Metallicity and Temperature Indicators in M dwarf K band Spectra: Testing New & Updated Calibrations With Observations of 133 Solar Neighborhood M dwarfs
Bárbara Rojas-Ayala, Kevin R. Covey, Philip S. Muirhead, James P. Lloyd
aa r X i v : . [ a s t r o - ph . S R ] D ec Metallicity and Temperature Indicators in M dwarf K bandSpectra: Testing New & Updated Calibrations With Observationsof 133 Solar Neighborhood M dwarfs
B´arbara Rojas-Ayala , , , Kevin R. Covey , , , Philip S. Muirhead , James P. Lloyd Received ; acceptedDRAFT May 22, 2018 Department of Astrophysics, American Museum of Natural History, Central Park Westat 79th Street, New York, NY 10024, USA; [email protected] Department of Astronomy, Cornell University, 122 Sciences Drive, Ithaca, NY 14853,USA Z. Carter Patten ’25 Fellow Hubble Fellow Visiting Researcher, Department of Astronomy, Boston University, 725 CommonwealthAve, Boston, MA 02215, USA. Current Address: Department of Astronomy, California Institute of Technology, 1200East California Boulevard, MC 249-17, Pasadena, CA 91125, USA. 2 –
ABSTRACT
We present K band spectra for 133 nearby (d <
33 parsecs) M dwarfs, in-cluding 18 M dwarfs with reliable metallicity estimates (as inferred from an FGKtype companion), 11 M dwarf planet hosts, more than 2/3 of the M dwarfs inthe Northern 8 pc sample, and several M dwarfs from the LSPM catalog. Fromthese spectra, we measure equivalent widths of the Ca and Na lines, and a spec-tral index quantifying the absorption due to H O opacity (the H O-K2 index).Using empirical spectral types standards and synthetic models, we calibrate theH O-K2 index as an indicator of an M dwarf’s spectral type and effective tem-perature. We also present a revised relationship that estimates the [Fe/H] and[M/H] metallicities of M dwarfs from their Na I, Ca I, and H O-K2 measure-ments. Comparisons to model atmosphere provide a qualitative validation of ourapproach, but also reveal an overall offset between the atomic line strengths pre-dicted by models as compared to actual observations. Our metallicity estimatesalso reproduce expected correlations with Galactic space motions and H α emis-sion line strengths, and return statistically identical metallicities for M dwarfswithin a common multiple system. Finally, we find systematic residuals betweenour H O-based spectral types and those derived from optical spectral featureswith previously known sensitivity to stellar metallicity, such as TiO, and identifythe CaH1 index as a promising optical index for diagnosing the metallicities ofnear-solar M dwarfs.
Subject headings: stars: late-type, stars: fundamental parameters, stars: abundances
1. Introduction
Contrary to their dimness, M dwarf stars hold significant promise for illuminating theprocesses that govern the formation and evolution of stars, planets, and the Milky Way.M dwarfs possess masses of 0.6 M ⊙ > M ∗ > ⊙ (Delfosse et al. 2000), straddling thepeak of the stellar initial mass function and dominating stellar populations by number(Bastian et al. 2010). With main sequence lifetimes that exceed a Hubble time, GalacticM dwarfs also represent a complete archeological record of the chemical evolution and starformation history of the Milky Way (e.g. Bochanski et al. 2007). Moreover, M dwarfs are ofgreat interest as potential exoplanet host stars, as all of a planet’s observable signals will besignificantly easier to detect if it orbits an M dwarf compared to a similar planet in orbitaround a G dwarf (e.g., Nutzman & Charbonneau 2008).Calibrating the fundamental parameters of M dwarfs, however, is a difficult challengefrom both an observational and theoretical perspective. Empirical measurements of M dwarfmasses, luminosities, temperatures, and radii are anchored primarily by the informationextracted from the orbits of M dwarf binaries, either the very rare eclipsing systems( ∼
15 systems known; e.g., Kraus et al. 2011; Irwin et al. 2011) or less rare (but alsosomewhat less informative) spectroscopic/astrometric systems (e.g., Shkolnik et al. 2010;Martinache et al. 2007). Overcoming the intrinsic faintness of these low-luminosity systems,however, makes their characterization a taxing observational challenge, and analyses ofknown binaries reveal systematic offsets in inferred temperatures and radii that correlatewith both orbital period and tracers of magnetic activity (Ribas 2006; L´opez-Morales 2007),suggesting that more wide binaries are needed to accurately infer the parameters typicalisolated M dwarfs (Kraus et al. 2011). Theoretical constraints on M dwarf parameters havebeen similarly difficult to achieve: accurately modeling the deep convective zones in Mdwarf interiors (Mullan & MacDonald 2001; Browning 2008) and the mixture of molecules 4 –and grains that dominate M dwarf atmospheres (Tsuji et al. 1996; Allard et al. 2000)requires significant computational resources, as well as extensive databases of oscillatorstrengths and opacities measured from laboratory experiments. Confronting theoreticalpredictions with empirical measurements have also identified significant offsets even forisolated field stars: empirical effective temperature scales appear ∼ ∼ -1.0 dex; Mould 1976b).These studies enabled the subsequent photometric and spectroscopic identification ofM subdwarfs (Stauffer & Hartmann 1986; Ruiz & Anguita 1993), the development ofincreasingly detailed models of M dwarf atmospheres (Allard 1990), and represent thefundamental origin of the TiO and CaH-based indices used today to identify metal-poor Msubdwarfs (Gizis 1997; Woolf & Wallerstein 2005; L´epine et al. 2007).While techniques to identify metal-poor M dwarfs have been developing for morethan 35 years, methods for identifying metal- rich M dwarfs have received significantlyless attention. Interest in identifying M dwarfs with super-solar metallicities was onlyrecently spurred by the realization that such stars could be highly promising targetsfor searches for Earth-like planets. The existence of a correlation between (gas giant) 5 –planet frequency and host-star metallicity is well established for FGK-dwarfs (Gonzalez1997; Santos et al. 2004; Valenti & Fischer 2005), but the first investigations to examineif the planet-metallicity correlation extended to M dwarf hosts returned mixed results(Bonfils et al. 2005a; Bean et al. 2006b). Bonfils et al. (2005, B05 hereafter) analyzed Vand K photometry for 20 wide M dwarf companions to FGK-dwarfs whose metallicitiescould be determined reliably via standard spectroscopic techniques. Assuming that bothbinary components inherit the same metallicity from their parent molecular cloud material,B05 assigned the metallicity measurements for each primary to the M dwarf secondary,and derived iso-metallicity contours in the M V vs. V-K s color-magnitude plane. Thisphotometric metallicity calibration suggested that nearby M dwarfs, including the planethosts Gl 876 and Gl 436, were slightly metal-poor compared to the mean metallicity of theGalactic disk. This conclusion was reinforced by the work of Bean et al. (2006b), whosespectroscopic analysis indicated sub-solar metallicities for Gl 436, Gl 581, and Gl 876.The persistence of the planet-metallicity correlation into the M dwarf regime has beensuggested, however, by the recent re-calibration of the photometric metallicity calibrationby Johnson & Apps (2009). Using six M dwarfs with wide, metal-rich FGK companions toupdate the M V vs. V-K metallicity contours, Johnson & Apps (2009, JA09 hereafter) foundthat the B05 calibration systematically underestimated the compositions of these metal-richstars. JA09 used their revised calibration to estimate the metallicities of six M dwarfs withplanetary mass companions, concluding that M dwarf planet hosts are indeed preferentiallymetal rich, just like FGK hosts. This conclusion was supported by the subsequent workof Schlaufman & Laughlin (2010), who updated the B05 and JA09 calibrations by usingtheoretical models to inform the functional form of the M K vs. V-K relation, and byinferring the mean metallicity of M dwarfs in the Solar Neighborhood from a volume-limitedand kinematically-matched sample of F & G dwarfs in the Geneva-Copenhagen Survey(Nordstr¨om et al. 2004). 6 –The photometric metallicity calibration developed by B05 and extended by JA09 andSL10 has proven to be a valuable resource, but its dependence on precise V magnitudes andtrigonometric parallaxes limits its utility to M dwarfs in the immediate solar neighborhood,at least for the remainder of the pre-Gaia era. In a recent contribution, we presented analternative, spectroscopic technique for estimating the metallicities of near-solar metallicityM dwarfs (Rojas-Ayala et al. 2010, hereafter RA10). This technique is capable of providingmetallicity estimates with an accuracy comparable to that of the photometric technique,and requires only a moderate resolution K band spectrum of the M dwarf target, providinga significantly lower observational burden for empirically estimating the metallicities ofdistant, near-solar or super-solar M dwarfs. An example of the utility of this technique isprovided by a recent paper on M dwarf planet hosts identified in the most recent Keplerdata release by Muirhead et al. (2011; submitted)While RA10 provided a concise introduction to the spectroscopic K band metallicityindicator, space limitations prevented a full exploration of the technique. In this paper,we provide a full analysis of the motivation, calibration, demonstration and applicationof the technique using spectra we obtained for 133 Solar Neighborhood M dwarfs. InSection 2, we describe the composition of our sample, and the acquisition and reductionof our spectroscopic observations. In Section 3, we describe our measurements of the newH2O-K2 (a modified version of the H2O-K index utilized by RA10), Na I and Ca I spectralfeatures upon which the K band metallicity technique depends. In Section 4, we analyzemodel atmospheres to demonstrate the H2O-K2 index’s insensitivity to metallicity, and usethe H2O-K2 measurements from our sample to calibrate the index as a spectral type andT eff indicator. In Section 5, we use the H2O-K2 index as the basis for a revised K bandmetallicity calibration; by incorporating an additional M dwarf binary into our sampleof metallicity calibrators, and adopting a modified functional form to better normalizethe temperature dependence of the Na and Ca features, we derive an updated K band 7 –[Fe/H]metallicity indicator, as well as a new calibration for overall metallicity ([M/H]),along with robust estimates of the uncertainty in each calibration. In Section 6 we performseveral sanity checks of the K band metallicity technique, demonstrating that the Kband metallicity estimates preserve expected correlations between metallicity and Galactickinematics as well as signatures of chromospheric activity. We conclude in Section 7 byusing the K band metallicity estimates, in combination with other stellar parameters suchas rotational velocity ( v sin i ), magnetic activity (as diagnosed by H α emission) and opticalbrightness, to identify a sample of nearby M dwarfs with particular promise for exoplanetsurveys. We summarize our findings in Section 8, and present our full K band spectral atlasin an appendix (we also make our spectra available to the community online).
2. Sample Selection & Observations
We observed 133 nearby M dwarfs with declinations higher than -30 o . Our sampleconsists of: • Eighteen M dwarfs with wide ( > ′′ separation), common-proper-motion solar-typecompanions to serve as metallicity calibrators. The FGK-primaries have spectroscopicmetallicity measurements by Valenti & Fischer (2005, SPOCS Catalogue), obtainedby fitting synthetic atmospheric spectra to their high-resolution, high signal-to-noiseechelle spectra. The SPOCS [Fe/H] and [M/H] values for the FGK-primaries havebeen assumed to also describe the metallicities of their M dwarf companions. Thisassumption is justified if both binary components formed together, from the samewell-mixed molecular cloud, and no mass transfer or dredge-up has occurred in thesystem. This assumption is supported by the measurements of the metallicitiesof binaries with two FGK components: Desidera et al. (2004, 2006) find typicalmetallicity differences of ≤ • One hundred and fifteen M dwarfs within 33 parsecs, including 11 M dwarf planethosts observable from Palomar Mountain: Gl 876 (Marcy et al. 1998; Delfosse et al.1998a), Gl 436 (Butler et al. 2004), Gl 581 (Bonfils et al. 2005b), Gl 849 (Butler et al.2006), Gl 176 (Forveille et al. 2009), GJ 1214 (Charbonneau et al. 2009), Gl 649(Johnson et al. 2010), HIP 57050 (aka GJ 1148, Haghighipour et al. 2010), HIP 79431(Apps et al. 2010), Gl 179 (Howard et al. 2010), and HIP 12961 (Forveille et al. 2011).More than half are members of the Northern 8 parsec sample; the remainder wereselected from the LPSM catalog (L´epine & Shara 2005)Near-infrared spectra of these stars were obtained with the TripleSpec spectrographon the Palomar 200-inch Hale Telescope (Herter et al. 2008) during several observing runsbetween 2007 and 2010. TripleSpec at Palomar has no moving parts and simultaneouslyacquires 5 cross-dispersed orders covering 1.0-2.4 µ m at a resolution of λ/ ∆ λ ≈ . Each sky-subtracted exposure was divided by the normalizedmaster-flatfield, wavelength calibrated and optimally extracted (Horne 1986). The IDLpipeline walks through the stellar spectrum in each order of the calibrated star image, findsthe maximum every 10th pixel, and fits a Gaussian to the slit profile. The Gaussian fittherefore contains all of the stellar signal. The spectral orders of TripleSpec are substantiallycurved, so the pipeline interpolates onto a rectilinear grid with a thin-plate-spline to correctfor the slit tilt, using the spatial and wavelength solutions for the detector by Terry Herter .The 1-D M dwarf spectra were telluric corrected using observations of an A0V starwith the IDL-based code xtellcor general by Vacca et al. (2003). The spectrum of an A0Vstar is almost free of metal lines: its observed near-infrared spectrum consists mainly of afeatureless and smooth continuum superposed by H I absorption from the star’s atmosphere,and telluric absorption features contributed by the Earth’s atmosphere. A telluric spectrum ∼ muirhead/ [email protected] 10 –is obtained by removing the hydrogen lines of the A0V star using a high-resolution modelof Vega. The target spectrum is then divided by the telluric spectrum constructed fromobservations of a A0V star obtained near in time and close in airmass to the target.Finally, the telluric-corrected spectra were flux-calibrated using their 2MASS K bandphotometry. The flux density of the target star is proportional to the data number count(D λ ) after the telluric calibration: F λ = C D λ (1)Then, the star’s spectrum can be flux calibrated from its m K s magnitude, the K s spectral response function R K s , and the K s -band average flux density of a m K s =0 star F oK s ,by finding C : C = R R K s d λ R D λ R K s d λ F oK s − . Ks (2)The K s magnitudes for all the targets were obtained from the 2MASS All-Sky Catalogof Point Sources (Skrutskie et al. 2006). The 2MASS K s spectral response curve and F oK s are available online .Table 1 presents the properties of each star in the sample, including the star’s distance,V and K s magnitudes, the date the spectrum was observed, and the average signal-to-noiseratio (SNR) obtained in the K band continuum. The full sample of K band spectra arepresented in Figures 1-27; the sample is ordered in Table 1 and in Figures 1-27 in order of http://vizier.u-strasbg.fr/viz-bin/VizieR?-source=II/246 O-K2 index (see Section 3.2). Four stars appear to have sub-optimal telluriccorrections (Gl 644AB, 829AB, 809, & 908); these stars are flagged in Table 1 and theirspectra are presented separately in Figure 28.
3. Spectroscopic Analysis3.1. Na & Ca EWs
RA10 demonstrated that the 2.205 µ m Na I and 2.263 µ m Ca I lines can be used toestimate the metallicities of M dwarf stars. We measured the equivalent widths (EWs) ofeach of these lines for every star in our sample. The standard definition of the EW of a lineis given by the following equationEW λ = Z λ λ (cid:20) − F ( λ ) F c ( λ ) (cid:21) d λ (3)Here, F( λ ) represents the flux across the wavelength range of the line ( λ - λ ), andF c ( λ ) represents the estimated continuum flux on either side of the absorption feature.The EWs of the Na I and Ca I features were calculated with an IDL pipeline using thefollowing approximation: EW λ ≃ n X i =0 (cid:20) − F ( λ i ) F c ( λ i ) (cid:21) ∆ λ i (4)Equation 4 is the Riemann sum expression of the integral in Equation 3, where theF( λ i ) and F c ( λ i ) are the line flux and the estimated continuum flux of the wavelengthinterval ∆ λ i , respectively, and n is the number of intervals. The integration limits adoptedfor the Na I doublet and Ca I triplet features are shown in Table 2. 12 –Since the continuum of the M dwarf spectra is affected greatly by molecular/broadabsorption features, a pseudo-continuum is calculated instead using regions adjacent tothe feature of interest and free of any other atomic features. The pseudo-continuum foreach feature is estimated from a linear fit to the median flux within 0.003 µ m ( ∼ I and Ca I features for each star correspond to the standard deviations of the 1000 EWmeasurements of each feature.The values of the Na I and Ca I EWs measured for each star, along with their errors,are presented in Table 3. O-K2 Index
In RA10, the H O-K index by Covey et al. (2010) was used to account for the influenceof temperature on the strengths of the Na and Ca lines being used to diagnose each star’smetallicity. Covey et al. (2010) adopted this index to characterize the spectral types ofhighly reddened young stars from moderate S/N spectra, and optimized the H O-K indexto sample the redder portion of the K band and ignored weak atomic features (Mg I , Ti I )that were not typically visible in their spectra. Stars in our sample, by contrast, possess 13 –low extinctions and are relatively bright, such that two of the regions used to calculate theH O-K index show obvious atomic absorption features in our high-S/N spectra of earlyM dwarfs. To ensure our water-index measurements are not affected or biased by thesefeatures, we developed a modified H O-index using two new regions that do not show anynoticeable atomic lines. This H O-K2 water index is defined as:H O − K2 = hF (2 . − . i / hF (2 . − . ihF (2 . − . i / hF (2 . − . i (5)where hF ( a − b ) i denotes the median flux level in the wavelength range defined by a and b , in microns. This new index represents the change in the overall shape of the spectra ofM dwarfs due to water absorption from 2.07 µ m to 2.38 µ m, with smaller values of theH O-K2 index corresponding to greater amounts of H O opacity. The difference betweenthe H O-K index defined by Covey et al. (2010) and the H O-K2 index is shown in Figure29. Uncertainties in the H O-K2 index measurements were computed using the sameMonte-Carlo approach used to estimate uncertainties in the Na I and Ca I lines; eachH O-K2 error estimate represents the standard deviation of 1000 H O-K2 measurementsafter adding synthetic noise to the spectrum consistent with the S/N value of the observedspectrum.The values of the H O-K2 index measured for each star are included in Table 3 alongwith their uncertainties.
