The Benchmark Ultracool Subdwarf HD 114762B: A Test of Low-Metallicity Atmospheric and Evolutionary Models
aa r X i v : . [ a s t r o - ph . S R ] O c t Accepted by ApJ 2009 October 7
Preprint typeset using L A TEX style emulateapj v. 08/22/09
THE BENCHMARK ULTRACOOL SUBDWARF HD 114762B:A TEST OF LOW-METALLICITY ATMOSPHERIC AND EVOLUTIONARY MODELS Brendan P. Bowler, Michael C. Liu, and Michael C. Cushing Institute for Astronomy, University of Hawai‘i2680 Woodlawn Drive, Honolulu, HI 96822, USA
Accepted by ApJ 2009 October 7
ABSTRACTWe present a near-infrared spectroscopic study of HD 114762B, the latest-type metal-poor compan-ion discovered to date and the only ultracool subdwarf with a known metallicity, inferred from theprimary star to be [Fe/H] = –0.7. We obtained a medium-resolution (R ∼ µ m spectrum and a low-resolution (R ∼ µ m spectrum of HD 114762Bto test atmospheric and evolutionary models for the first time in this mass-metallicity regime. HD114762B exhibits spectral features common to both late-type dwarfs and subdwarfs, and we assign ita spectral type of d/sdM9 ±
1. We use a Monte Carlo technique to fit PHOENIX/
GAIA syntheticspectra to the observations, accounting for the coarsely-gridded nature of the models. Fits to theentire OSIRIS J -band and to the metal-sensitive J -band atomic absorption features (Fe I , K I , andAl I lines) yield model parameters that are most consistent with the metallicity of the primary starand the high surface gravity expected of old late-type objects. The effective temperatures and radiiinferred from the model atmosphere fitting broadly agree with those predicted by the evolutionarymodels of Chabrier & Baraffe, and the model color-absolute magnitude relations accurately predictthe metallicity of HD 114762B. We conclude that current low-mass, mildly metal-poor atmosphericand evolutionary models are mutually consistent for spectral fits to medium-resolution J -band spectraof HD 114762B, but are inconsistent for fits to low-resolution near-infrared spectra of mild subdwarfs.Finally, we develop a technique for estimating distances to ultracool subdwarfs based on a singlenear-infrared spectrum. We show that this “spectroscopic parallax” method enables distance esti-mates accurate to .
10% of parallactic distances for ultracool subdwarfs near the hydrogen burningminimum mass.
Subject headings: stars: fundamental parameters — stars: individual (HD 114762B) — stars: low-mass, brown dwarfs — subdwarfs INTRODUCTION
A complete understanding of low-mass stars and browndwarfs is an important goal of astrophysics. Low-massstars (0.08 M ⊙ . M . M ⊙ ) are the most numerousobjects in our galaxy (Lada 2006) and make up nearlyhalf of its total mass. Brown dwarfs are objects that formlike stars but have insufficient mass to sustain core nu-clear reactions ( M . M ⊙ ) and represent the linkbetween low-mass stars and extra-solar giant planets.Objects with spectral types of M7 and later are knownas “ultracool” objects and encompass the lowest-massstars and brown dwarfs. Our understanding of theseobjects has dramatically improved over the last decade,but there remain several fundamental areas of parame-ter space that are relatively unexplored, one of which ismetallicity. Electronic address: [email protected] Some of the data presented herein were obtained at the W.M.Keck Observatory, which is operated as a scientific partnershipamong the California Institute of Technology, the University ofCalifornia and the National Aeronautics and Space Administra-tion. The Observatory was made possible by the generous financialsupport of the W.M. Keck Foundation. Visiting Astronomer at the Infrared Telescope Facility, whichis operated by the University of Hawaii under Cooperative Agree-ment no. NCC 5-538 with the National Aeronautics and SpaceAdministration, Science Mission Directorate, Planetary AstronomyProgram. Alfred P. Sloan Research Fellow
Sub-solar metallicity low-mass stars and brown dwarfsare referred to as ultracool subdwarfs. Like their solar-metallicity counterparts, ultracool subdwarfs have spec-tral energy distributions that peak in the near-infraredand are dominated by overlapping molecular absorp-tion bands. Their lower metallicities, however, dramati-cally alter their spectral properties compared to solar-metallicity objects and can ultimately provide insightinto the influence of metallicity on the chemistry, con-densate cloud formation, and temperature/pressure pro-files in the atmospheres of ultracool objects. Prominentspectral changes resulting from a reduced metallicity in-clude suppressed H - and K -band fluxes (i.e. bluer near-infrared colors) due to increased collision-induced ab-sorption by H (CIA H ; Linsky 1969; Borysow et al.1997), a suppression of metal-oxide bands, and an en-hancement of metal hydride bands (Bessell 1982). Ul-tracool subdwarfs exhibit large space motions consis-tent with thick disk or halo kinematics (Burgasser et al.2007), indicating that these objects are probably quiteold (see, e.g., Helmi 2008).The number of spectroscopically-confirmed ultracoolsubdwarfs has rapidly increased from the first identifica-tion over a decade ago (LHS 377, with a spectral type ofsdM7: Monet et al. 1992; Gizis 1997) to the ∼
45 cur-rently known, the vast majority of which have been foundin the past five years (see Table 7 of Burgasser et al.2007; Burgasser 2008). Many discoveries have been made
TABLE 1Age and Metallicity of HD 114762A:Literature Search (1995 – 2008)
Reference Age (Gyr) [Fe/H]Haywood (2008) 12.4 (2.8) · · ·
Holmberg et al. (2007) 10.6 (2.2) –0.76Gonzalez & Laws (2007) · · · –0.657 (0.051)Zhang & Zhao (2006) 14.1 –0.80 (0.10)Reddy et al. (2006) 11.3 (3.0) –0.71Saffe et al. (2005) 11.8 (3.6) · · ·
Valenti & Fischer (2005) 7.7 (2.3) –0.65 (0.02)Santos et al. (2004) · · · –0.70 (0.04)Gratton et al. (2003) · · · –0.79
Fe I
Laws et al. (2003) 14 (2) · · ·
Heiter & Luck (2003) · · · –0.78 (0.06)Sadakane et al. (2002) · · · –0.74 (0.07)Fulbright (2000) · · · –0.7 (0.08)Lachaume et al. (1999) 11 (1) · · ·
Th´evenin & Idiart (1999) · · · –0.72
LTE ; –0.56
NLTE
Clementini et al. (1999) · · · –0.66 (0.07)Gonzalez (1998) 14 (2) –0.6 (0.06)Fuhrmann (1998) · · · –0.71 ( ∼ · · · Henry et al. (1997) 5 · · ·
Adopted Values a
11 (3) –0.71 (0.07) a The adopted age and metallicity represent the mean and rms valueof the listed quantities. through searches of large near-infrared and proper mo-tion surveys including the Deep Near Infrared Survey ofthe Southern Sky (Epchtein et al. 1997), the Two MicronAll Sky Survey (2MASS, Skrutskie et al. 2006), and theDigitized Sky Survey (L´epine & Shara 2005). For exam-ple, L´epine & Scholz (2008) recently identified 23 newM-type ultracool subdwarfs through template matchingto Sloan Digital Sky Survey optical spectra. Many morefield ultracool subdwarfs are expected to be revealed withthe next generation of deep, multi-epoch all-sky surveyssuch as the Panoramic Survey Telescope & Rapid Re-sponse System (Kaiser et al. 2002) and the Large Syn-optic Survey Telescope (Tyson 2002).The absolute metallicities of ultracool subdwarfs arecurrently unknown. A commonly-used technique for es-timating the metallicities of late-type objects is to fit syn-thetic spectra to their red-optical spectra and to adoptthe metallicity of the best-fitting model (Schweitzer et al.1999; L´epine et al. 2004; Burgasser et al. 2007). Evolu-tionary models have also been used to estimate the metal-licities of ultracool subdwarfs in color-color and color-magnitude diagrams (Scholz et al. 2004b; Burgasser2008; Dahn et al. 2008; Schilbach et al. 2009). It is un-clear how reliable these methods are, however, becausemodels in this low-temperature, low-metallicity regimehave not been tested. There is thus a growing need forthe discovery of ultracool subdwarfs with independentlyderived metallicities.Benchmark objects whose fundamental parameters canbe independently determined enable valuable tests of at-mospheric and evolutionary models. Several