Accurate Gravities of F, G, and K stars from High Resolution Spectra Without External Constraints
John M. Brewer, Debra A. Fischer, Sarbani Basu, Jeff A. Valenti, Nikolai Piskunov
aa r X i v : . [ a s t r o - ph . S R ] M a r Accepted to ApJ: March 30, 2015
Preprint typeset using L A TEX style emulateapj v. 5/2/11
ACCURATE GRAVITIES OF F, G, AND K STARS FROM HIGH RESOLUTION SPECTRA WITHOUTEXTERNAL CONSTRAINTS
John M. Brewer, Debra A. Fischer, Sarbani Basu
Department of Astronomy, Yale University and260 Whitney Avenue, New Haven, CT 06511, USA
Jeff A. Valenti
Space Telescope Science Institute and3700 San Martin Drive, Baltimore, MD 21218, USA
Nikolai Piskunov
Uppsala University andDepartment of Physics and Astronomy, Box 516, 75120 Uppsala, Sweden
Accepted to ApJ:
March 30, 2015
ABSTRACTWe demonstrate a new procedure to derive accurate and precise surface gravities from highresolution spectra without the use of external constraints. Our analysis utilizes SpectroscopyMade Easy (SME) with robust spectral line constraints and uses an iterative process to miti-gate degeneracies in the fitting process. We adopt an updated radiative transfer code, a newtreatment for neutral perturber broadening, a line list with multiple gravity constraints andseparate fitting for global stellar properties and abundance determinations. To investigate thesources of temperature dependent trends in determining log g noted in previous studies, weobtained Keck HIRES spectra of 42 Kepler asteroseismic stars. In comparison to asteroseismi-cally determined log g our spectroscopic analysis has a constant offset of 0.01 dex with a rootmean square (RMS) scatter of 0.05 dex. We also analyzed 30 spectra which had publishedsurface gravities determined using the a/R ∗ technique from planetary transits and found aconstant offset of 0.06 dex and RMS scatter of 0.07 dex. The two samples covered effectivetemperatures between 5000K and 6700K with log g between 3.7 and 4.6. Subject headings: stars: fundamental parameters; stars: solar-type; techniques: spectroscopic;asteroseismology; methods: data analysis INTRODUCTION
For many planets, uncertainty in the stellar ra-dius is the largest contributor to uncertainty inplanet radius and density, limiting attempts to un-derstand planet formation theory. Ten years ago,the high quality Spectral Properties of Cool Stars(SPOCS) catalog (Valenti & Fischer 2005, hereafterVF05) provided a uniform analysis which enablednew insights into planet formation Fischer & Valenti(2005). However, the authors cautioned that offsets [email protected].fi[email protected]@[email protected]@physics.uu.se remained with other catalogs and that a temperaturedependent bias existed between the spectroscopic andmodel isochrone gravities for some stars.More recent analyses have used non spectroscopic(’external’) constraints on either T eff or log g to re-move this trend. Torres et al. (2012) showed that theSpectroscopy Made Easy (SME) (Valenti & Piskunov1996) analysis used in VF05 displayed degeneraciesbetween T eff and log g and that the surface gravitycould be off by up to 0.5 dex in regions of the HRdiagram where the Mg b triplet is a poor gravityconstraint. An offset of 0.5 dex in log g resulted inan a corresponding offset of 400K in T eff . One re-cently developed external constraint for stars withtransiting planets, used in Torres et al. (2012), is thestellar density derived from the a/R ∗ ratio (Sozzettiet al. 2007). Although transiting systems are fan-tastic laboratories, only 1% of planetary systems willbe favorably aligned for transits. Additionally, thismethod can suffer from inaccuracies due to contam-ination from the light of nearby companions (Seager& Mall´en-Ornelas 2003) as well as high impact pa-rameter or large eccentricity of the transiting planet(Huber et al. 2013). Angular diameter measurementsof stars are a gold standard for obtaining effectivetemperatures when the angular resolution of the in-terferometer can directly measure the angular stellardiameter and accurate distances are known. This isan important means of validation but is not possiblefor more distant stars.Valenti et al. (2009) externally constrained SMEby using parallax to determine the bolometric lumi-nosity of the star then combined that with derivedspectral parameters to interpolate in a grid of stel-lar models and obtain a constraint on gravity. Gaiawill