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Yuan-Sen Ting

Publications and source records attributed to Yuan-Sen Ting.

At least 199 records · Page 11Linked to original sources

Astronomical Image Quality Prediction based on Environmental and Telescope Operating Conditions

Intelligent scheduling of the sequence of scientific exposures taken at ground-based astronomical observatories is massively challenging. Observing time is over-subscribed and atmospheric conditions are constantly changing. We propose to guide observatory scheduling using machine learning. Leveraging a 15-year archive of exposures, environmental, and operating conditions logged by the Canada-France-Hawaii Telescope, we construct a probabilistic data-driven model that accurately predicts image quality. We demonstrate that, by optimizing the opening and closing of twelve vents placed on the dome of the telescope, we can reduce dome-induced turbulence and improve telescope image quality by (0.05-0.2 arc-seconds). This translates to a reduction in exposure time (and hence cost) of $\sim 10-15\%$. Our study is the first step toward data-based optimization of the multi-million dollar operations of current and next-generation telescopes.

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A new approach to observational cosmology using the scattering transform

Parameter estimation with non-Gaussian stochastic fields is a common challenge in astrophysics and cosmology. In this paper, we advocate performing this task using the scattering transform, a statistical tool sharing ideas with convolutional neural networks (CNNs) but requiring no training nor tuning. It generates a compact set of coefficients, which can be used as robust summary statistics for non-Gaussian information. It is especially suited for fields presenting localized structures and hierarchical clustering, such as the cosmological density field. To demonstrate its power, we apply this estimator to a cosmological parameter inference problem in the context of weak lensing. On simulated convergence maps with realistic noise, the scattering transform outperforms classic estimators and is on a par with state-of-the-art CNN. It retains the advantages of traditional statistical descriptors, has provable stability properties, allows to check for systematics, and importantly, the scattering coefficients are interpretable. It is a powerful and attractive estimator for observational cosmology and the study of physical fields in general.

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Data-driven spectroscopic estimates of absolute magnitude, distance and binarity -- method and catalog of 16,002 O- and B-type stars from LAMOST

We present a data-driven method to estimate absolute magnitudes for O- and B-type stars from the LAMOST spectra, which we combine with {\it Gaia} parallaxes to infer distance and binarity. The method applies a neural network model trained on stars with precise {\it Gaia} parallax to the spectra and predicts $K_{\rm s}$-band absolute magnitudes $M_{Ks}$ with a precision of 0.25\,mag, which corresponds to a precision of 12\% in spectroscopic distance. For distant stars (e.g. $>5$\,kpc), the inclusion of constraints from spectroscopic $M_{Ks}$ significantly improves the distance estimates compared to inferences from {\it Gaia} parallax alone. Our method accommodates for emission line stars by first identifying them via PCA reconstructions and then treating them separately for the $M_{Ks}$ estimation. We also take into account unresolved binary/multiple stars, which we identify through deviations in the spectroscopic $M_{Ks}$ from the geometric $M_{Ks}$ inferred from {\it Gaia} parallax. This method of binary identification is particularly efficient for unresolved binaries with near equal-mass components and thus provides an useful supplementary way to identify unresolved binary or multiple-star systems. We present a catalog of spectroscopic $M_{Ks}$, extinction, distance, flags for emission lines, and binary classification for 16,002 OB stars from LAMOST DR5. As an illustration of the method, we determine the $M_{Ks}$ and distance to the enigmatic LB-1 system, where Liu et al. (2019) had argued for the presence of a black hole and incorrect parallax measurement, and we do not find evidence for errorneous {\it Gaia} parallax.

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The Predicted Properties of Helium-Enriched Globular Cluster Progenitors at High Redshift

Globular cluster progenitors may have been detected by \textit{HST}, and are predicted to be observable with \textit{JWST} and ground-based extremely-large telescopes with adaptive optics. This has the potential to elucidate the issue of globular cluster formation and the origins of significantly helium-enriched subpopulations, a problem in Galactic astronomy with no satisfactory theoretical solution. Given this context, we use model stellar tracks and isochrones to investigate the predicted observational properties of helium-enriched stellar populations in globular cluster progenitors. We find that, relative to helium-normal populations, helium-enriched ($ΔY=+0.12$) stellar populations similar to those inferred in the most massive globular clusters, are expected, modulo some rapid fluctuations in the first $\sim$30 Myr, to be brighter and redder in the rest frame. At fixed age, stellar mass, and metallicity, a helium-enriched population is predicted to converge to being $\sim$0.40 mag brighter at $λ\approx 2.0\, μm$, and to be 0.30 mag redder in the \textit{JWST}-NIRCam colour $(F070W-F200W)$, and to actually be fainter for $λ\lesssim 0.50 \, μm$. Separately, we find that the time-integrated shift in ionizing radiation is a negligible $\sim 5\%$, though we show that the Lyman-$α$ escape fraction could end up higher for helium-enriched stars.

