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Hong Soo Park

Publications and source records attributed to Hong Soo Park.

At least 19 recordsLinked to original sources

3.5-meter Segmented-Mirror Robotic Space Telescope Mission White Paper I. Overall Architecture and Scientific Mission

We present the preliminary science concept and mission architecture of a 3.5-meter segmented-mirror robotic space telescope currently under study. The observatory is conceived as a versatile platform supporting wide-field cosmology and galaxy evolution, direct imaging and characterization of nearby planetary systems, time-domain and multi-messenger observations, compact-object studies, and Solar-System small-body science. These programs share requirements for angular resolution, photometric stability, rapid target acquisition, spectroscopy, and long-term observing efficiency. The telescope employs an 18-segment 3.5-meter primary mirror for high-angular-resolution imaging from the near-ultraviolet through the optical and near-infrared. The current baseline covers 0.2--1.5 $μ$m, with the wavelength for diffraction-limited performance to be set by the final wavefront-error budget. Wide-field imaging is intended for deep surveys, precision photometry, and repeated monitoring over approximately 10' $\times$ 10' to 30' $\times$ 30'. Spectroscopic modes with $R \sim 1000$ and higher-resolution options approaching $R \sim 5000$ are being considered for galaxy surveys, transient classification, compact-object spectroscopy, and targeted studies. A dedicated coronagraph is also being studied for direct observations of nearby exoplanetary systems, with a current raw-contrast goal of order $10^{-8}$ and further gains expected from calibration and post-processing. Candidate mission configurations include the Sun--Earth L2 region and alternative Earth orbits, with the final choice driven by science performance, thermal stability, communications, operations, and mission cost. This paper defines the current science requirements, baseline technical configuration, and engineering trade space for further development of the 3.5mST concept.

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3.5-meter Segmented-Mirror Robotic Space Telescope Mission White Paper II. Key Scientific Mission: Wide-Field Cosmology and Galaxy Evolution

The 3.5-meter Segmented-Mirror Robotic Space Telescope uses an image slicer for all spectroscopic observations. The planning baseline uses $R \simeq 1000$ for the wide survey and retains selectable $R \simeq 5000$ bands for precision line measurements. The central science case is a dense emission-line galaxy redshift survey for baryon acoustic oscillations and redshift-space distortions. Supernova and quasar programs exploit the stability, multiplexing, and repeatability of space operations. The supernova tier measures rest-frame U and near-ultraviolet magnitudes that separate optical twins at subgroup precision to $z \simeq 0.9$--$1.1$ in standard visits and to $z \simeq 1.3$--$1.5$ in ten-hour stacks. Every wide-survey tile receives three spectroscopic orientations, and a joint scene reconstruction uses their different overlap geometries to recover the spectra. The flagship survey covers 100--300 deg$^2$ and targets $10^6$--$3 \times 10^6$ emission-line galaxies. A deep pencil-beam tier and a supernova time-domain tier complement the wide survey. The same observations provide a census of ultra-diffuse and low-surface-brightness galaxies, map intracluster light, and test cold, self-interacting, and fuzzy dark matter through dwarf-galaxy structure and low-mass halo abundance.

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3.5-meter Segmented-Mirror Robotic Space Telescope Mission White Paper III. Key Scientific Mission: Exoplanet Science with a Coronagraph

This volume defines the exoplanet science program enabled by the dedicated high-contrast coronagraph in the baseline science payload of the 3.5-meter Segmented-Mirror Robotic Space Telescope. The observatory architecture incorporates the optical interfaces, wavefront sensing and control, pointing stability, and operations software required for coronagraphic observations from the outset. The observing strategy gives priority to the nearest stellar systems because they provide the most accessible laboratories for planetary exploration and the most likely destinations of future interstellar missions. The diffraction limit sets a reflected-light horizon of roughly 10--15 pc for planets at 1 AU and roughly 50--80 pc for Jupiter analogs. Within those horizons, the telescope can image nearby giant planets, obtain reflected-light spectra of their atmospheres, survey young systems and circumstellar disks, and support the habitability and biosignature programs that larger future missions will pursue. The wide-field imager complements the coronagraph through transit photometry, occurrence-rate statistics, and long-term monitoring of stellar magnetic activity. A systematic census of the nearest stellar neighbors provides a lasting reference for exoplanet science and future space exploration.