eventually give us precise distances for millionsof stars; however, many of the Kepler planet hosts donot have well-measured distances.To avoid using external constraints, we havesearched for the source of the inaccurate gravity de-terminations and correlated errors in temperatureand metallicity. Most of the gravity information inthe line list of VF05 is contained in the dampingwings of the Mg I b triplet lines, which are sensitive topressure changes in main sequence stars cooler thanabout 6200 K. The visual spectrum is dominated bylines of Fe I which is the minority species in the Sunand hotter stars. With few Fe II lines in the line listthe solution is less sensitive to the ionization equilib-rium. Our initial investigation showed that althoughthere were minor improvements which could be madeby improving the treatment of pressure broadeningthere was still a large degeneracy between temper-ature, gravity, and metallicity which could lead toinaccurate results.The line list of VF05 contains ∼ II lines. The upgrade of theHIRES CCD from one to three detectors extended thewavelength range and we take advantage of this inour new analysis. Our line list now contains roughly7500 lines covering more than 350 ˚A. The addition ofnew temperature and pressure sensitive lines, includ-ing 290 Fe II lines, has helped to break the degen-eracies between temperature, gravity, and metallic-ity. In addition to the large line list, we also use theprescription for broadening by neutral hydrogen from Barklem & O’Mara (1998) when available in VALD-3.This more accurate treatment of line wing broaden-ing provides a better fit to the wings of strong lines.Through two independent comparisons, we show thatthe procedure presented in this paper makes system-atic trends in derived surface gravities comparable toor smaller than random errors. OBSERVATIONS AND REDUCTIONS
Our purpose in this work was to improve spectralsynthesis modeling for accurate determination of ef-fective temperature and surface gravity.
Kepler as-teroseismic observations (Borucki et al. 2010) allowprecise determinations of stellar mass and radius giv-ing both accurate and precise surface gravities (Gaiet al. 2011; Basu et al. 2010). We obtained KeckHIRES spectra for a sample of 42 stars covering arange of temperatures, surface gravities, and activitylevels to explore how changes in the spectral anal-ysis affected our ability to recover the asteroseismicsurface gravity.
Spectra
We obtained 43 spectra of 42
Kepler asteroseismictargets using the Keck HIRES spectrograph in thered configuration at a resolution of R ≈ , >
200 perpixel column in the region around the Mg I b tripletfor all but 4 fainter targets that had S/N of ≈ ASTEROSEISMIC SURFACE GRAVITIES
Stellar oscillation frequencies were obtained usingshort cadence observations from the primary
Kepler mission (Borucki et al. 2010). The short cadence andprecision photometry of the
Kepler telescope allows∆ ν and ν max to be determined extremely accuratelyfor most stars (Chaplin et al. 2014).To close approximation the large frequency separa-tion, ∆ ν , scales as ρ / where ρ is the mean stellardensity and the frequency of maximum power, ν max ,scales as gT − / eff (Christensen-Dalsgaard et al. 2010).Combining these parameters with an externally de-termined effective temperature, we can use the scal-ing relations to find the surface gravity. The uncer-tainties in log g can be reduced by using a grid ofstellar evolutionary models with estimated frequen-cies instead of simply using the scaling relations. Weused the grid-based Yale-Birmingham pipeline (Gaiet al. 2011; Basu et al. 2010) which combines ∆ ν and ν max derived from Kepler lightcurves with the spec-troscopically determined T eff and [Fe/H]. Iterative Fitting
The asteroseismic surface gravities of main se-quence stars depend only weakly on the effective tem-perature and metallicity of the star (Gai et al. 2011)with their importance increasing slightly as the starevolves. We obtained temperature and metallicityfrom our spectral analysis, then used those valuesas initial inputs in the asteroseismic analysis. Wethen iterated once, fixing the gravity in our spectralanalysis to the value returned from asteroseismologyand used the newly derived T eff and [Fe/H] valuesin the asteroseismic analysis. The iteration resultedin changes of less than 0.05 dex in the final gravitiesfrom those initially determined from the asteroseis-mic analysis. SPECTROSCOPIC ANALYSIS TECHNIQUE