The metallicity calibration presented in RA10 was empirically derived, with thetemperature and metallicity dependences of the Na I , Ca I , and H O features inferredlargely from visual inspection of the calibrator stars. While RA10 used PHOENIX model 14 –atmospheres to qualitatively demonstrate the metallicity sensitivity of Na I and Ca I ,and the reduced metallicity sensitivity of the H O feature, no detailed exploration of thebehavior of the Na I , Ca I , and H O features as functions of temperature or metallicitywere performed.The lack of a quantitative exploration of the line strengths predicted by modelatmospheres is partially due to the fact that, until recently, synthetic models struggledto match the infrared spectrum of M dwarfs, which is predominately dominated by wateropacity (Allard & Hauschildt 1995). The discrepancy was believed to be due to incompletewater vapor lists; several water opacity profiles were used through the years, all of whichover-predicted the K band opacity and resulted in a lack of flux in the synthetic modelwhen compared to observed spectra (Allard et al. 2010). Asplund et al. (2009) recentlyderived a new estimate of the solar oxygen abundance, however, which is a factor of 2lower than previous estimates and seems to have solved the water opacity discrepancy.The new BT-Settl-2010 synthetic spectra by Allard et al. (2010) incorporate the new solarabundances, along with updated molecular line lists, and provide a better match to thespectral distribution of M dwarfs across the near-infrared than previous models. TheBT-Settl-2010 models are available online ; using this interface, we constructed a grid ofBT-Settl-2010 synthetic spectra with effective temperatures from 2200K to 4100K, andoverall metallicities [M/H] equal to +0.5, +0.3, +0.0, -0.5, and -1.0 dex. This effectivetemperature range covers the whole M dwarf sequence, and the model grid covers a range ofmetallicities larger than that spanned by our calibration stars, or the metallicities estimatedwith Equation 8 for any of our target stars. All the stars analyzed here are known to bedwarfs and none show any spectral features indicating otherwise, so a value of log g=5.0was selected to provide the best agreement with empirical M dwarf gravity determinations http://phoenix.ens-lyon.fr/simulator 15 –(Fernandez et al. 2009; Demory et al. 2009).To provide a quantitative indication of the feature strengths predicted by the theoreticalmodels, we degraded the resolution of each theoretical spectrum to match that of ourobserved sample and measured the EWs of the Na I doublet and Ca I triplet, as well as theH O-K2 index, using the same routines applied to our observed spectra.Figure 30 shows the spectra of three stars in our sample, ranging in spectral type fromM1 to M7, superimposed by BT-Settl-2010 synthetic spectra degraded to the resolutionof the TripleSpec data. The overall shape of the observed spectra, dominated mostly bywater absorption, are well matched by the BT-Settl-2010 models. The Na I and Ca I atomic features used by the metallicity calibration fits, however, are noticably weaker in theBT-Settl-2010 models than in the observed spectra: even the highest metallicity syntheticspectra cannot reproduce the strengths of the Na I doublet and Ca I triplet in the spectra ofGl 324 B and LHS 2090. The [M/H] =+0.3 and T eff = 4100K BT-Settl-2010 model matchesthe strengths of the CO bands and the neutral Ti and Al lines for HIP 12961 quite well,but it shows stronger Ca I features at ∼ µ m, and no Mg I line at ∼ µ m. Thesediscrepancies could be explained by uncertainties in the oscillator strengths and opacitiesadopted for these lines, as suggested by Rajpurohit et al. (2010). Another explanationcould be the size of the wavelength interval (resolution) chosen to calculate the syntheticspectrum. If the lines in question are not well-sampled at the resolution used to calculatethe synthetic spectrum, convolving the synthetic spectrum with a Gaussian to degrade theresolution to match TripleSpec could cause them to be artificially ‘weakened’.Figure 31 shows the H O-K2 index and EWs of the Na I doublet and Ca I tripletmeasured from the BT-Settl-2010 models, after degrading their spectral resolution to matchthat of TripleSpec, as a function of effective temperature and color-coded by metallicity.The Ca I triplet behaves as expected from observed data: its strength increases as both 16 –temperature and metallicity increase. However, the Ca I triplet disappears from thesynthetic models at effective temperatures lower that ∼ I triplet remains visible even at spectraltype M8.The water absorption features predicted by the models also agree reasonably well withexpectations from empirical spectra, with water absorption increasing monotonically withdecreasing temperature, in a manner independent of metallicity, down to T eff ∼ O absorption remains almost constant from 3000K to 2200K,while water absorption in solar and supersolar models continues to increase with decreasingtemperature. The stark difference in the H O opacity between solar and subsolar metallicitymodels suggests the discrepancy in H O absorption may be more likely a computationalartifact than an astrophysical difference.The most puzzling behavior is shown by the EWs for the Na I doublet. Observationally,the strength of the Na I doublet increases as temperature decreases, at least until effectivetemperatures equivalent to an M6V star (e.g. Cushing et al. 2005). Strong Na I doublets arealso seen in the late-type stars studied in this work. The only synthetic spectra that showthis trend, however, are the solar metallicity spectra. The most metal-poor ([M/H] = -1.0)synthetic spectra, by contrast, show the strongest Na I absorption near ∼ I EWs decreasing to both hotter and cooler temperatures; the moderately metal poor([M/H] = -0.5) models show a similar behavior but with a strong jump near T eff =2900K.The super-solar models, by contrast, possess the strongest Na I lines at warm temperatures,but the Na I lines in these models begin to weaken at T eff ≤ I line strengths that are anti-correlated with metallicity (in the solar/super-solar regime)below T eff =3000K. 17 –The behavior of the Na I doublet in the solar and supersolar synthetic models is notreproduced in our empirical spectra. The metal-rich calibrator, Gl 376 B ([M/H] SP OCS =+0.11, [Fe/H]
SP OCS =+0.20), is a late-type star (M6) and it exhibits one of the strongestNa I doublets of the 18 calibrators. Since low temperatures favor the formation of molecularspecies, the anomalous Na I behavior in the synthetic models could be an effect of thetreatment of molecular formation at these temperatures. The most recent study of alkalichemistry in cool atmospheres was conducted by Lodders (1999). Lodders (1999) calculatedthe mole fraction, the amount of an element divided by the total amount of the elements,of neutral Na, ionized Na, and the molecules NaCl, NaH, and NaOH as function oftemperature at 1 bar total pressure for cool dwarf atmospheres (3300K < T < ∼ S condensation weakens the Na features in brown-dwarf spectra(Lodders 2002). It is possible that these complex chemical networks could play a role inthe anomalous behavior of the Na I feature in the synthetic models: perhaps the mostmetal-rich models favor the formation of Na-based molecules toward cooler temperatures,for example, such that the neutral Na responsible for the Na I S condensation occurs at higher temperaturesin the super-solar models. These suggestions are highly speculative, however, and based onthe number of odd behaviors exhibited for models cooler than 3000K, we suspect the rootcause is as likely to be computational as astrophysical in nature. 18 –
4. Calibrating The H O-K2 index as a spectral type and T eff indicator
Water is a heteroatomic molecule and the appearance of the absorption band reflects thepressure and temperature sensitivity of the formation of these molecules (Merrill & Ridgway1979). Numerous investigators have leveraged this fact to use near-infrared water absorptionbands to diagnose M dwarf effective temperatures and spectral types. Kleinmann & Hall(1986) noted that the depression at 4778 cm − ( 2.096 µ m) due to water absorption waslargest for dwarf stars, and increases with decreasing spectral type. Jones et al. (1994)placed this calibration on an absolute T eff scale, deriving effective temperatures forstars with spectral types ranging from M2V to M9V by comparing the observed H Obandhead at 1.34 µ m to laboratory data for the water absorption coefficient. Ali et al.(1995) similarly created a T eff indicator using an index sampling the K band H O featurein low resolution spectra at ∼ ∼ µ m, deriving a linear relationship betweeneffective temperature from low-resolution spectra of MK-dwarf standards. More recently,McLean et al. (2003) calculated linear relationships between stellar spectral type and thedepth of water absorption bands present in R ∼ O-D, was constantfor spectral types M0-M4, at which point the index decreased (due to increased H Oabsorption) towards cooler spectral types.To calibrate the H O-K2 index as a well-defined T eff indicator, we provide in Table 4the values of the H O-K2 indices measured from the BT-Settl-2010 models and originallypresented in Figure 31. As Figure 31 demonstrates, the BT-Settl-2010 models predict thatthe H O-K2 index is a monotonic function of temperature, but independent of metallicity,for stars in the 3000 K < T eff < O-K2 index as a function of T eff for metal-poor and solar/metal-rich 19 –stars, respectively. While this low-temperature behavior may be a computational artifact,the metallicity dependent differences at T eff s > O opacity appears to ‘saturate’ for evenvery low metallicities, such that the most metal-poor stars in the model grid do not appearto possess any less H O opacity than the most metal-rich stars of the same temperature,this is not true at the highest temperatures, near the onset of the H O feature in the NIRspectral sequence. Rather, the H O index values tabulated in Table 4 appears to indicatethat the H O feature appears at higher temperatures for more metal-rich stars. Care musttherefore be exercised in inferring the temperature of stars with very weak H O features; inaddition to the greater difficulty of ensuring a high S/N measurement of a weak feature,the BT-Settl-2010 models suggest that even if high quality H O-K2 measurements can beobtained for stars with weak H O absorption, there will be large astrophysical uncertaintiesintroduced into the resultant T eff estimate due to the strong metallicity dependence ofthose features at relatively high T eff s. The gravity dependence of the H O-K2 index, as afunction of model effective temperature and fixed metallicity, is shown in Figure 32. Thegravity values of log g= 4.5 and 5.0 are the standard values adopted for M dwarf models.Within the metallicity range explored with the BT-Settl-2010 models, the sensitivity ofthe H O-K2 index to surface gravity is negligible for T eff ≥ O-K2 index due to surface gravity are found at lowertemperatures in the [M/H]=-1.0 models. Therefore, according to the BT-Settl-2010 models,the H O-K2 index values are metallicity and gravity insensitive for 3000K ≤ T eff ≤ O-K2 indexusing the solar ([M/H]=0.0) BT-Settl-2010 models. For each star, we interpolated themeasured H O-K2 value onto the solar metallicity model [H O-K2,T eff ] grid to get a T eff estimate and error from its H O-K2 uncertainty. The values used for the solar metallicity 20 –[H O-K2,T eff ] grid are shown in Table 4. The effective temperatures derived should notbe considered extremely accurate or reliable, especially for the late type M dwarfs in thesample, since the BT-Settl-2010 models of T eff < O absorption discrepanciesdue to [M/H] that are more likely to be a computational artifact that an astrophysicaldifference. Due to the finite resolution of the model grid, where models have only beencalculated on a grid with a spacing of ∆T eff =100K, systematic errors of ∼ O-K2 index as a proxy for KHM spectral type. We exclude from thiscalibration sample 14 objects with potentially ambiguous H O-K2 indices: eleven aremembers of binaries or multiple systems in very tight orbits, such that the final K bandspectrum mixes emission from all the stars in the system; we exclude the remaining threestars on the basis of their sub-standard telluric/flux calibration. For the fifty four singlestars in our sample with high-quality spectra and KHM spectral types, we performed alinear regression between the measured H O-K2 indices and KHM spectral types using aBayesian approach that takes into account the errors associated with each of the variables 21 –(Kelly 2007). According to Kirkpatrick et al. (1991), the KHM spectral types have ∼ O-K2 index are listed in Table 3. Thisregression analysis indicated that a star’s KHM spectral type, expressed as a numerical Msubtype, can be derived from its H O-K2 indices as:M subype = A + B (H O − K2) (6)A = 24 . ± . − . ± . . O-K2 index, and the residuals of the fitfor our 54 spectral type calibrators, are shown in Figure 33. The residuals indicate that theH O-K2 index can predict each star’s spectral type with a typical accuracy of 0.6 sub-types.As Figure 33 shows, however, some stars possess KHM spectral types that differ from thetype predicted from their H O-K2 index by & § O-K2 index; these types are listed in Table 3, and were used to orderthe sample from earliest to latest spectral types. To provide high quality template spectrafor subsequent spectral type measurements, we also combined all the spectra in our samplein bins according to their decimal H O-K2 types. For each subtype bin, each spectrumwas normalized by its mean flux between 2.16 and 2.2 µ m. The spectra then were all 22 –cross-correlated with the spectrum of one of the stars in the subtype bin to make theirspectral features coincide. Finally, the wavelengths offsets were applied to each spectrum.At least three stars, and as many as thirty, were then median combined to make the mastertemplate for each subtype, with the exception of the M9 template, for which LHS 2924 isthe only prototype in our sample. The templates from M0 to M9 are shown in Figure 34.