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The GALAH Survey: Using Galactic Archaeology to Refine our Knowledge of TESS Target Stars

An unprecedented number of exoplanets are being discovered by the Transiting Exoplanet Survey Satellite (TESS). Determining the orbital parameters of these exoplanets, and especially their mass and radius, will depend heavily upon the measured physical characteristics of their host stars. We have cross-matched spectroscopic, photometric, and astrometric data from GALAH Data Release 2, the TESS Input Catalog and Gaia Data Release 2, to create a curated, self-consistent catalog of physical and chemical properties for 47,285 stars. Using these data we have derived isochrone masses and radii that are precise to within 5\%. We have revised the parameters of three confirmed, and twelve candidate, TESS planetary systems. These results cast doubt on whether CTOI-20125677 is indeed a planetary system since the revised planetary radii are now comparable to stellar sizes. Our GALAH-TESS catalog contains abundances for up to 23 elements. We have specifically analysed the molar ratios for C/O, Mg/Si, Fe/Si and Fe/Mg, to assist in determining the composition and structure of planets with $R_p < 4R_\oplus$. From these ratios, 36% fall within 2 sigma of the Sun/Earth values, suggesting that these stars may host rocky exoplanets with geological compositions similar to planets found within our own Solar system.

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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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Discovery of ubiquitous lithium production in low-mass stars

The vast majority of stars with mass similar to the Sun are expected to only destroy lithium over the course of their lives, via low-temperature nuclear burning. This has now been supported by observations of hundreds of thousands of red giant stars (Brown et al. 1989, Kumar et al. 2011, Deepak et al. 2019, Singh et al. 2019, Casey et al. 2019). Here we perform the first large-scale systematic investigation into the Li content of stars in the red clump phase of evolution, which directly follows the red giant branch phase. Surprisingly we find that all red clump stars have high levels of lithium for their evolutionary stage. On average the lithium content increases by a factor of 40 after the end of the red giant branch stage. This suggests that all low-mass stars undergo a lithium production phase between the tip of the red giant branch and the red clump. We demonstrate that our finding is not predicted by stellar theory, revealing a stark tension between observations and models. We also show that the heavily studied (Brown et al. 1989, Reddy et al. 2005, Kumar et al. 2011, Singh et al. 2019, Casey et al. 2019) very Li-rich giants, with A(Li) $> +1.5$ dex, represent only the extreme tail of the lithium enhancement distribution, comprising 3% of red clump stars. Our findings suggest a new definition limit for Li-richness in red clump stars, A(Li) $> -0.9$ dex, which is much lower than the limit of A(Li) $> +1.5$ dex used over many decades (Brown et al. 1989, Castilho et al. 1995, Reddy et al. 2005, Carlberg et al. 2016, Casey et al. 2019, Holanda et al. 2020).

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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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Interpreting Stellar Spectra with Unsupervised Domain Adaptation

We discuss how to achieve mapping from large sets of imperfect simulations and observational data with unsupervised domain adaptation. Under the hypothesis that simulated and observed data distributions share a common underlying representation, we show how it is possible to transfer between simulated and observed domains. Driven by an application to interpret stellar spectroscopic sky surveys, we construct the domain transfer pipeline from two adversarial autoencoders on each domains with a disentangling latent space, and a cycle-consistency constraint. We then construct a differentiable pipeline from physical stellar parameters to realistic observed spectra, aided by a supplementary generative surrogate physics emulator network. We further exemplify the potential of the method on the reconstructed spectra quality and to discover new spectral features associated to elemental abundances.

