arXiv subjects

Jason S. Kalirai

Publications and source records attributed to Jason S. Kalirai.

At least 19 recordsLinked to original sources

arXiv2025

The JWST Resolved Stellar Populations Early Release Science Program. VIII. The Spatially Resolved Star Formation History of WLM

We measure radial stellar age gradients in the relatively isolated gas-rich dwarf irregular WLM, combining JWST NIRCam and NIRISS imaging with six archival Hubble fields over semi-major axis equivalent distances of 0$\lesssim$R$_{SMA}$$\lesssim$4 kpc ($\lesssim$3R$_{hl}$). Fitting lifetime star formation histories (SFHs) to resolved color-magnitude diagrams (CMDs), radial age gradients are quantified using $τ_{90}$ and $τ_{50}$, the lookback times to form 90\% and 50\% of the cumulative stellar mass. We find that globally, the outskirts of WLM are older on average, with ($δ$$τ_{90}$, $δ$$τ_{50}$)/$δ$R$_{SMA}=$(0.82$^{+0.10}_{-0.10}$, 1.60$^{+0.23}_{-0.22}$) Gyr/kpc (stat.), in good agreement with simulations. However, we also detect an azimuthal dependence of radial stellar age gradients, finding that stars on the leading edge of WLM (relative to its proper motion) are both younger and have a flatter age gradient compared to the trailing edge. This difference persists over 0.6$\lesssim$R$_{SMA}$$\lesssim$3.2 kpc ($\sim$0.5$-$2.5R$_{hl}$) and lookback times up to $\sim$8 Gyr, and is robust to assumed stellar evolutionary model. Our results are consistent with star formation triggered by ram pressure stripping from a circumgalactic and/or intergalactic medium, suggested by recent HI observations. If confirmed, processes typifying dense environments, such as ram pressure stripping, may be more relevant to the evolution of isolated galaxies than previously thought.

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arXiv2025

The structure of the stellar halo of the Andromeda galaxy explored with the NB515 for Subaru/HSC. I.: New Insights on the stellar halo up to 120 kpc

We analyse the M31 halo and its substructure within a projected radius of 120 kpc using a combination of Subaru/HSC $\textit{NB515}$ and CFHT/MegaCam $\textit{g}$- \& $\textit{i}$-bands. We succeed in separating M31's halo stars from foreground contamination with $\sim$ 90 \% accuracy by using the surface gravity sensitive $\textit{NB515}$ filter. Based on the selected M31 halo stars, we discover three new substructures, which associate with the Giant Southern Stream (GSS) based on their photometric metallicity estimates. We also produce the distance and photometric metallicity estimates for the known substructures. While these quantities for the GSS are reproduced in our study, we find that the North-Western stream shows a steeper distance gradient than found in an earlier study, suggesting that it is likely to have formed in an orbit closer to the Milky Way. For two streams in the eastern halo (Stream C and D), we identify distance gradients that had not been resolved. Finally, we investigate the global halo photometric metallicity distribution and surface brightness profile using the $\textit{NB515}$-selected halo stars. We find that the surface brightness of the metal-poor and metal-rich halo populations, and the all population can be fitted to a power-law profile with an index of $α=-1.65\pm0.02$, $-2.82\pm0.01$, and $-2.44\pm0.01$, respectively. In contrast to the relative smoothness of the halo profile, its photometric metallicity distribution appears to be spatially non-uniform with nonmonotonic trends with radius, suggesting that the halo population had insufficient time to dynamically homogenize the accreted populations.

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arXiv2023

The JWST Resolved Stellar Populations Early Release Science Program IV: The Star Formation History of the Local Group Galaxy WLM