solar metal-licity benchmark systems have already been used forsuch purposes. One of the best examples is the HD130948ABC system (Potter et al. 2002), which containstwo L4 brown dwarfs in a hierarchical triple system witha G2V primary. In this case the age and metallicity ofthe primary star along with the luminosities and dynam- ical masses of the brown dwarfs have been directly mea-sured and used to test brown dwarf evolutionary models(Dupuy et al. 2009). At sub-solar metallicities, however,there have not been any benchmark studies using verylow-mass objects. One possibility would be to use thelatest-type objects in globular clusters, which comprisecoeval stellar populations with uniform chemical compo-sitions. Their great distances, however, currently preventspectroscopic studies of the lowest-mass members forwhich even photometric detections have proven difficultto obtain (Richer et al. 2002; Richer 2006; Richer et al.2008). Another approach would be to use nearby ultra-cool subdwarfs in binary systems as sub-solar metallic-ity benchmarks. Companions to field subdwarfs couldalso act as metallicity calibrators for the field ultracoolsubdwarf population. This technique relies on the con-servative assumption that the components of binary sys-tems have the same metallicity. Observations of bina-ries in the field (Desidera et al. 2004) and in the Hyades(Paulson et al. 2003) have revealed that the componentshad differential [Fe/H] abundances of . . ′′ M P sin i = 11.68 ± M Jup ; Latham et al. 1989;Cochran et al. 1991; Hale 1995; Butler et al. 2006). Thepresence of a massive exoplanet candidate has led tonumerous studies of the primary’s metallicity ([Fe/H])and age, which have been well constrained to be –0.71 ± ± (Table 1).Age estimates in the literature for HD 114762A arebased on theoretical isochrones and chromospheric ac-tivity levels. This system may also harbor a debris diskbased on optical polarimetry and ISO far-IR photometry(Saffe & G´omez 2004).A Keck adaptive optics/NIRSPEC J -band spectrumof HD114762B was presented by Patience et al. (2002).They found inconsistent spectral features that appearedsimilar to a late-M/early L spectrum based on thestrength of the 1.4 µ m steam band, but also resembleda mid-M spectrum based on the strengths of the 1.189 µ m Fe I and 1.313 µ m Al I neutral metal lines and on acomparison to J -band spectra of other M dwarfs. How-ever, the dearth of ultracool subdwarfs known at thetime of discovery prevented a comparative analysis withother metal-poor objects, and the nature of their ob-servations made the analysis difficult because slit-based The quoted errors are rms values based on a literature searchrather than formal uncertainties. he Benchmark Companion HD 114762B 3spectroscopy with adaptive optics does not preserve thecontinuum shape (Goto et al. 2002; Goto et al. 2003;McElwain et al. 2007).Here we present a near-infrared spectroscopic studyof HD 114762B. Our goals are threefold: (1) to bettercharacterize this object through a comparison to knownsubdwarfs, (2) to test atmospheric models by compar-ing the results of the best-fitting models to the knownmetallicity of this object, and (3) to study the consis-tency of the predictions from atmospheric and evolu-tionary models. For our tests we use the
GAIA gridof synthetic spectra (Brott & Hauschildt 2005, basedon the PHOENIX atmospheric model code) and theChabrier & Baraffe (1997, CB97), Baraffe et al. (1997,BCAH97), and Baraffe et al. (1998, BCAH98) low-metallicity evolutionary models (all based on the sameinput physics). These models are widely used through-out the literature and are therefore important to validate.In § § χ fitting of the models to thedata and the way in which we derive the fundamentalparameters from the atmospheric and evolutionary mod-els. Finally, we summarize our results and discuss theimplications of our work in § OBSERVATIONS AND DATA REDUCTION
OSIRIS Spectrum
We obtained medium-resolution (R ∼ ≡ λ/ ∆ λ ) J -band spectra of HD 114762B with theOH-Suppressing InfraRed Integral-field Spectrograph(OSIRIS; Larkin et al. 2006) using the natural guide staradaptive optics system at Keck II on the night of 2008Jan 14 UT. The weather was poor with patchy cirrusclouds. Using HD 114762A as the natural guide star, weobtained four exposures of HD 114762B with an integra-tion time of 600 s and one with an integration time of 120s for a total integration time of 42 min. Immediately af-terwards we observed the A0V star HD 116960 for telluriccorrection with four exposures of 60 s each. We used the50 mas pixel scale for these observations. OSIRIS uses alenslet array to sample a rectangular region of sky, pro-ducing 16 ×
64 individual spectra which are later mergedinto a data cube covering both spatial and dispersion di-rections. The data were reduced and wavelength cali-brated using the OSIRIS data pipeline (Krabbe 2004).We extracted individual spectra from each observationby performing a robust third-order polynomial fit to thecentroids of each target in the dispersion direction forboth the the x- and y-coordinates. We then performedaperture photometry centered on the polynomial fit po-sitions at each wavelength slice using an aperture radiusof 3 pixels (0 . ′′
15) and an inner and outer sky annulus of7 pix (0 . ′′
35) and 10 pix (0 . ′′ SpeX Prism Spectrum
Observations
We obtained low-resolution (R ∼ µ m near-infrared spectra of HD 114762B using the near-infraredSpeX spectrograph (Rayner et al. 2003) in prism modeat IRTF on 2008 Jan 28 UT. Conditions were not photo-metric but the seeing was good with a typical FWHM of0 . ′′ ′′ and a slitwidth of 0 . ′′
5. The close angular separation (3 . ′′
3) and thehigh contrast (∆ J ∼ ∼ ′′ from the companion so ourobservations include a spectrum of a bright diffractionspike along with that of the much fainter science target(Figure 1, top panel).The data were taken by nodding on and off the targetin the ABBA configuration by about 13 ′′ , and consist of11 cycles of 120 s each for a total integration time of 22min. We subtracted the raw data in pairs to remove thenight sky lines, dark current, and bias offset. The sub-tracted pairs were then divided by a flat-field which wascreated by first scaling to a median-combined flat andthen taking the median of the scaled frames. A slightresidual sky signal was apparent across the entire spec-trum. We removed the residual sky at each column byfitting a line to the median-combined flux near both endsof the slit in the spatial direction and then subtracting offthe fitted line. This procedure simply flattened the datato zero at both ends of the spatial profile. The effect ofremoving the residual sky was small and the extraction ofthe companion spectrum (see below) was done with thisflattening and without it; the result on the final spec-trum was negligible. We accounted for chip defects inthe SpeX infrared array detector by using the bad pixelmask provided in Spextool. Extracting the Spectrum
Extracting the one-dimensional spectrum from thetwo-dimensional reduced data was not straightforward.The main difficulty lay in determining the spatial shapeof the diffraction spike spectrum whose tail the compan-ion was immersed. The peak of the diffraction spike was ∼ ′′ from that of the companion in the spatial direc-tion. Ideally we would like to know the exact functionalform of the bright tail so that we could simply subtractit off at each column. Practically this meant fitting sim-ple functions to the tail to determine the one that bestapproximated the data.The spatial profile of the diffraction spike was slightlyasymmetric so we could not use the opposite tail as a Fig. 1.—
Extraction of the HD 114762B spectrum from the SpeX/prism low-resolution data. The upper panel shows a single sky-subtracted and flat-fielded two-dimensional spectrum of the companion HD 114762B and the very bright diffraction spike of the primarystar HD 114762A. The x -axis is the dispersion direction and the y -axis is the spatial direction (the spatial scale is 0 . ′′