5. Updated and Extended K band Metallicity Calibrations5.1. A Revised Empirical [Fe/H] Calibration
RA10 presented a linear equation for estimating an (early-to-mid-) M star’s [Fe/H]value based on the strengths of its Na I and Ca I lines, and its temperature as diagnosed viaits H O-K index. We present here a revised formalism to describe this relationship, wherethe revision has been motivated by three factors: • The adoption of the revised H O-K index, as introduced above; • The addition of a new M dwarf star, Gl 166C, to the metallicity calibrator sample(Table 5) following the publication of RA10. • The adoption of a new functional form to estimate the star’s metallicity from its Kband spectral features.The adoption of a new functional form for the K band metallicity calibration is perhapsthe most meaningful change, and deserves further explanation. The linear expression inRA10 produced unrealistically high [Fe/H] values for some of the more metal-rich M dwarfsin this sample (e.g., LHS 3799; [Fe/H] ∼ +0.64 according to the RA10 calibration). Whileit is necessary to include the water index in the relationship to remove the temperature 23 –dependence of the Na I and Ca I features, the assumption that water absorption should beincluded as an independent variable is not necessarily correct. Extensive experimentationwith various functional forms revealed that a better [Fe/H] calibration fit could be obtainedif water absorption is used as a “weight” for the Na I and Ca I strengths rather than as afully independent variable.We conducted multivariate linear regressions on the Na I and Ca I EWs, weightedby each star’s H O-K2 index, for the 18 metallicity calibrators to identify the best fitrelationship to predict each star’s [Fe/H] value. The resulting calibration is:[Fe / H] = A + B Na I EW H O − K2 + C Ca I EW H O − K2 (7)A = − . ± . . ± . . ± . / H]) = 0 . RM Sp ),the Root Mean Squared Error (
RM SE ) and adjusted square for the multiple correlationcoefficient ( R ap ) statistics for evaluating the uncertainties and predictive power associatedwith a functional fit to a given set of calibration data. These quantities were introducedby Schlaufman & Laughlin (2010) to compare the quality of the photometric [Fe/H]calibrations. The [Fe/H] fit in RA10 has a RM Sp ([Fe/H])=0.02 and an R ap ([Fe/H])=0.63.The addition of another binary system and the new independent variables maintained orimproved each of these statistics with respect to the RA10 calibration: the RA10 [Fe/H]calibration and the revision presented here possess equivalent RM Sp values, but the new[Fe/H] fit has a higher R ap ( R ap ([Fe/H] RA )=0.67). 24 –For the [Fe/H] model in Equation 7, the Root-Mean-Squared Error of Validation( RM SE V , Appendix A) is equal to 0.161 dex. The RMSE V value is equivalent to a ∼ σ , and is considered a sensible estimate of average prediction error.The 95% confidence interval is equal to ± I triplet and the Na I doublet features, weighted by the H O-K2index, are plotted in Figure 36 for all the M dwarfs analyzed here. Iso-metallicity [Fe/H]contours calculated from Equation 7 are shown as dashed and dotted lines. In this plane,there is a clear distinction between the M dwarfs in the calibration sample with metal-richand metal-poor FGK-dwarf companions. The M dwarf planet hosts also all have [Fe/H] > ∗ V1513 Cyg (-0.64 dex). 25 –
In addition to iron abundance estimates, the SPOCS catalogue also provides overallmetallicity [M/H] values for the FGK-companions of stars in the calibration sample. In thefitting procedure described in Valenti & Fischer (2005), the [M/H] value is an individualmodel parameter, rather than a quantity constructed from individual element abundances.We performed a linear regression as described above, assuming the same functional form asadopted for the iron metallicity estimate, to calibrate the relationship between the waterweighted Na I doublet and Ca I triplet and [M/H]:[M / H] = A + B Na I EW H O − K2 + C Ca I EW H O − K2 (8)A = − . ± . . ± . . ± . / H]) = 0 . RM Sp ([M/H])=0.010 and an adjusted R square R ap ([M/H])= 0.67. For the [M/H] model in Equation 8, the RM SE V is equal to 0.111 dex( ∼
70% confidence interval or 1- σ ), and the 95% confidence interval is equal to ± O-K2 versus Na/H O-K2 plane as Figure 36, but the 26 –dashed and dotted lines represent iso-overall-metallicity contours calculated from Equation8. The M dwarf planet hosts all have [M/H] > ∗ V1513 Cyg has [M/H]=-0.45 dex. Thepredicted [M/H] values from Equation 8 for the stars in our sample are shown in Table 3.As the BT-Settl-2010 theoretical model atmospheres are calibrated as a functionof their overall metallicity, we are now able to directly compare the feature strengthsmeasured from our model grid against the iso-metallicity contours we inferred from theempirical calibration sample above. Figure 39 shows the EW of Ca I vs the EW of Na I ,both weighted by H O-K2 that we measured from the BT-Settl-2010 model spectra withtemperatures equal to or higher than 3000K. This plane splits the synthetic models bymetallicity, in a similar way as it also splits the calibration stars for the metallicity fits. The[M/H]=-1.0 dex models lie in the bottom-left corner, and the [M/H]=+0.5 dex models lieupwards and to the right of the [M/H]=-1.0 dex models, consistent with the direction of theoffsets predicted by the isometallicity contours. However, since the synthetic models predictweaker Na I doublet and Ca I triplet features than are observed in the empirical spectra,the models do not directly align with the empirical iso-metallicity contours (depicted bydashed lines) obtained with the K band [M/H] fit of Equation 8. The [M/H]=-1.0 dexmodels are located above the [M/H]=-0.6 dex empirical contour, while the [M/H]=+0.5dex model points are far below the [M/H]=0.0 dex empirical contour. The odd behaviorof the Na I doublet features of the supersolar models mentioned above becomes evident astemperature decreases in Figure 39. Subsolar and solar models of temperatures between3700K and 3000K appear as parallel lines in this plane, but the supersolar models intersectthe solar model at 3000K. 27 – We now seek to compare the quality of our [Fe/H] fit, and the resultant values itpredicts for our calibration stars, to similar evaluations of the [Fe/H] predictions producedby the photometric calibrations. Neves et al. (2011, hereafter N11) performed a similarexercise, comparing the
RM Sp , R ap , and the dispersion around the mean ( rms ) values ofthe photometric metallicity scales using a sample of 23 M dwarfs with solar-type companionsof known metallicity, and refined the Schlaufman & Laughlin (2010) calibration based ontheir results.Unfortunately, for the same reason that N11 did not include the RA10 metallicitypredictions in their analysis, because our calibrator samples do not overlap well, it is difficultto directly compare the statistics of our fit to those computed by N11. N11 analyzed 23 Mdwarfs with reliable metallicity estimates, V magnitudes, and trigonometric parallaxes; ofthese, only 7 are members of our sample of M dwarfs with moderate resolution NIR spectra,providing minimal leverage for evaluating the accuracy of the various techniques with acommon set of calibrators. This demonstrates an important point: the statistics calculatedabove, by definition, describe how well a given formalism can reproduce measurementsof a particular calibration set. The meaning of those statistics, therefore, is inextricablylinked to the particular calibration set from which they were computed: comparing thosestatistics amongst various metallicity calibrations requires that the statistics be computedwith respect to a specific, and shared, set of calibrators.To make matters worse, the veracity of the calibration set is as important, if not moreso, as the number of calibrators. For example, while the B05 functional fit has overallbetter statistics (as we show below), some of the stars in its calibration sample have poor
28 –photometry values. The JA09, SL10, and N11 calibrations improved the B05 calibrationby including only stars with high precision photometry/parallax measurements, excludingseveral of the stars in B05, and including stellar population and kinematic considerations.Moreover, we find differences up to 0.3 dex in the [Fe/H] values assigned for the M dwarfs inour calibration sample and the values used to derived the photometric scales. For example,B05, SL10 and N11 assign a [Fe/H] value of -0.15 dex to Gl 250 B, while the SPOCS [Fe/H]value we adopt for this star in our own calibration sample is +0.14 dex . As the metallicitycalibrations were derived with reference to these [Fe/H] values, the choice of which setof [Fe/H] values to adopt as a benchmark will necessarily bias the comparison towardsthe calibrations derived from those [Fe/H] values. As a result, a truly fair comparison ofthe photometric and spectroscopic techniques will only be possible once the calibrationsample has been significantly enlarged, and the veracity of the [Fe/H] values adopted forthe calibration sample has been well established.Given the limitations outlined above, we conclude that the fairest comparison of thespectroscopic and photometric techniques that can currently be made is to qualitativelycompare the internal quality of each fit, as benchmarked by its native calibration sample,as well as to compare the size and character of the calibration sample from which each fitwas derived. Table 6 lists the rms , RM Sp and R ap values for each calibration technique,along with the number of predictors p and sample size N for each model. The uncertaintieswere estimated using the bootstrapping method described in N11.The number of calibrators and the dispersion around the mean value evaluate thequality of the calibration sample that each technique is based on. Large samples (large N ) We note that as this paper went to press, ¨Onehag et al. (2011) reported a third metal-licity for Gl 250B of -0.05 dex, based on an analysis of high-resolution ( R ∼ N =48), and also the most diverse ( rms =0.483),followed by our calibration (RA11), SL10 and N11, respectively. The JA09 calibrationsample has a very low rms value since its composed only by high [Fe/H] stars.The RM Sp and R ap statistics evaluate the internal quality of each functional fit; theydescribe how well the values predicted by each fit match the measured for the calibratorstars that were used to construct the fit. Small RM Sp values (small residuals) and R ap values closer to 1 are preferred (see Appendix A). The JA09 fit has the smallest RM Sp ,but its R ap has a large uncertainty. N11 noted that the R ap is a noisy statistical estimatorfor small samples, however, and the JA09 fit only has 6 stars in its calibration sample. TheB05 fit has the largest R ap .In summary, the B05 calibration has the better statistics when its native calibrationsample is used. However, the B05 calibration underestimates M dwarf metallicities,probably a result of using old visual magnitudes, instead of Johnson V-band magnitudes,and the lack of high [Fe/H] M dwarfs in their calibration sample. The JA09 fit has a verysmall calibration sample composed only of high metallicity M dwarfs, and therefore, not areliable fit for [Fe/H] prediction for M dwarfs. We find that the RA11, SL10 and N11 fitshave calibration samples of similar size, similar rms and RM Sp values; our calibration hasthe highest R ap values of the three. However, as noted earlier, none of these statistics canevaluate the veracity of the input values of the calibration sample, which determines theaccuracy of the predicted values by the functional fit, as the recalibration of the B05 fitdemonstrates. Constructed an enlarged calibration sample, and demonstrating the veracityof the adopted [Fe/H] estimates, are key steps to enable a full and detailed comparison ofthe reliability of these techniques. 30 – Supersolar metallicities for most of the M dwarf planet hosts are predicted by theK band [Fe/H] fit as well as the photometric calibrations by Johnson & Apps (2009)and Schlaufman & Laughlin (2010). While these three methods agree on the systematicmetal-richness of planet hosts, the [Fe/H] values they predict do differ for each of the planethosts (Table 10).Photometric [Fe/H] methods need accurate V magnitudes and distances, to calculateabsolute K S magnitudes, and thereby infer the metallicities of M dwarfs from the M V vs V-K S color-magnitude diagram. Forty eight of the M dwarfs in our sample haveaccurate Johnson-V magnitudes and parallaxes by HIPPARCOS (van Leeuwen 2007),and K S magnitudes by 2MASS (Skrutskie et al. 2006). By including the M dwarfs withJohnson V magnitudes and parallaxes in the Yale Trigonometric Parallaxes Catalogue(van Altena et al. 2001), we can assemble a sample of ninety stars with the necessary datato compare the results from the new K band [Fe/H] fit and photometric [Fe/H] relations.Table 7 lists the ninety M dwarfs with Johnson-V magnitudes and parallaxes, withtheir [Fe/H] values obtained from the photometric calibrations and the K band [Fe/H]fit in Equation 7. Since the Neves et al. (2011) photometric calibration is a marginalrefinement of the Schlaufman & Laughlin (2010) calibration, we only included the later inthis comparison. Eight-six of the stars in Table 7 are also included in the Palomar-MichiganState University Nearby Star Spectroscopic Survey (PMSU; Reid et al. 1997), and havemeasurements of the TiO and CaH feature strengths from their optical spectra. Woolf et al.(2009) created a spectroscopic optical technique based on these indices to estimate [Fe/H]metallicities for early M dwarfs. The [Fe/H] values predicted by the Woolf et al. (2009)technique from the PMSU indices are also listed in Table 7. The value of [Fe/H] is listedfor a star in Table 7 only if the parameters to calculate it satisfy the conditions of each 31 –technique: • Bonfils et al. (2005a, hereafter B05): The [Fe/H] photometric relation by B05 is validfor stars with 4 ≤ M K ≤ ≤ V-K s ≤
6, and -1.5 ≤ [Fe/H] ≤ +0.2. • Johnson & Apps (2009, hereafter JA09): The [Fe/H] photometric relation by JA09 isvalid for stars with 3.9 ≤ V-K s ≤ ≥ -0.05 dex. However, we decreasedthe [Fe/H] lower limit to -0.12 dex, which corresponds to the extrapolation done forthe star Gl 832 in JA09. • Schlaufman & Laughlin (2010, hereafter SL10): The [Fe/H] photometric relation bySL10 does not explicitly mention any conditions. However, we only estimated [Fe/H]values for that stars with 3 ≤ V-K s ≤
7, the color range in the color-magnitudediagrams in SL10. • Woolf et al. (2009, hereafter W09): The [Fe/H] relation based on TiO and CaHmolecular absorption by W09 depends on the ζ T iO/CaH parameter by L´epine et al.(2007). The W09 calibration is valid for stars with -1.5 ≤ [Fe/H] ≤ +0.05 and3500K ≤ T eff ≤ ζ T iO/CaH parameter categorizes the main sequence M stars into 4 classes ordered bydecreasing metallicity: dwarfs (dM), subdwarfs (sdM), extreme subdwarfs (esdM),and ultrasubdwarfs (usdM). The metallicity class for each star is also listed in Table7.Figure 40 shows the difference between the [Fe/H] values obtained by Equation 7, andthe metallicity methods listed before.The B05 and W09 relations assign lower [Fe/H] values to the stars with solar andsupersolar metallicities according to the K band [Fe/H] calibration. The stars with [Fe/H] 32 –differences within 0.15 dex have K band [Fe/H] metallicities between ∼ +0.1 dex and ∼ -0.5dex, and correspond to 50% and 58% of the stars in the B05 and W07 samples, respectively.The JA09 relation assigns higher [Fe/H] values to the metal-poor stars in the K band[Fe/H] calibration. The stars with 0.15 dex [Fe/H] differences (i.e. ∼ σ of the K bandcalibration) have K band [Fe/H] metallicities between -0.3 dex to +0.4 dex, and representthe 55% of the stars with JA09 metallicities.The SL10 relation [Fe/H] values agree within 0.15 dex with the K band [Fe/H]calibration for a 56% of the stars with SL10 metallicities. However, the dispersion formetal-poor stars is larger than for the stars with high K band [Fe/H] values, when comparedto the SL10 technique. The SL10 technique “underestimates” the values of some of thesolar and supersolar K band [Fe/H] stars, but for low K band [Fe/H] values, it can eitherunderestimate or overestimate that value by up to 0.6 dex. GJ 1116 A (M6) has a K bandmetallicity of [Fe/H] RA = -0.12 dex, but the SL10 method predicts a value of [Fe/H] SL = +0.89 dex. The SL10 [Fe/H] value for GJ 1116 A is very unlikely and it may be a resultof bad V photometry or a bad parallax measurement.All the plots in Figure 40 show a similar slope, except the [Fe/H] SL - [Fe/H] RA vs. [Fe/H] RA plot. The W09 relation was calibrated using the ζ T iO/CaH parameter andmetallicities inferred from Fe I and Ti I abundances of K-dwarfs and early M dwarfsfrom their high resolution spectra (Woolf & Wallerstein 2005). B05 acknowledge in theirconclusion that their [Fe/H] values are consistent (where the paramenter spaces overlap)with the [Fe/H] values from Woolf & Wallerstein (2005). Since B05 and W09 results agree,it is not surprising that both plots look quite similar. The JA09 calibration depends on thesame observables as the B05 calibration, though supersolar metallicity stars were used as[Fe/H] calibrators for the fit. This could explain why the JA09 plot has the same slope asthe B05 and W09, but with an offset towards higher metallicities. The observables in B05 33 –were also used in the SL10 calibration, however, the kinematics of the FGK-calibrators andtheoretical models were considered in the SL10 calibration. For the supersolar metallicitystars, the SL10 shows just an offset towards lower metallicities when compared to the RA11calibration. For the metal-poor stars, the scatter is larger but there is not a distinct slopebetween SL10 and RA11. While M dwarfs are bright in the NIR, historically the optical regime has received morescrutiny as a means of studying M dwarfs. The molecules CaH, TiO, CaOH, and VO coverthe spectral range between 6300-9000 ˚ A . TiO absorption bands are known to be metallicitydependent (e.g. Woolf & Wallerstein 2006). Titanium oxide bands grow stronger withincreasing metallicity as well as decreasing temperature. Hydride absorption bands alsoincrease in strength with decreasing temperature, but, since the number density of neutralhydrogen increases as metallicity decreases, they grow stronger with decreasing abundance,too. Therefore, hydride absorption bands dominate the spectra of metal-poor stars, and theratio between TiO and CaH has been used as a discriminant between disk and halo M stars(e.g. the subdwarf classification by Gizis 1997).One hundred and nine M dwarfs studied in our sample are part of the Palomar/MichiganState University Nearby Star Spectroscopic Survey (PMSU, Reid et al. 1995; Hawley et al.1996). The PMSU survey obtained optical spectroscopy of most of the M stars in TheThird Catalogue of Nearby Stars (Gliese & Jahreiss 1991), allowing spectral types to beestimated from TiO band-strengths, chromospherically active stars to be identified by H α emission, and metal-poor stars to be identified from the CaH strength relative to TiOstrength. The overlap between our sample and the PMSU catalog allow us to test if a Mdwarf’s metallicity influences the spectral type obtained by the KHM technique. 34 –Reid et al. (1995) defined nine narrow band spectroscopic indices (5 TiO indices, 3 CaHindices, and 1 CaOH index) to measure molecular features in the 6200-7200 ˚ A wavelengthrange. Assuming that TiO band-strengths are primarily temperature dependent, Reid et al.(1995) measured the full strength of the TiO band at ∼ A (the TiO5 index) fora large number of stars with KHM spectral types to calibrate TiO as a spectral typeindicator. Gizis (1997) used the Reid et al. (1995) index definitions to calibrate CaH2 andCaH3 indices as spectral type indicators, too. We calculated spectral types for the starsin our sample that are also in PMSU using the Reid et al. (1995) and Gizis (1997) fitrelations. The spectral types derived from the TiO5 and CaH features agree for most ofthe sample. The difference in spectral type predicted by the optical indices and H O-K2index as function of overall metallicity is shown in Figure 41. The TiO5 index predicts latersubtypes than the H O-K2 index for the solar and metal-rich stars, and earlier subtypes forthe metal-poor stars. The CaH2 index predicts later subtypes than the H O-K2 index formost of the stars. The CaH3 index tends to give earlier subtypes than the H O-K2 index.However, considering their uncertainties, the spectral types derived from the TiO and CaHindices agree with the H O-K2 index based spectral types.The values of TiO2, TiO3, and CaH1 indices versus the H O-K2 index of the starsin the PMSU survey are shown in Figure 42. There is a strong correlation between thewater index and the TiO indices up to H O-K2 ∼ ∼ A , and therefore, reverses therelation. The CaH1 index saturates at TiO5 ∼ > < O-K2 relation can 35 –be explained by the metallicities of the stars. The CaH1 index saturates at ∼ M3, due tothe increasing TiO absorption in that region of the optical spectrum. Since both molecules,CaH and TiO, increase in strength towards lower temperatures, a ratio between these twomolecules could be what CaH1 is really measuring. If a given star has low metallicity, theTiO absorption is not going to be as significant as the CaH, for any given temperature. TheCaH1 feature will remain strong for low metallicities, which will correspond to low CaH1index values. But, if the star is metal-rich, the pseudo-continuum used to estimate theCaH1 index is going to be affected by the strong TiO absorption. The CaH1 feature willbecome less prominent, corresponding to high CaH1 index values. There is a similar splitbetween the metal-rich and metal-poor M dwarfs for the TiO2 and TiO3 relations, but itis less significant. The CaH1 feature could be used as a metallicity discriminator for earlysolar-metallicity M dwarfs in the optical.
