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Gregory N. Mace

Publications and source records attributed to Gregory N. Mace.

At least 55 records · Page 3Linked to original sources

New Y and T dwarfs from WISE identified by Methane Imaging

We identify new Y- and T-type brown dwarfs from the WISE All Sky data release using images obtained in filters that divide the traditional near-infrared H and J bands into two halves -- specifically CH4s & CH4l in the H and J2 & J3 in the J. This proves to be very effective at identifying cool brown dwarfs via the detection of their methane absorption, as well as providing preliminary classification using methane colours and WISE-to-near-infrared colours. New and updated calibrations between T/Y spectral types and CH4s-CH4l, J3-W2, and CH4s-W2 colours are derived, producing classification estimates good to a few spectral sub-types. We present photometry for a large sample of T and Y dwarfs in these filters, together with spectroscopy for 23 new ultra-cool dwarfs - two Y dwarfs and twenty one T dwarfs. We identify a further 8 new cool brown dwarfs, which we have high confidence are T dwarfs based on their methane photometry. We find that, for objects observed on a 4m-class telescope at J band magnitudes of ~20 or brighter, CH4s-CH4l is the more powerful colour for detecting objects and then estimating spectral types. Due to the lower sky background in the J-band, the J3 and J2 bands are more useful for identifying fainter cool dwarfs at J>22. The J3-J2 colour is poor at estimating spectral types. But fortunately, once J3-J2 confirms that an object is a cool dwarf, the J3-W2 colour is very effective at estimating approximate spectral types.

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Wolf 1130: A Nearby Triple System Containing a Cool, Ultramassive White Dwarf

Following the discovery of the T8 subdwarf WISEJ200520.38+542433.9 (Wolf 1130C), with common proper motion to a binary (Wolf 1130AB) consisting of an M subdwarf and a white dwarf, we set out to learn more about the old binary in the system. We find that the A and B components of Wolf 1130 are tidally locked, which is revealed by the coherence of more than a year of V band photometry phase folded to the derived orbital period of 0.4967 days. Forty new high-resolution, near-infrared spectra obtained with the Immersion Grating Infrared Spectrometer (IGRINS) provide radial velocities and a projected rotational velocity (v sin i) of 14.7 +/- 0.7 km/s for the M subdwarf. In tandem with a Gaia parallax-derived radius and verified tidal-locking, we calculate an inclination of i=29 +/- 2 degrees. From the single-lined orbital solution and the inclination we derive an absolute mass for the unseen primary (1.24+0.19-0.15 Msun). Its non-detection between 0.2 and 2.5 microns implies that it is an old (>3.7 Gyr) and cool (Teff<7000K) ONe white dwarf. This is the first ultramassive white dwarf within 25pc. The evolution of Wolf 1130AB into a cataclysmic variable is inevitable, making it a potential Type Ia supernova progenitor. The formation of a triple system with a primary mass >100 times the tertiary mass and the survival of the system through the common-envelope phase, where ~80% of the system mass was lost, is remarkable. Our analysis of Wolf 1130 allows us to infer its formation and evolutionary history, which has unique implications for understanding low-mass star and brown dwarf formation around intermediate mass stars.

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Characterizing TW Hydra

At 60 pc, TW Hydra (TW Hya) is the closest example of a star with a gas-rich protoplanetary disk, though TW Hya may be relatively old (3-15 Myr). As such, TW Hya is especially appealing to test our understanding of the interplay between stellar and disk evolution. We present a high-resolution near-infrared spectrum of TW Hya obtained with the Immersion GRating INfrared Spectrometer (IGRINS) to re-evaluate the stellar parameters of TW Hya. We compare these data to synthetic spectra of magnetic stars produced by MoogStokes, and use sensitive spectral line profiles to probe the effective temperature, surface gravity, and magnetic field. A model with T_eff= 3800 K, log g=4.2, and B=3.0 kG best fits the near-infrared spectrum of TW Hya. These results correspond to a spectral type of M0.5 and an age of 8 Myr, which is well past the median life of gaseous disks.