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3.5-meter Segmented-Mirror Robotic Space Telescope Mission White Paper IV. Key Scientific Mission: Solar-System Small Bodies and Planetary Defense

The baseline 0.2--1.5 $μ$m observatory provides rapid-response astrometry, visible and near-infrared taxonomy, rotation and phase curves, recovery, and long-arc orbit improvement for near-Earth objects and other small bodies. The instrument study also evaluates calibrated throughput to 2.70 $μ$m with a 3.0 $μ$m operational band-edge goal. A reduction to 2.5 $μ$m remains the formal engineering off-ramp if thermal, detector, cooling, mass, power, or cost constraints require it. The 3.5-meter Segmented-Mirror Robotic Space Telescope does not carry a mid-infrared channel. Coordinated ground-based mid-infrared telescopes provide the thermal fluxes required to infer diameter and albedo, while the space mission supplies contemporaneous reflected-light measurements and observing geometry. The program combines recovery, physical characterization, orbit refinement, and covariance-based hazard assessment. Its CODES dynamics system and OGFinder-to-OpenOrb processing path connect measured astrometry to reproducible orbit solutions and close-approach predictions.

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3.5-meter Segmented-Mirror Robotic Space Telescope Mission White Paper V. Key Scientific Mission: Compact-Object Time-Domain Science

An isolated compact object retains the point-source resolving power of the space-based slitless spectrograph. The baseline wavelength range is 0.2--1.5 $μ$m. The planning baseline uses $R \simeq 1000$ for broad and faint transient spectra and reserves selectable bands at $R \simeq 5000$ for accretion-disk profiles, velocity structure, and precision line ratios. Broad features can be measured after binning the native $R \simeq 5000$ data to lower resolution. Rapid-response spectroscopy follows gravitational-wave counterparts and kilonovae from hours to days. Repeated spectra of dwarf novae and compact binaries trace accretion state and orbital phase, while uninterrupted imaging of white dwarfs measures pulsation frequencies. The program combines mission-based monitoring with external alerts, including KGMT transient detections. The instrument study must preserve calibrated throughput to 2.70 $μ$m and evaluate a 3.0 $μ$m operational band edge, with 2.5 $μ$m retained as the formal engineering off-ramp. Mid-infrared imaging is not part of the adopted compact-object baseline.

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SN 2025fhm: A central-engine powered Ic-BL supernova associated with X-ray transient EP250304a

We present X-ray, optical, and radio follow-up observations of EP250304a, an extragalactic fast X-ray transient (EFXT) discovered by the Einstein Probe. Its X-ray light curve exhibits two broad pulses with comparable peak fluxes within the first $\sim$1~ks, a feature rarely seen among low-luminosity gamma-ray bursts or EFXTs. Optical follow-up observations were carried out using the Korea Microlensing Telescope Network, the Thai Robotic Telescope, the Las Cumbres Observatory 1~m global network, the Gemini Multi-Object Spectrograph on Gemini south telescope, and the Global Supernova Network. The fast-cooling phase (within 3 days) of optical data can be well fitted by a shocked cocoon model. However, during the supernova phase (SN 2025fhm, from 3 to 88 days), the late-time light curve cannot be explained solely by radioactive $^{56}$Ni decay, as demonstrated by a grid of simulations using the one-dimensional Lagrangian radiation hydrodynamics code SNEC, which reveals a significant energy excess at late epochs. To account for this excess, a central engine like a rapidly spinning, highly magnetized neutron star is needed to provide additional energy injection. This model yields a best-fit spin period of $\sim$12.60~ms and magnetic field strength of $\sim 3.52\times10^{15} \rm G$, and it successfully explains both the late-time bolometric light curve and the early X-ray pulse structures. Our results indicate that EP250304a/SN 2025fhm is likely powered by a central magnetar rather than by radioactive decay alone, offering new insights into the energy budget and physical origin of EFXTs and their associated supernovae.

