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Wei-Chun Jao

Publications and source records attributed to Wei-Chun Jao.

At least 19 recordsLinked to original sources

The Solar Neighborhood LVI: The RMSTAR Catalog of the Nearest 3352 M Dwarf Systems and 305 of their Wide Companions

We present the RMSTAR (RECONS M STAR) catalog, a 25 pc volume-limited and effectively volume-complete sample of the nearest 3352 M dwarf systems and their 305 wide stellar and 9 brown dwarf companions. RMSTAR has been created using only results from Gaia Data Releases 3 (GDR3) and 2 (GDR2), Hipparcos, and ground-based discoveries of M dwarf systems that are not available in the space-based results. The wide companions are identified using only results from GDR3 and GDR2, and have separations $ρ\ge0.''46$. There are 291 primaries with stellar companions, yielding a multiplicity rate of 8.68$\pm$0.49% for these widely separated systems, with a rate of 6.86$\pm$0.44% for projected separations $s\geq30$ au, where the sample of stellar companions is complete except perhaps for a few fringe cases. It is shown that the rate of stellar companions increases from the search limit of 30,000 au down to separations of 30 au, with a large set of companions to be characterized at closer separations in future work. We determine luminosity and mass functions for all stellar red dwarfs and their wide secondaries, finding that the luminosity function displays a classic turnover at $M_G\sim11$, whereas the mass function is described by an exponential function that rises from 0.60 M$_{\odot}$ to the end of the stellar main sequence at 0.075 M$_{\odot}$. We assess the large population of close, unresolved companions to M dwarfs by analyzing several Gaia parameters, identifying 1089 (30%) individual sources as having at least one of these elevated unresolved companion indication parameters.

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Visual Orbits of Spectroscopic Binaries with the CHARA Array. V. HD 210763 and HD 221950

We present the visual orbits and dynamical masses of two longer period spectroscopic binary stars, HD 210763 and HD 221950, using long baseline interferometry with the CHARA Array and high resolution spectroscopy with the APO 3.5 m and CTIO 1.5 m telescopes. By combining the astrometric and radial velocity observations, we solve for the full, three-dimensional orbits and determine the stellar masses to within 0.5% uncertainty and the distance to within 0.2% uncertainty. For HD 210763, we found component masses of M1 = 1.748 Msun and M2 = 1.492 Msun. For HD 221950, we found masses of M1 = 1.098 Msun and M2 = 1.031 Msun. We then estimate the effective temperature and radius of each component star through disentangling and spectral energy distribution analyses. We compare the observed stellar parameters to the predictions of the stellar evolution models and estimate the system ages. The primary component of HD 210763 is at the end of the main sequence while the secondary component is on the main sequence, providing a tight age constraint for this system at 1.6 Gyr. Both components of HD 221950 are still on the main sequence with an age of 3.76 Gyr. These systems have longer orbital periods, beyond the tidal circularization limit, and therefore are better proxies for single stars and tests of stellar evolution models than short period, eclipsing systems.

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The Debris Disk Host $β$ Piscis Austrinus is a Rapidly Rotating Star Seen Nearly Pole-On

Previous studies of $β$ Piscis Austrinus (PsA) have speculated that the narrow and saddle-like shapes of some of its weak metallic lines are a consequence of it being a rapidly rotating star viewed nearly pole-on. Here we use the \texttt{fastrot-spec} spectral synthesis code to model high-dispersion (R = 115,000) HARPS spectra of $β$ PsA in order to determine its inclination and photospheric properties, with additional constraints on the surface temperature set by measures of Fe II/Fe I line ratios. The analysis confirms that $β$ PsA is oriented nearly pole-on ($i = 4.75^{+0.75}_{-0.50}$$^o$) and experiences substantial gravity darkening caused by its rapid rotation ($Ω/Ω_{crit}=0.93\pm0.17$). $β$ PsA has a polar temperature of $10300^{+200}_{-250}$ K that is 24% hotter than its equatorial temperature ($8275^{+317}_{-400}$ K). This results in its apparent luminosity being 48% larger than its actual luminosity of 26.2$^{+1.9}_{-2.4}$ L$_\odot$. When this methodology is applied to high-dispersion spectra of the star Vega, the analysis determines a nearly pole-on orientation that is consistent with interferometric measurements, validating the technique. Based on comparisons with PARSEC evolutionary models of stars rotating at similar velocities, $β$ PsA has a mass of $2.20\pm0.03$ M$_{\odot}$ and an age of $141^{+113}_{-49}$ Myr; this age is consistent with the age inferred for its G5V companion star, CD-32 17127, based on lithium depletion models. The analysis demonstrates the potential for both identifying and determining the stellar properties of rapidly rotating stars viewed nearly pole-on via spectroscopy alone.