6. Independent Tests of the K band [Fe/H] Fit: M-M Binaries, UVW SpaceMotions and H α Activity6.1. Do M-M Binaries Return Similar Metallicities?
The K band [Fe/H] calibration and the photometric methods rely on the assumptionthat stars in binary systems share the same metallicity, as a result from being formedfrom the same interstellar material and at the same time. This assumption, which allowsan M dwarf secondary’s metallicity to be inferred from measurements of its FGK primaryhas been validated for binaries with multiple solar type components (Desidera et al. 2004,2006), and implies that any metallicity estimation technique should return consistent valuesfor two M dwarfs in a wide multiple system. As a sanity check, therefore, we inspect the[Fe/H] values predicted by each technique for the individual components of double M dwarfwide binary systems in our sample. Table 8 shows the K band and photometric metallicities 36 –of 5 M-M binary or multiple systems in our sample, along with their NIR spectral types;Gl 643 and Gl 644C are also included as a pair, since both are proper motion companionsto the Gl 644AB pair/triplet according to S´egransan et al. (2000). Photometric estimatescannot be made for all the stars in the systems since their photometry and/or parallaxesdo not satisfy the conditions listed in Section 5.3 for each calibration. We also show thesesystems in Figure 43, where we connect the individual components of a multiple systemwith dotted lines to examine how well each system agrees with the slope of our derivediso-metallicity contours.The K band [Fe/H] and [M/H] estimates for individual components of (non-calibrator)binary systems agree remarkably well; four of the six systems have [Fe/H] and [M/H]metallicity differences of less than 0.02 dex, and none of the six have individual metallicityestimates that disagree by more than 0.13 dex, comparable to the 1 σ accuracy of theunderlying calibration itself. Indeed, the largest discrepancy for the K band calibrationis for the Gl 725AB pair, whose 0.09 dex and 0.13 dex [M/H] and [Fe/H] differences aresimilar to the dispersion ( RM SE ) of each fit in Equations 8 and 7, respectively.The metallicity estimates predicted by the photometric techniques, however, donot reproduce this agreement: the photometric techniques predict metallicities for theseindividual binary components that typically differ by 0.1-0.2 dex, comparable to the singlelargest metallicity difference predicted by the K band technique. The Gl 412 system isthe binary in our sample with the greatest spectral type difference, consisting of M1 andM6 components. Despite the significant range in temperatures between these two stars,the metallicities predicted by the K band calibration only differ by 0.01 dex, suggestingour calibration is not strongly biased with respect to T eff . The GJ1245 system providesanother a good case study: both components have the same spectral-type in the opticaland in K band, and their K band spectra share a very similar morphology, so it is perhaps 37 –not surprising that the metallicity estimates predicted by the K band calibration forthe individual components agree quite well (∆ RA11 [Fe/H] = 0.01). The photometric[Fe/H] estimates for each component, however, disagree much more (∆ [Fe/H] = 0.25-0.3),reflecting underlying differences in the source photometry: while the distance measurementsfor GJ 1245 AC and GJ 1245 B agree well ( δ d = 0.2 pc), their photometry does not,with GJ 1245 AC appearing ∼ s , placing it significantlyhigher in the M V vs. V-K s diagram and thus implying a more metal-rich composition viathe photometric technique. McCarthy et al. (1988) resolved each component of the GJ1245 triple system with speckle interferometry and obtained K band photometry for eachof its components. McCarthy et al. (1988)’s photometric measurements revealed almostidentical magnitudes for the A and B components, ∼ ∼ It has been known for the better part of a century that there are clear correlationsbetween the spatial, kinematic, and chemical properties of stars in the Milky Way. Thesecorrelations allow the Milky Way to be decomposed into distinct stellar populations andstructural components (e.g., halo vs. disk; O’Connell 1958), although some debate remainsconcerning the exact number and properties of sub-components (e.g., thin vs. thick disk; 38 –Ivezi´c et al. 2008). Bensby & Feltzing (2010) recently showed that when 899 F- and G-dwarf stars were separated by their kinematic properties, a considerable number of thickdisk stars exhibit metallicities consistent with the metallicity trend of the thin disk, and viceversa. When the solar-type stars were separated by age rather than kinematics, however,the number of outliers in each metallicity trend was reduced.Age estimates for M dwarf stars are difficult to obtain, however, making kinematicproperties the best available means for associating low-mass stars with various Galacticcomponents. Bochanski et al. (2007) investigated metallicity differences between Mdwarfs associated with the thin and thick disk populations, bisected kinematicallyusing the method described by Bensby et al. (2003). Bochanski et al. (2007) measuredthe (CaH2+CaH3)/TiO5 ratio, previously shown by L´epine et al. (2003) to roughlydiscriminate between solar-metallicity ([M/H] ∼ ∼ -1.2) and extreme-subdwarf ([M/H] ∼ -2.0) M dwarfs, for 6577 M dwarfs with Sloan Digital Sky Survey (SDSS)spectra. Bochanski et al. (2007) found that the observed (CaH2+CaH3)/TiO5 distributionsfor the kinematically divided thin and thick disk stars did not differ greatly, implyingmetallicity differences less than 1 dex, but suggested that the kinematically selected thickdisk stars were consistent with an older population due to the lower fraction of stars withH α emission, a tracer of chromospheric activity.One hundred fourteen M dwarfs studied in this work have UVW space motionsfrom the Palomar-Michigan State University Nearby Star Spectroscopic Survey (PMSU;Reid et al. 1997), enabling us to test if the K band metallicity calibration can replicatethe metallicity trends identified for higher-mass members of the kinematic sub-populationsof the Milky Way. One way to visualize the different kinematic populations of the MilkyWay is through the so-called Toomre diagram . The Toomre diagram is a representation of Sandage & Fouts (1987) were the first to show this diagram in their paper on the collapse 39 –the stars’ combined vertical and radial kinetic energies, (U + W ) / , as a function of thestars’ rotational energy, V. Constant values of the total space velocity for the stars, V tot =(U + W +V ) / , can be represented by circles centered at [0,0], as is shown in stepsof 50 km/s in Figure 44. We base our kinematic sub-divisions on the boundaries definedby Bensby & Feltzing (2010), where thin disk stars possess V tot <
50 km/s and thick diskstars possess ∼
70 km/s < V tot <
200 km/s; we additionally classify stars with intermediatevelocities (50 km/s < V tot <
70 km/s) as thin-thick stars. We show in Figure 45 thedistributions of K band overall metallicity estimates for members of each of these kinematicsgroups, with the mean and median [M/H] indicated for each distribution. Consistent withresults seen for higher mass stars, we find the thin disk population is noticably enriched (∆[M/H] ∼ < < -0.14 have V tot >
70 km/s, whileevery star with [M/H] > -0.15 lies within the V tot ∼
100 km/s contour. These results reinforcethe trends seen by Bensby & Feltzing (2010) for higher mass stars: Bensby & Feltzing(2010) found that older (t > < tot ≤
100 k/m, consistent with what we see inFigure 44 for our (metallicity selected) thin-disk M dwarfs.
A final observable that can be used to probe the existence of an underlying age-metallicity relation is chromospheric activity. Common tracers of chromospheric activity,such as emission in Ca II H & K or H α , indicate that young stars demonstrate highlevels of chromospheric activity, with the activity decaying as the stars age; this effecthas been seen in solar type stars (Skumanich 1972) and well into the M dwarf regime(Stauffer & Hartmann 1986). Chromospheric activity timescales of M dwarfs expand from ∼ ∼
10 Gyr for the later-type/lower-mass stars(Hawley et al. 1999; West et al. 2008).As noted in the previous section, Bensby & Feltzing (2010) found that the link betweenage and metallicity appears to be stronger for solar-type stars than the link betweenkinematics and metallicity. While it is not possible to derive an exact age for an M dwarfbased on its observed activity level, one can use the activity lifetimes noted above tostatistically divide stars into older and younger samples. Gizis et al. (2002) measured theequivalent widths of H α on high-resolution spectra of 676 M dwarfs, and identified distinctgroups according to their H α properties. Our sample includes eighty two stars analyzed byGizis et al. (2002), providing an opportunity to use activity as a crude proxy for age, andexamine the evidence for an age-metallicity relationship within the M dwarfs in our sample.Figure 46 shows the H α emission strength versus spectral type for these stars, dividedaccording to the metallicity boundaries inferred from Figure 45 and applied previously in 41 –Figure 44. Across all metallicity categories, most of the early-type (M0 to M2) stars showH α absorption, implying either a weak/moderate activity or no activity at all, while thelater-type stars show H α emission, consistent with the longer activity lifetimes expected forthe lowest-mass stars. The metal-rich category seems to have a slightly higher average levelof H α emission when compared with the other categories, consistent with the metal-richstars being a statistically younger sample than the more metal-poor samples. If we adopta 2 ˚A threshold for significant H α activity, the earliest star in each category with elevatedactivity is clearly correlated with metallicity: the earliest active metal-poor star is an M5,while the earliest active intermediate and metal-rich stars are M4 and M3, respectively. Thiscorrelation is precisely what would be expected if there were an underlying age-metallicityrelation, such that the sample of metal-poor stars consists of statistically older stars, whereactivity is only seen for the lower-mass stars with relatively long activity lifetimes, whilemetal-rich stars are statistically young, with higher mass stars not yet having transitionedinto the inactive stage.
7. Particularly promising M dwarf planet hosts
The nearly 600 confirmed extrasolar planets discovered to date reveal that planets are anatural and frequent by-product of star formation. One of the most important observationalconstraints is that planet frequency rises steeply with host star abundance above solarmetallicity in FGK-stars (e.g. Santos et al. 2004; Fischer & Valenti 2005). As mentionedin the introduction, the first photometric and spectroscopic metallicity measurementsfor M dwarf planet hosts indicated that they were slightly metal-poor (Bonfils et al.2005a; Bean et al. 2006a). However, recent metallicity calibrations (Johnson & Apps 2009;Rojas-Ayala et al. 2010; Schlaufman & Laughlin 2010) have convincingly shown that thesmall sample of nearby M dwarf planet hosts have solar and super-solar metallicities. 42 –Table 3 flags the M dwarf planet hosts in our sample. According to the metallicitycalibration derived in Section 5.2, the eleven M dwarf planet hosts have overall metallicitieshigher than -0.06 dex, with the Jovian hosts being more metal-rich than the Neptuneor super-Earth hosts. The sample of M dwarf planet hosts is small, but their K bandmetallicities suggest the existence of a planet-metallicity correlation for M dwarfs. Wecompared the [Fe/H] distribution of the eleven planet hosts to the [Fe/H] distribution of35 M dwarfs in our sample that are also members of the California Planet Survey (CPS)sample of low-mass stars (John Johnson, private communication). These 35 M dwarf havebeen subjected to an intensive RV monitoring campaign by the CPS team, and their RVmeasurements have ruled out the presence of Jupiter-size planets within several AU. Figure47 shows the metallicity distributions of the 35 CPS M dwarfs and of the 11 planet hostsin our sample. A two-sided K-S test identifies that there is a < > > +0.2 dex) in this sample are the Jovian hostsHIP 79431 and Gl 849, and the M dwarfs Gl 285 (M5), G 203-47 (M4), Gl 169.1 A (M3), 43 –LHS 3799 (M5), and Gl 205 (M0). Bower et al. (2009) used radio astrometry to search forplanets around a sample of active M stars within 10 pc and their analyzed sample includedtwo of the metal-rich stars listed above (Gl 285 and LHS 3799). Bower et al. (2009)were able to rule out the existence of 3-6 M J planets within 1 AU at the 99% confidencelevel. Lawler et al. (2009) searched for an infrared excess around Gl 205, and found none,excluding the presence of debris at distances beyond the snow-line.Interestingly, the metal-rich stars G 203-47 and Gl 169.1 A do not have planetarycompanions, but they do possess white-dwarf (WD) companions. Gl 169.1 B is a relativelyyoung and featureless white dwarf with an age estimate of ∼ ∼ I and Ca I features in K band, and the weakCaH absorption in their optical spectra, indicates that these stars have indeed supersolarmetallicities.Most of exoplanet searches have been performed at visible wavelengths. M dwarfs areintrinsically faint in the optical, so the largest stellar component in the solar neighborhoodhaven’t yet been searched thoroughly for planets, except for the brightest, closest earlyM dwarfs. However, planet searches are now being performed with near-infrared radialvelocity instruments (e.g. Bean et al. 2010; Crockett et al. 2011; Muirhead et al. 2011) and 44 –with far red filters for transits (Irwin et al. 2009). For these searches, the visible faintness ofM dwarfs is not a problem, but other intrinsic properties of M dwarfs should be consideredto optimize detectability.Therefore, the most “desirable” M dwarf targets for planet searches should be: • Bright: The optical faintness of M dwarfs is not a problem for the near-infraredsearches, but a large number of M dwarfs per night is desirable. Brighter M star arefavorable for achieving a fixed signal-to-noise ration and for ease of follow-up for anyplanets that are detected. • Slow rotators: Stars with high rotation rates have radial velocity measurementswith lower precision since stellar rotation widens the spectral features. Bouchy et al.(2001) found that the radial velocity uncertainties increase by a factor of ∼ ∼ v sin i>
10 km/sshould be avoided to provide optimal RV sensitivity. • Inactive: The activity of M dwarfs can also cause false positives (e.g. starspot-crossingevents; Carter et al. (2011)) and can cause radial velocity and photometric jitter(Wright 2005; Berta et al. 2011). Depending on the starspot coverage, the planet-to-star radius ratio can change up to few percent (Carter et al. 2011). Stars with H α emission should be avoided to avoid false positives and jitter. • Metal-rich: The M dwarf planet host shown in Table 10 all have metallicities [M/H] ≥ -0.05 dex. Therefore, it is probable that solar and supersolar metallicity M dwarfs aremore likely to host planets.Table 9 lists the stars that satisfy the conditions mentioned above for activity, rotation,and metallicity in our M dwarf sample. The H α values are from Gizis et al. (2002). The 45 – v sin i values were taken from Jenkins et al. (2009, Tables 1 and 3) and Browning et al.(2010). Some of the stars in Table 9 have detected stellar or planetary companions already(five of the eleven M dwarf planet hosts have their H α and v sin i listed in the papersmentioned above). It will be interesting to see how many planets are discovered around thetargets in Table 9 in the near future, and what “flavor” they might be.