15 pix − ). The lowerpanel shows the image after fitting and subtracting the diffraction spike. The approximate locations of the J , H , and K bands are labeled. model. We first tested a method of spline interpolationacross the location of the science target. This techniquewas highly sensitive to both the “tension” parameter ofthe spline as well as the choice of anchor points along thetail; the result was a noisy and over-subtracted compan-ion spectrum. We tried constant values for the tensionparameter as well as tension values estimated from thebest-fitting spline interpolation over the same region onthe opposite tail. Both methods produced poor results.We tested a wide variety of standard functions includ-ing a Gaussian, a Moffat, and a number of polynomials(from 2 nd to 6 th order) in both normal- and log-space.The quality of each fit was judged based on a visual in-spection of the fit at each column and of the resultingsubtracted two-dimensional spectrum. The best resultwas a third-order polynomial fit to the logarithm of theintensity values. The functional form in linear flux unitsis I ( y ) = 10 a + by + cy + dy , (1)where I is the intensity at each pixel, y is the pixel coor-dinate in the spatial direction, and the values of a , b , c ,and d are the constants that are fit for at each column.In each fit the data were median-combined over 11 pixelsin the dispersion direction to create a higher signal-to-noise spatial profile. Anchor points used in the fit werecentered around the peak of the companion and were ad-justed for a small ( ∼ MPFITEXPR , a robust non-linear least squares curve fitting routine in IDL (Markwardt2009). Finally, the scaled fit was subtracted from thetail of the diffraction spike thereby revealing the spatialprofile of HD 114762B (Figure 1, bottom panel). Thisprocedure was applied to every column across the entirespectrum for each reduced frame.One-dimensional spectra were obtained for each indi-vidual frame by summing the flux within a width of 5pixels (0 . ′′
75) from either side of the peak of the spatialprofile of the target spectrum at each column. To ensurea smooth aperture radius along the dispersion direction,the peak of the spatial profile was determined by firstfitting a Gaussian to the spatial profile at each columnand then fitting a line in the dispersion direction to thepeak of each Gaussian fit. To combine the spectra fromthe individual frames the data were scaled to the median-combined spectrum over the H -band and were median-combined again. Telluric correction was performed usingthe Spextool IRTF data reduction and analysis package(v.3.4, Vacca et al. 2003; Cushing et al. 2004). We per-formed several trial extractions to test the influence ofthe aperture radius and anchor points of the fitted func-tion on the final coadded spectrum. The aperture radiiwere tested with values of 1, 3, 5, 7, and 10 pixels. Theshape of the spectra changed very little, especially foraperture radii > ∼ ∼ µ m (Figure 2). In this region small changes in thegoodness-of-fit of Equation 1 corresponded to large varia-he Benchmark Companion HD 114762B 5 Fig. 2.—
Extraction of the HD 114762B spectrum from theSpeX/prism low-resolution data. The spatial scale of the infraredarray is 0 . ′′
15 pix − . The science target is the small bump seen onthe steeply rising flux from the primary star’s diffraction spike. Ateach column we fit a function (red line, Equation 1) to the spatialprofile of the diffraction spike using anchor points (demarcatedby gray dashed lines) that were allowed to shift with the peak ofthe diffraction spectrum across the array. The fit was subtractedfrom the bright tail, revealing the spectrum of the companion(plotted as diamonds). The contrast between the science targetand the diffraction spike was worse in the J band than in the K band and may have led to a slight oversubtraction of flux at shortwavelengths, especially below ∼ µ m. See § tions in the resulting subtracted profile. For that reason, the companion spectrum is probably not reliable for λ . µ m. While general absorption features are apparent,the flux levels are probably not trustworthy.
Flux Calibration
We flux-calibrated the OSIRIS and SpeX spectra us-ing published photometry. Differential J , H , and K S magnitudes between HD 114762A and HD 114762B arelisted in Table 4 of Patience et al. (2002). Their imag-ing observations were obtained using Lick Observatory’sIRCAL camera with adaptive optics. We used the dif-ferential magnitudes combined with 2MASS photometryof the primary to compute the IRCAL magnitudes ofHD 114762B: J IRCALcom = ∆ J IRCAL + ( J + J corr ) , (2)where J corr is the correction term used to transform the2MASS J -band magnitude to the IRCAL photometricsystem. The same procedure was applied to the H and K S bands. The correction term was derived by calcu-lating the differential magnitude of an F9 star in bothphotometric systems. The choice of an F9 star is basedon the spectral type of HD 114762A (sdF9), which allowsus to avoid a color correction between the filter systems.We performed synthetic photometry on the infrared spec-trum of HD 27383 (F9V) which we obtained from theIRTF spectral library (Rayner et al., submitted). Thecorrection term for the J band is J corr = − . R λf F9 λ T IRCAL J ( λ ) dλ R λf Vega λ T IRCAL J ( λ ) dλ ! + 2 . R λf F9 λ T J ( λ ) dλ R λf Vega λ T J ( λ ) dλ ! . (3)Here T IRCAL J and T J are the transmission curvesof the J filter in the IRCAL and 2MASS systems, re-spectively, while f F9 λ and f Vega λ are the flux densities ofthe F9 star and Vega. The 2MASS transmission filtersinclude the filter profile together with the atmospherictransmission profile, so we multiplied the IRCAL filtertransmissions with an infrared telluric profile generatedusing ATRAN (Lord 1992). For Vega fluxes throughoutthis work we used the flux-calibrated spectrum of Vegaprovided in Spextool. The correction terms to convertfrom the 2MASS to the IRCAL systems were < K S -band magnitudelisted in Table 2. The K S band was chosen because anysystematic errors caused by the extraction of the spec-trum would be minimized in this bandpass (see § C fc was computed in aMonte Carlo fashion. An artificial spectrum was gener-ated by adding to the data noise drawn from a Gaussiandistribution with a standard deviation equal to the mea-surement error at each pixel. The flux calibration scalingfactor C fc was then computed for each artificial spectrumin the following manner: C fc ,i = R λf Vega λ T K S ( λ ) dλ R λf MC λ,i T K S ( λ ) dλ × − . K S ,i , (4)where f MC λ,i is the Monte Carlo-generated spectrum fortrial i , and f Vega λ and T K S ( λ ) are the same as in Equa-tion 3. For each trial i , a new K S ,i magnitude was drawnfrom a Gaussian distribution with a mean value equal tothe K S -band magnitude from Table 2 and a standard de-viation equal to the photometric uncertainty. The meanflux calibration scaling factor C fc and its error σ C fc wereobtained from the distribution of C fc values for 10 tri-als. The resulting values of C fc and σ C fc were 1.10 and0.10, respectively. The error in the final flux calibrationlevel is roughly 9% and is dominated by the K S -bandphotometric uncertainty.The OSIRIS spectrum does not cover the entire2MASS J band so we used the SpeX spectrum for fluxcalibration. We smoothed the OSIRIS spectrum to theresolution of the SpeX data and then scaled it to thesame flux level. We assume an identical flux calibrationuncertainty of 9% for the OSIRIS spectrum based on theSpeX spectrum. Synthetic Photometry
TABLE 2HD 114762B Infrared Photometry (2MASS System)
Type J ( σ J ) H ( σ H ) K S ( σ K S ) J − H ( σ J − H ) H − K S ( σ H − K S ) J − K S ( σ J − K S ) RefAperture Phot. 13.74 (0.10) 13.39 (0.10) 13.01 (0.10) 0.35 (0.14) 0.38 (0.14) 0.73 (0.15) 1, 2Synthetic Phot. 13.99 (0.10) 13.45 (0.10) 12.99 (0.10) 0.54 ( < < < References . — (1) Patience et al. (2002); (2) Cutri et al. (2003); (3) This work.
