 8 Gyr ago. These results suggest a scenario in which the Milky Way accreted a satellite galaxy at $z\approx2$ that merged with the early disk by $z\approx1$. This merger truncated star formation in the early high-$α$ disk and perturbed a fraction of that disk onto halo-like orbits. The merger enabled the formation of a chemically distinct, low-$α$ disk at $z\lesssim1$. The lack of any stars on halo-like orbits at younger ages indicates that this event was the last significant disturbance to the Milky Way disk.

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Measuring Star Formation Histories, Distances, and Metallicities with Pixel Color-Magnitude Diagrams II: Applications to Nearby Elliptical Galaxies

We present spatially-resolved measurements of star formation histories (SFHs), metallicities, and distances in three nearby elliptical galaxies and the bulge of M31 derived using the pixel color-magnitude diagram (pCMD) technique. We compute pCMDs from archival $\textit{HST}$ photometry of M87, M49, NGC 3377 and M31, and fit the data using the new code $\texttt{PCMDPy}$. We measure distances to each system that are accurate to $\sim 10\%$. The recovered non-parametric SFHs place reasonable ($\pm 1$ dex) constraints on the recent (< 2 Gyr) star formation in M31 and NGC 3377, both of which show evidence of inside-out growth. The SFHs in M87 and M49 are constrained only at the oldest ages. The pCMD technique is a promising new avenue for studying the evolutionary history of the nearby universe, and is highly complementary to existing stellar population modeling techniques.

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The Dragonfly Wide Field Survey. I. Telescope, Survey Design and Data Characterization

We present a description of the Dragonfly Wide Field Survey (DWFS), a deep photometric survey of a wide area of sky. The DWFS covers 330 $\mathrm{deg}^2$ in the equatorial GAMA fields and the Stripe 82 fields in the SDSS $g$ and $r$ bands. It is carried out with the 48-lens Dragonfly Telephoto Array, a telescope that is optimized for the detection of low surface brightness emission. The main goal of the survey is to study the dwarf galaxy population beyond the Local Group. In this paper, we describe the survey design and show early results. We reach $1σ$ depths of $μ_g\approx 31$ mag arcsec$^{-2}$ on arcminute scales and show that Milky Way satellites such as Sextans, Bootes, and Ursa Major should be detectable out to $D\gtrsim 10$ Mpc. We also provide an overview of the elements and operation of the 48-lens Dragonfly telescope and a detailed description of its data reduction pipeline. The pipeline is fully automated, with individual frames subjected to a rigorous series of quality tests. The sky subtraction is performed in two stages, ensuring that emission features with spatial scales up to $\sim 0.^{\circ}9 \times 0.^{\circ}6$ are preserved. The DWFS provides unparalleled sensitivity to low surface brightness features on arcminute scales.

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SPECULATOR: Emulating stellar population synthesis for fast and accurate galaxy spectra and photometry

We present SPECULATOR - a fast, accurate, and flexible framework for emulating stellar population synthesis (SPS) models for predicting galaxy spectra and photometry. For emulating spectra, we use principal component analysis to construct a set of basis functions, and neural networks to learn the basis coefficients as a function of the SPS model parameters. For photometry, we parameterize the magnitudes (for the filters of interest) as a function of SPS parameters by a neural network. The resulting emulators are able to predict spectra and photometry under both simple and complicated SPS model parameterizations to percent-level accuracy, giving a factor of $10^3$-$10^4$ speed up over direct SPS computation. They have readily-computable derivatives, making them amenable to gradient-based inference and optimization methods. The emulators are also straightforward to call from a GPU, giving an additional order-of-magnitude speed-up. Rapid SPS computations delivered by emulation offers a massive reduction in the computational resources required to infer the physical properties of galaxies from observed spectra or photometry and simulate galaxy populations under SPS models, whilst maintaining the accuracy required for a range of applications.