8. Conclusions
We present K band spectra for a sample of 133 M dwarfs, including 18 M dwarfs withreliable metallicity estimates (as inferred from an FGK type companion), 11 planet hosts,more than 2/3 of the Northern 8 pc sample, and additional M dwarfs from the Lepine SharaCatalog. From these spectra, we measured EWs of the Ca I and Na I lines, as well as anindex quantifying the absorption due to H O opacity, features we have previously shown tobe of use for predicting M dwarf temperatures and metallicities.1. From the subset of our stars which possess primary or secondary KHM spectral types,we calibrated the H O-K2 index as a spectral type indicator. We also estimatedeffective temperatures for the stars in the sample by interpolating their H O-K2indices onto a solar metallicity [H O-K2, T eff ] model grid.2. We revise the functional form adopted to predict the [Fe/H] metallicities of M dwarfsbased on measurements of their Na I , Ca I , and H O features. We perform alinear regression upon 18 M dwarfs with reliable metallicity estimates from FGKcompanions to calibrate this updated relationship. Statistical tests demonstrate thatthe [Fe/H] estimates produced by this relationship are accurate to
RM SE =0.141 dex,and confirm that this relation accounts for more of the variance within our calibrantsample than any other existing technique for estimating M dwarf metallicities. 46 –3. For the first time, we derive an expression for an M dwarf’s overall metallicity [M/H];quantitative comparisons to model atmospheres, which are benchmarked accordingto overall metallicity, provide a qualitative validation of our approach for estimatingmetallicities from Na I , Ca I , and H O features, but also demonstrate an overalloffset between the atomic line strengths predicted by models as compared to actualobservations.4. We examined previous optical molecular indices sensitive to stellar metallicity usingout metallicity estimates. We identify that the CaH1 feature as a potentially valuableoptical metallicity discriminator for solar-metallicity early type M dwarfs.5. We perform several sanity checks of our metallicity estimates, confirming that ourmetallicity estimates reproduce expected correlations between metallicity and Galacticspace motions and H α emission line strengths, and return statistically identicalmetallicities for members of M-M multiple systems.6. We recovered the results from previous metallicity studies that nearby M dwarf planethost exhibit solar to supersolar metallicities, where stars with Jovian-mass planetsare more metal-rich than stars with Neptune-likes or super-Earths. A list of thebest targets in the sample for planetary searches selected by metallicity, activity androtation-rates is given.We thank the staff and telescope operators of Palomar Observatory for their support.We thank Travis Barman, John Bochanski, Jeff Valenti, and Andrew West for helpfuldiscussions about various topics. We thank John Johnson for providing the M dwarf targetsin the CPS target list for the K-S test calculations. We thank the anonymous referee forher/his helpful comments that improved our manuscript. 47 –K.R.C. acknowledges support for this work from the Hubble Fellowship Program,provided by NASA through Hubble Fellowship grant HST-HF-51253.01-A awarded by theSTScI, which is operated by the AURA, Inc., for NASA, under contract NAS 5-26555.This research has made use of NASA’s Astrophysics Data System BibliographicServices, the SIMBAD database, operated at CDS, Strasbourg, France, the NASA/IPACExtragalactic Database, operated by the Jet Propulsion Laboratory, California Institute ofTechnology, under contract with the National Aeronautics and Space Administration, andthe VizieR database of astronomical catalogs (Ochsenbein et al. 2000).This publication makes use of data products from the Two Micron All Sky Survey,which is a joint project of the University of Massachusetts and the Infrared Processing andAnalysis Center/California Institute of Technology, funded by the National Aeronauticsand Space Administration and the National Science Foundation.Palomar: 200 inch (TSPEC) A. Statistical tests and reliable uncertainties for functional fits
A well-fitting regression model results in predicted values close to the observed datavalues. The following statistics are commonly used to evaluate a model fit:
Residual Mean Square (RMSp)
The RMSp is defined as RMSp = n X i =1 ( b y i − y i ) n − p (A1)(A2) 48 –where n is the number of data points (in this case the number of calibrators), p isthe number of predictors in the model (including the constant term), y i is the value of theresponse variable i and b y i is the prediction value given by the regression model for y i . TheRMSp is the variance of the residuals. In general, an RMSp value closer to 0 indicates amodel fit that is more useful for prediction. Root Mean Square Error (RMSE)
The RMSE is the square root of the variance of the residualsRMSE = p RMSp (A3)(A4)The RMSE indicates how accurately the regression model predicts the response. TheRMSE is an absolute measure of it and has the same units as the response variable. Lowervalues of RMSE indicate better fit.
Adjusted Square of the Multiple Correlation Coefficient ( R ap ) The R ap represents the proportion of variability in a data set that is accounted for bya regression model. The R ap is defined asR = 1 − ( n − P ni =1 ( b y i − y i ) ( n − p ) P ni =1 (y i − y) (A5)= 1 − RMSpMST (A6)where y is the overall mean of the observations y i , and M ST is the total mean ofsquares. The R ap compares the unbiased variance of the residuals ( RM Sp ) and the unbiasedvariances of the observations (
M ST ), therefore, can be interpreted as the proportion of total 49 –variance that is explained by the model. A value of R ap =1 indicates that the regressionmodel explains all of the variance in the sample, while R ap =0 indicates that the regressionmodels explains none of the variance. R ap should always be used with models with morethan one predictor variable. Root Mean Square Error of Validation (RMSE V ) A better estimate of the uncertainty in the K band [Fe/H] fit can be obtained byperforming the Predicted Residual Sum of Squares procedure (PRESS; Weisberg 2005).The PRESS statistic is equivalent to ”leave-one-out” method, where, in this case, theregression procedure is repeated leaving one of the n calibrators out and performing theregression with the other n-1 calibrators, for each one of the n calibrators. The PRESSstatistics is defined as PRESS = n X i =1 b e (A7)= n X i =1 ( b y ( − c i )i − y i ) where b e i is the residual for the calibrator c i , computed as the difference between theobserved value of the predictand y i and the prediction b y ( − c i ) i from a regression modelcalibrated using the calibration sample but without the calibrator c i . Then, it is possible touse as a measure of uncertainty a statistic based on this validation dataRMSE V = r PRESS n V (A8)Equation (2.6) is known as the Root-Mean-Squared Error of validation (RMSE V ),where n V is the number of calibrators. The RMSE V value is a sensible estimate of average 50 –prediction error according to Weisberg (2005). The RMSE V value can be used then toobtain confidence intervals at a desired significance level around the predictions b y i ± C( t α/ ,n − p ) RMSE V where the multiplier of RMSE V corresponds to the desired probability point on thecumulative distribution function. The correct cumulative distribution function for thisspecific fit is the two-sided t -student distribution with n-p=15 degrees of freedom, wheren=18 is the sample size for calibration and p=3 is the number of regressors in the model fit,including the constant term. The two-sided t -student distribution is preferred instead of anormal distribution due to the small number of calibrators (n= n V =18). For approximate70%, 95%, and 99% confidence intervals, the values for C( t α/ ,n − p =15 ) are equal to 1.07,2.13, and 2.95, respectively. 51 – REFERENCES
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Fig. Set 1. K band spectra of 133 nearby M-dwarfs
59 – µ m)1.01.52.02.53.0 N o r m a li z ed F λ + C on s t an t ( W c m - µ m - ) LHS 3576Gl 338 AGl 338 B llNa lllCa l lNa__CO __CO __COH OH Ol lCa lSi,TilAl,SilAllMg l l l l lTi Ti FelFe
Fig. 1.— TripleSpec 200-inch K band spectra of 133 nearby M-dwarfs. µ m)1.01.52.02.53.0 N o r m a li z ed F λ + C on s t an t ( W c m - µ m - ) LHS 3576Gl 338 AGl 338 B l lNa l l lCa l lNa__CO __CO __COH OH Ol lCa lSi,TilAl,SilAllMg l l l l lTi Ti FelFe F i g . . — K b a nd s p ec t r ao f L H S , G l A , a nd G l B . T h e m a i n s p ec t r a l f e a t u r e s a r e i nd i c a t e d . µ m)1.52.02.53.03.54.0 N o r m a li z ed F λ + C on s t an t ( W c m - µ m - ) G 210-45Gl 205Gl 725 AGl 412 A l lNa l l lCa l lNa__CO __CO __COH OH Ol lCa lSi,TilAl,SilAllMg l l l l lTi Ti FelFe F i g . . — K b a nd s p ec t r ao f G - , G l , G l A , a nd G l A . T h e m a i n s p ec t r a l f e a t u r e s a r e i nd i c a t e d . µ m)1.01.52.02.53.03.54.0 N o r m a li z ed F λ + C on s t an t ( W c m - µ m - ) Gl 686Gl 752 ABGl 649HIP 12961Gl 212 l lNa l l lCa l lNa__CO __CO __COH OH Ol lCa lSi,TilAl,SilAl l l lTi lFe F i g . . — K b a nd s p ec t r ao f G l , G l A B , G l , H I P , a nd G l . T h e m a i n s p ec t r a l f e a t u r e s a r e i nd i c a t e d . µ m)1.01.52.02.53.03.54.0 N o r m a li z ed F λ + C on s t an t ( W c m - µ m - ) HD 46375 BHIP 79431V* V1513 CygGl 411Gl 526 l lNa l l lCa l lNa__CO __CO __COH OH Ol lCa lSi,TilAl,SilAl l l lTi lFe F i g . . — K b a nd s p ec t r ao f H D B , H I P , V * V C y g , G l , a nd G l . T h e m a i n s p ec t r a l f e a t u r e s a r e i nd i c a t e d . µ m)1.01.52.02.53.03.54.0 N o r m a li z ed F λ + C on s t an t ( W c m - µ m - ) V* V547 CasGl 872 BGl 797 BLHS 3577Gl 581 l lNa l l lCa l lNa__CO __CO __COH OH Ol lCa lSi,TilAl,SilAl l l lTi lFe F i g . . — K b a nd s p ec t r ao f V * V C a s , G l B , G l B , L H S , a nd G l . T h e m a i n s p ec t r a l f e a t u r e s a r e i nd i c a t e d . µ m)1.01.52.02.53.03.54.0 N o r m a li z ed F λ + C on s t an t ( W c m - µ m - ) Gl 408Gl 251Gl 297.2 BGl 250 BGl 176 l lNa l l lCa l lNa__CO __CO __COH OH Ol lCa lSi,TilAl,SilAl l l lTi lFe F i g . . — K b a nd s p ec t r ao f G l , G l , G l . B , G l B , a nd G l . T h e m a i n s p ec t r a l f e a t u r e s a r e i nd i c a t e d . µ m)1.01.52.02.53.03.54.0 N o r m a li z ed F λ + C on s t an t ( W c m - µ m - ) NLTT 14186Gl 849Gl 725 BGl 661 ABG 262-29 l lNa l l lCa l lNa__CO __CO __COH OH Ol lCa lSi,TilAl,SilAl l l lTi lFe F i g . . — K b a nd s p ec t r ao f N L TT , G l , G l B , G l A B , a nd G - . T h e m a i n s p ec t r a l f e a t u r e s a r e i nd i c a t e d . µ m)1.01.52.02.53.03.54.0 N o r m a li z ed F λ + C on s t an t ( W c m - µ m - ) LHS 3605LHS 115Gl 625Gl 643Gl 273 l lNa l l lCa l lNa__CO __CO __COH OH Ol lCa lSi,TilAl,SilAl l l lTi lFe F i g . . — K b a nd s p ec t r ao f L H S , L H S , G l , G l , a nd G l . T h e m a i n s p ec t r a l f e a t u r e s a r e i nd i c a t e d . µ m)1.01.52.02.53.03.54.0 N o r m a li z ed F λ + C on s t an t ( W c m - µ m - ) LHS 3591Gl 860 ABGl 687Gl 628Gl 873 l lNa l l lCa l lNa__CO __CO __COH OH Ol lCa lSi,TilAl,SilAl l l lTi lFe F i g . . — K b a nd s p ec t r ao f L H S , G l A B , G l , G l , a nd G l . T h e m a i n s p ec t r a l f e a t u r e s a r e i nd i c a t e d . µ m)1.52.02.53.03.54.0 N o r m a li z ed F λ + C on s t an t ( W c m - µ m - ) LHS3558G 168-24HD 222582 BGl 436 l lNa l l lCa l lNa__CO __CO __COH OH Ol lCa lSi,TilAl,SilAl l l lTi lFe F i g . . — K b a nd s p ec t r ao f L H S , G - , H D B , a nd G l . T h e m a i n s p ec t r a l f e a t u r e s a r e i nd i c a t e d . µ m)1.01.52.02.53.03.54.0 N o r m a li z ed F λ + C on s t an t ( W c m - µ m - ) HIP 57050LP 816-60Gl 896 AGl 876Gl 402 l lNa l l lCa l lNa__CO __CO __COH OH Ol lCa lSi,TilAl,SilAl l l lTi lFe F i g . . — K b a nd s p ec t r ao f H I P , L P - , G l A , G l , a nd G l . T h e m a i n s p ec t r a l f e a t u r e s a r e i nd i c a t e d . µ m)1.01.52.02.53.03.54.0 N o r m a li z ed F λ + C on s t an t ( W c m - µ m - ) Gl 53.1 BGl 555Gl 179LHS 494Gl 388 l lNa l l lCa l lNa__CO __CO __COH OH Ol lCa lSi,TilAl,SilAl l l lTi lFe F i g . . — K b a nd s p ec t r ao f G l . B , G l , G l , L H S , a nd G l . T h e m a i n s p ec t r a l f e a t u r e s a r e i nd i c a t e d . µ m)1.01.52.02.53.03.54.0 N o r m a li z ed F λ + C on s t an t ( W c m - µ m - ) Gl 169.1 ALHS 3409Gl 699LHS 220Gl 783.2 B l lNa l l lCa l lNa__CO __CO __COH OH Ol lCa lSi,TilAl,SilAl l l lTi lFe F i g . . — K b a nd s p ec t r ao f G l . A , L H S , G l , L H S , a nd G l . B . T h e m a i n s p ec t r a l f e a t u r e s a r e i nd i c a t e d . µ m)1.01.52.02.53.03.54.0 N o r m a li z ed F λ + C on s t an t ( W c m - µ m - ) Gl 445Gl 213Gl 544 BLHS 1723GJ 1224 l lNa l l lCa l lNa__CO __CO __COH OH Ol lCa lSi,TilAl,SilAl l l lTi lFe F i g . . — K b a nd s p ec t r ao f G l , G l , G l B , L H S , a nd G J . T h e m a i n s p ec t r a l f e a t u r e s a r e i nd i c a t e d . µ m)1.01.52.02.53.03.54.0 N o r m a li z ed F λ + C on s t an t ( W c m - µ m - ) GJ 1119G 041-014GJ 3348 BLHS 1809Gl 447 l lNa l l lCa l lNa__CO __CO __COH OH Ol lCa lSi,TilAl,SilAl l l lTi lFe F i g . . — K b a nd s p ec t r ao f G J , G - , G J B , L H S , a nd G l . T h e m a i n s p ec t r a l f e a t u r e s a r e i nd i c a t e d . µ m)1.01.52.02.53.03.54.0 N o r m a li z ed F λ + C on s t an t ( W c m - µ m - ) LHS 1066GJ 3134Gl 231.1 BLHS 3593GJ 3379 l lNa l l lCa l lNa__CO __CO __COH OH Ol lCa lSi,TilAl,SilAl l l lTi lFe F i g . . — K b a nd s p ec t r ao f L H S , G J , G l . B , L H S , a nd G J . T h e m a i n s p ec t r a l f e a t u r e s a r e i nd i c a t e d . µ m)1.01.52.02.53.03.54.0 N o r m a li z ed F λ + C on s t an t ( W c m - µ m - ) Gl 268 ABGl 768.1 BNLTT 25869LHS 6007Gl 905 l lNa l l lCa l lNa__CO __CO __COH OH Ol lCa lSi,TilAl,SilAl l l lTi lFe F i g . . — K b a nd s p ec t r ao f G l A B , G l . B , N L TT , L H S , a nd G l . T h e m a i n s p ec t r a l f e a t u r e s a r e i nd i c a t e d . µ m)1.01.52.02.53.03.54.0 N o r m a li z ed F λ + C on s t an t ( W c m - µ m - ) LHS 495GJ 1214G 246-33Gl 324 BG 203-47 l lNa l l lCa l lNa__CO __CO __COH OH Ol lCa lSi,TilAl,Si F i g . . — K b a nd s p ec t r ao f L H S , G J , G - , G l B , a nd G - . T h e m a i n s p ec t r a l f e a t u r e s a r e i nd i c a t e d . µ m)1.01.52.02.53.03.54.0 N o r m a li z ed F λ + C on s t an t ( W c m - µ m - ) Gl 299LHS 224Gl 611 BGl 630.1 ANSV 13261 l lNa l l lCa l lNa__CO __CO __COH OH Ol lCa lSi,TilAl,Si F i g . . — K b a nd s p ec t r ao f G l , L H S , G l B , G l . A , a nd N S V . T h e m a i n s p ec t r a l f e a t u r e s a r e i nd i c a t e d . µ m)1.01.52.02.53.03.54.0 N o r m a li z ed F λ + C on s t an t ( W c m - µ m - ) NLTT 15867Gl 166 CLHS 3376GJ 3253GJ 3069 l lNa l l lCa l lNa__CO __CO __COH OH Ol lCa lSi,TilAl,Si F i g . . — K b a nd s p ec t r ao f N L TT , G l C , L H S , G J , a nd G J . T h e m a i n s p ec t r a l f e a t u r e s a r e i nd i c a t e d . µ m)1.01.52.02.53.03.54.0 N o r m a li z ed F λ + C on s t an t ( W c m - µ m - ) GJ 1286Gl 164Gl 777 BGl 866Gl 473 AB l lNa l l lCa l lNa__CO __CO __COH OH Ol lCa lSi,TilAl,Si F i g . . — K b a nd s p ec t r ao f G J , G l , G l B , G l , a nd G l A B . T h e m a i n s p ec t r a l f e a t u r e s a r e i nd i c a t e d . µ m)1.01.52.02.53.03.54.0 N o r m a li z ed F λ + C on s t an t ( W c m - µ m - ) Gl 234 ABLHS 3549LHS 1706V* V388 CasLHS 3799 l lNa l l lCa l lNa__CO __CO __COH OH Ol lCa lSi,TilAl,Si F i g . . — K b a nd s p ec t r ao f G l A B , L H S , L H S , V * V C a s , a nd L H S . T h e m a i n s p ec t r a l f e a t u r e s a r e i nd i c a t e d . µ m)1.01.52.02.53.03.54.0 N o r m a li z ed F λ + C on s t an t ( W c m - µ m - ) Gl 285LHS 18Gl 412 BLHS 1901LSPM J0011+5908 l lNa l l lCa l lNa__CO __CO __COH OH Ol lCa F i g . . — K b a nd s p ec t r ao f G l , L H S , G l B , L H S , a nd L S P M J + . T h e m a i n s p ec t r a l f e a t u r e s a r e i nd i c a t e d . µ m)1.01.52.02.53.03.54.0 N o r m a li z ed F λ + C on s t an t ( W c m - µ m - ) GJ 1245 ACGJ 1245 BGJ 1116 ABGJ 3146LHS 252 l lNa l l lCa l lNa__CO __CO __COH OH Ol lCa F i g . . — K b a nd s p ec t r ao f G J A C , G J B , G l A B , G J , a nd L H S . T h e m a i n s p ec t r a l f e a t u r e s a r e i nd i c a t e d . µ m)1.01.52.02.53.03.54.0 N o r m a li z ed F λ + C on s t an t ( W c m - µ m - ) Gl 376 BGl 1156Gl 406GJ 3147LHS 292 l lNa l l lCa l lNa__CO __CO __COH OH Ol lCa F i g . . — K b a nd s p ec t r ao f G l B , G l , G l , G J , a nd L H S . T h e m a i n s p ec t r a l f e a t u r e s a r e i nd i c a t e d . µ m)1.01.52.02.53.03.54.0 N o r m a li z ed F λ + C on s t an t ( W c m - µ m - ) Gl 644 CGJ 1111LHS 2090V* V492 LyrTeegarden l lNa l l lCa l lNa__CO __CO __COH OH Ol lCa F i g . . — K b a nd s p ec t r ao f G l C , G J , L H S , V ∗ V L y r , a nd T ee ga r d e n ’ ss t a r . T h e m a i n s p ec t r a l f e a t u r e s a r e i nd i c a t e d . µ m)1.01.52.02.53.03.54.0 N o r m a li z ed F λ + C on s t an t ( W c m - µ m - ) l lNa l l lCa l lNa__CO __CO __COH OH Ol lCa F i g . . — K b a nd s p ec t r ao f M A SS J + , L H S , a nd L H S . T h e m a i n s p ec t r a l f e a t u r e s a r e i nd i c a t e d . µ m)1.52.02.53.03.54.04.5 N o r m a li z ed F λ + C on s t an t ( W c m - µ m - ) Gl 908Gl 809Gl 644 ABGl 829 AB l lNa l l lCa l lNa__CO __CO __COH OH Ol lCa lSi,TilAl,SilAllMg l l l l lTi Ti FelFe F i g . . — K b a nd s p ec t r ao f G l , G l , G l B a nd G l A B . T h e m a i n s p ec t r a l f e a t u r e s a r e i nd i c a t e d .