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Zodiacal Exoplanets in Time (ZEIT) VI: a three-planet system in the Hyades cluster including an Earth-sized planet

Planets in young clusters are powerful probes of the evolution of planetary systems. Here we report the discovery of three planets transiting K2-136 (EPIC 247589423), a late K dwarf in the Hyades (~800 Myr) cluster, and robust detection limits for additional planets in the system. The planets were identified from their K2 light curves, as part of our survey of young clusters and star forming regions. The smallest planet has a radius comparable to Earth (0.99 +/- 0.05 Earth radii), making it one of the few Earth-sized planets with a known, young age. The two larger planets are likely a mini-Neptune and a super-Earth, with radii of 2.91+/-0.11 and 1.45+/-0.10 Earth radii, respectively. The predicted radial velocity signals from these planets are between 0.4 and 2 m/s, achievable with modern precision RV spectrographs. Because the target star is bright (V=11.2) and has relatively low-amplitude stellar variability for a young star (2-6 mmag), EPIC 247589423 hosts the best planets known in a young open cluster for precise radial velocity follow-up, enabling a robust test of earlier claims that young planets are less dense than their older counterparts.

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Magnetic Inflation and Stellar Mass I: Revised Parameters for the Component Stars of the Kepler Low-mass Eclipsing Binary T-Cyg1-12664

Several low-mass eclipsing binary stars show larger than expected radii for their measured mass, metallicity and age. One proposed mechanism for this radius inflation involves inhibited internal convection and starspots caused by strong magnetic fields. One particular eclipsing binary, T-Cyg1-12664, has proven confounding to this scenario. \citet{Cakirli2013a} measured a radius for the secondary component that is twice as large as model predictions for stars with the same mass and age, but a primary mass that is consistent with predictions. \citet[][]{Iglesias2017} independently measured the radii and masses of the component stars and found that the radius of the secondary is not in fact inflated with respect to models, but that the primary is, consistent with the inhibited convection scenario. However, in their mass determinations, \citet[][]{Iglesias2017} lacked independent radial velocity measurements for the secondary component due to the star's faintness at optical wavelengths. The secondary component is especially interesting as its purported mass is near the transition from partially-convective to a fully-convective interior. In this article we independently determined the masses and radii of the component stars of T-Cyg1-12664 using archival {\it Kepler} data and radial velocity measurements of both component stars obtained with IGRINS on the Discovery Channel Telescope and NIRSPEC and HIRES on the Keck Telescopes. We show that neither of the component stars is inflated with respect to models. Our results are broadly consistent with modern stellar evolutionary models for main-sequence M dwarf stars and do not require inhibited convection by magnetic fields to account for the stellar radii.

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The Role of Gender in Asking Questions at Cool Stars 18 and 19

We examine the gender balance of the 18th and 19th meetings of the Cambridge Workshop on Cool Stellar Systems and the Sun (CS18 and CS19). The percent of female attendees at both meetings (31% at CS18 and 37% at CS19) was higher than the percent of women in the American Astronomical Society (25%) and the International Astronomical Union (18%). The representation of women in Cool Stars as SOC members, invited speakers, and contributed speakers was similar to or exceeded the percent of women attending the meetings. We requested that conference attendees assist in a project to collect data on the gender of astronomers asking questions after talks. Using this data, we found that men were over-represented (and women were under-represented) in the question sessions after each talk. Men asked 79% of the questions at CS18 and 75% of the questions at CS19, but were 69% and 63% of the attendees respectively. Contrary to findings from previous conferences, we did not find that the gender balance of questions was strongly affected by the session chair gender, the speaker gender, or the length of the question period. We also found that female and male speakers were asked a comparable number of questions after each talk. The contrast of these results from previous incarnations of the gender questions survey indicate that more data would be useful in understanding the factors that contribute to the gender balance of question askers. We include a preliminary set of recommendations based on this and other work on related topics, but also advocate for additional research on the demographics of conference participants. Additional data on the intersection of gender with race, seniority, sexual orientation, ability and other marginalized identities is necessary to fully address the role of gender in asking questions at conferences.