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Rapid Reionization by the Oligarchs: The Case for Massive, UV-Bright, Star-Forming Galaxies with High Escape Fractions

The protagonists of cosmic reionization remain elusive. Faint star-forming galaxies are leading candidates because they are numerous and may have significant ionizing photon escape fractions ($f_{esc}$). Here we update this picture via an empirical model that successfully predicts latest observations (e.g., the drop in star-formation density at z>8). We generate an ionizing spectrum for each galaxy in our model and constrain $f_{esc}$ using latest measurements of the reionization timeline (e.g., Ly$α$ damping of quasars and galaxies at z>7). Assuming a constant $f_{esc}$, we find $M_{UV}$<-13.5 galaxies need $f_{esc}=0.21^{+0.06}_{-0.04}$ to complete reionization. The inferred IGM neutral fraction is [0.9, 0.5, 0.1] at z=[8.2, 6.8, 6.2]$\pm$0.2, i.e., the bulk of reionization transpires in 300 Myrs. Inspired by the emergent sample of Lyman Continuum (LyC) leakers that overwhelmingly displays higher-than-average star-formation surface density ($Σ$), we propose a model relating $f_{esc}$ to $Σ$ and find $f_{esc}\proptoΣ^{0.4\pm0.1}$. Since $Σ$ falls by ~2.5 dex between z=8 and z=0, our model explains the humble upper limits on $f_{esc}$ at lower redshifts and its required evolution to ~0.2 at z>6. Within this model, strikingly, <5% of galaxies with $M_{UV}$<-18 (the `oligarchs') account for >80% of the reionization budget. In fact, faint sources ($M_{UV}$>-16) must be relegated to a limited role to ensure high neutral fractions at z=7-8. Shallow faint-end slopes of the UV luminosity function ($α$>-2) and/or $f_{esc}$ distributions skewed toward bright galaxies produce the required late and rapid reionization. We predict LyC leakers like COLA1 (z=6.6, $f_{esc}$~30%, $M_{UV}$=-21.5) become increasingly common towards z~6 and that the drivers of reionization do not lie hidden across the faint-end of the luminosity function, but are already known to us. (abridged)

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A New Census of the 0.2 < z < 3.0 Universe, Part I: The Stellar Mass Function

There has been a long-standing factor-of-two tension between the observed star formation rate density and the observed stellar mass buildup after $z\sim2$. Recently we have proposed that sophisticated panchromatic SED models can resolve this tension, as these methods infer systematically higher masses and lower star formation rates than standard approaches. In a series of papers we now extend this analysis and present a complete, self-consistent census of galaxy formation over $0.2 < z < 3$ inferred with the \texttt{Prospector} galaxy SED-fitting code. In this work, Paper I, we present the evolution of the galaxy stellar mass function using new mass measurements of $\sim$10$^5$ galaxies in the 3D-HST and COSMOS-2015 surveys. We employ a new methodology to infer the mass function from the observed stellar masses: instead of fitting independent mass functions in a series of fixed redshift intervals, we construct a continuity model that directly fits for the redshift evolution of the mass function. This approach ensures a smooth picture of galaxy assembly and makes use of the full, non-Gaussian uncertainty contours in our stellar mass inferences. The resulting mass function has higher number densities at a fixed stellar mass than almost any other measurement in the literature, largely owing to the older stellar ages inferred by \texttt{Prospector}. The stellar mass density is $\sim$50% higher than previous measurements, with the offset peaking at $z\sim1$. The next two papers in this series will present the new measurements of star-forming main sequence and the cosmic star formation rate density, respectively.

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High-resolution spectroscopy of the GD-1 stellar stream localizes the perturber near the orbital plane of Sagittarius

The $100^\circ$-long thin stellar stream in the Milky Way halo, GD-1, has an ensemble of features that may be due to dynamical interactions. Using high-resolution MMT/Hectochelle spectroscopy we show that a spur of GD-1-like stars outside of the main stream are kinematically and chemically consistent with the main stream. In the spur, as in the main stream, GD-1 has a low intrinsic radial velocity dispersion, $σ_{V_r}\lesssim1\,\rm km\,s^{-1}$, is metal-poor, $\rm [Fe/H]\approx-2.3$, with little $\rm [Fe/H]$ spread and some variation in $\rm [α/Fe]$ abundances, which point to a common globular cluster progenitor. At a fixed location along the stream, the median radial velocity offset between the spur and the main stream is smaller than $0.5\,\rm km\,s^{-1}$, comparable to the measurement uncertainty. A flyby of a massive, compact object can change orbits of stars in a stellar stream and produce features like the spur observed in GD-1. In this scenario, the radial velocity of the GD-1 spur relative to the stream constrains the orbit of the perturber and its current on-sky position to $\approx5,000\,\rm deg^2$. The family of acceptable perturber orbits overlaps the stellar and dark-matter debris of the Sagittarius dwarf galaxy in present-day position and velocity. This suggests that GD-1 may have been perturbed by a globular cluster or an extremely compact dark-matter subhalo formerly associated with Sagittarius.