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A New WZ Sagittae-type Dwarf Nova KSP-OT-202104a Near the Period Minimum from the KMTNet Supernova Program

We present photometric and spectroscopic studies of a new WZ Sagittae (Sge)-type dwarf nova (DN) KSP-OT-202104a discovered by the Korea Microlensing Telescope Network Supernova Program. The source exhibits outburst amplitudes of $\sim 8$ mag with a duration of $\sim 28.5$ days in the $V$-band. It is a type D DN among WZ Sge-types, and we estimate the superhump period to be $P_{\rm sh} \approx 71.7$ minutes ($=0.04978$ days). Its spectrum shows blue continuum as often found in optically-thick accretion disks of DNe during outbursts with hydrogen absorption lines from H$β$ to H$ζ$. Since the orbital period in WZ Sge-type DNe is typically very close to the superhump period, we consider that this target would belong to the small sample of DNe below the period minimum and may be evolving toward AM Canum Venaticorum (AM CVn) stars. This system therefore adds an example of a short-period dwarf nova with a low mass-transfer rate to the known sample.

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K-DRIFT Science Theme: New Theoretical Framework Using the Galaxy Replacement Technique for LSB studies

Low-surface-brightness (LSB) structures provide critical insights into the hierarchical formation of galaxies and galaxy clusters. The KASI Deep Rolling Imaging Fast Telescope (K-DRIFT) is designed to detect such diffuse features through deep, wide-field optical imaging with a surface brightness reaching $\sim$$30~\rm{mag}~\rm{arcsec}^{-2}$. To interpret the observation data expected from K-DRIFT, we have developed the Galaxy Replacement Technique (GRT), an $N$-body simulation framework optimized for tracing the gravitational evolution of stellar components. The GRT works by inserting high-resolution galaxy models, including a dark matter (DM) halo and stellar disk, in place of multiple low-resolution DM halos in the base $N$-body cosmological simulation. It allows us to achieve very high mass ($m_{star}=5.4\times10^4\msun\ h^{-1}$) and spatial resolution (10~$\rm{pc}~h^{-1}$) with shorter computation time compared to full hydrodynamic cosmological simulations. Therefore, this technique is particularly well-suited for studying LSB structures, with a surface brightness reaching $\sim$$31~\rm{mag}~\rm{arcsec}^{-2}$. In this paper, we present the motivation and methodology of the GRT, summarize key results from previous studies, and highlight its synergy with K-DRIFT observations. We further discuss planned science cases using the GRT, aiming to build a theoretical basis for interpreting LSB features in various environments.

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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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K-DRIFT Science Theme: Galactic Cirrus Clouds and Circumgalactic Medium

In this paper, we review the extended halo material and the circumgalactic medium (CGM), including both dust and gas, and discuss promising science cases that could be realized using the KASI Deep Rolling Imaging Fast Telescope (K-DRIFT). Scattered starlight from cirrus clouds in our Galaxy poses one of the major challenges to studying the low surface brightness features of extragalactic sources. Therefore, it is essential to investigate how to discriminate extragalactic sources from the cirrus cloud features. At the same time, interstellar dust clouds themselves are fundamental to understanding dust properties and the interstellar radiation field, both of which are essential for studies of chemical evolution and star formation in our Galaxy. Measuring the reddening of background sources, such as quasars, with K-DRIFT, which benefits from its broad field of view and accurate background subtraction, allows for effective detection of extended dust in galactic halos, the CGM, and intracluster space. Observations of the H-alpha emission lines can be used to identify signatures of star formation activity within galaxies, as well as the environmental effects acting on them. Galactic winds driven by active galactic nuclei and starbursts can be traced through H-alpha emission. Strong ram pressure stripping effectively removes the interstellar medium (ISM) from galaxies. The stripped ISM becomes ionized or dissociated through mixing with the hot intracluster medium (ICM), forming H-alpha tails. The surface brightness of these H-alpha tails correlates not only with the presence of star formation in the tails but also the mixing stage of the stripped ISM and ICM. The H-alpha survey with K-DRIFT will enable the investigation of the evolutionary stages of ram pressure stripped galaxies in cluster environments, as well as the multiphase gas reservoir around galaxies and in the CGM.