SME combines a stellar atmosphere grid, an atomicand molecular line list, and a radiative transfer codeto create model spectra based on specified physi-cal parameters such as effective temperature, sur-face gravity, metallicity, and rotation. Additionally,SME can fit an observed spectrum using Levenberg-Marquardt least-squares fitting with any number offree global stellar parameters combined with zero ormore free elemental abundances.VF05 analyzed nearly 2000 spectra using ≈ ∼
170 ˚A to produce the SPOCS catalog.Initial line parameters were obtained from the ViennaAtomic Line Database (VALD) (Kupka et al. 2011).Then VF05 tuned line position as well as log( gf )and van der Waals broadening coefficients to fit asolar atlas. In addition, 78 strong molecular MgHand C2 lines from (Kurucz 1993) were also included.Their analysis solves simultaneously for the global pa-rameters surface gravity (log g ), effective temperature( T eff ), metallicity ([M/H]), projected rotational ve-locity ( v sin i ), and radial velocity ( v rad ). In additionto the global parameters, VF05 solved for elementalabundances for Na, Si, Ti, Fe, and Ni. Microtur-bulence was fixed at 0.85 km/s and they derived anempirical relation for macroturbulence as a functionof effective temperature. The resulting parametershad good relative precision, though for some stars thespectroscopically determined gravities were inconsis-tent with isochrone gravities, especially for warmerstars. This later motivated the use of external con-straints on surface gravity in a more recent analysisto reduce parameter degeneracy (Valenti et al. 2009). Baseline Analysis with New Code
As a baseline, we began by analyzing the spectrausing the line list of VF05 with the same version ofSME they used. We then updated the line list overthe same wavelength region and updated the versionof SME to v439 , which uses an updated radiativetransfer code and updated atmosphere interpolationalgorithm. These changes reduced the differences inspectroscopic gravities relative to our asteroseismicreference values by about half; however, trends inthese differences as a function of both metallicity andtemperature remained. Between 5000 K and 6500K, ∆ log g (spectroscopic minus asteroseismic log g )spanned 0.5 dex.We then included additional spectral intervals anddecreased the number of simultaneously free parame-ters in our model to decouple the fitting of global pa-rameters from individual abundances. These changesdramatically improved the accuracy in our derivedlog g values, reducing the RMS scatter in ∆ log g to0.1 dex and removing the trend with respect to T eff .Further improvements were achieved by iterating thefitting procedure using the derived abundance pat-tern and allowing the abundances of alpha elementsto be free while fitting the global parameters. Thisapproach removed the trend in derived gravity withrespect to [M/H] and reduced the RMS scatter in ∆log g to only 0.05 dex. Expanded Line List
The line list now includes more than 350 ˚A in 20segments between 5160 ˚A and 7800 ˚A and includesnearly 7500 atomic and molecular lines (Table 1).The lines were obtained from the VALD-3 database(Kupka et al. 2011) and then tuned to better matcha high resolution disk-integrated solar atlas (Wallaceet al. 2011). The VALD-3 data contains many as-trophysically tuned line parameters, but we foundthat about 15% of the VALD-3 lines still needed ad-justment in one or more of line position, log( gf ),or neutral perturber broadening coefficients in orderto match the solar spectrum. Where available, wealso used VALD-3 values for the temperature depen-dent broadening prescription of Barklem & O’Mara(1998), which gives better fits to the line profiles thanthe traditional van der Waals formulation.We added wavelength regions to increase the num-ber and quality of gravity and temperature dependentlines and to allow abundance determinations for ad-ditional elements. SME calculates χ from the differ- Release versions of SME can be downloaded from
Deeper lines withdecreasing T eff
Shallower lines withdecreasing T eff ( × C u m u l a t i ve I n f o r m a t i on a b c d e f g h i j k l m n o pq r s t Deeper lines withdecreasing log g ( × C u m u l a t i ve I n f o r m a t i on a b c d e f g h i j k l m n o pq r s t Figure 1.