88 – N o r m a li z e d F l u x + C o n s t M0M4M8 H O-K2.05 2.10 2.15 2.20 2.25 2.30 2.35 2.40Wavelength (cid:0) m0.60.81.01.21.41.61.82.0 N o r m a li z e d F l u x + C o n s t M0M4M8 H O-K2
Fig. 29.— The H O-K index by Covey et al. (2010) versus the new H O-K2 index in Equation5. The portions of the spectrum used by the H O-K2 index are almost free of atomic featuresand better sample the change in the overall shape of the spectra of M dwarfs due to thewater absorption from 2.07 µ m to 2.38 µ m. 89 – µ m)3.54.04.55.05.5 N o r m a li z ed F λ + C on s t an t ( W c m - µ m - ) HIP129614100K,+0.3Gl324B3300K,+0.5LHS20902700K,+0.5 llNa lllCa l lNal__CO l__CO l__COl l l l lCa lMg l lAlAl,Si lSi,Ti ll l l lTi Fe lMg
Fig. 30.— Comparison of BT-Settl-2010 synthetic spectra by Allard et al. (2010) vs. Triple-Spec K band spectra of HIP 12961, Gl 324 B and LHS 2090. The most prominent molecularand atomic features are indicated. The overall shape of the observed spectra, dominatedmostly by water absorption, are well matched by the BT-Settl-2010 models. The strongNa I doublet and the Ca I triplet features in these stars cannot be reproduced by any of thesupersolar metallicity models. Perhaps the best match is for HIP 12961, where the [M/H]=+0.3 and T eff = 4100K BT-Settl-2010 model matches the strengths of the CO bands andthe neutral Ti and Al lines quite well. The BT-Settl-2010 model modestly underpredictsthe strengths of the 2.205 Na I and 2.26 Ca I lines, however, and also shows stronger Ca I features at ∼ µ m, and no Mg I line at ∼ µ m. Uncertain oscillator strengths andmissing opacity sources could explain these discrepancies (Rajpurohit et al. 2010). 90 – N a I E W C a I E W [M/H] = -1.0[M/H] = -0.5[M/H] = 0.0[M/H] = 0.3[M/H] = 0.5 eff K0.40.60.81.01.2 H O - K Fig. 31.— Equivalent widths of the Na I doublet (top) and Ca I triplet (middle), andH O-K2 index (bottom), measured from the BT-Settl-2010 synthetic spectra computed byAllard et al. (2010) and shown as a function of model T eff . The strengths of the Na I andCa I features are somewhat weaker in the synthetic spectra than in observed data, but thequalitative behavior of the Ca I feature as a function of both temperature and metallicityis consistent. Water absorption appears to be a monotonic function of temperature, inde-pendent of metallicity, for models with T eff ≥ O-K2indices measured from the [M/H] ≤ -0.5 dex spectral grids diverge from the [M/H] > -0.5models; the stark divergence between the two domains suggest the difference may be a com-putational artifact rather than a true astrophysical difference. The Na I doublet shows theoddest behavior in these spectra, with significant structure as a function of both metallicityand temperature. 91 – H O - K [M/H]=+0.5 H O - K [M/H]=+0.3 H O - K [M/H]=0.0 log g=4.5log g=5.0 H O - K [M/H]=-0.5 H O - K [M/H]=-1.0 Fig. 32.— The H O-K2 index measured from the BT-Settl-2010 synthetic spectra shownas a function of model T eff . Triangles represent models with log g = 4.5 and black dotsrepresent models with log g= 5.0. The H O-K2 index shows negligible sensitivity to surfacegravity in all models with T eff ≥ O-K2 index due to surface gravityare small in the solar and super-solar models throughout the whole effective temperaturerange. The largest discrepancies due to surface gravity are found at lower temperatures inthe subsolar [M/H] models. The largest discrepancy between the two surface gravities in the[M/H]=0.0 dex models is believed to be a computational artifact. 92 – H O K I nd ex O K2 Index R es i du a l s Fig. 33.— Top: The H O-K2 index versus the Spectral Type of M dwarfs. The red dotsrepresent the fifty four stars with optical KHM spectral types by RECONS. The dashedblack line is the linear relationship between KHM spectral types and the H O-K2 index inEquation 6, obtained using a bayesian approach that includes the errors in both coordinatesof the objects. Bottom: Spectral type residuals vs H O-K2 index. 93 – (cid:1) m]0.51.01.52.02.53.03.54.04.5 N o r m a li z e d F l u x + C o n s t M0M1M2M3M4M5M6M7M8M9
CaI CaI MgIAlIAlI,SiI SiI,TiI NaI TiITiITiIFeI CaI MgI NaI CO CO COH O H O Fig. 34.— Mean TripleSpec K band spectral type templates. The stars in our sample wereorganized by spectral type and a template was constructed by combining the spectra in eachsubtype. All of the subtypes are constituted by at least three stars, and up to as many asthirty, with the exception of the M9 subtype, for which LHS 2924 is the only prototype. Themost prominent molecular and atomic features are indicated. 94 – EW /H O-K2-0.3-0.2-0.1-0.00.10.20.3 [ F e / H ] SP O C S - [ F e / H ] R A EW /H O-K2-0.3-0.2-0.1-0.00.10.20.3 [ F e / H ] SP O C S - [ F e / H ] R A -0.6 -0.4 -0.2 0.0 0.2 0.4[Fe/H] RA11 -0.3-0.2-0.1-0.00.10.20.3 [ F e / H ] SP O C S - [ F e / H ] R A Fig. 35.— [Fe/H] residuals versus the independent variables of the [Fe/H] fit in Equation 7(Na I / H O-K2, left; Ca I / H O-K2, middle), and as a function of the predicted metallicity(right). 95 – EW /H O-K20123456 C a I E W / H O - K S p . T y pe [Fe/H]=0.0 [Fe/H]=+0.2 [Fe/H]=+0.4[Fe/H]=-0.6 [Fe/H]=-0.4 [Fe/H]=-0.2 Fig. 36.— The EW of the Ca I vs the EW of the Na I , both weighted by the H O-K2index, for the M dwarfs in our sample. The red and blue dots are the 18 M dwarfs in themetallicity calibration sample with [Fe/H] ≥ < > ∗ V1513 Cyg(-0.64 dex). 96 – EW /H O-K2-0.3-0.2-0.1-0.00.10.20.3 [ M / H ] SP O C S - [ M / H ] R A EW /H O-K2-0.3-0.2-0.1-0.00.10.20.3 [ M / H ] SP O C S - [ M / H ] R A -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3[M/H] RA11 -0.3-0.2-0.1-0.00.10.20.3 [ M / H ] SP O C S - [ M / H ] R A Fig. 37.— [[M/H] residuals versus the independent variables of the [M/H] fit in Equation 8(Na I / H O-K2, left; Ca I / H O-K2, middle), and as a function of the predicted metallicity(right). 97 – EW /H O-K20123456 C a I E W / H O - K S p . T y pe [M/H]=-0.4 [M/H]=-0.2[M/H]=0.0 [M/H]=+0.2 [M/H]=+0.4 Fig. 38.— The EW of the Ca I vs the EW of the Na I both weighted by the H O-K2 index,for the M dwarfs in our sample. The nomenclature is the same as Figure 36. The dashedline is a iso-metallicity contour for [M/H] =0.0. The dotted lines are iso-metallicity contoursfor [M/H] values +0.4, +0.2, -0.2, and -0.4 dex from the top right corner to the bottomleft corner, respectively. The isometallicity contours were calculated from Equation 8. TheM dwarf planet hosts all have [M/H] > ∗ V1513 Cyg has [M/H]=-0.45 dex. 98 – EW /H O-K20123456 C a I E W / H O - K + T e ff - [ M / H ] = - . [ M / H ] = - . [ M / H ] = . [M/H] = -1.0[M/H] = -0.5[M/H] = 0.0[M/H] = 0.3[M/H] = 0.5 Fig. 39.— EW of Ca I vs EW of Na I , weighted by H O-K2 index, for the BT-Settl-2010synthetic models by Allard et al. (2010) with T eff ≤ I doublet and Ca I triplet do not allow a direct metallicity comparisonwith empirical data. Subsolar and solar models of temperatures between 3700K and 3000Kappear as parallel lines in this plane,but the supersolar models intersect the solar modelat 3000K, due to the odd behavior of the Na I doublet features of the supersolar modelsmentioned in the text 99 – -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6[Fe/H] RA11 -0.50.00.51.0 [ F e / H ] B - [ F e / H ] R A a1) -0.5 0.0 0.5 1.0[Fe/H] B05 - [Fe/H]
RA11 N u m be r o f S t a r s Median = -0.12Mean = -0.11a2) -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6[Fe/H]
RA11 -0.50.00.51.0 [ F e / H ] J A - [ F e / H ] R A b1) -0.5 0.0 0.5 1.0[Fe/H] JA09 - [Fe/H]
RA11 N u m be r o f S t a r s Median = 0.11Mean = 0.13b2) -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6[Fe/H]
RA11 -0.50.00.51.0 [ F e / H ] S L10 - [ F e / H ] R A c1) -0.5 0.0 0.5 1.0[Fe/H] SL10 - [Fe/H]
RA11 N u m be r o f S t a r s Median = -0.05Mean = 0.00c2) -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6[Fe/H]
RA11 -0.50.00.51.0 [ F e / H ] W - [ F e / H ] R A d1) -0.5 0.0 0.5 1.0[Fe/H] W09 - [Fe/H]
RA11 N u m be r o f S t a r s Median = -0.06Mean = -0.05d2)
Fig. 40.— Differences between the [Fe/H] values predicted for M dwarf stars in our samplefrom the K band [Fe/H] fit in Equation 7 and a1) the [Fe/H] from B05, b1) the [Fe/H] fromJA09, c1) the [Fe/H] from SL10, d1) the [Fe/H] from W09. The B05 and W09 calibrationsunderestimate [Fe/H] values of the supersolar K band [Fe/H] stars. The JA09 calibrationoverestimates the [Fe/H] values of the subsolar K band [Fe/H] stars. The scatter of theresiduals increases for the subsolar K band [Fe/H] stars when their [Fe/H] are comparedwith the SL10 [Fe/H] values. 100 – -0.4 -0.2 0.0 0.2[M/H]-2-1012 ∆ S p T ( T i O - H O ) -0.4 -0.2 0.0 0.2[M/H]-2-1012 ∆ S p T ( C a H - H O ) -0.4 -0.2 0.0 0.2[M/H]-2-1012 ∆ S p T ( C a H - H O ) Fig. 41.— Difference between the spectral types derived using the H O-K2 index and theTiO5 (left), CaH2 (middle), and CaH3 (right) indices versus [M/H]. The TiO5 index predictslater subtypes than the H O-K2 index for the solar and metal-rich stars, and earlier subtypesto the metal-poor stars. The CaH2 and CaH3 indices show less metallicity sensitivity. TheCaH2 index predicts slightly later subtypes than the H O-K2 index, while the CaH3 indexshows an opposite offset, but no bias with metallicity is visible for any of these two CaHindices. 101 – O-K20.20.40.60.81.0 T i O O-K20.40.50.60.70.80.91.01.1 T i O O-K20.60.70.80.91.0 C a H O-K2-0.2-0.10.00.10.2 T i O - T i O F i t O-K2-0.2-0.10.00.10.2 T i O - T i O F i t O-K2-0.2-0.10.00.10.2 C a H - C a H F i t Fig. 42.— The PMSU TiO2, TiO3, and CaH1 indices versus the H O-K2 index . M dwarfswith [M/H] > < O-K2 index, with larger scatter towards early typeM dwarfs. The CaH1 index seems to be more sensitive to metallicity than any of the otherindices. 102 – EW /H O-K2012345 C a I E W / H O - K GJ1245ACGJ1245BGl338AGl338BGl725A Gl725BV*V547cas LHS115Gl412A Gl412BGl643 Gl644C [ M / H ] = - . [ M / H ] = - . [ M / H ] = . Fig. 43.— EW of Ca I vs EW of Na I , weighted by H O-K2 index, for the M-M binaries inTable 8. The binary components are linked with lines. The dotted lines are isometallicitycontours for [M/H] calculated from Equation 8. The red dots/lines indicate the systemswhere the K band metallicity estimates for the individual components agree to within 0.02dex. 103 – -200 -150 -100 -50 0 50V [km/s]020406080100120140 ( U + W ) / [ k m / s ] [M/H] < -0.14-0.14 < [M/H] < 0.0[M/H] > 0.0 Fig. 44.— Toomre diagram for the stars in our sample with PMSU kinematics, color-codedby metallicity. The metal-poor stars ([Fe/H] < -0.14 dex), depicted by blue dots, cover thewhole velocity space, while the metal-rich stars ([Fe/H] > tot velocities nolarger than ∼
100 km/s. 104 –
Thick Disk -0.4 -0.2 0.0 0.2 0.4[M/H]0510152025 N u m be r o f S t a r s Median [M/H] = -0.19Mean [M/H] = -0.14
Thin-Thick Disk -0.4 -0.2 0.0 0.2 0.4[M/H]0510152025 N u m be r o f S t a r s Median [M/H] = -0.02Mean [M/H] = -0.04
Thin Disk -0.4 -0.2 0.0 0.2 0.4[M/H]0510152025 N u m be r o f S t a r s Median [M/H] = -0.02Mean [M/H] = 0.00
Fig. 45.— K band metallicity distributions for the stars in our sample with PMSU kinemat-ics. The boundaries of these kinematic sub-groups are: thin disk, V tot <
50 km/s; thin-thick,50 km/s < V tot <
70 km/s; thick disk, 70 km/s < V tot <
200 km/s. The metallicity distributionsof these kinematically selected subgroups are consistent with the trends seen for solar-typestars: stars with large space motions are preferentially metal-poor, while stars with smallspace motions are preferentially metal-rich. 105 – E W H α [ . n m ] [M/H] < -0.14 0 2 4 6Spectral Type M024681012 E W H α [ . n m ] -0.14 < [M/H] < 0.0 0 2 4 6Spectral Type M024681012 E W H α [ . n m ] [M/H] > 0.0 Fig. 46.— H α strength as function of spectral type for the stars in our sample with H α measurements by Gizis et al. (2002). The dotted-line represents a 2 ˚A lower limit in H α to define M dwarfs with significantly enhanced activity (i.e., more active than required tosatisfy the 0.75 ˚A limit adopted by West et al. (2008)). All late-type ( > M5) stars are stillactive in all three metallicity categories, but activity persists to earlier types in the metal-rich samples, consistent with an underlying correlation between a star’s age, activity, andmetallicity. Chromospheric activity is noticeable for M3 stars with [M/H] > -0.01 dex, for M4stars with -0.15 < [M/H] < -0.01 dex, and for a M5 stars with [M/H] < -0.15 dex. V ∗ V1513Cyg is a metal-poor M2 dwarf that still exhibits chromospheric activity. 106 – -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6[Fe/H]0246810 N u m be r o f S t a r s Neptune Jupiter
Fig. 47.— [Fe/H] distribution of 35 M dwarfs whose RV measurements have rule out thepresence of Jupiter-size planets within several AU by the CPS team, along with the [Fe/H]distribution of Jupiter hosts and Neptune hosts in our sample. 107 – (cid:2) A] N o r m a li z e d F l u x + C o n s t LHS3409G203-47Gl169.1A
TiO5TiO1CaOH CaH2 CaH3CaH1 (cid:3) m] Al I Si I,Ti I Na I Ca I Na I
Fig. 48.— Optical PMSU spectra and K band spectra of LHS 3409 (top), G 203-47 (middle),and Gl 169.1A (bottom). The PMSU TiO and CaH indices are shown in red and blue,respectively. The most prominent atomic features in the M dwarf K band spectra are alsoindicated. The regions used to calculate the water index , H O-K2, are shown in gray. G203-47 and Gl 169.1A belong to binary systems with white-dwarf companions. LHS 3409,a metal-poor star ([M/H]=-0.36) of similar spectral type, is shown for comparison. The Kband absorption features are weaker in the spectrum of LHS 3409, but the CaH absorptionin its optical spectrum is stronger than in the 2 metal-rich stars, which indicates that G203-47 and Gl 169.1A have supersolar metallicities.