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Combined Effects of Rotation and Age Spreads on Extended Main Sequence Turn Offs

The extended main sequence turn offs (eMSTOs) of several young to intermediate age clusters are examined in the Magellanic Clouds and the Milky Way. We explore the effects of extended star formation (eSF) and a range of stellar rotation rates on the behavior of the color-magnitude diagram (CMD), paying particular attention to the MSTO. We create synthetic stellar populations based on MESA stellar models to simulate observed Hubble Space Telescope and Gaia star cluster data. We model the effect of rotation as a non-parametric distribution, allowing for maximum flexibility. In our models the slow rotators comprise the blueward, and fast rotators the redward portion of the eMSTO. We simulate data under three scenarios: non-rotating eSF, a range of rotation rates with a single age, and a combination of age and rotation effects. We find that two of the five clusters (the youngest and oldest) favor an age spread, but these also achieve the overall worst fits of all clusters. The other three clusters show comparable statistical evidence between rotation and an age spread. In all five cases, a rotation rate distribution alone is capable of qualitatively matching the observed eMSTO structure. In future work, we aim to compare our predicted Vsin(i) with observations in order to better constrain the physics related to stellar rotation.

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Resolving the Metallicity Distribution of the Stellar Halo with the H3 Survey

The Galactic stellar halo is predicted to have formed at least partially from the tidal disruption of accreted dwarf galaxies. This assembly history should be detectable in the orbital and chemical properties of stars. The H3 Survey is obtaining spectra for 200,000 stars, and, when combined with Gaia data, is providing detailed orbital and chemical properties of Galactic halo stars. Unlike previous surveys of the halo, the H3 target selection is based solely on magnitude and Gaia parallax; the survey therefore provides a nearly unbiased view of the entire stellar halo at high latitudes. In this paper we present the distribution of stellar metallicities as a function of Galactocentric distance and orbital properties for a sample of 4232 kinematically-selected halo giants to 100 kpc. The stellar halo is relatively metal-rich, [Fe/H]=-1.2, and there is no discernable metallicity gradient over the range $6 30$ kpc, respectively. Metal-poor stars with [Fe/H]$<-2$ are a small population of the halo at all distances and orbital categories. We associate the "in-situ" stellar halo with stars displaying thick-disk chemistry on halo-like orbits; such stars are confined to $|z|<10$ kpc. The majority of the stellar halo is resolved into discrete features in orbital-chemical space, suggesting that the bulk of the stellar halo formed from the accretion and tidal disruption of dwarf galaxies. (ABRIDGED)

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A Lower Limit on the Mass of Our Galaxy from the H3 Survey

The timing argument provides a lower limit on the mass of the Milky Way. We find, using a sample of 32 stars at $R > 60$ kpc drawn from the H3 Spectroscopic Survey and mock catalogs created from published numerical simulations, that M$_{200} > 0.91\times 10^{12}$ M$_\odot$ with 90% confidence. We recommend using this limit to refine the allowed prior mass range in more complex and sophisticated statistical treatments of Milky Way dynamics. The use of such a prior would have significantly reduced many previously published uncertainty ranges. Our analysis suggests that the most likely value of M$_{200}$ is $\sim 1.4 \times 10^{12}$ M$_\odot$, but establishing this as the Milky Way mass requires a larger sample of outer halo stars and a more complete analysis of the inner halo stars in H3. The imminent growth in the sample of outer halo stars due to ongoing and planned surveys will make this possible.

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