We increased the amount of T eff sensitive regionsby 51% and log g sensitive regions by 28% by including addi-tional wavelength segments. The dotted red line are for thosesegments which correspond to the original wavelength range ofVF05 and the solid blue line corresponds to the newly addedwavelength coverage. The gray vertical lines denote the bound-aries of the wavelength segments and the letters at the topdenote are keys to the wavelength ranges listed in Table 1. ence between observed and model spectra. To evalu-ate the influence that the new segments had on fittingfor log g and T eff we created a model spectrum withsolar parameters, two models with log g adjusted by ± . ± T eff . Wedifferenced pairs of models and used the squared dif-ference at each unmasked spectrum point as a proxyfor the information contributed to χ when fittingto spectra. We then plotted the cumulative distri-bution of these squared differences to examine this gravity and temperature information as a functionof the increasing wavelength point in our unmaskedspectrum (Figure 1). The information content ofeach segment is also detailed in Table 1. The ex-panded line list added 28% more gravity informationand 51% more temperature information. Addition-ally, although deep gravity sensitive lines tend to getstronger with increasing log g and temperature sen-sitive lines stronger with decreasing T eff , there aresome lines which display the opposite behavior. Asnoted by Gray (2008), weak lines of ions or atoms ofan element that is predominantly found in the sameionization state (e.g. weak Fe II lines) provide im-portant gravity information because these lines be-come stronger with decreasing gravity. The opposingline growth of these lines is especially helpful in con-straining T eff and log g and we more than doubledthe number of these spectral lines. Since Fe I is inthe next lower energy state than the dominant Fe II ,weak lines of Fe I will not be very pressure sensitiveand so ionization equilibrium provides an additionalgravity constraint to the Mg I b wings, for lines wherenon-LTE effects do not significantly affect ionizationequilibrium.In preparing the spectra for analysis we use thesame continuum normalization procedure as VF05but also mask out telluric lines as our spectral rangenow includes regions with significant telluric contam-ination. We perform cross correlation with the solaratlas (Wallace et al. 2011) to find an approximate ra-dial velocity and before shifting the spectrum to ob-servatory wavelengths, we apply a telluric mask basedon telluric lines found in the Wallace et al. (2011)atlas. This masking had a beneficial effect on con-tinuum normalization in some segments for spectrawhere telluric lines fell on continuum features nearthe ends of the segment. The New Analysis Procedure
Initial stellar parameters are all set to solar val-ues except for the temperature, determined by V-Kor B-V color relation (Boyajian et al. 2013), andgravity which is arbitrarily set to 4.5. In the firststep (“Step 1”), we allow the global parameters T eff ,log g , [M/H], and macroturbulence ( v mac ) to be freealong with individual abundances for Ca, Si, and Ti.These alpha elements represent the largest number ofnon iron peak lines in the spectral regions we are an-alyzing. They also have relatively high abundancesthat can differ greatly from the solar abundance pat-tern especially for low metallicity stars. In our ini-tial fits, overall metallicity is strongly correlated with Decreasing log g Decreasing T eff Segment λ start λ end lines grow lines weaken lines grow lines weaken VF05a 5164 5190 0.17% 67.07% 48.14% 0.00% xj 5190 5207 0.63% 