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Excitation of Molecular Hydrogen in the Orion Bar Photodissociation Region From a Deep Near-Infrared IGRINS Spectrum

We present a deep near-infrared spectrum of the Orion Bar Photodissociation Region (PDR) taken with the Immersion Grating INfrared Spectrometer (IGRINS) on the 2.7 m telescope at the McDonald Observatory. IGRINS has high spectral resolution (R~45000) and instantaneous broad wavelength coverage (1.45-2.45 microns), enabling us to detect 87 emission lines from rovibrationally excited molecular hydrogen (H_2) that arise from transitions out of 69 upper rovibration levels of the electronic ground state. These levels cover a large range of rotational and vibrational quantum numbers and excitation energies, making them an excellent probe of the excitation mechanisms of H_2 and physical conditions within the PDR. The Orion Bar PDR is thought to consist of cooler high density clumps or filaments (T=50-250 K, n_H = 10^5 - 10^7 cm^-3) embedded in a warmer lower density medium (T=250-1000 K, n_H=10^4 - 10^5 cm^-3). We fit a grid of simple constant-temperature and constant-density Cloudy models, which recreate the observed H_2 level populations well, to constrain the temperature to a range of 600 to 650 K and the density to n_H = 2.5 x 10^3 to 10^4 cm^-3. The best fit model gives T = 625 K and n_H = 5x10^3 cm^-3. This well constrained warm temperature is consistent with kinetic temperatures found by other studies for the Orion Bar's lower density medium. However, the range of densities well fit by the model grid is marginally lower than those reported by other studies. We could be observing lower density gas than the surrounding medium, or perhaps a density-sensitive parameter in our models is not properly estimated.

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Fluorescent H_2 Emission Lines from the Reflection Nebula NGC 7023 Observed with IGRINS

We have analyzed the temperature, velocity and density of H2 gas in NGC 7023 with a high-resolution near-infrared spectrum of the northwestern filament of the reflection nebula. By observing NGC 7023 in the H and K bands at R ~ 45,000 with the Immersion GRating INfrared Spectrograph (IGRINS), we detected 68 H2 emission lines within the 1" x 15" slit. The diagnostic ratios of 2-1 S(1)/1-0 S(1) is 0.41-0.56. In addition, the estimated ortho-to-para ratios (OPR) is 1.63-1.82, indicating that the H2 emission transitions in the observed region arises mostly from gas excited by UV fluorescence. Gradients in the temperature, velocity, and OPR within the observed area imply motion of the photodissociation region (PDR) relative to the molecular cloud. In addition, we derive the column density of H2 from the observed emission lines and compare these results with PDR models in the literature covering a range of densities and incident UV field intensities. The notable difference between PDR model predictions and the observed data, in high rotational J levels of v = 1, is that the predicted formation temperature for newly-formed H2 should be lower than that of the model predictions. To investigate the density distribution, we combine pixels in 1" x 1" areas and derive the density distribution at the 0.002 pc scale. The derived gradient of density suggests that NGC 7023 has a clumpy structure, including a high clump density of ~10^5 cm^-3 with a size smaller than ~5 x 10^-3 pc embedded in lower density regions of 10^3-10^4 cm^-3.

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Surface Gravities for 228 M, L, and T Dwarfs in the NIRSPEC Brown Dwarf Spectroscopic Survey

We combine 131 new medium-resolution (R~2000) J-band spectra of M, L, and T dwarfs from the Keck NIRSPEC Brown Dwarf Spectroscopic Survey (BDSS) with 97 previously published BDSS spectra to study surface-gravity-sensitive indices for 228 low-mass stars and brown dwarfs spanning spectral types M5-T9. Specifically, we use an established set of spectral indices to determine surface gravity classifications for all M6-L7 objects in our sample by measuring equivalent widths (EW) of the K I lines at 1.1692, 1.1778, 1.2529 um, and the 1.2 um FeHJ absorption index. Our results are consistent with previous surface gravity measurements, showing a distinct double peak - at ~L5 and T5 - in K I EW as a function of spectral type. We analyze K I EWs of 73 objects of known ages and find a linear trend between log(Age) and EW. From this relationship, we assign age ranges to the very low gravity, intermediate gravity, and field gravity designations for spectral types M6-L0. Interestingly, the ages probed by these designations remain broad, change with spectral type, and depend on the gravity sensitive index used. Gravity designations are useful indicators of the possibility of youth, but current datasets cannot be used to provide a precise age estimate.