Fig. 3.—
Line identification in HD 114762B from the medium-resolution OSIRIS spectrum (top) and the low-resolution SpeX/prismspectrum (bottom). Major molecular bands are from H O, FeH, and CO, while prominent atomic features originate from K I , Al I , Na I ,and Fe I . Measurement errors for both spectra are shown as dotted lines. The portion of the SpeX spectrum that may have been alteredby the spectral extraction technique is demarcated by the gray shaded region (see § We computed synthetic magnitudes and colors fromour flux-calibrated SpeX spectrum and compared themto the published photometry to test whether the ex-traction technique altered the slope of the final spec-trum. Synthetic magnitudes were derived in a MonteCarlo fashion incorporating measurement errors andflux-calibration errors. For each trial, an artificial spec-trum was generated in the manner described in § C fc and a standard deviation of σ C fc . Synthetic J , H , and K S magnitudes were then computed using2MASS transmission profiles. This process was repeated10 times. The mean synthetic magnitudes and the stan-dard deviations of the resulting distributions are listed inTable 2. Synthetic colors and errors were computed in asimilar manner and are presented in the same table.The synthetic colors and magnitudes from our SpeX spectrum disagree with those derived from thePatience et al. (2002) differential photometry. The dis-agreement appears to progressively worsen at shorterwavelengths in the form of a shallower spectral slope inthe SpeX spectrum. It is unclear whether this differenceoriginates in the spectral extraction method used in thiswork or whether it originates with the published pho-tometry. A greater offset with decreasing wavelength,however, is consistent with an oversubtraction of fluxin our extraction technique of the companion spectrum( § K -band region but would be significant forthe high contrast J -band region. We accounted for thisdifference by dividing the SpeX spectrum into three sec-tions and adjusting each section’s relative flux to matchthe J -, H -, and K S -band photometry. The sections werechosen to approximate the near-infrared bandpasses: a J section (1.1-1.33 µ m), an H section (1.5-1.8 µ m), and a K section (2.0-2.35 µ m). We left the K -band spectrumhe Benchmark Companion HD 114762B 7stationary as it was probably least affected by the ex-traction process. We refer to the resulting spectrum asthe “shifted SpeX spectrum” throughout this work. RESULTS
Spectroscopic Characterization of HD 114762B
The spectra of HD 114762B reveal that it is a late-type object with a spectral energy distribution domi-nated by strong overlapping molecular absorption bands,most notably the deep 1.4 and 1.9 µ m H O steambands. The strongest atomic absorption lines and themajor molecular absorption bands are labeled in Fig-ure 3. The OSIRIS J -band spectrum shows a pseudo-continuum that originates mostly from H O but that alsocontains defining FeH band heads at 1.1939 and 1.2389 µ m (Phillips et al. 1987; Jones et al. 1996; Cushing et al.2003; McLean et al. 2007) and a noticeable Q-branchfeature at 1.222 µ m (Cushing et al. 2003). Prominentatomic lines are from Fe I at 1.1886/1.1887 (blended)and 1.1976 µ m, K I at 1.2436 and 1.2526 µ m, and Al I at 1.3127 and 1.3154 µ m. The SpeX spectrum exhibits arich molecular band structure which includes the Wing-Ford FeH band at 0.99 µ m (Wing & Ford 1969), otherstrong FeH band heads at 1.239 and 1.194 µ m, and the2.3 µ m CO band. Neutral atomic lines are also visible,including a blended K I doublet at 1.177 and 1.245 µ m,a blended Al I doublet at 1.314 µ m, and a deep Na I doublet at 1.14 µ m.In Figure 4 we compare the SpeX spectrum of HD114762B to spectra of late-type dwarfs, to so-called “mildsubdwarfs” which are believed to be only slightly metal-poor, and to subdwarfs in the top, middle, and bot-tom panels, respectively. The spectra are from theSpeX Prism Spectral Library and are normalized at1.275 µ m. HD 114762B closely resembles the M9 ob-ject 2MASS 17072343–0558249 (McElwain & Burgasser2006) between 1.00-1.35 µ m, but has a deeper 1.4 µ mH O steam band than any of the normal dwarfs. A muchbetter fit is obtained when compared to the mild subd-warfs. The general shape of the spectral energy distribu-tion matches quite well, except in the K band, where thespectrum of HD 114762B appears slightly higher than themild subdwarfs. This may be caused by a slight oversub-traction at shorter wavelengths (see § µ m, would result in a raised K -bandflux. Finally, a comparison to subdwarf templates showspoor matches across the entire wavelength range.The best overall fit appears to be to the d/sdM9 object2MASS 00412179+3547133 (Burgasser et al. 2004). Wetherefore adopt a spectral type of d/sdM9 ± J and K bands, but the H band is significantlylower. This reduced H band flux would only worsen theagreement between the shifted spectrum and the spectrafrom Figure 4; we therefore suspect that this lowered fluxis an artifact of shifting the segments of the SpeX datato published photometry which had large uncertainties(color errors were ∼ spectra shown in Figure 6 based on the strength of the1.4 µ m steam band and the strengths of the 1.2436 and1.2526 µ m K I lines.Another line of evidence independently bolsters themetal-poor nature of HD 114762B. This object has a blue J – K S color (0.73 mag) compared to normal dwarfs with(optical) spectral types later than ∼ M6, which have J – K S values & caused by a reduced metallicity. It can alsooriginate from thin or large grain condensate clouds(Burgasser et al. 2008a). Clouds begin to appear in thelatest M dwarfs (Jones & Tsuji 1997; Allard et al. 2001),but their influence on the near-infrared spectral slopeonly becomes significant in L dwarfs, as is evident by theincreased spread in J – K S color in that spectral class.The blue near-infrared colors observed in HD 114762Bare therefore indicative of a reduced metallicity. Physical Parameters From Atmospheric Models
There is no standard method for fitting a coarsely-sampled grid of synthetic spectra (e.g., ∆[M/H] ∼ T eff ∼
100 K, and ∆log g ∼ χ statistic, equal to P i ( f i – M i ) / σ i , where f i , M i , and σ i are the data, themodel prediction, and the measurement error at point i ,respectively. When the random variable ( f i – M i )/ σ i is astandard normal deviate, the χ statistic approximatesa χ distribution. In that case confidence regions forthe best-fitting parameters may be approximated by cal-culating the χ -plus-constant value (e.g., Press et al.2007).Atmospheric models have known systematic errors inthe form of incomplete opacity sources, in which casethe χ method of error analysis may not be applicable.Thus the question arises of how correct the models mustbe for this χ technique to remain reliable. Small devia-tions from “truth” in the model will have little influenceon the resulting confidence regions, but large deviationswill make this method more and more incorrect. Oneway to assess this applicability is to study the normal-ity of the distribution of deviates ( f i – M i )/ σ i for thebest-fitting model. A near-perfect model will have devi-ates that are approximately normally distributed, but aninadequate model will have non-normally distributed de-viates. Note that the condition of normally distributeddeviates does not guarantee that the model is good, buta good model should have normally distributed deviates.A test for normality of the deviates may therefore serveas a useful assessment of the correctness of a best-fittingmodel. Reduced χ values are also used as a goodness-of-fit measure, but they rely on an accurate determinationof measurement errors, a task that is difficult to correctlyperform. Method
In this study we first determine the synthetic spec-trum that best fits the data using a Monte Carlo ap-proach described below. We then make use of two pa-rameters to determine the goodness-of-fit: the reduced χ value and the significance level of the D’Agostino-Pearson normality test (D’Agostino et al. 1990) applied Fig. 4.—
Comparison of HD 114762B (black) to spectra of late-type objects using the same instrument at IRTF (SpeX/prism). The toppanel is a comparison to late-type dwarfs, the middle to mild subdwarfs, and the bottom to subdwarfs. The deep 1.4 and 1.9 µ m H Osteam bands are poorly matched by the dwarfs and the subdwarfs. We assign a spectral type d/sdM9 ± § Fig. 5.—
SpeX spectrum shifted to the photometry ofPatience et al. (2002, solid black) and compared to 2MASS0041+35 (d/sdM9, gray), which is the best-fitting referenceobject to the original unshifted SpeX spectrum (dotted black).All spectra are normalized to 1.275 µ m. The H -band flux ofthe shifted SpeX spectrum is significantly lower than that of2MASS 0041+35, which is probably a result of scaling the spectralsegments of HD 114762B to the published photometry which hadlarge errors. to the best-fitting model deviates. The latter test com-pares the skewness and kurtosis of a distribution to thatof a normal distribution. If the deviates are normallydistributed and the reduced χ value is low (we impose acutoff of 2.0) then the model is deemed “good” and ap-proximately Gaussian confidence limits can be derivedusing the aforementioned χ -plus-constant method. Ifthese criteria are not satisfied then we simply report thephysical parameters of the top few best-fitting modelswithout errors.We use the GAIA grid of synthetic spectra, derivedfrom the PHOENIX stellar atmosphere code (