10.20% 16.17% 0.00%k 5232 5262 1.93% 5.77% 10.78% 0.01%b 6000 6015 0.08% 0.33% 1.68% 0.02% xc 6015 6030 0.02% 0.78% 2.20% 0.00% xd 6030 6050 0.29% 0.03% 0.35% 0.03% xe 6050 6070 0.10% 0.35% 1.08% 0.02% xf 6100 6120 0.21% 0.65% 1.88% 0.01% xg 6121 6140 0.30% 2.92% 3.89% 0.00% xh 6143 6160 0.60% 0.14% 1.11% 0.04% xi 6160 6180 0.04% 4.09% 5.42% 0.00% xl 6295 6305 0.11% 0.67% 0.78% 0.00%m 6311 6320 0.02% 0.11% 1.34% 0.01%n 6579 6599 0.16% 0.09% 1.13% 0.04%o 6688 6702 0.00% 0.01% 0.22% 0.00%p 6703 6711 0.00% 0.00% 0.43% 0.00%q 6711 6718 0.01% 0.09% 0.63% 0.00%r 7440 7470 0.16% 0.55% 1.16% 0.01%s 7697 7702 0.00% 0.30% 0.20% 0.00%t 7769 7799 0.64% 0.36% 0.53% 0.68% Table 1
Wavelength ranges of spectral regions used in this analysis. Those with a check in the VF05 column cover the same wavelengthsas segments from VF05. The letters correspond to those at the tops of the plots in Figure 1. The columns for decreasing log g and T eff quantify the total amount of information contributed to the χ determination for each segment as plotted in the figure. [Fe/H] due to the preponderance of iron lines. By let-ting these alpha elements be independent of overallmetallicity, we partially account for non-solar abun-dance patterns in fitting the global parameters. VF05showed that microturbulence, important in equiva-lent width analysis, seems not to play a large role inforward modeling and is degenerate with [M/H] sowe fixed it to our adopted solar value of 0.85 km/s.After fitting, we perturb the temperature ± T eff log g , and [M/H] for thestars in our sample.In the next step (“Step 2”) we fix the global param-eters to the χ weighted average of the three modelsfrom Step 1. We then allow all of our elemental abun-dances to be free including the three alpha elementswhich were free in Step 1. We have a total of 15free elemental abundances (C, N, O, Na, Mg, Al, Si,Ca, Ti, V, Cr, Mn, Fe, Ni, Y), which were selectedbased on our interest in the element, the number oflines available in our spectral range, the sensitivity of those lines to small changes in abundances, andthe reliability of recovering the solar abundances inour asteroid spectra (see below). A few of those ele-ments, carbon, nitrogen, oxygen, and magnesium arealso components of molecular species with lines inour spectral range and our inclusion of molecules inthe spectral synthesis model provide additional con-straints on these elemental abundances. The resul-tant model now has the full set of global parametersand individual abundances.We then iterate, repeating Step 1 and Step 2 usingthe abundance pattern derived from the output of thefirst iteration instead of solar values. The differencesin the models between the first and second iterationsare small but serve to erase a subtle trend in ∆ log g as a function of metallicity that was seen at the endof the first iteration. The standard deviation of thedifferences between the first and second iteration is0.056 dex in log g and only 0.01 dex for [M/H].To evaluate the accuracy of our returned param-eters, we analyzed 20 spectra of reflected sunlightfrom 4 different asteroids taken on 6 different epochs.These spectra were obtained in the same manner asour other targets. Because we calibrated the atomicline data to the high resolution NSO solar spectrum,we expect that we should recover the solar parameterswhen we fit the reflected solar spectra in the asteroidobservations. We found that our procedure recoversthe solar parameters for the asteroid spectra (Figure2) with χ weighted mean offsets of only 1K in T eff ,0.02 dex in log g , and 0.02 dex in [Fe/H] and RMSscatter of 5K, 0.006 dex, and 0.003 dex respectively. Figure 2.