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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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Forecasting Chemical Abundance Precision for Extragalactic Stellar Archaeology

Increasingly powerful and multiplexed spectroscopic facilities promise detailed chemical abundance patterns for millions of resolved stars in galaxies beyond the Milky Way (MW). Here, we employ the Cramér-Rao Lower Bound (CRLB) to forecast the precision to which stellar abundances for metal-poor, low-mass stars outside the MW can be measured for 41 current (e.g., Keck, MMT, VLT, DESI) and planned (e.g., MSE, JWST, ELTs) spectrograph configurations. We show that moderate resolution ($R\lesssim5000$) spectroscopy at blue-optical wavelengths ($λ\lesssim4500$ Å) (i) enables the recovery of 2-4 times as many elements as red-optical spectroscopy ($5000\lesssimλ\lesssim10000$ Å) at similar or higher resolutions ($R\sim 10000$) and (ii) can constrain the abundances of several neutron capture elements to $\lesssim$0.3 dex. We further show that high-resolution ($R\gtrsim 20000$), low S/N ($\sim$10 pixel$^{-1}$) spectra contain rich abundance information when modeled with full spectral fitting techniques. We demonstrate that JWST/NIRSpec and ELTs can recover (i) $\sim$10 and 30 elements, respectively, for metal-poor red giants throughout the Local Group and (ii) [Fe/H] and [$α$/Fe] for resolved stars in galaxies out to several Mpc with modest integration times. We show that select literature abundances are within a factor of $\sim$2 (or better) of our CRLBs. We suggest that, like ETCs, CRLBs should be used when planning stellar spectroscopic observations. We include an open source python package, \texttt{Chem-I-Calc}, that allows users to compute CRLBs for spectrographs of their choosing.

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The GALAH Survey: A new constraint on cosmological lithium and Galactic lithium evolution from warm dwarf stars

Lithium depletion and enrichment in the cosmos is not yet well understood. To help tighten constraints on stellar and Galactic evolution models, we present the largest high-resolution analysis of Li abundances A(Li) to date, with results for over 100 000 GALAH field stars spanning effective temperatures $5900\,\mathrm{K} \lesssim \rm{T_{eff}} \lesssim7000\,\mathrm{K}$ and metallicities $-3 \lesssim \rm[Fe/H] \lesssim +0.5$. We separated these stars into two groups, on the warm and cool side of the so-called Li-dip, a localised region of the Kiel diagram wherein lithium is severely depleted. We discovered that stars in these two groups show similar trends in the A(Li)-[Fe/H] plane, but with a roughly constant offset in A(Li) of 0.4 dex, the warm group having higher Li abundances. At $\rm[Fe/H]\gtrsim-0.5$, a significant increasing in Li abundance with increasing metallicity is evident in both groups, signalling the onset of significant Galactic production. At lower metallicity, stars in the cool group sit on the Spite plateau, showing a reduced lithium of around 0.4 dex relative to the primordial value predicted from Big Bang nucleosynthesis (BBN). However, stars in the warm group between [Fe/H] = -1.0 and -0.5, form an elevated plateau that is largely consistent with the BBN prediction. This may indicate that these stars in fact preserve the primordial Li produced in the early Universe.

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Chemically peculiar A and F stars with enhanced s-process and iron-peak elements: stellar radiative acceleration at work

We present $\gtrsim 15,000$ metal-rich (${\rm [Fe/H]}>-0.2$dex) A and F stars whose surface abundances deviate strongly from Solar abundance ratios and cannot plausibly reflect their birth material composition. These stars are identified by their high [Ba/Fe] abundance ratios (${\rm [Ba/Fe]}>1.0$dex) in the LAMOST DR5 spectra analyzed by Xiang et al. (2019). They are almost exclusively main sequence and subgiant stars with $T_{\rm eff}\gtrsim6300$K. Their distribution in the Kiel diagram ($T_{\rm eff}$--$\log g$) traces a sharp border at low temperatures along a roughly fixed-mass trajectory (around $1.4M_\odot)$ that corresponds to an upper limit in convective envelope mass fraction of around $10^{-4}$. Most of these stars exhibit distinctly enhanced abundances of iron-peak elements (Cr, Mn, Fe, Ni) but depleted abundances of Mg and Ca. Rotational velocity measurements from GALAH DR2 show that the majority of these stars rotate slower than typical stars in an equivalent temperature range. These characteristics suggest that they are related to the so-called Am/Fm stars. Their abundance patterns are qualitatively consistent with the predictions of stellar evolution models that incorporate radiative acceleration, suggesting they are a consequence of stellar internal evolution particularly involving the competition between gravitational settling and radiative acceleration. These peculiar stars constitute 40% of the whole population of stars with mass above 1.5$M_\odot$, affirming that "peculiar" photospheric abundances due to stellar evolution effects are a ubiquitous phenomenon for these intermediate-mass stars. This large sample of Ba-enhanced chemically peculiar A/F stars with individual element abundances provides the statistics to test more stringently the mechanisms that alter the surface abundances in stars with radiative envelopes.