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Placing the spotted T Tauri star LkCa 4 on an HR diagram

Ages and masses of young stars are often estimated by comparing their luminosities and effective temperatures to pre-main sequence stellar evolution tracks, but magnetic fields and starspots complicate both the observations and evolution. To understand their influence, we study the heavily-spotted weak-lined T-Tauri star LkCa 4 by searching for spectral signatures of radiation originating from the starspot or starspot groups. We introduce a new methodology for constraining both the starspot filling factor and the spot temperature by fitting two-temperature stellar atmosphere models constructed from Phoenix synthetic spectra to a high-resolution near-IR IGRINS spectrum. Clearly discernable spectral features arise from both a hot photospheric component $T_{\mathrm{hot}} \sim4100$ K and to a cool component $T_{\mathrm{cool}} \sim2700-3000$ K, which covers $\sim80\%$ of the visible surface. This mix of hot and cool emission is supported by analyses of the spectral energy distribution, rotational modulation of colors and of TiO band strengths, and features in low-resolution optical/near-IR spectroscopy. Although the revised effective temperature and luminosity make LkCa 4 appear much younger and lower mass than previous estimates from unspotted stellar evolution models, appropriate estimates will require the production and adoption of spotted evolutionary models. Biases from starspots likely afflict most fully convective young stars and contribute to uncertainties in ages and age spreads of open clusters. In some spectral regions starspots act as a featureless veiling continuum owing to high rotational broadening and heavy line-blanketing in cool star spectra. Some evidence is also found for an anti-correlation between the velocities of the warm and cool components.

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Zodiacal Exoplanets in Time (ZEIT) IV: seven transiting planets in the Praesepe cluster

Open clusters and young stellar associations are attractive sites to search for planets and to test theories of planet formation, migration, and evolution. We present our search for, and characterization of, transiting planets in the ~800 Myr old Praesepe (Beehive, M44) Cluster from K2 light curves. We identify seven planet candidates, six of which we statistically validate to be real planets, the last of which requires more data. For each host star we obtain high-resolution NIR spectra to measure its projected rotational broadening and radial velocity, the latter of which we use to confirm cluster membership. We combine low-resolution spectra with the known cluster distance and metallicity to provide precise temperatures, masses, radii, and luminosities for the host stars. Combining our measurements of rotational broadening, rotation periods, and our derived stellar radii, we show that all planetary orbits are consistent with alignment to their host star's rotation. We fit the K2 light curves, including priors on stellar density to put constraints on the planetary eccentricities, all of which are consistent with zero. The difference between the number of planets found in Praesepe and Hyades (8 planets) and a similar dataset for Pleiades (0 planets, ~125 Myr) suggests a trend with age, but may be due to incompleteness of current search pipelines for younger, faster-rotating stars. We see increasing evidence that some planets continue to lose atmosphere past 800 Myr, as now two planets at this age have radii significantly larger than their older counterparts from Kepler.

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Zodiacal Exoplanets in Time (ZEIT) III: A short-period planet orbiting a pre-main-sequence star in the Upper Scorpius OB Association

We confirm and characterize a close-in ($P_{\rm{orb}}$ = 5.425 days), super-Neptune sized ($5.04^{+0.34}_{-0.37}$ Earth radii) planet transiting K2-33 (2MASS J16101473-1919095), a late-type (M3) pre-main sequence (11 Myr-old) star in the Upper Scorpius subgroup of the Scorpius-Centaurus OB association. The host star has the kinematics of a member of the Upper Scorpius OB association, and its spectrum contains lithium absorption, an unambiguous sign of youth (<20 Myr) in late-type dwarfs. We combine photometry from K2 and the ground-based MEarth project to refine the planet's properties and constrain the host star's density. We determine \name's bolometric flux and effective temperature from moderate resolution spectra. By utilizing isochrones that include the effects of magnetic fields, we derive a precise radius (6-7%) and mass (16%) for the host star, and a stellar age consistent with the established value for Upper Scorpius. Follow-up high-resolution imaging and Doppler spectroscopy confirm that the transiting object is not a stellar companion or a background eclipsing binary blended with the target. The shape of the transit, the constancy of the transit depth and periodicity over 1.5 years, and the independence with wavelength rules out stellar variability, or a dust cloud or debris disk partially occulting the star as the source of the signal; we conclude it must instead be planetary in origin. The existence of K2-33b suggests close-in planets can form in situ or migrate within $\sim 10$ Myr, e.g., via interactions with a disk, and that long-timescale dynamical migration such as by Lidov-Kozai or planet-planet scattering is not responsible for all short-period planets.