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K-DRIFT Science Theme: Illuminating the Next Era of Galaxy Cluster Science

The KASI Deep Rolling Imaging Fast Telescope (K-DRIFT) is a pioneering instrument designed to explore low-surface-brightness (LSB) phenomena. This white paper presents a compelling array of science cases that showcase K-DRIFT's unique capabilities in unraveling the mysteries of intracluster light (ICL) and other LSB components within galaxy clusters. Exploring the origin of ICL in galaxy clusters and comparing the spatial distributions of ICL and dark matter will offer new insights into galaxy cluster dynamics. Moreover, investigating LSB objects in galaxy clusters, such as LSB structures in the brightest cluster galaxy, ultra-diffuse galaxies, and tidal features, will enhance our understanding of galaxy evolution within the cluster environment. We present our strategies for addressing scientific queries, encompassing LSB observation and analysis techniques, specialized simulations, and machine-learning approaches. Additionally, we examine the potential synergies between K-DRIFT and other ongoing or forthcoming multi-wavelength surveys. This white paper advocates for the recognition and support of K-DRIFT as a dedicated tool for advancing our understanding of the universe's subtlest phenomena.

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K-DRIFT: Unveiling New Imagery of the Hidden Universe

Low-surface-brightness (LSB) structures play a crucial role in understanding galaxy evolution by providing significant insights into galaxy interactions, the histories of mass assembly, and the distribution of dark matter. Nevertheless, their inherently faint nature, coupled with observational difficulties such as stray light interference and variations in the sky background, has significantly impeded comprehensive studies of LSB features. The KASI Deep Rolling Imaging Fast Telescope (K-DRIFT) project aims to address these observational challenges by developing off-axis freeform three-mirror telescopes and observational strategies specifically designed for LSB imaging surveys. The first generation of the K-DRIFT (K-DRIFT G1) has been successfully completed, and the forthcoming survey, scheduled to commence shortly, is expected to yield novel insights into the LSB universe. This paper outlines the scientific motivations of the project, discusses the technical challenges encountered, highlights the innovative solutions devised, and describes the future trajectory of the K-DRIFT.

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Infant Core-collapse Supernovae with Circumstellar Interactions from KMTNet I: Luminous Transitional Case of KSP-SN-2022c

We present $BVi$ multi-band high-cadence observations of a Type II supernova (SN) KSP-SN-2022c from a star-forming galaxy at $z$ $\simeq$ 0.041 from its infant to nebular phase. Early light curve fitting with a single power-law is consistent with the first detection of roughly 15 minutes after shock breakout. The SN light curves feature a rapid rise and decline across its luminous ($V$ $\simeq$ -18.41 mag) peak together with a short plateau. The presence of the short plateau and rapid post-peak decline place the SN within a small group of transitional type between Type II-P and II-L subtypes. Its (i) broad and asymmetric H profiles with large emission-to-absorption ratios and (ii) near-peak luminosity in excess of predictions from SN shock cooling models both point to circumstellar interactions in this SN. Early colour evolution exhibits a short-lived blueward motion in $B-V$ within the first few days and continuous reddening in $V-i$, inconsistent with simple blackbody heating. Our simulations of SN light curves estimate 13 $M_\odot$ and 680 $R_\odot$ for the mass and radius of the progenitor, respectively, together with CSM of 0.73 $M_\odot$ to account for the excess luminosity and rapid post-peak declines. We discuss the origin of its short plateau and early colour evolution in the context of partial envelope stripping of the progenitor star and a delayed SN shock breakout near the edge of the CSM, respectively, as indicated by our simulations. We establish a correlation between post-peak decline rates and CSM mass in Type II SNe, highlighting that CSM interactions play a major role in shaping the post-peak evolution of transitional types.