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The GALAH survey: Characterization of emission-line stars with spectral modelling using autoencoders

We present a neural network autoencoder structure that is able to extract essential latent spectral features from observed spectra and then reconstruct a spectrum from those features. Because of the training with a set of unpeculiar spectra, the network is able to reproduce a spectrum of high signal-to-noise ratio that does not show any spectral peculiarities even if they are present in an observed spectrum. Spectra generated in this manner were used to identify various emission features among spectra acquired by multiple surveys using the HERMES spectrograph at the Anglo-Australian telescope. Emission features were identified by a direct comparison of the observed and generated spectra. Using the described comparison procedure, we discovered 10,364 candidate spectra with a varying degree of H$α$/H$β$ emission component produced by different physical mechanisms. A fraction of those spectra belongs to the repeated observation that shows temporal variability in their emission profile. Among emission spectra, we find objects that feature contributions of a nearby rarefied gas (identified through the emission of [NII] and [SII] lines) that was identified in 4004 spectra, which were not all identified as having H$α$ emission. Positions of identified emission-line objects coincide with multiple known regions that harbour young stars. Similarly, detected nebular emission spectra coincide with visually-prominent nebular clouds observable in the red all-sky photographic composites.

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From the Inner to Outer Milky Way: A Photometric Sample of 2.6 Million Red Clump Stars

Large pristine samples of red clump stars are highly sought after given that they are standard candles and give precise distances even at large distances. However, it is difficult to cleanly select red clumps stars because they can have the same T$_{\mathrm{eff}}$ and log $g$ as red giant branch stars. Recently, it was shown that the asteroseismic parameters, $\rmΔ$P and $\rm{Δν}$, which are used to accurately select red clump stars, can be derived from spectra using the change in the surface carbon to nitrogen ratio ([C/N]) caused by mixing during the red giant branch. This change in [C/N] can also impact the spectral energy distribution. In this study, we predict the $\rmΔ$P, $\rm{Δν}$, T$_{\mathrm{eff}}$ and log $g$ using 2MASS, AllWISE, \gaia, and Pan-STARRS data in order to select a clean sample of red clump stars. We achieve a contamination rate of $\sim$20\%, equivalent to what is achieved when selecting from T$_{\mathrm{eff}}$ and log $g$ derived from low resolution spectra. Finally, we present two red clump samples. One sample has a contamination rate of $\sim$ 20\% and $\sim$ 405,000 red clump stars. The other has a contamination of $\sim$ 33\% and $\sim$ 2.6 million red clump stars which includes $\sim$ 75,000 stars at distances $>$ 10 kpc. For |b|>30 degrees we find $\sim$ 15,000 stars with contamination rate of $\sim$ 9\%. The scientific potential of this catalog for studying the structure and formation history of the Galaxy is vast given that it includes millions of precise distances to stars in the inner bulge and distant halo where astrometric distances are imprecise.

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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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A Mystery in Chamaeleon: Serendipitous Discovery of a Galactic Symbiotic Nova

We present the serendipitous discovery of a low luminosity nova occurring in a symbiotic binary star system in the Milky Way. We lay out the extensive archival data alongside new follow-up observations related to the stellar object V$^*$ CN Cha in the constellation of Chamaeleon. The object had long period ($\sim\! 250\,$day), high amplitude ($\sim\! 3\,$mag) optical variability in its recent past, preceding an increase in optical brightness by $\sim\! 8\,$magnitudes and a persistence at this luminosity for about 3 years, followed by a period of $\sim\! 1.4\,{\rm mag}\,{\rm yr}^{-1}$ dimming. The object's current optical luminosity seems to be dominated by H$α$ emission, which also exhibits blue-shifted absorption (a P-Cygni-like profile). After consideration of a number of theories to explain these myriad observations, we determine that V$^*$ CN Cha is most likely a symbiotic (an evolved star-white dwarf binary) system which has undergone a long-duration, low luminosity, nova. Interpreted in this way, the outburst in V$^*$ CN Cha is among the lowest luminosity novae ever observed.

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