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The Solar Neighborhood LIV: 54 Orbits of M Dwarf Multiples within 30 Parsecs with Speckle Interferometry at SOAR

We present 1066 speckle measurements of M dwarf multiples observed over 2021-2024, all taken with HRCam on the Southern Astrophysical Research 4.1 m telescope. Among these, 900 observations resolve companions in 212 pairs, with separations spanning 17 milliarcseconds to 3.4 arcsec and brightness differences ranging from 0 to 4.9 magnitudes in the I filter. We have characterized the orbits of 54 of these companions, spanning periods of 0.67-30 yr, by combining our data with literature astrometry, radial velocities, and, in four cases, Hipparcos-Gaia accelerations. Among the orbits presented here are 28 that are the first-ever such characterizations for their systems, and 26 that revise previously-published orbits, thus providing a significant update to the observed dynamics of M dwarfs in the solar neighborhood. From these orbits, we provide new and updated dynamical total masses for these systems, precise to 0.7-7% in nearly all cases. Future mass derivations for components in these systems will contribute to efforts in refining the mass-luminosity relation for the smallest stars, and will enhance investigations of age, magnetism, and metallicity effects on luminosities at a given mass.

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The Solar Neighborhood LV: Spectral Characterization of an Equatorial Sample of 580 K Dwarfs

We present a spectroscopic characterization of 580 K dwarfs within 33 pc, observed with the CHIRON echelle spectrograph (R=80,000) on the SMARTS 1.5m telescope. This volume-limited sample is part of the RKSTAR survey of $\sim$4400 K dwarf primaries within 50 pc. Using Empirical SpecMatch and the diagnostic lines H-alpha (6562.8 Angstrom) and Li I (6707.8 Angstrom), we derive stellar properties, activity status, and age indicators calibrated against 35 benchmark K dwarfs with ages from 20 Myr to 5 Gyr. We find that 7.4% (43 stars) exhibit signatures of youth and/or chromospheric activity: 19 stars show lithium absorption indicating ages $<$1 Gyr, and 36 display H$α$ emission. Kinematic analysis using BANYAN $Σ$ identifies 8 additional young stars through membership in the AB Doradus moving group and the Hyades cluster, bringing the total young/active population to 8.8% (51 stars). Stellar parameters span 3600--5500 K in \teff, $-$0.60 to $+$0.55 dex in [Fe/H], and $<$10 to $>$25 km s$^{-1}$ in $v\sin i$. A metal-poor population ([Fe/H] $\leq -$0.50 dex) comprises 4\% of the sample. Galactic kinematics place 80% in the thin disk and 18.4% in the thick disk, with one halo member (HD 134439). Young and active stars are predominantly thin disk members, with two thick disk exceptions. Cross-matching with NASA's Exoplanet Archive reveals only 7.5% (44 stars) host confirmed planets as of July 2025. Our results identify 529 mature, inactive K dwarfs as prime targets for terrestrial planet searches, providing a crucial resource for exoplanet habitability studies in the solar neighborhood.

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TESS Investigation -- Demographics of Young Exoplanets (TI-DYE) IV: a Jovian radius planet orbiting a 34 Myr Sun-like star in the Vela association

The discovery of infant (< 50 Myr), close-in (<30-day period) planets is vital in understanding the formation mechanisms that lead to the distribution of mature transiting planets as discovered by Kepler. Despite several discoveries in this age bin, the sample is still too small for a robust statistical comparison to older planets. Here we report the validation of TOI-6448 b, an 8.8 +/- 0.8 Re planet on a 14.8 day orbit. TOI-6448 was previously identified to be a likely member of Vela Population IV. We confirm the star's membership and re-derive the age of the cluster using isochrones, variability, and gyrochronology. We find the star, and thus planet, to be 34 +/- 3 Myr. Like other young planets, TOI-6448 b lands in a region of parameter space with few older planets. While just one data point, this fits with prior findings of an excess of 5-11Re planets around young stars far beyond what can be explained by reduced sensitivity at young ages. Our ongoing search of Vela, Taurus-Auriga, Sco-Cen, and Orion are expected to reveal dozens more < 50 Myr transiting planets.

