arXiv subjects

Soung-Chul Yang

Publications and source records attributed to Soung-Chul Yang.

At least 19 recordsLinked to original sources

arXiv2026

The SPHEREx Ices Investigation: An Overview

SPHEREx is a NASA mission designed to perform an all-sky spectroscopic survey in the 0.75 - 5 $μ$m wavelength range. Its primary science objectives are to investigate: (1) inflationary cosmology, (2) the history of galaxy formation, and (3) the abundance of molecular ices - critical for prebiotic chemistry - found on the surfaces of interstellar dust grains within planet-forming regions. This paper focuses on the third theme, the SPHEREx Ices investigation, for which SPHEREx is conducting a spectroscopic survey of nearly ten million preselected sources throughout the Milky Way and Magellanic Clouds to characterize their ice absorption features. By selecting targets based on infrared color, spatial isolation, and brightness, the Ices Investigation secures high-signal-to-noise spectra across a broad range of astrophysical environments that are relatively free of spectral contamination. Rather than attempting to decompose each spectrum into its individual ice components, the Ices Investigation prioritizes accurate measurements of the integrated optical depths of key molecular ice absorption features. This approach enables statistically powerful correlation studies between ice abundances and environmental parameters - including extinction, temperature, gas composition, radiation field strength, cosmic ray flux, and star formation activity. The data pipeline developed for this purpose incorporates machine learning for continuum estimation, drawing on both SPHEREx and ancillary datasets. Ultimately, the expansive spectral archive produced by SPHEREx, combined with targeted follow-up from facilities like JWST, will transform our understanding of Galactic ice formation, evolution, abundance and their inheritance into planetary systems and prebiotic inventories.

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arXiv2026

K-DRIFT Science Theme: Galaxies in the Faint Universe

Low-surface-brightness (LSB) structures serve as evidence of the intricate mass assembly of galaxies, and dedicatedly studying them promises to give us profound insights into the evolutionary history of galaxies. Furthermore, delving into the properties of star formation (SF) in the LSB regime can broaden our understanding of SF activity in regions characterized by low surface gas density, thereby shedding light on fundamental cosmic processes. However, systematic uncertainties may hamper the exploration of the LSB universe by limiting detectable SB levels. Indeed, despite dedicated advancements in telescope and observing techniques over decades, achieving ultra-deep photometric depths in optical wavelengths remains a formidable challenge. To overcome this challenge and explore the LSB universe that we have yet to see, we have been developing a novel telescope called K-DRIFT. This paper outlines the telescope's specification and describes various LSB features we aim for, explicitly focusing on nearby individual galaxies. To further advance the capabilities of the K-DRIFT survey, focused on LSB detection, we present several feasible research topics that utilize other survey data together and discuss the role of LSB observation in understanding the evolution of galaxies.

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arXiv2025

The SPHEREx Target List of Ice Sources (SPLICES)

One of the primary objectives of the SPHEREx mission is to understand the origin of molecules such as H2O, CO2, and other volatile compounds at the early stages of planetary system formation. Because the vast majority of these compounds -- typically exceeding 95% -- exist in the solid phase rather than the gaseous phase in the systems of concern here, the observing strategy planned to characterize them is slightly unusual. Specifically, SPHEREx will target highly obscured sources throughout the Milky Way, and observe the species of concern in absorption against background illumination. SPHEREx spectrophotometry will yield ice column density measurements for millions of obscured Milky Way sources of all ages and types. By correlating those column densities with source ages, the SPHEREx mission will shed light on whether those molecules were formed in situ along with their nascent stellar systems, or whether instead they formed elsewhere and were introduced into those systems after their formation. To that end, this work describes version 7$.$1 of the SPHEREx Target List of Ice Sources (SPLICES) for the community. It contains about 8$.$6 million objects brighter than W2~12 Vega mag over much of the sky, principally within a broad strip running the length of the Milky Way midplane, but also within high-latitude molecular clouds and even the Magellanic Clouds.