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IGRINS spectroscopy of Class I sources: IRAS 03445+3242 and IRAS 04239+2436

We have detected molecular and atomic line emission from the hot and warm disks of two Class I sources, IRAS 03445+3242 and IRAS 04239+2436 using the high resolution Immersion GRating INfrared Spectrograph (IGRINS). CO overtone band transitions and near-IR lines of Na I and Ca I, all in emission, trace the hot inner disk while CO rovibrational absorption spectra of the first overtone transition trace the warm gas within the inner few AU of the disk. The emission-line profiles for both sources show evidence for Keplerian disks. A thin Keplerian disk with power-law temperature and column density profiles with a projected rotational velocity of $\sim$60--75 km s$^{-1}$ and a gas temperature of $\sim$3500 K at the innermost annulus can reproduce the CO overtone band emission. Na I and Ca I emission lines also arise from this disk, but they show complicated line features possibly affected by photospheric absorption lines. Multi-epoch observations show asymmetric variations of the line profiles on one-year (CO overtone bandhead and atomic lines for IRAS 03445+3242) or on one-day (atomic lines for IRAS 04239+2436) time scales, implying non-axisymmetric features in disks. The narrow CO rovibrational absorption spectra ($v$=0$\rightarrow$2) indicate that both warm ($>$ 150 K) and cold ($\sim$20--30 K) CO gas are present along the line of sight to the inner disk. This study demonstrates the power of IGRINS as a tool for studies of the sub-AU scale hot and AU-scale warm protoplanetary disks with its simultaneous coverage of the full H and K bands with high spectral resolution ($R$= 45,000) allowing many aspects of the sources to be investigated at once.

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The AllWISE Motion Survey, Part 2

We use the AllWISE Data Release to continue our search for WISE-detected motions. In this paper, we publish another 27,846 motion objects, bringing the total number to 48,000 when objects found during our original AllWISE motion survey are included. We use this list, along with the lists of confirmed WISE-based motion objects from the recent papers by Luhman and by Schneider et al. and candidate motion objects from the recent paper by Gagne et al. to search for widely separated, common-proper-motion systems. We identify 1,039 such candidate systems. All 48,000 objects are further analyzed using color-color and color-mag plots to provide possible characterizations prior to spectroscopic follow-up. We present spectra of 172 of these, supplemented with new spectra of 23 comparison objects from the literature, and provide classifications and physical interpretations of interesting sources. Highlights include: (1) the identification of three G/K dwarfs that can be used as standard candles to study clumpiness and grain size in nearby molecular clouds because these objects are currently moving behind the clouds, (2) the confirmation/discovery of several M, L, and T dwarfs and one white dwarf whose spectrophotometric distance estimates place them 5-20 pc from the Sun, (3) the suggestion that the Na 'D' line be used as a diagnostic tool for interpreting and classifying metal-poor late-M and L dwarfs, (4) the recognition of a triple system including a carbon dwarf and late-M subdwarf, for which model fits of the late-M subdwarf (giving [Fe/H] ~ -1.0) provide a measured metallicity for the carbon star, and (5) a possible 24-pc-distant K5 dwarf + peculiar red L5 system with an apparent physical separation of 0.1 pc.

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The First Detection of Photometric Variability in a Y Dwarf: WISE J140518.39+553421.3

We present the first detection of photometric variability of a spectroscopically-confirmed Y dwarf. The Infrared Array Camera on board the Spitzer Space Telescope was used to obtain times series photometry at 3.6 and 4.5 microns over a twenty four hour period at two different epochs separated by 149 days. Variability is evident at 4.5 um in the first epoch and at 3.6 and 4.5 um in the second epoch which suggests that the underlying cause or causes of this variability change on the timescales of months. The second-epoch [3.6] and [4.5] light curves are nearly sinusoidal in form, in phase, have periods of roughly 8.5 hours, and have semi-amplitudes of 3.5%. We find that a simple geometric spot model with a single bright spot reproduces these observations well. We also compare our measured semi-amplitudes of the second epoch light curves to predictions of the static, one-dimensional, partly cloudy and hot spot models of Morley and collaborators and find that neither set of models can reproduce the observed [3.6] and[4.5] semi-amplitudes simultaneously. More advanced two- or three-dimensional models that include time-dependent phenomena like vertical mixing, cloud formation, and thermal relaxation are therefore sorely needed in order to properly interpret our observations.