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The Solar Neighborhood. LV. M Dwarf Twin Binaries -- One in Five Twin Sibling Pairs Are Mismatched in Activity and/or Rotation

We report on a study of 36 pairs of `twin' M dwarfs in wide binaries and assess how similarly the stars behave. Stars in each twin pair have BP, RP, $J$, $H$, and $K_s$ differing by $<$0.10 mag, mass estimates matching within $<$3%, and presumably the same age and composition. We utilize short- and long-term photometry, multi-epoch spectroscopy, and archival data to measure rotation periods, photometric activity levels, and H$α$ equivalent widths for many systems. Speckle imaging, radial velocities, and long-term astrometry are used to identify unresolved companions, yielding three systems with unseen components. Among the 33 remaining twin systems, numerous remarkable pairs show nearly identical rotation rates and activity levels between their twin components, including cases throughout the lower main sequence and across a broad range of rotation-activity parameter space. In contrast, mismatches with $>$25% differences exist in rotation period for $21\%_{-7\%}^{+14\%}$ of twin pairs, in rotation amplitude for $67\%_{-15\%}^{+10\%}$ of pairs, in multi-year photometric variability for $33\%_{-9\%}^{+12\%}$ of pairs, and in H$α$ activity for $21\%_{-6\%}^{+9\%}$ of pairs, with fully convective systems generally mismatched more often. Thus, roughly one out of five M dwarf twin sets does not match in rotation and/or activity despite otherwise identical fundamental parameters. Furthermore, we compile three key systems showing larger relative active/inactive H$α$ mismatches. We propose the various mismatches likely stem from factors such as dynamo stochasticity, activity cycles, formative disk aspects, and/or star-planet interactions, depending on the system. These well-vetted twins offer ripe targets for many future investigations.

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Abundance Measurements of the Metal-poor M subdwarf LHS 174 Using High-resolution Optical Spectroscopy

Metal-poor M subdwarfs are among the oldest stellar populations and carry valuable information about the chemical enrichment history of the Milky Way. The measurements of chemical abundances of these stars therefore provide essential insights into the nucleosynthesis in the early stages of the Galaxy's formation. We present the detailed spectroscopic analysis of a nearby metal-poor M subdwarf, LHS 174 from its high-resolution optical spectrum, and apply our previously developed spectral fitting code, \texttt{AutoSpecFit}, to measure the abundances of five elements:[O/H]=$-$0.519$\pm$0.081, [Ca/H]=$-$0.753$\pm$0.177, [Ti/H]=$-$0.711$\pm$0.144, [V/H]=$-$1.026$\pm$0.077, and [Fe/H]=$-$1.170$\pm$0.135. We compare the abundances of O, Ti, and Fe derived from this work and those from previous studies and demonstrate the observed data is clearly better matched with the synthetic model generated based on our abundances than those from the other analyses. The accuracy of inferred stellar abundances strongly depends on the accuracy of physical parameters, which motivates us to develop a reliable technique to determine the parameters of low-mass M dwarfs more accurately ever than before and infer abundances with smaller uncertainties.

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Mind the Gap II: the near-UV fluxes of M dwarfs

Because of the continuous variations in mass, metallicity, and opacity, dwarf stars are distributed along the main sequence on optical and near-IR color-magnitude diagrams following a smooth polynomial. In this study of utilizing a catalog of cross-matched GALEX and Gaia sources, we identify two distinct populations of M dwarfs in the near-ultraviolet (NUV) band on the $M_{NUV}$ vs. $M_G$ diagram. We also reveal a pronounced increase in the number of stars exhibiting high NUV fluxes near the spectral type M2 or $M_G\sim9.4$, coinciding with the $H_2$ formation in the atmosphere to improve the energy transportation at the surface. This suggests that certain yet-to-be-understood stellar mechanisms drive heightened activity in the NUV band around the effective temperature of M2 and later types of M dwarfs. Through examination of archival Hubble Space Telescope spectra, we show that Fe II line forests at $\sim$2400A and 2800A dominate the spectral features in the GALEX NUV bandpass, contributing to the observed excess fluxes at a given mass between the two populations. Additionally, our investigation indicates that fast rotators and young stars likely increase brightness in the NUV band, but not all stars with bright NUV fluxes are fast rotators or young stars.