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arXiv2023

Search for Extremely Metal-Poor Stars with GEMINI-N/GRACES I. Chemical-Abundance Analysis

We present stellar parameters and abundances of 13 elements for 18 very metal-poor (VMP; [Fe/H] $<$ -2.0) stars, selected as extremely metal-poor (EMP; [Fe/H] $<$ -3.0) candidates from SDSS and LAMOST survey. High-resolution spectroscopic observations were performed using GEMINI-N/GRACES. We find ten EMP stars among our candidates, and we newly identify three carbon-enhanced metal poor (CEMP) stars with [Ba/Fe] $<$ 0. Although chemical abundances of our VMP/EMP stars generally follow the overall trend of other Galactic halo stars, there are a few exceptions. One Na-rich star ([Na/Fe] = +1.14) with low [Mg/Fe] suggests a possible chemical connection with second-generation stars in a globular cluster. The progenitor of an extremely Na-poor star ([Na/Fe] = -1.02) with an enhancement of K- and Ni-abundance ratios may have undergone a distinct nucleosynthesis episode, associated with core-collapse supernovae (CCSNe) having a high explosion energy. We have also found a Mg-rich star ([Mg/Fe] = +0.73) with slightly enhanced Na and extremely low [Ba/Fe], indicating that its origin is not associated with neutron-capture events. On the other hand, the origin of the lowest Mg abundance ([Mg/Fe] = -0.61) star could be explained by accretion from a dwarf galaxy, or formation in a gas cloud largely polluted by SNe Ia. We have also explored the progenitor masses of our EMP stars by comparing their chemical-abundance patterns with those predicted by Population III SNe models, and find a mass range of 10 - 26 $M_\odot$, suggesting that such stars were primarily responsible for the chemical enrichment of the early Milky Way.

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arXiv2021

Optical and near-infrared pulsation properties of RR Lyrae and Population II Cepheid variables in the Messier 15 globular cluster

Messier 15 (NGC 7078) is an old and metal-poor post core-collapse globular cluster which hosts a rich population of variable stars. We report new optical ($gi$) and near-infrared (NIR, $JK_s$) multi-epoch observations for 129 RR Lyrae, 4 Population II Cepheids (3 BL Herculis, 1 W Virginis), and 1 anomalous Cepheid variable candidate in M15 obtained using the MegaCam and the WIRCam instruments on the 3.6-m Canada-France-Hawaii Telescope. Multi-band data are used to improve the periods and classification of variable stars, and determine accurate mean magnitudes and pulsational amplitudes from the light curves fitted with optical and NIR templates. We derive optical and NIR period-luminosity relations for RR Lyrae stars which are best constrained in the $K_s$-band, $m_{K_s} = -2.333~(0.054) \log P + 13.948~(0.015)$ with a scatter of only $0.037$ mag. Theoretical and empirical calibrations of RR Lyrae period-luminosity-metallicity relations are used to derive a true distance modulus to M15: $15.196~\pm~0.026$~(statistical)~$\pm~ 0.039$~(systematic) mag. Our precise distance moduli based on RR Lyrae stars and Population II Cepheid variables are mutually consistent and agree with recent distance measurements in the literature based on {\it Gaia} parallaxes and other independent methods.

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arXiv2021

RR Lyrae variables in Messier 53: Near-infrared Period--Luminosity relations and the calibration using Gaia Early Data Release 3

We present new near-infrared, $JHK_s$, Period--Luminosity relations (PLRs) for RR Lyrae variables in the Messier 53 (M53 or NGC 5024) globular cluster. Multi-epoch $JHK_s$ observations, obtained with the WIRCam instrument on the 3.6-m Canada France Hawaii Telescope, are used for the first time to estimate precise mean-magnitudes for 63 RR Lyrae stars in M53 including 29 fundamental-mode (RRab) and 34 first-overtone modes (RRc) variables. The $JHK_s$-band PLRs for RR Lyrae stars are best constrained for RRab types with a minimal scatter of 22, 23, and 19 mmag, respectively. The combined sample of RR Lyrae is used to derive the $K_s$-band PLR, $K_s = -2.303 (0.063) \log P + 15.212 (0.016)$ exhibiting a $1σ$ dispersion of only $0.027$ mag. Theoretical Period--Luminosity--Metallicity (PLZ) relations are used to predict parallaxes for 400 Galactic RR Lyrae resulting in a median parallax zero-point offset of $-7\pm3~μ$as in {\it Gaia} Early Data Release 3 (EDR3), which increases to $22\pm2~μ$as if the parallax corrections are applied. We also estimate a robust distance modulus, $μ_\textrm{M53} = 16.403 \pm 0.024$ (statistical) $\pm 0.033$ (systematic) mag, to M53 based on theoretical calibrations. Homogeneous and precise mean-magnitudes for RR Lyrae in M53 together with similar literature data for M3, M4, M5, and $ω$ Cen are used to empirically calibrate a new RR Lyrae PLZ$_{K_s}$ relation, $K_s = -0.848 (0.007) -2.320 (0.006) \log P + 0.166 (0.011) {\rm[Fe/H]}$, anchored with {\it Gaia} EDR3 distances and theoretically predicted relations, and simultaneously estimate precise RR Lyrae based distances to these globular clusters.