We present the first star formation history (SFH) and age-metallicity relation (AMR) derived from resolved stellar populations imaged with the JWST NIRCam instrument. The target is the Local Group star-forming galaxy WLM at 970 kpc. The depth of the color-magnitude diagram (CMD) reaches below the oldest main sequence turn-off with a SNR=10 at M_F090W=+4.6 mag; this is the deepest CMD for any galaxy that is not a satellite of the Milky Way. We use Hubble Space Telescope (HST) optical imaging that overlaps with the NIRCam observations to directly evaluate the SFHs derived based on data from the two great observatories. The JWST and HST-based SFHs are in excellent agreement. We use the metallicity distribution function measured from stellar spectra to confirm the trends in the AMRs based on the JWST data. Together, these results confirm the efficacy of recovering a SFH and AMR with the NIRCam F090W-F150W filter combination and provide validation of the sensitivity and accuracy of stellar evolution libraries in the near-infrared relative to the optical for SFH recovery work. From the JWST data, WLM shows an early onset to star formation, followed by an extended pause post-reionization before star formation re-ignites, which is qualitatively similar to what has been observed in the isolated galaxies Leo~A and Aquarius. Quantitatively, 15% of the stellar mass formed in the first Gyr, while only 10% formed over the next ~5 Gyr; the stellar mass then rapidly doubled in ~2.5 Gyr, followed by constant star formation over the last ~5 Gyr.

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arXiv2022

The JWST Resolved Stellar Populations Early Release Science Program I.: NIRCam Flux Calibration

We use globular cluster data from the Resolved Stellar Populations Early Release Science (ERS) program to validate the flux calibration for the Near Infrared Camera (NIRCam) on the James Webb Space Telescope (JWST). We find a significant flux offset between the eight short wavelength detectors, ranging from 1-23% (about 0.01-0.2 mag) that affects all NIRCam imaging observations. We deliver improved zeropoints for the ERS filters and show that alternate zeropoints derived by the community also improve the calibration significantly. We also find that the detector offsets appear to be time variable by up to at least 0.1 mag.

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arXiv2022

Kinematics and Metallicity of Red Giant Branch Stars in the Northeast Shelf of M31

We obtained Keck/DEIMOS spectra of 556 individual red giant branch stars in 4 spectroscopic fields spanning $13-31$ projected kpc along the Northeast (NE) shelf of M31. We present the first detection of a complete wedge pattern in the space of projected M31-centric radial distance versus line-of-sight velocity for this feature, which includes the returning stream component of the shelf. This wedge pattern agrees with expectations of a tidal shell formed in a radial merger and provides strong evidence in favor of predictions of Giant Stellar Stream (GSS) formation models in which the NE shelf originates from the second orbital wrap of the tidal debris. The observed concentric wedge patterns of the NE, West (W), and Southeast (SE) shelves corroborate this interpretation independently of the models. We do not detect a kinematical signature in the NE shelf region corresponding to an intact progenitor core, favoring GSS formation models in which the progenitor is completely disrupted. The shelf's photometric metallicity distribution implies that it is dominated by tidal material, as opposed to the phase-mixed stellar halo or the disk. The metallicity distribution ([Fe/H]$_{\rm phot}$ = $-0.42$ $\pm$ $0.01$) also matches the GSS, and consequently the W and SE shelves, further supporting a direct physical association between the tidal features.

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arXiv2021

Relative Ages of Nine Inner Milky Way Globular Clusters from Proper Motion Cleaned Color-Magnitude Diagrams

Our picture of the age-metallicity relation for Milky Way globular clusters (MWGCs) is still highly incomplete, and the majority of MWGCs lack self-consistent age measurements. Here, we exploit deep, homogenous multi-epoch Hubble Space Telescope (HST) imaging of nine MWGCs located towards the inner Milky Way to measure their relative ages, in most cases for the first time. Our relative age measurements are designed to be directly comparable to the large set of MWGC ages presented by VandenBerg et al. (2013, V13), using identical filters, evolutionary models, and bolometric corrections, extended to the higher extinction values relevant to our target clusters. Adopting the V13 MWGC age scale, our relative age measurements imply that our target clusters are consistently very old, with a mean age of 12.9$\pm$0.4 Gyr, with the exception of the young metal-rich MWGC NGC 6342. We perform two tests to validate the precision of our methodology, and discuss the implications of our target cluster loci in the MWGC age-metallicity plane. In addition, we use our fully self-consistent bolometric corrections to assess the systematic impact of variations in the total-to-selective extinction ratio $R_{V}$ on relative age measurements.