GAIA ver-sion 2.6.1, Brott & Hauschildt 2005; Hauschildt et al.1999), as models for our observations. We made use of4030 models with zero α -element enrichment comparedto solar values covering the cool stellar and substellarregime: –4.0 ≤ [M/H] ≤ ≤ T eff ≤ T eff = 100 K), –0.5 ≤ log g ≤ g = 0.5). Examples of these models over a rangeof metallicities, temperatures, and surface gravities arepresented in Figure 7.Our approach for fitting the synthetic spectra to theobservations makes use of a Monte Carlo method previ-ously used by several authors (e.g., Saumon et al. 2006,Cushing et al. 2008). The GAIA models were Gaussianhe Benchmark Companion HD 114762B 9
Fig. 6.— J -band spectra of increasingly later-type metal-poorobjects compared to our OSIRIS spectrum of HD 114762B.The data for LHS 3409, LHS 1135, and LSR 2036+5059 arefrom Cushing & Vacca (2006) taken with SpeX in SXD modeat IRTF. Spectra are normalized to 1.27 µ m and are shiftedby a constant. HD 114762B is consistent with a spectral typelater than LSR 2036+5059 (sdM7.5) based on the depth ofthe 1.2436 and 1.2526 µ m K I lines and the strength of the1.4 µ m H O steam band. The spectrum of HD 114762B hasbeen Gaussian smoothed to the same resolution as the other data. smoothed to the resolution of the SpeX and OSIRIS dataand were resampled onto the same wavelength grids. Thesynthetic spectra provide the emergent flux density at thesurface of a star and have to be scaled to the flux densityobserved at Earth. For each model k we compute thescaling factor C k by minimizing the χ statistic χ = n X i =1 (cid:18) f i − C k E k,i σ i (cid:19) , (5)where f i and σ i are the observed flux density and themeasurement error, respectively, E k,i is the emergent fluxdensity for model k and pixel i , and n is the number ofdata points used in the fit. The scaling factor is given by C k = P f i E k,i /σ i P E k,i /σ i (6)and is related to the stellar radius R and the distance d to the source by C k = ( R/d ) .The GAIA model with the lowest χ value may changefor different observations of the same source as a result ofrandom noise in the data. To account for this uncertaintywe generated a large set of simulated data and then de-termined the best-fitting model for each new spectrum.The simulated data were created by adding noise to theoriginal spectrum using the measurement errors. To ac-count for the uncertainty in the flux calibration, which isimportant for the error in the model scaling factor σ C k ,the artificial spectrum was adjusted by a flux calibrationscaling factor drawn from a Gaussian distribution with amean C fc and a standard deviation σ C fc . Following theapproach of Cushing et al. (2008), the 20 models withthe lowest original χ values were then refit to the arti-ficial data sets for 10,000 trials of simulated spectra. Weadopted the model with the highest fraction of χ val- ues as the best-fitting model; we refer to that fraction as f MC , the “Monte Carlo fraction” (Cushing et al. 2008).A mean scaling factor C k was calculated by averagingthe individual C k values for trials where the model withthe highest resulting Monte Carlo fraction had the lowest χ value. The scaling factor uncertainty σ C k representsthe standard deviation of the distribution of C k values. Results
Accurate atmospheric models should yield similar best-fitting physical properties for fits to observations of thesame target at different wavelengths and spectral resolu-tions. We fit the
GAIA synthetic spectra to the OSIRISspectrum (from 1.18-1.35 µ m) and to the SpeX spectrum(from 1.00-2.35 µ m; Figure 8). We also fit the shiftedSpeX spectrum (Figure 9, see § µ m for J , 1.50-1.80 µ m for H ,and from 2.05-2.35 µ m for K ) to study the wavelengthdependence of the fits. Our Monte Carlo fitting of theshifted SpeX spectrum incorporated measurement errorsfrom both the observed spectrum and the published pho-tometry. For the shifted SpeX spectrum, each spectralsegment was adjusted by a scaling factor drawn from anormal distribution with a standard deviation equal tothe error in the published photometry. Then measure-ment errors were drawn and added back to the data.Results from the fits are presented in Table 3. In Figures10 and 11 we present contour plots of slices of the χ cubes near the best-fitting models for fits to the entireOSIRIS and SpeX spectra.The resulting metallicities and surface gravities varygreatly among the best-fitting models from Table 3, butthere is good agreement in the derived effective temper-atures (2500-2800 K). The fitting results that suggest alow surface gravity for this object are inconsistent withthe known high surface gravities of old low-mass starsand brown dwarfs (L´opez-Morales 2007; see Figure 2of Jao et al. 2008 for a graphical version of the data).The fit to the OSIRIS spectrum resulted in a best-fittingmodel with [M/H] = –0.5 and log g = 5.5, in accordwith the metallicity of the primary and the high surfacegravities of late-type objects. Reduced χ values are gen-erally quite high and the significance levels ( p ) from theD’Agostino-Pearson normality tests are mostly low, in-dicating that the best-fitting models do not match theobservations well. A visual inspection confirms this, al-though visually the OSIRIS fit appears to be quite good(“chi-by-eye”). If the p value is lower than 0.005 then wereject the null hypothesis that the deviates are normallydistributed. In no case were both p > χ /ν< ≤ [M/H] ≤ –0.5 dex) and surfacegravities (1.0 ≤ log g ≤ GAIA models or originate from the SpeX data themselves, e.g.as a result of the atypical spectral extraction technique We do not differentiate between [Fe/H] and [M/H] for our tests,although we note that Valenti & Fischer (2005) derive a value of[M/H] = –0.52 for HD 114762A. This difference does not affect theanalysis nor the results, however. Fig. 7.—
The PHOENIX/
GAIA v.2.6.1 atmospheric models (Brott & Hauschildt 2005) showing the variations in emergent flux densitywith metallicity (top), temperature (middle), and surface gravity (bottom). The result of a reduced metallicity includes a suppression of H and K -band flux from collision-induced H absorption, producing bluer near-infrared colors. The model notation is as follows: [[M/H], T eff (K), log g ]. Fig. 8.—
Results of fitting the OSIRIS (top) and SpeX (bot-tom) spectra. The best-fitting
GAIA model to the 1.18-1.35 µ mregion of the OSIRIS spectrum was [–0.5/2800/5.5]. The best-fitting model to the SpeX spectrum from 1.00-2.35 µ m was [–2.0/2500/1.0]. The metallicity from fitting the OSIRIS spectrum([M/H] = –0.5) is consistent with that of the primary star HD114762A ([Fe/H] = –0.70). The gray regions at the bottom in-dicate the sections of the observations that were used in the fit. ( § Fig. 9.—
The best-fitting model (red) to the shifted SpeX spec-trum (solid black) compared to the original unshifted SpeX spec-trum (dotted black). The resulting metallicity ([M/H] = +0.5) isinconsistent with the value of the primary star ([Fe/H] = –0.70).The gray regions at the bottom indicate the sections of the obser-vations that were used in the fit. only small variations in each parameter then that wouldindicate that it is our SpeX spectrum that may beskewing the results of the fits. We examined the spec-tra of three mildly metal-poor d/sdM8 objects (2MASS01151621+3130061, 2MASS 15561873+1300527, 2MASS15590462-0356280; NIR spectral types) and one d/sdM9he Benchmark Companion HD 114762B 11
TABLE 3Best-Fit PHOENIX/
GAIA
Models
Spectral RegionUsed in Fit [M/H] T eff (K) log g f MC p χ /ν OSIRIS1.18 - 1.35 µ m –0.5 2800 5.5 0.998 a < − b –0.5 2600 5.0 0.824 a < − < − µ m –2.0 2500 1.0 0.500 a < − < − < − µ m –1.5 2600 3.5 0.697 a µ m –1.5 2600 1.5 0.422 a µ m –0.5 2500 5.0 0.527 a < − < − c J / H / K bands < − a < − Note . — Synthetic spectra are from the PHOENIX/
GAIA v.2.6.1 model atmo-sphere code (Brott & Hauschildt 2005). Column 1 lists the region of the spectrumused in the fit. The resulting metallicities, effective temperatures, and surface grav-ities are listed in Columns 2, 3, and 4, respectively. The Monte Carlo fraction ( f MC )is listed in Column 5 ( § f MC ≥ p of the null hypoth-esis, that the deviates are normally distributed, is listed in Column 6. The nullhypothesis is rejected for values of p below 0.005. Reduced χ values for fits to the observed data rather than the simulated data are listed in Column 6, where ν = n – m –1 for n data points and m parameters used in the model. Note that m = 4for all fits except for fits to the absorption lines, in which case m = 7 ( T eff , [M/H],log g , and one scaling factor for each of the four wavelength ranges). a This model had the lowest χ value in a fit to the observed data. b Five lines were used: Fe I (1.1886/1.1887 µ m; blended), K I (1.2436 µ m), K I(1.2526 µ m), Al I (1.3127 µ m), Al I (1.3154 µ m). c Shifted to match photometry from Patience et al. (2002). The χ fit wasperformed to the J , H , and K S bands, skipping over the steam bands. See § object (2MASS 00412179+3547133; NIR spectral type)from Burgasser et al. (2004), made available through theSpeX Prism Spectral Library. We used the measurementerrors from our SpeX observations scaled to the squareroot of the ratio of the respective integration times todetermine f MC values . We first fit the entire 0.80-2.35 µ m range of the prism spectra, presented in Figure 12.The resulting metallicities were 0.5, 0.0, 0.5, and –3.0dex for the four (presumably) mildly metal-poor objects.To test the wavelength dependence of the predictionswe also fit the mild subdwarfs from 1.00-2.35 µ m andover the individual J , H , and K bandpasses (Table 4).The resulting metallicities and surface gravities variedconsiderably among the four objects. Fits to differentspectral regions of the same object also produced highlydiscrepant results. The effective temperatures were rela-tively constant, however, with most fits giving 2500 K or Initially we used the errors provided in the SpeX Prism Spec-tral Library which were derived from the observations, but reducedchi-squared values were quite high, indicating that the errors werelikely underestimated. the metal-licities and surface gravities resulting from χ fits to low-resolution near-infrared spectra of ultracool subdwarfs areprobably not reliable .We also fit the metal-sensitive absorption lines in ourOSIRIS spectrum to determine whether this fitting tech-nique was superior to fitting the entire J band spectralregion, which emphasizes the overall shape of the spec-trum rather than the strengths of the individual absorp-tion lines. We identified prominent lines in the OSIRISobservations which were sensitive to metallicity, temper-ature, and surface gravity in the GAIA models (see Fig-ure 13). Five lines were chosen: Fe I (1.1887 µ m), K I (1.2436 µ m), K I (1.2526 µ m), Al I (1.3127 µ m), andAl I (1.3154 µ m). We fit these lines in the OSIRIS datausing a fitting range of ±