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arXiv2020

Exploring the nature and synchronicity of early cluster formation in the Large Magellanic Cloud V: Multiple Populations in ancient Globular Clusters

We examine four ancient Large Magellanic Cloud (LMC) globular clusters (GCs) for evidence of multiple stellar populations using the Advanced Camera for Surveys and Wide Field Camera 3 on the Hubble Space Telescope Programme GO-14164. NGC 1466, NGC 1841, and NGC 2257 all show evidence for a redder, secondary population along the main-sequence. Reticulum does not show evidence for the presence of a redder population, but this GC has the least number of stars and Monte Carlo simulations indicate that the sample of main sequence stars is too small to robustly infer whether a redder population exists in this cluster. The second, redder, population of the other three clusters constitutes $\sim30-40\%$ of the total population along the main-sequence. This brings the total number of ancient LMC GCs with known split or broadened main-sequences to five. However, unlike for Hodge 11 and NGC 2210 (see arXiv:1904.01434), none of the clusters show evidence for multiple populations in the horizontal branch. We also do not find evidence of a second population along the Red Giant Branch (RGB).

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arXiv2019

Exploring the nature and synchronicity of early cluster formation in the Large Magellanic Cloud IV: Evidence for Multiple Populations in Hodge 11 and NGC 2210

We present a multiple population search in two old Large Magellanic Cloud (LMC) Globular Clusters, Hodge 11 and NGC 2210. This work uses data from the Advanced Camera for Surveys and Wide Field Camera 3 on the Hubble Space Telescope from programme GO-14164 in Cycle 23. Both of these clusters exhibit a broadened main sequence with the second population representing ($20 \pm \! \sim \! 5$)% for NGC 2210 and ($30 \pm \! \sim \! 5$)% for Hodge 11. In both clusters, the smaller population is redder than the primary population, suggesting CNO variations. Hodge 11 also displays a bluer second population in the horizontal branch, which is evidence for helium enhancement. However, even though NGC 2210 shows similarities to Hodge 11 in the main sequence, there does not appear to be a second population on NGC 2210's horizontal branch. This is the first photometric evidence that ancient LMC Globular Clusters exhibit multiple stellar populations.

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arXiv2019

RR Lyrae Stars in the Field of Sagittarius II

We present the detection of RR Lyrae variable stars in the field of the Sagittarius II (Sgr II) ultra-faint dwarf (UFD) galaxy. Using B, V time-series photometry obtained with the Korea Microlensing Telescope Network (KMTNet) 1.6 m telescope at CTIO and G-band data from Gaia Data Release 2 (DR2), we identified and characterized two ab-type and four c-type RR Lyrae variables. Five out of the six stars are clustered within three half-light radii (~4.8') of the galaxy indicating their association with Sgr II, while the RRab star V4 is located ~22' from the galaxy center. By excluding V4, the high c-type fraction (0.8) and the period of the only RRab star V3 (P_V3 = 0.666 days) suggest an Oosterhoff II (Oo II) classification for Sgr II. Located close to the locus of Oo II clusters in the period-amplitude diagram, V3 is similar to RRab stars in other UFDs having Oosterhoff-intermediate and Oo II properties. Sgr II is, however, more compact than usual UFDs, placed in between star clusters and dwarf galaxies in the size-luminosity plane, and therefore spectroscopic studies are eventually required to ascertain the true nature of this stellar system. We derive the metallicity ([Fe/H]_RRab = -2.1 +- 0.3) and heliocentric distance (~64 +- 3 kpc) of Sgr II from the RR Lyrae stars, and estimate its age (~12 Gyr) based on our stellar population models. The Oosterhoff properties of UFDs can be explained with the evolution effect of RR Lyrae stars in the instability strip.