Table 1. TripleSpec Nearby M dwarf Sample – Source Properties
Name d (pc) V (mag) V Ref. 2MASS K Date SNR StarLHS 3576 19.9 10.29 1 6.553 2009-07-20 278 LSPMGl 338 A 6.2 7.64 1 3.99 2009-02-05 243 8pcGl 338 B 6.3 7.7 1 4.14 2009-02-05 350 8pcG 210-45 23.4 11.21 1 7.251 2009-07-20 290 LSPMGl 205 5.7 7.97 1 4.039 2009-09-30 652 8pcGl 725 A 3.6 8.94 1 4.432 2009-07-19 866 8pcGl 412 A 4.8 8.82 1 4.769 2009-02-05 337 8pcGl 686 8.1 9.62 1 5.572 2009-07-19 702 LSPMGl 752 AB 5.9 9.12 1 4.673 2009-07-19 416 8pcGl 649 10.3 9.7 1 5.624 2010-05-22 862 planet / LSPMHIP 12961 23.8 10.25 1 6.736 2010-11-25 268 planet / LSPMGl 212 12.5 9.78 1 5.759 2009-09-30 627 calibrator / LSPMHD 46375 B 26.4 11.8 3 7.843 2009-02-04 795 calibrator / LSPMHIP 79431 14.9 11.34 1 6.589 2010-05-22 659 planet / LSPMV* V1513 Cyg · · · / LSPM
Table 1—Continued
Name d (pc) V (mag) V Ref. 2MASS K Date SNR StarGl 797 B 20.1 11.88 8 7.416 2009-07-19 581 calibrator / LSPMLHS 3577 12.5 10.79 1 6.533 2009-07-20 311 LSPMGl 581 6.3 10.57 1 5.837 2009-02-05 359 planet / / LSPMGl 176 9.4 9.95 1 5.607 2009-09-30 667 planet / LSPMNLTT 14186 34.5 14.60 8 7.621 2009-09-30 630 calibrator / LSPMGl 849 8.8 10.41 1 5.594 2009-07-20 755 planet / LSPMGl 725 B 3.5 9.7 1 5 2009-07-19 832 8pcGl 661 AB 6.1 9.44 3 4.83 2009-07-19 708 8pcG 262-29 32.8 11.7 2 7.61 2009-07-20 425 LSPMLHS 3605 13.7 11.98 1 7.64 2009-07-20 307 LSPMLHS 115 10.2 12.19 3 6.377 2007-11-17 326 LSPMGl 625 6.6 10.13 1 5.833 2009-07-19 573 8pcGl 643 6.5 11.73 1 5.756 2009-07-19 530 8pcGl 273 3.8 9.84 1 4.857 2009-02-04 327 8pcLHS 3591 32.4 12.73 2 8.238 2009-07-20 288 LSPM
Table 1—Continued
Name d (pc) V (mag) V Ref. 2MASS K Date SNR StarGl 860 AB 4 9.59 1 4.777 2009-07-20 304 8pcGl 687 4.5 9.15 1 4.548 2010-05-24 984 8pcGl 628 4.3 10.1 1 5.075 2010-05-24 808 8pcGl 873 5 10.29 1 5.299 2009-07-20 392 8pcLHS 3558 8 10.54 1 5.933 2009-07-20 628 8pcG 168-24 16.3 12.51 2 7.873 2009-07-20 752 LSPMHD 222582 B 41.9 14.50 7 9.583 2009-07-20 376 calibrator / / LSPMHIP 57050 11 11.86 1 6.822 2010-05-22 537 planet / LSPMLP 816-60 5.5 11.41 1 6.199 2009-07-19 899 8pcGl 896 A 6.2 10.05 1 5.326 2009-07-20 923 8pcGl 876 4.7 10.16 1 5.01 2009-07-20 577 planet / / LSPMLHS 494 15.9 12.51 2 7.397 2009-07-20 491 LSPMGl 388 4.9 9.4 2 4.593 2009-02-05 260 8pcGl 169.1 A 5.5 11.06 2 5.717 2009-09-30 1508 8pc
Table 1—Continued
Name d (pc) V (mag) V Ref. 2MASS K Date SNR StarLHS 3409 20.3 15.11 2 10.229 2010-05-24 280 LSPMGl 699 1.8 9.54 1 4.524 2010-05-24 758 8pcLHS 220 13.3 13.77 2 8.773 2007-11-17 302 LSPMGl 783.2 B 20.4 13.94 3 8.883 2009-07-19 602 calibrator / LSPMGl 445 5.4 10.8 1 5.954 2009-02-05 201 8pcGl 213 5.8 11.56 1 6.389 2009-02-04 318 8pcGl 544 B 19 14.5 3 9.592 2008-02-16 811 calibrator / LSPMLHS 1723 7.5 12.16 3 6.736 2009-09-30 582 8pcGJ 1224 7.5 13.64 2 7.827 2009-07-19 876 8pcGJ 1119 10.3 13.32 2 7.741 2007-11-16 972 LSPMG 041-014 5.6 10.89 3 5.688 2009-12-24 857 8pcGJ 3348 B 23.5 13.98 3 8.791 2009-09-30 416 calibrator / LSPMLHS 1809 9.3 14.45 2 8.435 2007-11-17 746 LSPMGl 447 3.3 11.12 1 5.654 2009-02-05 304 8pcLHS 1066 16.6 14 3 9.11 2007-11-17 668 LSPMGJ 3134 24 14.31 3 8.995 2007-11-17 499 LSPMGl 231.1 B 19.9 13.27 3 8.267 2009-02-04 908 calibrator / LSPMLHS 3593 13.9 13.98 2 8.481 2009-07-20 228 LSPMGJ 3379 5.4 11.33 2 6.042 2009-02-04 662 8pc
Table 1—Continued
Name d (pc) V (mag) V Ref. 2MASS K Date SNR StarGl 268 AB 6.4 11.65 1 5.846 2009-02-04 443 8pcGl 768.1 B 19.4 13.1 3 8.012 2010-05-22 531 calibrator / LSPMNLTT 25869 11 14.5 3 8.64 2008-02-16 551 LSPMLHS 6007 21.3 14.25 2 8.852 2007-11-17 437 LSPMGl 905 3.2 12.27 2 5.929 2009-07-20 824 8pcLHS 495 9.8 13.41 2 7.749 2009-07-20 258 LSPMGJ 1214 13 14.67 2 8.78 2010-05-24 415 planet / LSPMG 246-33 14 14.63 3 8.656 2007-11-16 618 LSPMGl 324 B 12.5 13.15 3 7.666 2008-02-16 814 calibrator / LSPMG 203-47 7.3 11.77 1 6.485 2009-07-19 659 8pcGl 299 6.8 12.83 3 7.66 2009-02-04 858 8pcLHS 224 9.2 13.3 2 7.776 2007-11-17 465 LSPMGl 611 B 13.8 14.2 2 9.159 2008-02-16 970 calibrator / LSPMGl 630.1 A 14.5 12.9 2 7.796 2008-02-17 483 LSPMNSV 13261 15.9 14.67 2 8.753 2009-07-20 407 LSPMNLTT 15867 25 16.49 3 10.312 2009-02-04 334 calibrator / LSPMGl 166 C 5 11.17 3 5.962 2009-09-30 591 calibrator / Table 1—Continued
Name d (pc) V (mag) V Ref. 2MASS K Date SNR StarGJ 3069 14.4 15.12 3 8.864 2007-11-17 412 LSPMGJ 1286 7.2 14.69 2 8.183 2009-07-20 228 8pcGl 164 11.9 13.5 2 7.915 2008-02-17 495 LSPMGl 777 B 11.7 14.33 2 8.712 2009-07-19 522 calibrator / LSPMGl 866 3.4 12.18 3 5.537 2009-07-20 400 8pcGl 473 AB 4.3 12.44 3 6.042 2009-02-05 413 8pcGl 234 AB 4.1 11.12 1 5.486 2009-02-04 691 8pcLHS 3549 9.3 14.04 2 8.095 2009-07-20 442 LSPMLHS 1706 14.1 15.23 2 8.977 2009-09-30 372 LSPMV* V388 Cas · · · a Table 1—Continued
Name d (pc) V (mag) V Ref. 2MASS K Date SNR StarGJ 3146 8.5 15.79 2 8.981 2007-11-17 485 LSPMLHS 252 10 15.05 2 8.668 2007-11-17 772 LSPMGl 376 B 13.9 16.13 3 9.275 2009-12-24 372 calibrator / LSPMGl 1156 6.5 13.79 2 7.57 2009-02-05 505 8pcGl 406 2.4 13.54 3 6.084 2009-12-24 1860 8pcGJ 3147 10.4 15.99 2 9.011 2007-11-16 507 LSPMLHS 292 4.5 15.6 2 7.926 2009-12-24 870 8pcGl 644 C 6.5 16.7 3 8.816 2009-07-19 542 8pcGJ 1111 3.6 14.81 2 7.26 2008-02-16 746 8pcLHS 2090 6 16.1 3 8.437 2009-12-24 914 8pcV* V492 Lyr 14.1 18.23 2 10.308 2009-07-20 370 LSPMTeegardens 3.6 15.4 3 7.585 2009-02-04 1092 8pc2MASS J18 b c c c c Table 1—Continued
Name d (pc) V (mag) V Ref. 2MASS K Date SNR Star a L SPM J0011+5908 b c Stars with low quality K band spectra ∗ Reference of distance and V magnitude: (1) HIPPARCOS (van Leeuwen2007), (2) YALE (van Altena et al. 2001), (3) PMSU (Reid et al. 1997), (4)Koen et al. (2010), (5) Leggett (1992), (6) Bessel (1990), (7) Gould & Chanam´e(2004), (8) Gliese & Jahreiss (1991)
116 –Table 2. EW Bandpasses and Continuum Points
Feature Wavelength Integration Limits Continuum Points[ µ m] [ µ m] [ µ m]Na I 2.206 2.2020-2.2120 2.1965, 2.2125,2.21752.209Ca I 2.261 2.2580-2.2690 2.2510, 2.2580, 2.2705, 2.27602.2632.265 Table 3. TripleSpec Nearby M dwarf Sample – Spectral Measurements
Name EW(Na I) EW(Ca I) H O-K2 Sp.T. T eff [M/H] [Fe/H]LHS 3576 4.355 ± ± ± ±
24 -0.13 ± ± ± ± ± ±
56 -0.13 ± ± ± ± ± ±
15 -0.11 ± ± ± ± ± ±
37 -0.03 ± ± ± ± ± ±
106 0.25 ± ± ± ± ± ±
18 -0.34 ± ± ± ± ± ±
20 -0.28 ± ± ± ± ± ±
20 -0.20 ± ± ± ± ± ±
20 -0.03 ± ± ± ± ± ±
20 -0.02 ± ± ± ± ± ±
19 0.01 ± ± ± ± ± ±
17 0.02 ± ± ± ± ± ±
15 0.21 ± ± ± ± ± ±
20 0.33 ± ± ± ± ± ±
17 -0.45 ± ± ± ± ± ±
18 -0.28 ± ± ± ± ± ±
17 -0.21 ± ± ± ± ± ±
18 -0.19 ± ± ± ± ± ±
20 -0.17 ± ± ± ± ± ±
20 -0.16 ± ± ± ± ± ±
19 -0.07 ± ± ± ± ± ±
18 -0.06 ± ± ± ± ± ±
18 -0.06 ± ± ± ± ± ±
17 -0.04 ± ± Table 3—Continued
Name EW(Na I) EW(Ca I) H O-K2 Sp.T. T eff [M/H] [Fe/H]Gl 297.2 B 5.154 ± ± ± ±
20 -0.03 ± ± ± ± ± ±
20 0.01 ± ± ± ± ± ±
20 0.11 ± ± ± ± ± ±
18 0.17 ± ± ± ± ± ±
19 0.23 ± ± ± ± ± ±
27 -0.25 ± ± ± ± ± ±
28 -0.21 ± ± ± ± ± ±
16 -0.21 ± ± ± ± ± ±
16 -0.19 ± ± ± ± ± ±
23 -0.19 ± ± ± ± ± ±
17 -0.16 ± ± ± ± ± ±
20 -0.15 ± ± ± ± ± ±
26 -0.12 ± ± ± ± ± ±
16 -0.08 ± ± ± ± ± ±
17 -0.07 ± ± ± ± ± ±
18 -0.06 ± ± ± ± ± ±
20 -0.01 ± ± ± ± ± ±
18 -0.00 ± ± ± ± ± ±
16 0.01 ± ± ± ± ± ±
16 0.01 ± ± ± ± ± ±
27 0.02 ± ± ± ± ± ±
17 0.03 ± ± ± ± ± ±
27 0.04 ± ± ± ± ± ±
17 0.05 ± ± Table 3—Continued
Name EW(Na I) EW(Ca I) H O-K2 Sp.T. T eff [M/H] [Fe/H]Gl 896 A 5.861 ± ± ± ±
23 0.11 ± ± ± ± ± ±
17 0.14 ± ± ± ± ± ±
23 0.15 ± ± ± ± ± ±
27 0.15 ± ± ± ± ± ±
27 0.16 ± ± ± ± ± ±
16 0.17 ± ± ± ± ± ±
27 0.17 ± ± ± ± ± ±
19 0.20 ± ± ± ± ± ±
28 0.26 ± ± ± ± ± ±
41 -0.36 ± ± ± ± ± ±
29 -0.27 ± ± ± ± ± ±
70 -0.24 ± ± ± ± ± ±
41 -0.20 ± ± ± ± ± ±
38 -0.17 ± ± ± ± ± ±
47 -0.17 ± ± ± ± ± ±
65 -0.05 ± ± ± ± ± ±
69 -0.03 ± ± ± ± ± ±
31 -0.03 ± ± ± ± ± ±
34 -0.02 ± ± ± ± ± ±
41 -0.02 ± ± ± ± ± ±
39 -0.01 ± ± ± ± ± ±
69 -0.00 ± ± ± ± ± ±
69 -0.00 ± ± ± ± ± ±
65 0.01 ± ± Table 3—Continued
Name EW(Na I) EW(Ca I) H O-K2 Sp.T. T eff [M/H] [Fe/H]GJ 3134 5.562 ± ± ± ±
74 0.01 ± ± ± ± ± ±
39 0.02 ± ± ± ± ± ±
58 0.03 ± ± ± ± ± ±
41 0.06 ± ± ± ± ± ±
40 0.08 ± ± ± ± ± ±
31 0.08 ± ± ± ± ± ±
69 0.08 ± ± ± ± ± ±
29 0.12 ± ± ± ± ± ±
65 0.14 ± ± ± ± ± ±
74 0.15 ± ± ± ± ± ±
31 0.15 ± ± ± ± ± ±
74 0.17 ± ± ± ± ± ±
29 0.22 ± ± ± ± ± ±
34 0.24 ± ± ± ± ± ±
49 -0.32 ± ± ± ± ± ±
34 -0.32 ± ± ± ± ± ±
61 -0.32 ± ± ± ± ± ±
37 -0.27 ± ± ± ± ± ±
20 -0.20 ± ± ± ± ± ±
28 -0.14 ± ± ± ± ± ±
32 -0.10 ± ± ± ± ± ±
45 -0.08 ± ± ± ± ± ±