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The Solar Neighborhood LII: M Dwarf Twin Binaries -- Presumed Identical Twins Appear Fraternal in Variability, Rotation, H$α$, and X-rays

We present an investigation into the rotation and stellar activity of four fully convective M dwarf `twin' wide binaries. Components in each pair have (1) astrometry confirming they are common-proper-motion binaries, (2) Gaia $BP$, $RP$, and 2MASS $J$, $H$, and $K_s$ magnitudes matching within 0.10 mag, and (3) presumably the same age and composition. We report long-term photometry, rotation periods, multi-epoch H$α$ equivalent widths, X-ray luminosities, time series radial velocities, and speckle observations for all components. Although it might be expected for the twin components to have matching magnetic attributes, this is not the case. Decade-long photometry of GJ 1183 AB indicates consistently higher spot activity on A than B, a trend matched by A appearing 58$\pm$9% stronger in $L_X$ and 26$\pm$9% stronger in H$α$ on average -- this is despite similar rotation periods of A=0.86d and B=0.68d, thereby informing the range in activity for otherwise identical and similarly-rotating M dwarfs. The young $β$ Pic Moving Group member 2MA 0201+0117 AB displays a consistently more active B component that is 3.6$\pm$0.5 times stronger in $L_X$ and 52$\pm$19% stronger in H$α$ on average, with distinct rotation at A=6.01d and B=3.30d. Finally, NLTT 44989 AB displays remarkable differences with implications for spindown evolution -- B has sustained H$α$ emission while A shows absorption, and B is $\geq$39$\pm$4 times stronger in $L_X$, presumably stemming from the surprisingly different rotation periods of A=38d and B=6.55d. The last system, KX Com, has an unresolved radial velocity companion, and is therefore not a twin system.

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The Solar Neighborhood LI: A Variability Survey of Nearby M Dwarfs with Planets from Months to Decades with TESS and the CTIO/SMARTS 0.9 m Telescope

We present the optical photometric variability of 32 planet-hosting M dwarfs within 25 parsecs over timescales of months to decades. The primary goal of this project, ATLAS -- A Trail to Life Around Stars, is to follow the trail to life by revealing nearby M dwarfs with planets that are also "quiet", which may make them more amiable to habitability. There are 69 reported exoplanets orbiting the 32 stars discussed here, providing a rich sample of worlds for which environmental evaluations are needed. We examine the optical flux environments of these planets over month-long timescales for 23 stars observed by TESS, and find that 17 vary by less than 1% ($\sim$11 mmag). All 32 stars are being observed at the CTIO/SMARTS 0.9 m, with a median duration of 19.1 years of optical photometric data in the $VRI$ bands. We find over these extended timescales that six stars show optical flux variations less than 2%, 25 vary from 2--6% ($\sim$22-67 mmag), and only one, Proxima Centauri, varies by more than 6%. Overall, LHS 1678 exhibits the lowest optical variability levels measured over all timescales examined, thereby providing one of the most stable photometric environments among planets reported around M dwarfs within 25 parsecs. More than 600 of the nearest M dwarfs are being observed at the 0.9 m in the RECONS program that began in 1999, and many more planet hosts will undoubtedly be revealed, providing more destinations to be added to the ATLAS sample in the future.

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Mind the Gap I: H$α$ Activity of M Dwarfs Near the Partially/Fully Convective Boundary and a New H$α$ Emission Deficiency Zone on the Main Sequence