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arXiv2018

RR Lyrae Variable Stars in the Crater II Dwarf Galaxy

We report the detection of RR Lyrae variable stars in Crater II, a recently discovered large and diffuse satellite dwarf galaxy of the Milky Way (MW). Based on B, V time-series photometry obtained with the Korea Microlensing Telescope Network (KMTNet) 1.6-m telescope at CTIO, we identified 83 ab-type and 13 c-type pulsators by fitting template light curves. The detected RR Lyrae stars are centrally concentrated, which ensures that most of them are members of Crater II. In terms of the distribution of RRab stars in the period-amplitude diagram, Crater II is clearly different from ultra-faint dwarf (UFD) galaxies, but very similar to the two classical MW dwarf spheroidal (dSph) galaxies Draco and Carina with Oosterhoff-intermediate (Oo-int) properties. Combined with the mean period of ab-type variables ( = 0.631+-0.004 d) and the c-type fraction (~0.14) in Crater II, this suggests an Oo-int classification for Crater II and implies that its nature is more like a dSph rather than a UFD. We also estimated the mean metallicity, reddening, and distance of Crater II, from the photometric and pulsation properties of the RR Lyrae stars. The stellar population model we have constructed indicates that Crater II is dominated by an old population, but is relatively younger than the oldest globular clusters in the MW. With a lack of high-amplitude short-period RRab stars, Crater II, like most of the other less massive dSphs, is probably not a surviving counterpart of the major building blocks of the MW halo.

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arXiv2017

Exploring the nature and synchronicity of early cluster formation in the Large Magellanic Cloud: III. Horizontal Branch Morphology

We leverage new high-quality data from Hubble Space Telescope program GO-14164 to explore the variation in horizontal branch morphology among globular clusters in the Large Magellanic Cloud (LMC). Our new observations lead to photometry with a precision commensurate with that available for the Galactic globular cluster population. Our analysis indicates that, once metallicity is accounted for, clusters in the LMC largely share similar horizontal branch morphologies regardless of their location within the system. Furthermore, the LMC clusters possess, on average, slightly redder morphologies than most of the inner halo Galactic population; we find, instead, that their characteristics tend to be more similar to those exhibited by clusters in the outer Galactic halo. Our results are consistent with previous studies showing a correlation between horizontal branch morphology and age.

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arXiv2017

Exploring the nature and synchronicity of early cluster formation in the Large Magellanic Cloud: II. Relative ages and distances for six ancient globular clusters

We analyze Hubble Space Telescope observations of six globular clusters in the Large Magellanic Cloud from program GO-14164 in Cycle 23. These are the deepest available observations of the LMC globular cluster population; their uniformity facilitates a precise comparison with globular clusters in the Milky Way. Measuring the magnitude of the main sequence turnoff point relative to template Galactic globular clusters allows the relative ages of the clusters to be determined with a mean precision of 8.4%, and down to 6% for individual objects. We find that the mean age of our LMC cluster ensemble is identical to the mean age of the oldest metal-poor clusters in the Milky Way halo to 0.2 $\pm$ 0.4 Gyr. This provides the most sensitive test to date of the synchronicity of the earliest epoch of globular cluster formation in two independent galaxies. Horizontal branch magnitudes and subdwarf fitting to the main sequence allow us to determine distance estimates for each cluster, and examine their geometric distribution in the LMC. Using two different methods, we find an average distance to the LMC of 18.52 $\pm$ 0.05.

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arXiv2016

The Carnegie-Chicago Hubble Program. I. An Independent Approach to the Extragalactic Distance Scale Using only Population II Distance Indicators

We present an overview of the Carnegie-Chicago Hubble Program, an ongoing program to obtain a 3 per cent measurement of the Hubble constant using alternative methods to the traditional Cepheid distance scale. We aim to establish a completely independent route to the Hubble constant using RR Lyrae variables, the tip of the red giant branch (TRGB), and Type Ia supernovae (SNe Ia). This alternative distance ladder can be applied to galaxies of any Hubble Type, of any inclination, and, utilizing old stars in low density environments, is robust to the degenerate effects of metallicity and interstellar extinction. Given the relatively small number of SNe Ia host galaxies with independently measured distances, these properties provide a great systematic advantage in the measurement of the Hubble constant via the distance ladder. Initially, the accuracy of our value of the Hubble constant will be set by the five Galactic RR Lyrae calibrators with Hubble Space Telescope Fine-Guidance Sensor parallaxes. With Gaia, both the RR Lyrae zero point and TRGB method will be independently calibrated, the former with at least an order of magnitude more calibrators and the latter directly through parallax measurement of tip red giants. As the first end-to-end "distance ladder" completely independent of both Cepheid variables and the Large Magellanic Cloud, this path to the Hubble constant will allow for the high precision comparison at each rung of the traditional distance ladder that is necessary to understand tensions between this and other routes to the Hubble constant.