30 ˚A from the center of each ab-sorption line, except for the aluminum doublet, for whichthe range was −
30 ˚A from the 1.3127 µ m line to +30 ˚Afrom the 1.3154 µ m line. The data were normalized tounity at the shortest wavelength of the fitting range foreach line and a separate scaling factor was computed for2 TABLE 4PHOENIX/
GAIA
Model Fits to Published Late-Type Mild Subdwarf SpeXSpectra
Object a [M/H] T eff (K) log g f MC p χ /ν Fit from 0.80-2.35 µ m2MASS 0115+31 (d/sdM8) 0.5 2600 4.0 0.999 < − < − < − < − µ m2MASS 0115+31 0.0 2700 4.5 1.000 < − < − < − < − µ m2MASS 0115+31 –1.5 2600 3.0 0.231 0.206 3.472MASS 1556+13 –2.5 2600 1.5 0.398 0.484 3.212MASS 1559–03 –1.5 2600 2.5 0.637 0.866 3.282MASS 0041+35 –1.0 2300 4.0 0.373 0.404 5.26Fit from 1.50-1.80 µ m2MASS 0115+31 –0.5 2700 4.0 0.822 0.060 3.252MASS 1556+13 –2.0 2600 1.0 0.852 0.920 4.682MASS 1559–03 0.0 2700 4.5 0.429 0.664 6.482MASS 0041+35 0.0 2500 5.0 0.782 0.702 5.38Fit from 2.05-2.35 µ m2MASS 0115+31 0.0 2800 5.0 0.498 0.865 1.672MASS 1556+13 0.5 2800 5.5 0.855 0.022 2.172MASS 1559–03 –0.5 2700 4.0 0.370 0.708 4.242MASS 0041+35 –1.0 2700 4.5 0.487 < − a The full names of the objects are 2MASS 01151621+3130061, 2MASS15561873+1300527, 2MASS 15590462–0356280, and 2MASS 00412179+3547133.
Fig. 10.—
Contour plots of χ values from fitting the GAIA syn-thetic spectra to our OSIRIS spectrum. The top row shows slices inmetallicity near the global minimum; the bottom row shows slicesin surface gravity. The global minimum is located at [M/H] = –0.5, T eff = 2800 K, log g = 5.5. The contour levels represent 1.02, 1.3,1.9, 2.5, 3.1, and 3.7 times the χ value, where χ = 8222.7(dof = 1128). Although confidence regions of contours cannot becomputed using the χ -plus-constant method (see § Fig. 11.—
Contour plots of χ values from fits to our SpeXspectrum (similar to Figure 10). The global minimum is located at[M/H] = –2.0, T eff = 2500 K, log g = 1.0. The contours representvalues of 1.02, 2.0, 4.0, 6.0, 8.0, and 10.0 times the χ value,where χ = 2324.4 (dof = 359). each of the four spectral segments. Each model was thenfit independently to the four regions and the resulting χ values were summed to produce a final χ value forthat model. The parameters from the best-fitting mod-els using this technique are similar to those for fits to thehe Benchmark Companion HD 114762B 13 Fig. 12.—
Spectral fits to SpeX/prism data for objects with sim-ilar spectral types to HD 114762B (from Burgasser et al. 2004).The metallicities and surface gravities from the best-fitting mod-els vary considerably among the objects for fits to the 0.80-2.35 µ m region. The full names of the mild subdwarfs are2MASS J01151621+3130061, 2MASS J15561873+130027, 2MASSJ15590462–0356280, and 2MASS J00412179+3547133. The graylines at the bottom indicate the sections of the observations thatwere used in the fit. entire OSIRIS J band spectrum (Figure 14), although inthis case the effective temperature is reduced by 200 Kto 2600 K .The effective temperatures of the best-fitting GAIA models (2500-2800 K) are systematically hotter thanthe temperatures of other late M-type objects whichhave been derived using other techniques. For example,Gautier et al. (2007) use 24 µ m photometry from SpitzerSpace Telescope to derive effective temperatures of Mdwarfs using the infrared flux method. They find effec-tive temperatures of 2150-2450 K for spectral types be-tween M8 and M9.5. Similarly, Golimowski et al. (2004)derive effective temperatures between 2000-2525 for spec-tral types between M8.5 and M9.5 based on L Bol - T eff relations from evolutionary models. The hotter effec-tive temperatures we inferred from this study may havetwo (non-mutually exclusive) causes: systematic errors inthe models or different temperature scales caused by themetal-poor nature of HD 114762B. The GAIA modelsdo not include the effects of dust, which can be a signif-icant source of continuum opacity in late M-type andL-type objects (Tsuji et al. 1996; Jones & Tsuji 1997;Leinert et al. 2000; Allard et al. 2001; Pavlenko et al.2006). We also tried fitting the models using the pseudo-equivalentwidths of the model absorption lines relative to those of the data.We calculated a chi squared statistic χ EW = X l =1 ( EW f,l − EW M ,l ) EW M ,l (7)over lines l = 1 to 5. Here EW f,l is the pseudo-equivalent width ofthe observed data for line l , and EW M ,l is the pseudo-equivalentwidth of the model line. A Monte Carlo simulation was used todetermine Monte Carlo fractions. f MC values were quite low, in-dicating that this method did a poor job of distinguishing amongthe best-fitting models. The results were also dependent on theway the pseudo-equivalent widths were calculated, as the pseudo-continuum is far from smooth. This method seems to be inferiorto χ fits over the absorption lines. The AMES-Dusty grid (Allard et al. 2001) is a popularalternative set of low-temperature models which includethe limiting effects of dust, but the sub-solar metallic-ity AMES-Dusty models only extend as cool as 2800 K.Nevertheless, to gauge the differences between non-dustyand dusty models, we fit the solar-metallicity AMES-Dusty models (∆ T eff = 100 K; ∆log g = 0.5) to our J -band OSIRIS and 1.00-2.35 µ m SpeX/prism spectra ofHD 114762B. The best-fitting AMES-dusty model to theOSIRIS spectrum is [2800/5.5] and to the SpeX spectrumis [2600/4.0]. These effective temperatures are similar tothose of the best-fitting GAIA models and so the useof non-dusty models does not appear to be the primarycause of the hotter temperatures. However, it remainspossible that both sets of models produce systematicallyhot effective temperatures.An alternative explanation for the hotter effective tem-peratures is the metal-poor nature of HD 114762B com-pared to the solar-metallicity M dwarfs used in previousstudies. As we discuss in § The Luminosity of HD 114762B
We calculated the luminosity of HD 114762B using itsbolometric flux and the (revised) HIPPARCHOS paral-lax measurement of HD 114762A (25.87 ± +1 . − . pc; van Leeuwen 2007; Perryman et al. 1997).The bolometric flux was computed twice using the origi-nal and shifted SpeX spectra to test whether shifting thespectrum significantly influenced the resulting luminos-ity. To determine the bolometric flux of the unshifteddata we first created an artificial spectrum by addingnoise drawn from the measurement errors. We then usedthe best-fitting model as a bolometric correction by at-taching a short-wavelength segment (10 − µ m < λ < µ m) and a long-wavelength segment (2.35 µ m < λ< µ m) to the artificial spectrum. To account forthe uncertainty in the flux calibration we adjusted thespectrum by a scaling factor drawn from a Gaussian dis-tribution with a mean C fc and error σ C fc . The bolomet-ric flux was then computed by integrating the spectrum.This process was repeated 10,000 times, from which amean bolometric flux and error were determined. A sim-ilar process was carried out for the shifted spectrum.Each artificial shifted spectrum consisted of J , H , and K spectral regions to which noise was added. In addition,short-wavelength (10 − µ m < λ < µ m) and long-wavelength (2.35 µ m < λ < µ m) segments from thebest-fitting model were attached to the artificial data, aswere model contributions between the J to H and H to K filter bandpasses. The spectrum was multiplicativelyscaled by a Monte Carlo-generated flux-calibration scal-ing factor and the bolometric flux was computed. Thisprocess was repeated 10,000 times.The uncertainty in the bolometric luminosity incorpo-rates the error in the parallactic distance measurement( σ d ) and the error in the bolometric flux ( σ F Bol ) in thefollowing way:4
Fig. 13.—
Relative strengths of the J -band absorption lines in the GAIA model atmospheres for changing physical parameters. Thedepth of the lines are sensitive to changes in metallicity (top), temperature, (middle), and surface gravity (bottom). The combination ofthese lines provides a good estimator of all three parameters when fitting synthetic spectra to observations. The models are smoothed forbetter rendering.