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The origin and evolution of the normal Type Ia SN 2018aoz with infant-phase reddening and excess emission

SN~2018aoz is a Type Ia SN with a $B$-band plateau and excess emission in the infant-phase light curves $\lesssim$ 1 day after first light, evidencing an over-density of surface iron-peak elements as shown in our previous study. Here, we advance the constraints on the nature and origin of SN~2018aoz based on its evolution until the nebular phase. Near-peak spectroscopic features show the SN is intermediate between two subtypes of normal Type Ia: Core-Normal and Broad-Line. The excess emission could have contributions from the radioactive decay of surface iron-peak elements as well as ejecta interaction with either the binary companion or a small torus of circumstellar material. Nebular-phase limits on H$α$ and He~I favour a white dwarf companion, consistent with the small companion size constrained by the low early SN luminosity, while the absence of [O~I] and He~I disfavours a violent merger of the progenitor. Of the two main explosion mechanisms proposed to explain the distribution of surface iron-peak elements in SN~2018aoz, the asymmetric Chandrasekhar-mass explosion is less consistent with the progenitor constraints and the observed blueshifts of nebular-phase [Fe~II] and [Ni~II]. The helium-shell double-detonation explosion is compatible with the observed lack of C spectral features, but current 1-D models are incompatible with the infant-phase excess emission, $B_{\rm max}-V_{\rm max}$ color, and absence of nebular-phase [Ca~II]. Although the explosion processes of SN~2018aoz still need to be more precisely understood, the same processes could produce a significant fraction of Type Ia SNe that appear normal after $\sim$ 1 day.

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Origin of high-velocity ejecta and early red excess emission in the infant Type Ia supernova 2021aefx

SN~2021aefx is a normal Type Ia Supernova (SN) with red excess emission over the first $\sim$ 2 days. We present detailed analysis of this SN using our high-cadence KMTNet multi-band photometry, spectroscopy, and publicly available data. We provide the first measurements of its epochs of explosion (MJD 59529.32 $\pm$ 0.16) as well as ``first light'' (MJD 59529.85 $\pm$ 0.55) associated with the main ejecta ${\rm{^{56}Ni}}$ distribution. This places our first detection of SN 2021aefx at $\sim -$0.5 hours since ``first light'', indicating the presence of additional power sources. Our peak-spectrum confirms its Type Ia sub-classification as intermediate between Core-Normal and Broad-Line, and we estimate the ejecta mass to be $\sim$ 1.34 $M_{\odot}$. The pre-peak spectral evolution identifies fast-expanding material reaching $>$ 40,000 km s$^{-1}$ (the fastest ever observed in Type Ia SNe) and at least two distinct homologously-expanding ejecta components: (1) a normal-velocity (12,400 km s$^{-1}$) component consistent with the typical photospheric evolution of Chandrasekhar-mass ejecta; and (2) a high-velocity (23,500 km s$^{-1}$) component visible during the first $\sim$ 3.6 days post-explosion, which locates the component within the outer $<$ 16\% of the ejecta mass. Asymmetric, subsonic explosion processes producing a non-spherical photosphere provide an explanation for the simultaneous presence of the two components, as well as the red excess emission via a slight ${\rm{^{56}Ni}}$ enrichment in the outer $\sim$ 0.5\% of the ejecta mass. Our spectrum from 300 days post-peak advances the constraint against non-degenerate companions and further supports a near-Chandrasekhar-mass explosion origin. Off-center ignited delayed-detonations of Chandrasekhar-mass white dwarfs may be responsible for the observed features of SN 2021aefx in some normal Type Ia SNe.

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Infant Type Ia Supernovae from the KMTNet I. Multi-Color Evolution and Populations