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arXiv2014

Measurable Relationship Between Bright Galaxies and Their Faint Companions in WHL J085910.0+294957, a Galaxy Cluster at z = 0.30: Vestiges of Infallen Groups?

The properties of satellite galaxies are closely related to their host galaxies in galaxy groups. In cluster environments, on the other hand, the interaction between close neighbors is known to be limited. Our goal is to examine the relationships between host and satellite galaxies in the harsh environment of a galaxy cluster. To achieve this goal, we study a galaxy cluster WHL J085910.0+294957 at z = 0.30 using deep images obtained with CQUEAN CCD camera mounted on the 2.1-m Otto Struve telescope. After member selection based on the scaling relations of photometric and structural parameters, we investigate the relationship between bright (M_i < -18) galaxies and their faint (-18 < M_i < -15) companions. The weighted mean color of faint companion galaxies shows no significant dependence (< 1 sigma to Bootstrap uncertainties) on cluster-centric distance and local luminosity density as well as the luminosity and concentration of an adjacent bright galaxy. However, the weighted mean color shows marginal dependence (~ 2.2 sigma) on the color of an adjacent bright galaxy, when the sample is limited to bright galaxies with at least 2 faint companions. By using a permutation test, we confirm that the correlation in color between bright galaxies and their faint companions in this cluster is statistically significant with a confidence level of 98.7%. The statistical significance increases if we additionally remove non-members using the SDSS photometric redshift information (~ 2.6 sigma and 99.3%). Our results suggest three possible scenarios: (1) vestiges of infallen groups, (2) dwarf capturing, and (3) tidal tearing of bright galaxies.

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arXiv2014

The RR Lyrae Variable Population in the Phoenix Dwarf Galaxy

We present the first detailed study of the RR Lyrae variable population in the Local Group dSph/dIrr transition galaxy, Phoenix, using previously obtained HST/WFPC2 observations of the galaxy. We utilize template light curve fitting routines to obtain best fit light curves for RR Lyrae variables in Phoenix. Our technique has identified 78 highly probable RR Lyrae stars (54 ab-type; 24 c-type) with about 40 additional candidates. We find mean periods for the two populations of $\langle P_{ab}\rangle = 0.60 \pm 0.03$ days and $\langle P_{c}\rangle = 0.353 \pm 0.002$ days. We use the properties of these light curves to extract, among other things, a metallicity distribution function for ab-type RR Lyrae. Our analysis yields a mean metallicity of $\langle [Fe/H]\rangle = -1.68 \pm 0.06$ dex for the RRab stars. From the mean period and metallicity calculated from the ab-type RR Lyrae, we conclude that Phoenix is more likely of intermediate Oosterhoff type; however the morphology of the Bailey diagram for Phoenix RR Lyraes appears similar to that of an Oosterhoff type I system. Using the RRab stars, we also study the chemical enrichment law for Phoenix. We find that our metallicity distribution is reasonably well fitted by a closed-box model. The parameters of this model are compatible with the findings of Hidalgo et al. (2009) further supporting the idea that Phoenix appears to have been chemically enriched as a closed-box-like system during the early stage of its formation and evolution.