The wings of the Mg I b triplet contain significantgravity information in our spectral region. As can be seen inthis fit (heavy red line) to a spectrum from the asteroid Vesta(thin black line), we obtain a good fit using our new analysis.Gray regions are excluded from the fit and residuals (observed- model) are shown below.
Microturbulence
Our analysis is one of differential solar measure-ments made after tuning our line list against a solaratlas. In doing so, we adopted a microturbulencevalue of 0.85 km/s for the sun and left that fixed inthe analysis of other stars. After fitting using ournew procedure, we analyzed the effects of this deci-sion to follow VF05 in fixing the microturbulence tothe value we adopted for the sun with two tests. Thefirst fixed v mic using the final parameters from ouranalysis in the empirical formula of Ramirez et al.(2013) v mic = 1 . . × − × ( T eff − − . × (log g − . − . × [ F e/H ] (1) and then ran our analysis as before. For the aster-oid spectra v mic = 1.07 was 0.2 km/s higher than ourvalue of 0.85 and resulted in models on average 30Khotter and 0.03 dex higher in log g . For the astero-seismic stars, the resultant gravities were discrepantfrom asteroseismic values by up to 0.35 dex and therewere clear trends in ∆ log g with both T eff and [M/H].Temperatures also increased for hotter stars by up to200K. Allowing for the possibility that the offset in v mic at solar from our adopted value could be re-sponsible for the differences, we re-ran this test aftersubtracting a constant 0.22 km/s from the v mic val-ues. By construction, this then returned the solarparameters for the asteroid spectra but the trend in∆ log g with T eff remained with a slightly shallowerslope (∆ log g up to 0.23 dex).The second test allowed v mic to be an additionalfree parameter in the global parameter step with itsinitial value set to 0.85 km/s and our procedure wasthen run as before. There was a systematic offsetof ∼ . km/s lower in the returned v mic with re-spect to the fixed test values. The asteroid spectrareturned the solar parameters with only [M/H] in-creasing slightly by 0.01 dex. However, asteroseismicstars again showed clear trends in ∆ log g with both T eff and [M/H] though slightly less (∆ log g up to 0.25dex) than the fixed v mic case.The first step in our analysis was to empiricallytune our line data against a solar atlas using fixedsolar parameters including 0.85 km/s for microtur-bulence. Using the formula of Ramirez et al. (2013)for microturbulence when fitting stellar spectra de-graded our gravity accuracy because our lines hadbeen tuned at this constant, lower value. It is possiblethat self-consistent use of the Ramirez et al. (2013)formula to tune the line data and fit stellar spectramight improve the accuracy of our abundance deter-minations without compromising the accuracy of thegravity.In our models, microturbulence is partially degen-erate with log g , T eff and [M/H]. Including it as anadditional free parameter reduces our ability to re-cover accurate surface gravities. Solving for micro-turbulence while tuning the atomic line data mightallow us to solve for microturbulence when fittingspectra without compromising the fit for solar-typestars. From these tests it is clear that we have toleave v mic set at the value we adopted for the sunsince this is the value used in tuning our lines againstthe solar atlas. RESULTS ∆ logg vs T eff eff [K]−0.4−0.20.00.20.4 ∆ l og g ( S p ec t r o sc op i c − A s t e r o se i s m i c ) This WorkVF05 analysis procedurev rot > 15 km/s
Figure 3.
The unconstrained values of log g determined byour new analysis are much closer to the asteroseismic valuesthan those returned by our analysis using the VF05 Line list.Moreover, there are no trends with temperature and compar-isons with gravity and metallicity also show no trends. Thelone outlier in our new analysis comes from a star with totalrotational broadening ( v rot ) greater than 25 km/s. Comparing all of the stellar parameters derivedfrom spectral analysis to known stellar parametersis only possible for the Sun, where we have indepen-dent methods for determining age and composition.Even then, debate continues surrounding the accu-racy of abundance patterns. However, for individualparameters such as surface gravity, we now have twomethods that provide consistency checks for our anal-ysis.