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arXiv2020

Structure and Internal Kinematics of Nine Inner Milky Way Globular Clusters

This study constitutes part of a larger effort aimed at better characterizing the Galactic globular clusters (GGCs) located towards the inner Milky Way bulge and disk. Here, we focus on internal kinematics of nine GGCs, obtained from space-based imaging over time baselines of $>$9 years. We exploit multiple avenues to assess the dynamical state of the target GGCs, constructing radial profiles of projected stellar density, proper motion dispersion, and anisotropy. We posit that two-thirds (6/9) of our target GGCs are in an advanced dynamical state, and are close to (or have recently undergone) core collapse, supported by at least two lines of evidence: First, we find relatively steep proper motion dispersion profiles, in accord with literature values for core-collapsed GGCs. Second, we find that our sample is, in the mean, isotropic even out to their half-light radii, although one of our target clusters (NGC 6380) is tangentially anisotropic at $>$1$σ$ beyond its half-light radius, in accord with theoretical predictions for clusters evolving in strong tidal fields. Our proper motion dispersion and anisotropy profiles are made publicly available.

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arXiv2020

Project AMIGA: The Circumgalactic Medium of Andromeda

Project AMIGA (Absorption Maps In the Gas of Andromeda) is a large ultraviolet Hubble Space Telescope program, which has assembled a sample of 43 QSOs that pierce the circumgalactic medium (CGM) of Andromeda (M31) from R=25 to 569 kpc (25 of them probing gas from 25 kpc to about the virial radius-Rvir = 300 kpc-of M31). Our large sample provides an unparalleled look at the physical conditions and distribution of metals in the CGM of a single galaxy using ions that probe a wide range of gas phases (Si II, Si III, Si IV, C II, C IV, and O VI, the latter being from the Far Ultraviolet Spectroscopic Explorer). We find that Si III and O VI have near unity covering factor maintained all the way out to 1.2Rvir and 1.9Rvir, respectively. We show that Si III is the dominant ion over Si II and Si IV at any R. While we do not find that the properties of the CGM of M31 depend strongly on the azimuth, we show that they change remarkably around 0.3-0.5Rvir, conveying that the inner regions of the CGM of M31 are more dynamic and have more complicated multi-phase gas-structures than at R>0.5Rvir. We estimate the metal mass of the CGM within Rvir as probed by Si II, Si III, and Si IV is 2x10^7 Msun and by O VI is >8x10^7 Msun, while the baryon mass of the 10^4-10^5.5 K gas is ~4x10^10 (Z/0.3 Zsun)^(-1) Msun within Rvir. We show that different zoom-in cosmological simulations of L* galaxies better reproduce the column density profile of O VI with R than Si III or the other studied ions. We find that observations of the M31 CGM and zoom-in simulations of L* galaxies have both lower ions showing higher column density dispersion and dependence on R than higher ions, indicating that the higher ionization structures are larger and/or more broadly distributed.

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arXiv2019

Cool white dwarfs as standards for infrared observations

In the era of modern digital sky surveys, uncertainties in the flux of stellar standards are commonly the dominant systematic error in photometric calibration and can often affect the results of higher-level experiments. The Hubble Space Telescope (HST) spectrophotometry, which is based on computed model atmospheres for three hot (Teff > 30,000 K) pure-hydrogen (DA) white dwarfs, is currently considered the most reliable and internally consistent flux calibration. However many next generation facilities (e.g. Harmoni on E-ELT, Euclid and JWST) will focus on IR observations, a regime in which white dwarf calibration has not yet been robustly tested. Cool DA white dwarfs have energy distributions that peak close to the optical or near-IR, do not have shortcomings from UV metal line blanketing, and have a reasonably large sky density ($\simeq$ 4 deg$^{-2}$ at G < 20), making them, potentially, excellent calibrators. Here we present a pilot study based on STIS+WFC3 observations of two bright DA white dwarfs to test whether targets cooler than current hot primary standards (Teff < 20,000 K) are consistent with the HST flux scale. We also test the robustness of white dwarf models in the IR regime from an X-shooter analysis of Paschen lines and by cross-matching our previously derived Gaia white dwarf catalogue with observations obtained with 2MASS, UKIDSS, VHS, and WISE.