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arXiv2014

The Early Chemical Enrichment Histories of Two Sculptor Group Dwarf Galaxies as Revealed by RR Lyrae Variables

We present the results of our analysis of the RR Lyrae (RRL) variable stars detected in two transition-type dwarf galaxies (dTrans), ESO294-G010 and ESO410-G005 in the Sculptor group, which is known to be one of the closest neighboring galaxy groups to our Local Group. Using deep archival images from the Advanced Camera for Surveys (ACS) onboard the Hubble Space Telescope (HST), we have identified a sample of RR Lyrae candidates in both dTrans galaxies [219 RRab (RR0) and 13 RRc (RR1) variables in ESO294-G010; 225 RRab and 44 RRc stars in ESO410-G005]. The metallicities of the individual RRab stars are calculated via the period-amplitude-[Fe/H] relation derived by Alcock et al. This yields mean metallicities of <[Fe/H]>_{ESO294} = -1.77 +/- 0.03 and <[Fe/H]>_{ESO410} = -1.64 +/- 0.03. The RRL metallicity distribution functions (MDFs) are investigated further via simple chemical evolution models; these reveal the relics of the early chemical enrichment processes for these two dTrans galaxies. In the case of both galaxies, the shapes of the RRL MDFs are well-described by pre-enrichment models. This suggests two possible channels for the early chemical evolution for these Sculptor group dTrans galaxies: 1) The ancient stellar populations of our target dwarf galaxies might have formed from the star forming gas which was already enriched through "prompt initial enrichment" or an "initial nucleosynthetic spike" from the very first massive stars, or 2) this pre-enrichment state might have been achieved by the end products from more evolved systems of their nearest neighbor, NGC 55.

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arXiv2012

WIYN Open Cluster Study : Wide-Field CCD Photometry of the Old Open Cluster NGC 6819

We present a comprehensive photometric study of the old open cluster, NGC 6819 using 1x1 degree field VI MOSAIC CCD imaging taken with the WIYN 0.9m telescope. The resultant color-magnitude diagram (CMD) shows a well developed main sequence (MS) extending from V~14.5 mag down to our photometric limit of V~21 mag. Fitting theoretical isochrones with adopted values of the reddening and metallicity (E(B-V)=0.14, [Fe/H]=+0.09 dex) to the observed CMD yields a distance modulus of (m-M)_{0}=11.93+/-0.10 and an age of ~2.6 Gyr for NGC 6819. Our wide-field imaging reveals that NGC 6819 is larger in areal extent (R=13') than previously thought. The wide-field also benefits our estimate of the degree of field star contamination, and ultimately yields improved measurements of the structural parameters (r_c=2.80', r_t=38.2', and r_h=7') and tidal mass of the cluster (M_{tid}=3542.4 M(sun)). The flattened luminosity and mass functions indicate that NGC 6819 has experienced mass segregation as a result of its dynamical evolution. Our variability study of the cluster blue straggler star (BSS) population using the Welch-Stetson variability index (I_{WS}) has revealed a number of variable BSS candidates.

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arXiv2012

An Ancient Metal-Poor Population in M32, and Halo Satellite Accretion in M31, Identified by RR Lyrae Stars

We present time-series photometry of two fields near M32 using archival observations from ACS/WFC onboard HST. One field is centered about 2 arcmin from M32 while the other is located 15 arcmin to the southeast of M31. We identify a total of 1139 RR Lyrae variables of which 821 are ab-type and 318 are c-type. In the field near M32, we find a radial gradient in the density of RR Lyraes relative to the center of M32. This gradient is consistent with the surface brightness profile of M32 suggesting that a significant number of the RR Lyraes in this region belong to M32. This provides further confirmation that M32 contains an ancient stellar population formed around the same time as the oldest population in M31 and the Milky Way. The RR Lyrae stars in M32 exhibit a mean metal abundance of [Fe/H] ~ -1.42 +/- 0.02, which is ~15 times lower than the metal abundance of the overall M32 stellar population. Moreover, the abundance of RR Lyrae stars normalized to the luminosity of M32 in the field analyzed further indicates that the ancient metal-poor population in M32 represents only a very minor component of this galaxy, consistent with the 1% to 4.5% in mass inferred from the CMD analysis of Monachesi et al. In the other field, we find unprecedented evidence for two populations of RR Lyraes in M31 as shown by two distinct sequences among the ab-type variables in the Bailey Diagram. When interpreted in terms of metal abundance, one population exhibits a peak at [Fe/H] ~ -1.3 and the other is at [Fe/H] ~ -1.9. One possible interpretation of this result is that the more metal-rich population represents the dominant M31 halo, while the metal-poorer group could be a disrupted dwarf satellite galaxy orbiting M31. If true, this represents a further indication that the formation of the M31 spheroid has been significantly influenced by the merger and accretion of dwarf galaxy satellites. [abridged]

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