Fig. 14.—
Results from fitting the OSIRIS data to the absorp-tion lines. The metallicity and surface gravity are consistent withthe metallicity of the primary star ([Fe/H] = –0.70) and the highsurface gravity of late-type objects. The effective temperature isconsistent with that predicted by the CB97 evolutionary models.Note that the depth to the 1.1887 µ m Fe I line is overestimated inthe model. σ L Bol = 4 πd F Bol s(cid:18) σ F Bol F Bol (cid:19) + (cid:18) σ d d (cid:19) . (8)The resulting bolometric flux and luminosity from theoriginal spectrum are 9.11 ± × − W m − Fig. 15.—
Bolometric corrections for HD 114762B. The toppanel shows the original SpeX/prism spectrum (dark grey) andthe best-fitting model used for the bolometric correction (lightgrey; [[M/H]/ T eff /log g ] = [–2.0/2500/1.0]). The bottom panelshows the SpeX spectral segments shifted to the published pho-tometry (dark grey) and the best-fitting model for the correction([+0.5/2600/3.0]). The models have been smoothed to the resolu-tion of the data. and log( L Bol /L ⊙ ) = –3.37 ± ± × − W m − andlog( L Bol /L ⊙ ) = –3.32 ± L Bol / L ⊙ ) from choosing different modelatmospheres was less than 0.01 dex for the original SpeXspectrum and was near 0.02 dex for the shifted spectrum.In addition, we computed the luminosities using the[–0.5/2600/5.5] GAIA model. This model was chosenbecause its parameters are the closest to those predictedby the evolutionary models (see § ∼ ∼ The Luminosities of Other Ultracool Subdwarfs
Using the same method described in § J -band magnitudesand the best-fitting GAIA models were used to de-termine bolometric corrections. Parallaxes for LSR2036+5059, SSSPM 1013–1356, and 2MASS 1626+3945are from Schilbach et al. (2009) and the parallax for LHS377 is from Monet et al. (1992). The spectra were origi-nally published by Burgasser (2004) and Burgasser et al.(2004). The best-fitting models used for the short-and long-wavelength corrections were [0.5/3200/5.5], [–1.0/2900/5.0], [–1.5/2600/5.0], and [–2.5/2200/3.0] forLHS 377, LSR 2036+5059, SSSPM 1013–1356, and2MASS 1626+3945, respectively. We added in quadra-ture the resulting luminosity measurement errors and anestimated systematic error of 0.02 dex to account for thechoice of atmospheric model used for the bolometric cor-rection. The results are summarized in Table 6. Theluminosity of LHS 377 has previously been calculated byLeggett et al. (2000) using an observationally-derived K -band bolometric correction; the luminosity we obtained(–3.08 ± ± ± ± Fig. 16.—
Bolometric luminosity as a function of spectral typefor ultracool dwarfs (gray) and ultracool subdwarfs (red). Thedata for the dwarfs are from Dahn et al. (2002), Golimowski et al.(2004), and Cushing et al. (2005). Objects that have since beendiscovered to be resolved close binaries have been removed fromthe samples. The subdwarf data are from this work (Table 6) andBurgasser et al. (2008b, for 2MASS 05325346+8246465 (sdL7)).The solid black line and the dashed black curves show the linearfit and ± σ uncertainty (Equation 9). the following coefficients:log( L/L ⊙ ) = − . − . × SpT, (9)
Cov = (cid:18) . − . − .
369 0 . (cid:19) × − , where SpT is the ultracool subdwarf numerical spectraltype beginning at M0 = 0 and increasing by 1 for everyspectral subclass (e.g., L5 = 15).
Cov is the covariantmatrix of the fit.There are several explanations for the apparent over-luminosity of ultracool subdwarfs in the luminosity-spectral type diagram. Unresolved binarity is one possi-bility, but it is unlikely that the few late-type subdwarfssampled thus far all happen to be unresolved binaries.An alternative explanation is that the effective temper-atures and/or radii of ultracool subdwarfs are differentthan those of normal dwarfs in the same spectral sub-class. Ultracool subdwarfs appear to be ∼ ∼
26% larger than those of dwarfs. If, on theother hand, the increased luminosity were caused by adifference in effective temperature, then ultracool sub-dwarfs would need effective temperatures that were ∼
12% hotter than dwarfs from the same spectral sub-class. This translates into temperature differences of ∼ TABLE 5Luminosity and Radius of HD 114762B C k ( × − ) R ( R ⊙ ) R ( R ⊙ )Spectrum [[M/H]/ T eff /log g ] { = R / d } { = d p C k } { = q L Bol / (4 πσT ) } log( L Bol /L ⊙ ) a SpeX (1.00 - 2.35 µ m) [–2.0/2500/1.0] 4.6 ± ± ± ± J / H / K ) [0.5/2600/3.0] 4.4 ± ± ± ± a We adopt a value of 3.86 × W m − for L ⊙ . TABLE 6Luminosities and Bolometric Corrections of Ultracool Subdwarfs
Best-Fitting BC J BC K S SpectrumObject SpT
GAIA
Model a log( L Bol /L ⊙ ) (mag) (mag) Ref.LHS 377 sdM7 [0.5/3200/5.5] –3.08 ± ± ± ± ± ± ± ± ± ± ± ± References . — (1) Burgasser (2004), (2) Burgasser et al. (2004) a For fits to the 0.80-2.35 µ m spectral region; model parameters are [[M/H]/ T eff (K)/log g ]. temperature scales for objects with the same spectraltype but different luminosity class is not new: M dwarfsand M giants, for example, to exhibit this trait (see, e.g.,di Benedetto 1993). Bolometric Corrections for Ultracool Subdwarfs
Using our computed bolometric fluxes, we can derivebolometric corrections for ultracool subdwarfs. The J -band bolometric correction is defined as BC J ≡ M Bol – M J = m Bol – J , where M Bol is the absolute bolomet-ric magnitude, M J is the J -band absolute magnitude, m Bol is the apparent bolometric magnitude, and J isthe J -band apparent magnitude. Following Bessell et al.(1998, Appendix D), we define M Bol , ⊙ to be 4.74 and weassume L Bol , ⊙ = 3.86 × W, in which case the J -bandbolometric correction becomes BC J = − . F Bol ) − . − J , where F Bol is the bolometric flux in W. J - and K S -band bolometric corrections for ultracoolsubdwarfs are plotted in Figure 17 and are tabulated inTable 6. We use the values from Burgasser et al. (2008b)for 2MASS 05325346+8246465 (sdL7) to derive bolomet-ric corrections for that object. A linear fit to the J -bandbolometric corrections yield the following relation: BC J = 1 .
75 + 0 . × SpT, (10)
Cov = (cid:18) . − . − .
461 0 . (cid:19) × − , where SpT is the numerical spectral type beginning atM7 = 7 and increasing by 1 for each spectral subclassthrough L7. The rms scatter about the fit is 0.007 mags.Similarly, a quadratic fit to the K S bolometric correctiongives BC K S = 5 . − . × SpT + 0 . × SpT , (11) Cov = − . . − . . − . . − .