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arXiv2019

Elemental Abundances in M31: First Alpha and Iron Abundance Measurements in M31's Giant Stellar Stream

We present the first measurements of [Fe/H] and [$α$/Fe] abundances, obtained using spectral synthesis modeling, for red giant branch stars in M31's giant stellar stream. The spectroscopic observations, obtained at a projected distance of 17 kpc from M31's center, yielded 61 stars with [Fe/H] measurements, including 21 stars with [$α$/Fe] measurements, from 112 targets identified as M31 stars. The [Fe/H] measurements confirm the expectation from photometric metallicity estimates that stars in this region of M31's halo are relatively metal-rich compared to stars in the MW's inner halo: more than half the stars in the field, including those not associated with kinematically identified substructure, have [Fe/H] abundances $> -1.0$. The stars in this field are $α$-enhanced at lower metallicities, while [$α$/Fe] decreases with increasing [Fe/H] above metallicities of [Fe/H] $\gtrsim -0.9$. Three kinematical components have been previously identified in this field: the giant stellar stream, a second kinematically cold feature of unknown origin, and M31's kinematically hot halo. We compare probabilistic [Fe/H] and [$α$/Fe] distribution functions for each of the components. The giant stellar stream and the second kinematically cold feature have very similar abundance distributions, while the halo component is more metal-poor. Although the current sample sizes are small, a comparison of the abundances of stars in the giant stellar stream field with abundances of M31 halo and dSph stars from the literature indicate that the progenitor of the stream was likely more massive, and experienced a higher efficiency of star formation, than M31's existing dSphs or the dEs NGC147 and NGC185.

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arXiv2019

A Novel Approach to Constrain Rotational Mixing & Convective-Core Overshoot in Stars Using the Initial-Final Mass Relation

The semi-empirical initial-final mass relation (IFMR) connects spectroscopically analyzed white dwarfs in star clusters to the initial masses of the stars that formed them. Most current stellar evolution models, however, predict that stars will evolve to white dwarfs $\sim$0.1 M$_\odot$ less massive than that found in the IFMR. We first look at how varying theoretical mass-loss rates, third dredge-up efficiencies, and convective-core overshoot may help explain the differences between models and observations. These parameters play an important role at the lowest masses (M$_{\rm initial}$ $<$ 3 M$_\odot$). At higher masses, only convective-core overshoot meaningfully affects white dwarf mass, but alone it likely cannot explain the observed white dwarf masses nor why the IFMR scatter is larger than observational errors predict. These higher masses, however, are also where rotational mixing in main sequence stars begins to create more massive cores, and hence more massive white dwarfs. This rotational mixing also extends a star's lifetime, making faster rotating progenitors appear like less massive stars in their semi-empirical age analysis. Applying the observed range of young B-dwarf rotations to the MIST or SYCLIST rotational models demonstrates a marked improvement in reproducing both the observed IFMR data and its scatter. The incorporation of both rotation and efficient convective-core overshoot significantly improves the match with observations. This work shows that the IFMR provides a valuable observational constraint on how rotation and convective-core overshoot affect the core evolution of a star.

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arXiv2018

Project AMIGA: Distance and Metallicity Gradients Along Andromeda's Giant Southern Stream from the Red Clump

The Giant Southern Stream (GSS) of M31, a keystone signature of a major accretion event, yields crucial constraints on M31 formation and evolution models. Currently, our understanding of the GSS, in terms of both its geometry and its chemistry, results from either wide-field imaging probing only a few magnitudes below the red giant branch tip, or deep imaging or spectroscopy of isolated regions. Here, we take an alternative approach, using Hubble Space Telescope (HST) imaging to characterize the horizontal branch red clump (RC) using unbinned maximum likelihood fits to luminosity functions (LFs) from observed color-magnitude diagrams (CMDs). Comparing the RC mean magnitude across three fields at projected distances of 21, 52 and 80 kpc from M31, we find a line of sight distance gradient identical to recent literature measurements in fields along the core. We also find tentative evidence that the line of sight distance dispersion increases with projected distance from M31. Meanwhile, the metallicity in the 52 kpc field westward of the GSS core is at least as high as that in the 21 kpc GSS core field, and the peak colors of the RC in these two fields imply identical metallicities to within 0.2 dex. We discuss implications for distance and metallicity gradients both along and perpendicular to the GSS in the context of recent ground-based photometric and spectroscopic results, including evidence for a dropoff in metallicity moving westward from the GSS, as well as prospects for further constraining stellar populations in the vicinity of the GSS.