Since identifying the gap in the H-R Diagram (HRD) marking the transition between partially and fully convective interiors, a unique type of slowly pulsating M dwarf has been proposed. These unstable M dwarfs provide new laboratories in which to understand how changing interior structures can produce potentially observable activity at the surface. In this work, we report the results of the largest high-resolution spectroscopic H$α$ emission survey to date spanning this transition region, including 480 M dwarfs observed using the CHIRON spectrograph at CTIO/SMARTS 1.5-m. We find that M dwarfs with H$α$ in emission are almost entirely found 0 to 0.5 magnitude above the top edge of the gap in the HRD, whereas effectively no stars in and below the gap show emission. Thus, the top edge of the gap marks a relatively sharp activity transition, and there is no anomalous H$α$ activity for stars in the gap. We also identify a new region at 10.3 $<M_{G}<$ 10.8 on the main sequence where fewer M dwarfs exhibit H$α$ emission compared to M dwarfs above and below this magnitude range. Careful evaluation of literature results indicates that 1) rotation and H$α$ activity distributions on the main sequence are closely related, and 2) fewer stars in this absolute magnitude range rotate in less than $\sim$13 days than populations surrounding this region. This result suggests that the most massive fully convective stars lose their angular momentum faster than both partially convective stars and less massive fully convective stars.

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Enabling Exoplanet Demographics Studies with Standardized Exoplanet Survey Meta-Data

Goal 1 of the National Academies of Science, Engineering and Mathematics Exoplanet Science Strategy is "to understand the formation and evolution of planetary systems as products of the process of star formation, and characterize and explain the diversity of planetary system architectures, planetary compositions, and planetary environments produced by these processes", with the finding that "Current knowledge of the demographics and characteristics of planets and their systems is substantially incomplete." One significant roadblock to our ongoing efforts to improve our demographics analyses is the lack of comprehensive meta-data accompanying published exoplanet surveys. The Exoplanet Program Analysis Group (ExoPAG) Science Interest Group 2: Exoplanet Demographics has prepared this document to provide guidance to survey architects, authors, referees and funding agencies as to the most valuable such data products for five different exoplanet detection techniques - transit, radial velocity, direct imaging, microlensing and astrometry. We find that making these additional data easily available would greatly enhance the community's ability to perform robust, reproducible demographics analyses, and make progress on achieving the most important goals identified by the exoplanet and wider astronomical community.

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Estimating the Convective Turnover Time

The introduction of the Rossby number (R$_0$), which incorporates the convective turnover time ($τ$), in 1984 was a pioneering idea for understanding the correlation between stellar rotation and activity. The convective turnover time, which cannot be measured directly, is often inferred using existing $τ$-mass or $τ$-color relations, typically established based on an ensemble of different types of stars by assuming that $τ$ is a function of mass. In this work, we use {\it Gaia} Early Data Release 3 to demonstrate that the masses used to establish one of the most cited $τ$-mass relations are overestimated for G type dwarfs and significantly underestimated for late M dwarfs, offsets that affect studies using this $τ$-mass relation to draw conclusions. We discuss the challenges of creating such relations then and now. In the era of {\it Gaia} and other large datasets, stars used to establish these relations require characterization in a multi-dimensional space, rather than via the single-characteristic relations of the past. We propose that new multi-dimensional relations should be established based on updated theoretical models and all available stellar parameters for different interior structures from a set of carefully vetted single stars, so that the convective turnover time can be estimated more accurately.

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Visual Orbits of Spectroscopic Binaries with the CHARA Array. IV. HD 61859, HD 89822, HD 109510, and HD 191692

We present the visual orbits of four spectroscopic binary stars, HD 61859, HD 89822, HD 109510, and HD 191692, using long baseline interferometry with the CHARA Array. We also obtained new radial velocities from echelle spectra using the APO 3.5 m, CTIO 1.5 m, and Fairborn Observatory 2.0 m telescopes. By combining the astrometric and spectroscopic observations, we solve for the full, three-dimensional orbits and determine the stellar masses to 1-12% uncertainty and distances to 0.4-6% uncertainty. We then estimate the effective temperature and radius of each component star through Doppler tomography and spectral energy distribution analyses. We found masses of 1.4-3.5 Msun, radii of 1.5-4.7 Rsun, and temperatures of 6400-10300K. We then compare the observed stellar parameters to the predictions of the stellar evolution models, but found that only one of our systems fits well with the evolutionary models.