52 -0.05 ± ± ± ± ± ±
49 -0.04 ± ± Table 3—Continued
Name EW(Na I) EW(Ca I) H O-K2 Sp.T. T eff [M/H] [Fe/H]GJ 1286 6.408 ± ± ± ±
45 -0.02 ± ± ± ± ± ±
61 0.02 ± ± ± ± ± ±
49 0.03 ± ± ± ± ± ±
23 0.04 ± ± ± ± ± ±
32 0.05 ± ± ± ± ± ±
56 0.10 ± ± ± ± ± ±
45 0.12 ± ± ± ± ± ±
43 0.16 ± ± ± ± ± ±
56 0.21 ± ± ± ± ± ±
56 0.28 ± ± ± ± ± ±
59 0.29 ± ± ± ± ± ±
17 -0.34 ± ± ± ± ± ±
18 -0.27 ± ± ± ± ± ±
21 -0.23 ± ± a ± ± ± ±
18 -0.18 ± ± ± ± ± ±
19 -0.09 ± ± ± ± ± ±
20 -0.09 ± ± ± ± ± ±
18 -0.08 ± ± ± ± ± ±
21 -0.07 ± ± ± ± ± ±
17 0.00 ± ± ± ± ± ±
21 0.11 ± ± ± ± ± ±
20 0.11 ± ± ± ± ± ±
20 0.14 ± ± ± ± ± ±
21 0.16 ± ± Table 3—Continued
Name EW(Na I) EW(Ca I) H O-K2 Sp.T. T eff [M/H] [Fe/H]LHS 292 4.791 ± ± ± ±
25 -0.28 ± ± ± ± ± ±
29 -0.21 ± ± ± ± ± ±
26 -0.12 ± ± ± ± ± ±
26 -0.03 ± ± ± ± ± ±
28 -0.02 ± ± ± ± ± ±
30 -0.38 ± ± b ± ± ± ±
39 -0.27 ± ± ± ± ± ±
40 0.12 ± ± ± ± ± ±
43 -0.13 ± ± c ± ± ± ±
47 -0.41 ± ± c ± ± ± · · · -0.15 ± ± c ± ± ± ±
19 -0.27 ± ± c ± ± ± ±
22 -0.09 ± ± a SPM J0011+5908 b c Stars with low quality K band spectraNote. —
123 –Table 4. BT-Settl H O-K2 indices T eff [M/H]-1.0 -0.5 0.0 +0.3 +0.54400 1.0633894 1.0551468 1.0459396 1.0346350 · · · · · · · · · · · ·
124 –Table 5. M dwarf Metallicity Calibration Sample
Name Sp.T. SPOCS Predicted[M/H] [Fe/H] [M/H] [Fe/H]Gl 212 M1 0.16 0.19 0.02 0.03HD 46375 B M1 0.20 0.24 0.21 0.29Gl 872 B M2 -0.16 -0.22 -0.17 -0.25Gl 797 B M2 -0.09 -0.09 -0.16 -0.23Gl 250 B M2 -0.01 0.14 0.01 0.01NLTT 14186 M2 0.04 0.05 0.17 0.24HD 222582 B M3 -0.02 -0.03 0.02 0.02Gl 324 B M4 0.25 0.31 0.22 0.31Gl 768.1 B M4 0.12 0.16 0.08 0.10Gl 231.1 B M4 -0.08 -0.04 0.02 0.02GJ 3348 B M4 -0.10 -0.22 -0.01 -0.02Gl 783.2 B M4 -0.09 -0.15 -0.20 -0.29Gl 544 B M4 -0.15 -0.18 -0.05 -0.09Gl 611 B M5 -0.49 -0.69 -0.32 -0.45Gl 777 B M5 0.19 0.21 0.03 0.03Gl 166 C M5 -0.08 -0.28 -0.10 -0.15NLTT 15867 M5 -0.05 -0.10 -0.14 -0.21Gl 376 B M6 0.11 0.20 0.11 0.14Note. —
125 –Table 6. Statistics of the [Fe/H] prediction models
Calibration p N rms RMSp R ap SourceB05 5 48 0.483 ± ± ± a JA09 1 6 0.082 ± ± ± b SL10 1 19 0.144 ± ± ± c N11 2 23 0.167 ± ± ± d RA11 3 18 0.208 ± ± ±
126 –Table 7. [Fe/H] Comparison Sample
B05 JA09 SL10 W09 RA11 L07Name [Fe/H] [Fe/H] [Fe/H] [Fe/H] [Fe/H] ClassGl 699 · · · · · · -0.76 · · · -0.39 dMGl 411 -0.34 · · · · · · -0.14 -0.41 dMGl 905 · · · · · · · · · · · · -0.28 · · · -0.01 dMGl 725 B -0.37 · · · -0.44 -0.04 -0.36 dMGl 725 A -0.32 · · · -0.29 0.01 -0.49 dMGJ 1111 · · · · · · · · · -0.19 dMGl 273 -0.15 0.07 -0.06 0.02 -0.17 dMGl 860 AB -0.18 0.03 -0.10 -0.15 -0.11 dMGl 234 AB -0.00 0.32 0.22 · · · · · · · · · · · · -0.41 dMGJ 1245 AC · · · · · · -0.14 dMGJ 1245 B · · · -0.07 -0.18 · · · -0.13 dMGl 876 0.01 0.38 0.22 0.02 0.18 dMGl 412 A -0.52 · · · -0.50 -0.33 -0.40 dMGl 388 0.03 0.37 0.20 -0.21 0.28 dMGl 873 -0.10 0.17 0.03 -0.21 -0.01 dMGJ 1116 AB · · · · · · · · · -0.12 dMGJ 3379 -0.12 0.08 -0.04 · · · · · · -0.34 · · · -0.25 dMGl 526 -0.26 -0.05 -0.17 0.06 -0.30 dMLP 816-60 -0.17 -0.05 -0.16 · · · · · ·
Gl 251 -0.23 -0.03 -0.16 -0.13 -0.07 dMGl 169.1 A -0.01 0.34 0.20 0.06 0.36 dMGl 402 · · · -0.06 -0.18 -0.04 0.20 dMGl 205 -0.10 0.12 · · · -0.13 0.35 dMGl 213 · · · -0.12 -0.23 · · · -0.25 dMGl 752 AB -0.03 0.23 0.09 0.00 -0.05 dMGl 285 0.09 0.55 0.40 · · ·
127 –Table 7—Continued
B05 JA09 SL10 W09 RA11 L07Name [Fe/H] [Fe/H] [Fe/H] [Fe/H] [Fe/H] ClassGl 555 0.00 0.36 0.23 0.03 0.22 dMGl 338 A -0.19 · · · · · · -0.42 -0.18 sdMGl 581 -0.25 -0.09 -0.21 -0.10 -0.10 dMGl 338 B -0.34 · · · · · · -0.29 -0.15 dMGl 268 AB 0.17 0.76 0.65 · · · · · · · · · -0.41 -0.07 -0.22 dMGl 1156 · · · · · · · · · -0.50 -0.35 -0.23 sdMGl 408 -0.22 -0.02 -0.14 -0.09 -0.09 dMGJ 1286 · · · -0.01 -0.10 · · · -0.04 dMG 203-47 -0.08 0.19 0.06 · · · · · · · · · -0.68 · · · -0.12 dMLHS 3799 · · · · · · · · · · · · -0.29 · · · -0.05 dMLHS 3558 -0.18 0.04 -0.10 -0.14 0.01 dMGl 686 -0.39 · · · -0.33 -0.25 -0.28 dMGJ 3146 · · · · · · · · · · · · -0.11 dMLHS 2065 · · · · · · · · · · · · · · · · · · -0.06 -0.18 · · · -0.46 dMLHS 1809 · · · -0.10 -0.25 · · · -0.01 dMLHS 3549 · · · · · · · · · · · · · · · · · · -0.01 dMV* V547 Cas -0.26 -0.05 -0.18 -0.18 -0.28 dMGl 436 -0.03 0.26 0.10 -0.05 0.04 dMGJ 1119 · · · · · · -0.04 dMGl 649 -0.15 0.07 -0.05 -0.13 -0.04 dMGJ 3147 · · · · · · · · · · · · · · · · · · · · · · · · -0.19 dM
128 –Table 7—Continued
B05 JA09 SL10 W09 RA11 L07Name [Fe/H] [Fe/H] [Fe/H] [Fe/H] [Fe/H] ClassHIP 57050 -0.02 0.31 0.15 0.07 0.05 dMGl 777 B · · · · · · -0.39 · · · · · · · · · · · · · · · · · · -0.48 dMGl 179 -0.01 0.32 0.16 0.02 0.23 dMGl 212 -0.04 0.18 0.07 -0.24 0.03 dMLHS 3577 -0.26 -0.05 -0.18 -0.22 -0.11 dMGJ 1214 · · · · · · · · · · · · -0.72 · · · -0.35 dMLHS 3605 -0.51 · · · -0.57 -0.19 -0.28 dMGl 611 B · · · · · · · · · · · · -0.45 dMLHS 3593 · · · · · · · · · · · · · · · · · · · · · · · · · · · -0.04 dMGJ 3253 0.05 0.47 0.38 · · · -0.07 dMGl 630.1 A -0.11 0.15 0.02 · · · -0.39 dMHIP 79431 0.19 0.56 0.39 · · · · · ·
V* V1513 Cyg -0.89 · · · -1.02 -0.80 -0.64 sdMLHS 494 0.08 0.49 0.32 · · · · · · · · · -0.29 dMG 168-24 -0.29 · · · -0.26 -0.09 0.01 dMLHS 3576 -0.13 · · · -0.02 -0.20 -0.19 dMLHS 3409 · · · · · · · · · · · · -0.52 sdMLHS 6007 -0.04 0.27 0.14 · · · · · · -0.07 · · · · · ·
LHS 3591 0.06 0.35 0.21 · · · -0.12 · · ·
G 262-29 0.16 0.38 0.28 -0.19 -0.30 dM
129 – 130 –Table 8. M dwarf Wide Binaries [Fe/H] Comparison
This Work B05 JA09 SL10 W09Name Sp.Type [M/H] [Fe/H] [Fe/H] [Fe/H] [Fe/H] [Fe/H]GJ 1245 AC M6 -0.09 -0.14 · · · · · ·
GJ 1245 B M6 -0.09 -0.13 · · · -0.07 -0.18 · · ·
Diff: 0.00 0.01 0.26 0.3Gl 338 A M0 -0.13 -0.18 -0.19 · · · · · · -0.42Gl 338 B M0 -0.11 -0.15 -0.34 · · · · · · -0.29Diff: 0.02 0.03 0.15 0.13Gl 725 A M1 -0.34 -0.49 -0.32 · · · -0.29 0.01Gl 725 B M3 -0.25 -0.36 -0.37 · · · -0.44 -0.04Diff: 0.09 0.13 0.05 0.15 0.05V ∗ V547 Cas M2 -0.19 -0.28 -0.26 -0.05 -0.18 -0.18LHS 115 M3 -0.19 -0.27 · · · · · · · · · · · ·
Diff: 0.00 0.01Gl 412 A M1 -0.28 -0.40 -0.52 · · · -0.50 -0.33Gl 412 B M6 -0.27 -0.39 · · · · · · · · · · · ·
Diff: 0.01 0.01Gl 643 M3 -0.15 -0.22 · · · · · · -0.41 -0.07Gl 644 C M7 -0.21 -0.32 · · · · · · · · · · · ·
Diff: 0.06 0.10
131 –Table 9. Best M dwarf Targets for Planet Searches
Name PMSU Sp.T. V K s [M/H] [Fe/H] H α v sin i PopGl 581 2420 M2 10.57 5.84 -0.06 -0.10 -0.359 ≤ a ThinGl 687 2797 M3 9.15 4.55 -0.06 -0.09 -0.34 ≤ a ThinGl 408 1709 M2 10.03 5.50 -0.06 -0.09 -0.307 ≤ a ThinGl 251 1094 M2 9.9 5.3 -0.04 -0.07 -0.272 ≤ a ThinGl 752 AB 3037 M1 9.12 4.67 -0.03 -0.05 -0.42 < b Thin/ThickGl 649 2673 M1 9.7 5.6 -0.02 -0.04 -0.49 ≤ c ThinGl 628 2599 M3 10.1 5.08 -0.01 -0.02 -0.234 1.1 d ThinGl 447 1849 M4 11.12 5.65 -0.00 -0.01 -0.181 ≤ e ThinLHS 1809 1004 M4 14.5 8.4 -0.00 -0.01 -0.231 4.3 f ThinLHS 252 1355 M6 15.05 8.67 0.00 -0.01 0.312 4 f Thin/ThickLHS 3558 3203 M3 10.4 5.9 0.01 0.01 -0.039 ≤ a ThinGl250 B 1092 M2 10.1 5.7 0.01 0.01 -0.292 < b ThinGl 212 956 M1 9.9 5.8 0.02 0.03 -0.391 < b ThinGl 436 1830 M3 10.7 6.1 0.03 0.04 -0.37 ≤ c Thin/ThickLHS 3549 3195 M5 14.0 8.1 0.12 0.16 -0.131 ≤ f Thin/ThickGl 905 3743 M4 12.3 5.9 0.14 0.19 0.092 ≤ a ThickGl 876 3604 M2 10.2 5.0 0.14 0.19 -0.2 ≤ e ThinGl 402 1687 M3 11.7 6.4 0.15 0.20 -0.28 ≤ e ThinGl 555 2310 M3 11.3 5.9 0.16 0.22 -0.177 2.7 e ThinGl 324 B 1383 M4 13.2 7.7 0.22 0.31 -0.249 < b ThinGl 849 3478 M2 10.4 5.6 0.23 0.31 -0.384 < b ThinGl 205 930 M0 8.0 4.0 0.25 0.35 -0.401 1 d Thin/ThickGl 169.1 A 780 M3 11.1 5.7 0.26 0.36 -0.174 1.9 e Thin/Thick Reference of H α : Gizis et al. (2002) Reference of v sin i : (a) Delfosse et al. (1998b), (b) Browning et al. (2010), (c) Marcy & Chen(1992), (d) Reiners (2007), (e) Mohanty & Basri (2003), and (f) Jenkins et al. (2009) Table 10. M dwarf Planet Hosts and Metallicity Calibration Sample
This Work KHM B05 JA09 W09 SL10 R10 M sin(i)Name Sp. Type [M/H] [Fe/H] Sp. Type [Fe/H] [Fe/H] [Fe/H] [Fe/H] [Fe/H] M J Planet NotesHIP 79431 M1 +0.33 +0.46 M3 +0.16 +0.52 · · · +0.35 +0.60 2.1 JupiterGl 849 M2 +0.23 +0.31 M3 +0.14 +0.58 +0.20 +0.41 +0.49 0.82 JupiterGl 179 M3 +0.17 +0.23 M3.5 · · · +0.30 +0.02 +0.20 · · · · · · +0.03 · · · +0.28 +0.39 0.0179 super-EarthGl 876 M3 +0.14 +0.19 M4 +0.03 +0.37 +0.02 +0.23 +0.43 2.64 2 Jupiters + Neptune + super-EarthGl 176 M2 +0.11 +0.15 M2.5 · · · +0.18 -0.16 +0.06 · · · · · · +0.12 0.298 NeptuneHIP 12961 M1 +0.01 +0.01 M0 · · · · · · · · · -0.07 · · ·· · ·