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arXiv2018

The White Dwarf Initial-Final Mass Relation for Progenitor Stars From 0.85 to 7.5 M$_\odot$

We present the initial-final mass relation (IFMR) based on the self-consistent analysis of Sirius B and 79 white dwarfs from 13 star clusters. We have also acquired additional signal on eight white dwarfs previously analyzed in the NGC 2099 cluster field, four of which are consistent with membership. These reobserved white dwarfs have masses ranging from 0.72 to 0.97 M$_\odot$, with initial masses from 3.0 to 3.65 M$_\odot$, where the IFMR has an important change in slope that these new data help to observationally confirm. In total, this directly measured IFMR has small scatter ($σ$ = 0.06 M$_\odot$) and spans from progenitors of 0.85 to 7.5 M$_\odot$. Applying two different stellar evolutionary models to infer two different sets of white dwarf progenitor masses shows that when the same model is also used to derive the cluster ages, the resulting IFMR has weak sensitivity to the adopted model at all but the highest initial masses ($>$5.5 M$_\odot$). The non-linearity of the IFMR is also clearly observed with moderate slopes at lower masses (0.08 M$_{\rm final}$/M$_{\rm initial}$) and higher masses (0.11 M$_{\rm final}$/M$_{\rm initial}$) that are broken up by a steep slope (0.19 M$_{\rm final}$/M$_{\rm initial}$) between progenitors from 2.85 to 3.6 M$_\odot$. This IFMR shows total stellar mass loss ranges from 33\% of M$_{\rm initial}$ at 0.83 M$_\odot$ to 83\% of M$_{\rm initial}$ at 7.5 M$_\odot$. Testing this total mass loss for dependence on progenitor metallicity, however, finds no detectable sensitivity across the moderate range of -0.15 $<$ [Fe/H] $<$ +0.15.

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arXiv2018

Improved Main Sequence Turnoff Ages of Young Open Clusters: Multicolor UBV Techniques & the Challenges of Rotation

Main sequence turnoff ages in young open clusters are complicated by turnoffs that are sparse, have high binarity fractions, can be affected by differential reddening, and typically include a number of peculiar stars. Furthermore, stellar rotation can have a significant effect on a star's photometry and evolutionary timescale. In this paper we analyze in 12 nearby open clusters, ranging from ages of 50 Myr to 350 Myr, how broadband UBV color-color relations can be used to identify turnoff stars that are Be stars, blue stragglers, certain types of binaries, or those affected by differential reddening. This UBV color-color analysis also directly measures a cluster's E(B-V) and estimates its [Fe/H]. The turnoff stars unaffected by these peculiarities create a narrower and more clearly defined cluster turnoff. Using four common isochronal models, two of which consider rotation, we fit cluster parameters using these selected turnoff stars and the main sequence. Comparisons of the photometrically fit cluster distances to those based on Gaia DR2 parallaxes find that they are consistent for all clusters. For older (>100 Myr) clusters, like the Pleiades and the Hyades, comparisons to ages based on the lithium depletion boundary method finds that these cleaned turnoff ages agree to within ~10% for all four isochronal models. For younger clusters, however, only the Geneva models that consider rotation fit turnoff ages consistent with lithium-based ages, while the ages based on non-rotating isochrones quickly diverge to become 30% to 80% younger. This illustrates the importance of rotation for deriving ages in the youngest (<100 Myr) clusters.

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arXiv2018

The Age of the Old Metal-Poor Globular Cluster NGC6397 Using WFC3/IR Photometry

Globular Clusters (GCs) in the Milky Way represent the ideal laboratory to establish the age of the oldest stellar populations and to measure the color-magnitude relation of stars. Infrared (IR) photometry of these objects provides a new opportunity to accomplish this task. In particular, at low stellar masses, the stellar main sequence (MS) in an IR color-magnitude diagram (CMD) exhibits a sharp "kink" (due to opacity effects in M dwarfs), such that lower mass and cooler dwarfs become bluer in the F110W - F160W color baseline and not redder. This inversion of the color-magnitude relation offers the possibility to fit GC properties using IR imaging, and to reduce their uncertainties. Here, we used the IR channel of the Wide Field Camera 3 onboard the Hubble Space Telescope to obtain new, deep high-resolution photometry of the old metal-poor GC NGC6397. From the analysis of the GC CMD, we revealed below the MS "kink" the presence of two MSs with different chemical composition. We derived the cluster fiducial line and we compared it with a grid of isochrones over a large range of parameter space, allowing age, metallicity, distance and reddening to vary freely within reasonable selected ranges. We derived an age of 12.6 Gyr with a random uncertainty sigma ~ 0.7 Gyr. These results confirm that the analysis of the IR color-magnitude of stars provide a valuable tool to measure the GC ages and offers a new venue to determine their absolute age to sub-Gyr accuracy with next generation IR telescopes.