Comparison to Asteroseismic Surface Gravity
The first of these is to compare our spectroscopicgravity with the surface gravity from the grid basedasteroseismic method described in § g between the asteroseimically and spectroscopi-cally determined values with respect to T eff , log g , ormetallicity (Figure 4). Errors in these three param-eters have been shown to be correlated in previousspectral synthesis modeling analyses using the VF05line list and an older SME version (Torres et al. 2012).The extreme outlier at ∆ log g = -0.2 dex (Figure 4)is a star with total rotational broadening ( v sin i and v mac ) greater than 25 km/s which smooths away mostof the information needed to determine gravity andtemperature. Comparison with Published Results
A second comparison of our spectroscopic analysiscomes from the gravity constraint of transiting ex-oplanets. We compared our spectroscopic log g val-ues with those derived by Torres et al. (2012) usingthe a/R ∗ density method (Sozzetti et al. 2007) forstars with transiting planets. Most of the spectrahave SNR >
100 per wavelength bin, though a quar-ter of them have SNR below 100. Torres et al. (2012)found systematic trends between their gravities basedon a/R ∗ and SME gravities obtained using the VF05procedure. In contrast, we find no systematic trendsbetween Torres et al. (2012) gravities and our SMEgravities obtained using more spectral segments anda two-stage fitting procedure. Our SME methodologyworks better than the VF05 procedure for the Torreset al. (2012) stars, which are generally warmer thanthe original VF05 sample. We find a constant offsetof 0.06 dex in log g , relative to Torres et al. (2012).Such a small offset could be a result of errors in ourspectroscopic analysis or may be the result of smallerrors in the a/R ∗ analysis that arise because of in-accuracies in the impact parameters or eccentricities(Huber et al. 2013). DISCUSSION
We believe that the largest improvement in our de-termination of surface gravity was a result of addingnew wavelength segments. The expanded line listadded new gravity and temperature dependent linesthat helped reduce parameter degeneracy. We alsoincluded a factor of 10 more iron lines in the mask,bringing the total to ∼
900 with almost one thirdof them Fe II lines. All of the iron lines, regardlessof ionization state or excitation potential, are mod-eled with the same iron abundance. Because mostof the iron is in an ionized state at the temperatureswe are interested in, weak Fe II lines will becomestronger with decreasing gravity while weak Fe I linesare largely gravity insensitive. Having a large num-ber of lines in both states provides another importantconstraint on the gravity and helps to further limitthe parameter space. The addition of the expandedwavelength range gave us very accurate gravities andleft us with only a small residual trend with metal-licity.The wings of the Mg I b triplet lines provide awealth of information on the surface gravity of a cool ∆ l og ( g ) ( S p ec t r o − A s t e r o ) eff from This Work −0.6 −0.4 −0.2 0.0 0.2 0.4[M/H] from This Work Figure 4.
The spectroscopically determined gravities return the asteroseismically determined gravities with only 0.05 dex RMSscatter and show no trends with log g , T eff , or [M/H]. In the first panel there is no trend in derived gravity for subgiants throughsolar type dwarfs. In the second panel, we see no trends in derived gravity for stellar temperatures between early K and late Fobjects. In the final panel we see no trends for stars with metallicities between -0.5 and 0.3 dex. The outlier at -0.2 dex is a starwith total rotational broadening greater than 25 km/s ∆ l og ( g ) ( Th i s − To rr es ) eff from This Analysis −0.4 −0.2 0.0 0.2 0.4[M/H] from This Analysis Figure 5.