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The LHS 1678 System: Two Earth-Sized Transiting Planets and an Astrometric Companion Orbiting an M Dwarf Near the Convective Boundary at 20 pc

We present the TESS discovery of the LHS 1678 (TOI-696) exoplanet system, comprised of two approximately Earth-sized transiting planets and a likely astrometric brown dwarf orbiting a bright ($V_J$=12.5, $K_s$=8.3) M2 dwarf at 19.9 pc. The two TESS-detected planets are of radius 0.70$\pm$0.04 $R_\oplus$ and 0.98$\pm$0.06 $R_\oplus$ in 0.86-day and 3.69-day orbits, respectively. Both planets are validated and characterized via ground-based follow-up observations. HARPS RV monitoring yields 97.7 percentile mass upper limits of 0.35 $M_\oplus$ and 1.4 $M_\oplus$ for planets b and c, respectively. The astrometric companion detected by the CTIO/SMARTS 0.9m has an orbital period on the order of decades and is undetected by other means. Additional ground-based observations constrain the companion to being a high-mass brown dwarf or smaller. Each planet is of unique interest; the inner planet has an ultra-short period, and the outer planet is in the Venus zone. Both are promising targets for atmospheric characterization with the JWST and mass measurements via extreme-precision radial velocity. A third planet candidate of radius 0.9$\pm$0.1 $R_\oplus$ in a 4.97-day orbit is also identified in multi-Cycle TESS data for validation in future work. The host star is associated with an observed gap in the lower main sequence of the Hertzsprung-Russell diagram. This gap is tied to the transition from partially- to fully-convective interiors in M dwarfs, and the effect of the associated stellar astrophysics on exoplanet evolution is currently unknown. The culmination of these system properties makes LHS 1678 a unique, compelling playground for comparative exoplanet science and understanding the formation and evolution of small, short-period exoplanets orbiting low-mass stars.

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An Adaptive Optics Census of Companions to Northern Stars Within 25 pc with Robo-AO

In order to assess the multiplicity statistics of stars across spectral types and populations in a volume-limited sample, we censused nearby stars for companions with Robo-AO. We report on observations of 1157 stars of all spectral types within 25 pc with decl. $>-13^{\circ}$ searching for tight companions. We detected 154 companion candidates with separations ranging from $\sim$0.15$''$ to 4.0$''$ and magnitude differences up to $Δ$m$_{\textit{i'}}\le$7 using the robotic adaptive optics instrument Robo-AO. We confirmed physical association from Gaia EDR3 astrometry for 53 of the companion candidates, 99 remain to be confirmed, and 2 were ruled out as background objects. We complemented the high-resolution imaging companion search with a search for co-moving objects with separations out to 10,000 AU in Gaia EDR3, which resulted in an additional 147 companions registered. Of the 301 total companions reported in this study, 49 of them are new discoveries. Out of the 191 stars with significant acceleration measurements in the Hipparcos-Gaia catalog of accelerations, we detect companions around 115 of them, with the significance of the acceleration increasing as the companion separation decreases. From this survey, we report the following multiplicity fractions (compared to literature values): 40.9%$\pm$3.0% (44%) for FGK stars and 28.2%$\pm$2.3% (27%) for M stars, as well as higher-order fractions of 5.5%$\pm$1.1% (11%) and 3.9%$\pm$0.9% (5%) for FGK stars and M type stars, respectively.

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The Solar Neighborhood XLIX: New Discoveries and Orbits of M Dwarf Multiples with Speckle Interferometry at SOAR

We present the first results of a multi-year program to map the orbits of M dwarf multiples within 25 parsecs. The observations were conducted primarily during 2019 - 2020 using speckle interferometry at the Southern Astrophysical Research (SOAR) Telescope in Chile, using the High-Resolution Camera mounted on the adaptive optics module (HRCam+SAM). The sample of nearby M dwarfs is drawn from three sources: multiples from the RECONS long-term astrometric monitoring program at the SMARTS 0.9m, known multiples for which these new observations will enable or improve orbit fits, and candidate multiples flagged by their astrometric fits in Gaia Data Release 2 (DR2). We surveyed 333 of our 338 M dwarfs via 830 speckle observations, detecting companions for 63% of the stars. Most notably, this includes new companions for 76% in the subset selected from Gaia DR2. In all, we report the first direct detections of 97 new stellar companions to the observed M dwarfs. Here we present the properties of those detections, the limits of each non-detection, and five orbits with periods 0.67 - 29 yr already observed as part of this program. Companions detected have projected separations of 0.024 - 2.0 arcsec (0.25 - 66 AU) from their primaries and have $ΔI \lesssim 5.0$ mag. This multi-year campaign will ultimately map complete orbits for nearby M dwarfs with periods up to 3 yr, and provide key epochs to stretch orbital determinations for binaries to 30 yr.

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