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arXiv2018

Deep Hubble Space Telescope Imaging of Globular Clusters Towards the Galactic Bulge: Observations, Data Reduction and Color-Magnitude Diagrams

The Galactic globular clusters (GGCs) located towards the Galactic bulge have generally been excluded from large-scale photometric GGC surveys due to severe total and differential extinction. Here, we present an overview of a Hubble Space Telescope program designed to obtain deep, high spatial resolution multiband imaging of 16 poorly studied GGCs located towards the inner Galactic bulge and disk. In this first paper of a series resulting from these observations, we give an overview of target cluster selection, observations and data reduction procedures for optimizing the resulting photometric catalogs. Artificial star tests are used to compare the respective advantages of different data reduction strategies in terms of photometric and astrometric precision and photometric incompleteness. We present the resulting color-magnitude diagrams (CMDs) of all target clusters in several color-magnitude planes, along with CMDs of comparison fields from parallel observations. For each target cluster, we summarize existing studies, and discuss their CMDs qualitatively in the context of these results.

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arXiv2018

Evidence of a non universal stellar Initial Mass Function. Insights from HST optical imaging of 6 Ultra Faint Dwarf Milky Way Satellites

Using deep HST/ACS observations, we demonstrate that the sub-solar stellar initial mass function (IMF) of 6 ultra-faint dwarf Milky Way Satellites (UFDs) is more bottom light than the IMF of the Milky Way disk. Our data have a lower mass limit of about 0.45 M$_{\odot}$, while the upper limit is $\sim 0.8$ M$_\odot$, set by the turn-off mass of these old, metal poor systems. If formulated as a single power law, we obtain a shallower IMF slope than the "Salpeter" value of $-2.3$, ranging from $-1.01$ for Leo IV, to $-1.87$ for Boötes I. The significance of such deviations depends on the galaxy and is typically 95\% or more. When modeled as a log-normal, the IMF fit results in a larger peak mass than in the Milky Way disk, however a Milky Way disk value for the characteristic system mass ($\sim0.22$ M$_{\odot}$) is excluded only at 68\% significance, and only for some UFDs in the sample. We find that the IMF slope correlates well with the galaxy mean metallicity and, to a lesser degree, with the velocity dispersion and the total mass. The strength of the observed correlations is limited by shot noise in the number of observed stars, but future space-based missions like JWST and WFIRST will both enhance the number of dwarf Milky Way Satellites that can be studied in such detail, and the observation depth for individual galaxies.

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arXiv2017

Stellar Stream and Halo Structure in the Andromeda Galaxy From a Subaru/Hyper Suprime-Cam Survey

We present wide and deep photometry of the northwest part of the halo of the Andromeda galaxy (M31) using Hyper Suprime-Cam on the Subaru Telescope. The survey covers 9.2 deg$^{2}$ field in the $g$, $i$, and $NB515$ bands and shows a clear red giant branch (RGB) of M31's halo stars and a pronounced red clump (RC) feature. The spatial distribution of RC stars shows a prominent stream feature, the North Western (NW) Stream, and a diffuse substructure in the south part of our survey field. We estimate the distances based on the RC method and obtain $(m-M)$ = 24.63$\pm 0.191$(random)$\pm0.057$(systematic) and 24.29$\pm 0.211$(random)$\pm0.057$(systematic) mag for the NW stream and diffuse substructure, respectively, implying that the NW Stream is located behind M31, whereas the diffuse substructure is located in front. We also estimate line-of-sight distances along the NW Stream and find that the south part of the stream is $\sim$20 kpc closer to us relative to the north part. The distance to the NW Stream inferred from the isochrone fitting to the color-magnitude diagram favors the RC-based distance, but the TRGB-based distance estimated for $NB515$-selected RGB stars does not agree with it. The surface number density distribution of RC stars across the NW Stream is found to be approximately Gaussian with a FWHM of $\sim$25 arcmin (5.7 kpc), with a slight skew to the south-west side. That along the NW Stream shows a complicated structure including variations in number density and a significant gap in the stream.

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