A comparison of stars analyzed by Torres et al. (2012) made use of a/R ∗ for transiting planets. There does not appearto be any trend in derived surface gravity with respect to the parameters log g , T eff or [Fe/H]. This sample contains several lowmass stars missing in the asteroseismology sample. Spectra with SNR <
100 per wavelength bin have square markers. dwarf star, but the gravity information is degeneratewith the Mg abundance. This led us to separate theglobal parameter fitting from the abundance determi-nations. However, because the particular atmosphereused is tied to the metallicity, a scaled solar abun-dance pattern (dominated by [Fe/H]) will not workfor all stars. By allowing the most abundant alphaelements (minus Mg) to be independent of the overallmetallicity we obtained a closer match to the correctatmosphere on the first iteration. The magnesiumabundance, however, will be the scaled solar value inthis step and not necessarily accurate. In the sec-ond iteration, we have a direct determination of themagnesium abundance and so obtain more accurategravity information from the Mg I b wings. In Fig-ure 6 we see that the changes in the magnesium tometallicity ratio between the first step (scaled solarvalue) and the final (independently determined Mgabundance) are inversely proportional to the changein gravity. −0.20 −0.15 −0.10 −0.05 0.00 0.05 0.10 ∆ log g: First − Final−0.10−0.050.000.050.100.15 ∆ [ M g / M ]: F i r s t − F i n a l Figure 6.
During the first iteration of our analysis, the Mgabundance is just the solar abundance pattern scaled to theoverall metallicity. After obtaining a close estimate of theglobal parameters we get more detailed abundances for 15 el-ements including Mg and this new abundance pattern is usedin fitting for the final global parameters. Because Mg linesconstitute the bulk of the surface gravity information for cooldwarfs, this iterative process allowed us to remove subtle trendsin derived log( g ) with metallicity in our sample. As K and M dwarfs are some of the most promis-ing candidates for finding Earth-like planets in thehabitable zone a robust spectroscopic analysis of cooldwarfs is an important improvement to the work pre-sented here. We are currently finishing the analysis of all stars observed by the California Planet Searchsince late 2004 using this procedure and will includeour updated line list in that paper. CONCLUSIONS
Accurate stellar parameters can be obtained fromhigh resolution spectroscopic analysis when spectralsegments contain adequate constraints and care istaken to decouple degeneracies in the fitting process.The results improve upon our past analyses wherecorrelated errors led to surface gravity determinationoff by more than 0.3 dex for stars where Mg I b isno longer a good gravity constraint. Our techniquereturns gravities consistent with those determined byasteroseismic analysis with an RMS scatter of only0.05 dex. It is also consistent with gravities deter-mined using a/R ∗ constraints from planetary transitswith a small systematic offset of 0.06 dex.This work was supported by a NASA Keck PI DataAward, administered by the NASA Exoplanet Sci-ence Institute. The authors thank the anonymousreferee for their insightful comments which greatlyimproved the quality of this work. Data presentedherein were obtained at the W. M. Keck Observa-tory from telescope time allocated to the NationalAeronautics and Space Administration through theagency’s scientific partnership with the California In-stitute of Technology and the University of Califor-nia. The Observatory was made possible by the gen-erous financial support of the W. M. Keck Founda-tion.The authors wish to recognize and acknowledge thevery significant cultural role and reverence that thesummit of Mauna Kea has always had within the in-digenous Hawaiian community. We are most fortu-nate to have the opportunity to conduct observationsfrom this mountain.DF and JMB acknowledged NASA grantNNX12AC01G. SB acknowledges support from NSFgrant AST-1105930 which also partially supportedJMB. SB was further supported by NASA grantNNX13AE70G. REFERENCESBarklem, P. S., & O’Mara, B. J. 1998, Monthly Notices of theRoyal Astronomical Society, 300, 863 [1, 4.2]Basu, S., Chaplin, W. J., & Elsworth, Y. 2010, TheAstrophysical Journal, 710, 1596 [2, 3]Borucki, W. J., et al. 2010, Science, 327, 977 [2, 3]Boyajian, T. S., et al. 2013, The Astrophysical Journal, 771,40 [4.3]0