We conduct a systematic analysis of the early multi-band light curves and colors of 19 Type Ia Supernovae (SNe) from the Korea Microlensing Telescope Network SN Program, including 16 previously unpublished events. Seven are detected $\lesssim$ 1 day since the estimated epoch of first light and the rest within $\lesssim$ 3 days. Some show excess emission within $<$ 0.5 days to $\sim$ 2 days, but most show pure power-law rises. The colors are initially diverse before $\sim$ 5 days, but converge to a similar color at $\sim$ 10 days. We identify at least three populations based on 2--5-day color evolution: (1) "early-blues" exhibit slowly-evolving colors consistent with a $\sim$ 17,000 K blackbody; (2) "early-reds" have initially blue $B-V$ and red $V-i$ colors that cannot simultaneously be fit with a blackbody -- likely due to suppression of $B$- and $i$-band flux by Fe II/III and Ca II -- and evolve more rapidly; and (3) "early-yellows" evolve blueward, consistent with thermal heating from $\sim$ 8,000 to 13,000 K. The distributions of early-blue and early-red colors are compatible with them being either distinct populations -- with early-reds comprising (60 $\pm$ 15)% of them -- or extreme ends of one continuous population; whereas the early-yellow population identified here is clearly distinct. Compared to the other populations, early-blues in our sample differ by exhibiting excess emission within 1--2 days, nearly constant peak brightness regardless of $ΔM_{15}(B)$ after standardization, and shallower Si II features. Early-blues also prefer star-forming host environments, while early-yellows and, to a lesser extent, early-reds prefer quiescent ones. These preferences appear to indicate at least two Type Ia SN production channels based on stellar population age, while early-reds and early-blues may still share a common origin.

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Helium-deficient ER UMa-type dwarf nova below the period minimum with a hot secondary

We present the discovery of a peculiar dwarf nova KSP-OT-201712a using high-cadence, multi-color observations made with the Korea Microlensing Telescope Network. KSP-OT-201712a exhibits a rare presence of outbursts during standstills as well as strong H$α$ emission for a dwarf nova below the period minimum with an orbital period of 58.75 $\pm$ 0.02 minutes. The outburst cycles are ~ 6.6 days within standstills but increase to ~ 15 days outside of them. Both B-V and V-I colors become bluer and redder as the outburst luminosities increase and decrease, respectively, for the outburst within standstill, while they evolve in the opposite directions outside of the standstills. The presence of strong double-peaked H$α$ and weak He I emission lines with He/H flux ratio of 0.27, together with absorption lines of Mg b and Na D in the source, leads to the estimation Teff ~ 4570 $\pm$ 40 K, [Fe/H] ~ 0.06 $\pm$ 0.15 dex, and log g ~ 4.5 $\pm$ 0.1 for its secondary. KSP-OT-201712a is the second He-deficient dwarf nova below the period minimum, while the temperature of the secondary is measured for the first time in such objects. We identify it to be an ER UMa type dwarf nova suggesting that the evolution of dwarf novae across the period minimum is accompanied by large mass transfers. The high temperature of the secondary indicates that the system started its mass transfer when the secondary was about 93$\%$ of its main sequence age. The system will evolve to a helium cataclysmic variable or to AM CVn once its hydrogen envelope is exhausted before it explodes as a Type Ia supernova.

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Dwarf Galaxy Discoveries from the KMTNet Supernova Program III. the Milky-Way Analog NGC~2997 Group

We present the discovery of 48 new and the analysis of 55, including 7 previously discovered, dwarf galaxy candidates around the giant spiral galaxy NGC~2997 using deep $BVI$ images from the KMTNet Supernova Program. Their $V$-band central surface brightness and total absolute magnitudes are in the range of 20.3--26.7 mag arcsec$^{-2}$ and --(8.02--17.69) mag, respectively, while the $I$-band effective radii are 0.14--2.97 kpc. We obtain $α$ $\simeq$ --1.43 $\pm$ 0.02 for the faint-end slope of their luminosity function, comparable to previously measured values but shallower than theoretical predictions based on $Λ$CDM models. The distance-independent distributions of their mass and color suggest that the group could have recently accreted new massive members from the surrounding fields. The systematically bluer colors of the brighter members indicate younger stellar population and higher star formation activities in them, which appears to be consistent with similar findings from the SAGA or ELVES survey. We suggest that the massive and bluer dwarf galaxies in the group have experienced less environmental quenching due to their recent accretion, while environmental quenching is more effective for the low-mass members. The interpretation of NGC~2997 being populationally young with recent accretion of massive members is also consistent with the overall morphological distribution of the dwarf galaxies showing a lack of morphologically evolved candidates but a plethora of irregularly shaped ones. Our detection rate of dwarf galaxy candidates in the NGC~2997 group and their inferred star formation activities are comparable to those found in Milky Way analog systems from recent surveys within the magnitude limit M$_{V}$ $\lesssim$ --13 mag.

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