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Zodiacal Exoplanets In Time (ZEIT) I: A Neptune-sized planet orbiting an M4.5 dwarf in the Hyades Star Cluster

Studying the properties of young planetary systems can shed light on how the dynamics and structure of planets evolve during their most formative years. Recent K2 observations of nearby young clusters (10-800 Myr) have enabled the discovery of such planetary systems. Here we report the discovery of a Neptune-sized planet transiting an M4.5 dwarf (K2-25) in the Hyades cluster (650-800 Myr). The lightcurve shows a strong periodic signal at 1.88 days, which we attribute to spot coverage and rotation. We confirm the planet host is a member of the Hyades by measuring the radial velocity of the system with the high-resolution near-infrared spectrograph IGRINS. This enables us to calculate a distance based on EPIC 210490365's kinematics and membership to the Hyades, which in turn provides a stellar radius and mass to 5-10%, better than what is currently possible for most Kepler M dwarfs (12-20%). We use the derived stellar density as a prior on fitting the K2 transit photometry, which provides weak constraints on eccentricity. Utilizing a combination of adaptive optics imaging and high-resolution spectra we rule out the possibility that the signal is due to a bound or background eclipsing binary, confirming the transits' planetary origin. EPIC 210490365b has a radius ($3.43^{+0.95}_{-0.31}$R$_{E}$) much larger than older Kepler planets with similar orbital periods (3.484 days) and host-star masses (0.29$M_{\odot}$). This suggests that close-in planets lose some of their atmospheres past the first few hundred Myr. Additional transiting planets around the Hyades, Pleiades, and Praesepe clusters from K2 will help confirm if this planet is atypical or representative of other close-in planets of similar age.

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The Chemical Compositions of Very Metal-Poor Stars HD 122563 and HD 140283; A View From the Infrared

From high resolution (R = 45,000), high signal-to-noise (S/N > 400) spectra gathered with the Immersion Grating Infrared Spectrograph (IGRINS) in the H and K photometric bands, we have derived elemental abundances of two bright, well-known metal-poor halo stars: the red giant HD 122563 and the subgiant HD 140283. Since these stars have metallicities approaching [Fe/H] = -3, their absorption features are generally very weak. Neutral-species lines of Mg, Si, S and Ca are detectable, as well as those of the light odd-Z elements Na and Al. The derived IR-based abundances agree with those obtained from optical-wavelength spectra. For Mg and Si the abundances from the infrared transitions are improvements to those derived from shorter wavelength data. Many useful OH and CO lines can be detected in the IGRINS HD 122563 spectrum, from which derived O and C abundances are consistent to those obtained from the traditional [O I] and CH features. IGRINS high resolutions H- and K-band spectroscopy offers promising ways to determine more reliable abundances for additional metal-poor stars whose optical features are either not detectable, or too weak, or are based on lines with analytical difficulties.

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Direct Spectral Detection: An Efficient Method to Detect and Characterize Binary Systems

Young, intermediate-mass stars are experiencing renewed interest as targets for direct-imaging planet searches. However, these types of stars are part of multiple systems more often than not. Close stellar companions affect the formation and orbital evolution of any planets, and the properties of the companions can help constrain the binary formation mechanism. Unfortunately, close companions are difficult and expensive to detect with imaging techniques. In this paper, we describe the direct spectral detection method wherein a high-resolution spectrum of the primary is cross-correlated against a template for a companion star. Variants of this method have previously been used to search for stellar, brown dwarf, and even planetary companions. We show that the direct spectral detection method can detect companions as late as M-type orbiting A0 or earlier primary stars in a single epoch on small-aperture telescopes. In addition to estimating the detection limits, we determine the sources of uncertainty in characterizing the companion temperature, and find that large systematic biases can exist. After calibrating the systematic biases with synthetic binary star observations, we apply the method to a sample of 34 known binary systems with an A- or B-type primary star. We detect nine total companions, including four of the five known companions with literature temperatures between $4000$ K $ < T < 6000$ K, the temperature range for which our method is optimized. We additionally characterize the companion for the first time in two previously single-lined binary systems and one binary identified with speckle interferometry. This method provides an inexpensive way to use small-aperture telescopes to detect binary companions with moderate mass-ratios, and is competitive with high-resolution imaging techniques inside $\sim 100-200$ mas.

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