545 0 . ! × − . Fig. 17.— J - and K S -band bolometric correction as a functionof spectral type for ultracool subdwarfs. The gray dashed curve inthe bottom panel shows the K -band bolometric correction (not K S )for ultracool dwarfs derived by Golimowski et al. (2004). The dot-ted gray lines represent the typical rms scatter of ultracool dwarfs(0.13 mags) about the best-fitting polynomial relation. Ultracoolsubdwarf names and their individual corrections are tabulated inTable 6. The coefficients and covariance matrices of the fits aregiven in Equations 10 and 11. These relations are only applicablefor mildly metal-poor “sd”-type subdwarfs. The rms scatter about the quadratic fit is 0.04 mags. Wenote that these relations are only applicable for moder-ately metal-poor ultracool subdwarfs and should not beapplied for “usd”- or “esd”-type objects.
The Radius of HD 114762B
The radius of HD 114762B can be calculated in twoways using the model atmospheres. One way is to use thescaling factor C k which scales the emergent flux densityof the best-fitting model to the flux-calibrated spectra.The radius R and the error σ R can be computed usingthe following relations:he Benchmark Companion HD 114762B 17 Fig. 18.—
Predictions from the CB97 evolutionary models based on the bolometric luminosity of HD 114762B (log( L Bol /L ⊙ ) = –3.37 ± ± R = d q C k , (12) σ R = R s(cid:18) σ C k C k (cid:19) + (cid:16) σ d d (cid:17) , (13)where d and σ d are the distance and uncertainty in thedistance to the object, and C k and σ C k are the modelscaling factor and its error. The radii computed usingthis method are 0.116 ± R ⊙ and 0.113 ± R ⊙ for the original and shifted SpeX spectra, respectively,where R ⊙ = 6.960 × cm.The radius may also be computed using the bolometricluminosity and the effective temperature derived fromthe best-fitting atmospheric model: R = (cid:18) L Bol πσT (cid:19) / (14) σ R = R s(cid:18) σ L Bol L Bol (cid:19) + (cid:18) σ T eff T eff (cid:19) (15)In this work we do not estimate the errors of the fun-damental parameters derived from fitting atmosphericmodels; instead we merely report the best few modelsas a triplet of [[M/H], T eff , log g ]. To compute the un-certainty of the radius we estimate σ T eff to be ∼
100 K based on the narrow range of resulting temperatures fromthe best-fitting models. This gives radii of 0.111 ± R ⊙ and 0.110 ± R ⊙ for the original and shiftedSpeX spectra, respectively. These values are consistentwith the radii derived using the model scaling factor. Comparing Physical Parameters From Atmosphericand Evolutionary Models
Evolutionary models predict the change in stellar lu-minosity, effective temperature, and radius as a functionof mass, age, and metallicity. When testing evolution-ary models, the interpretation of discrepancies betweenobservations and model predictions must be made withcare. Evolutionary models depend on atmospheric mod-els to account for the way that radiative flux escapesfrom a central luminosity source, so the choice of atmo-spheric models can influence the predictions of the evolu-tionary models. It may therefore be difficult to untangleinadequate atmospheric models from missing or incorrectphysics in the evolutionary models.These models can be unraveled to some extent bystudying their predictions in various diagrams. Thefundamental physical parameters predicted by the evo-lutionary models ( L Bol , T eff , and R ) are more depen-dent on the input physics than on the atmospheric mod-els used (Chabrier et al. 2000). However, converting L and T eff into observable quantities (magnitudes andcolors) relies on the emergent spectral energy distribu-tions, so the predictive accuracy of color-magnitude di-8 TABLE 7Results From CB97 Evolutionary Models for HD114762B T eff (K) R ( R ⊙ ) M ( M ⊙ ) log g ±
42 0.100 ± ± ± Note . — Errors are derived in a Monte Carlo fashion using thebolometric luminosity from the original SpeX data (log( L Bol /L ⊙ )= –3.37 ± ± agrams reflects the accuracy of the atmospheric mod-els more so than do L - T eff HR diagrams. This depen-dency on correct atmospheric models is especially strongfor low-mass stars and brown dwarfs, for which the in-clusion of clouds in the models is required to even ap-proximately match the observed trends of late-M, L,and T dwarfs in the near-infrared color-absolute mag-nitude diagrams (Allard et al. 2001; Tsuji & Nakajima2003; Burrows et al. 2006; Saumon & Marley 2008). Inthis study we use the fundamental parameters from bythe Chabrier & Baraffe (1997, CB97) models and thecolor-magnitude relations from the Baraffe et al. (1997,BCAH97) and Baraffe et al. (1998, BCAH98) models, allof which incorporate the same (PHOENIX/
N extGen )model atmospheres and are based on the same inputphysics. These models are widely used throughout theliterature so it is crucial to test them at low masses andmetallicities, a task that we perform here for the firsttime.Using the metallicity and the now well-measured lumi-nosity of HD 114762B, we compared the effective temper-atures, radii, and surface gravities from our atmosphericmodel fitting to the values predicted by the evolutionarymodels to test for consistency. Mutually consistent pre-dictions do not prove that the models are correct (bothmay predict the wrong values), but inconsistent resultsindicate that at least one set of models needs improve-ment.There are a large number of age estimates in the lit-erature for the primary star HD 114762A, the majorityof which are based on evolutionary model isochrones orchromospheric activity levels. Most estimates are greaterthan 10 Gyr (Table 1). For the low mass evolutionarytracks that are relevant to HD 114762B, there is littledifference between the 1 Gyr and 10 Gyr isochrones (Fig-ure 18). We chose the 10 Gyr evolutionary tracks for ouranalysis. The properties of HD 114762B were derived ina Monte Carlo fashion by first randomly choosing a lu-minosity from a Gaussian distribution with mean valuesof –3.37 dex and a standard deviation of 0.04 dex. Simi-larly, a metallicity was chosen from a Gaussian distribu-tion with a mean value of –0.71 dex and a standard devi-ation of 0.07 dex. We created a new metallicity track atthe chosen value by interpolating the evolutionary mod-els. Then using the luminosity and the new metallicitytrack, we determined a temperature, radius, mass, andsurface gravity for that trial. This process was repeated10,000 times and the resulting distributions are summa-rized in Table 7. The CB97 models yielded the following While masses can be inferred from the atmospheric modelsusing the radius and surface gravity, the results are not practicalfor comparison because the models are coarsely gridded (∆log g =0.5). results for log( L Bol /L ⊙ ) = –3.37 ± ± T eff = 2645 ±
42 K, R = 0.100 ± R ⊙ , M = 0.0879 ± M ⊙ , and log g = 5.381 ± GAIA atmospheric models and the CB97 evolu-tionary models generally predicted consistent effectivetemperatures (between 2500 and 2700 K for the for-mer and 2645 K for the latter) and radii, but the in-ferred surface gravities were largely inconsistent. Theexceptions were the fits to the OSIRIS data. Fittingthe entire OSIRIS spectrum with the
GAIA models re-sulted in a temperature of 2800 K (or ∼
150 K abovethat of the CB97 evolutionary models) and a surfacegravity of 5.5 dex (similar to 5.38 dex from the CB97evolutionary models). The fit to the J -band absorptionlines yielded T eff = 2600 K and log g = 5.0. Jao et al.(2008) used the radii and masses of low-mass stars fromL´opez-Morales (2007) to construct a mass-gravity rela-tionship, which exhibited an increasing trend of surfacegravity with lower mass. For a mass of ∼ M ⊙ , wecan therefore expect HD 114762B to have a surface grav-ity above ∼ g . ∼ R ⊙ )is statistically slightly larger than the value predicted bythe evolutionary models ( ∼ R ⊙ ).The color-magnitude diagram (CMD) provides anothertest of the atmospheric models. In Figure 19 we plot theposition of HD 114762B with respect to the BCAH97and BCAH98 evolutionary models in the M K S vs J – K S CMD. The [M/H] = { } metallicity tracksare from BCAH98 while the [M/H] = { –1.0, –1.3, –1.5,–2.0 } tracks are from BCAH97. These evolutionary mod-els make use of an earlier version of the PHOENIX code(the NextGen models) than the
GAIA grid that we stud-ied in this work. The location of HD 114762B in thisdiagram is comfortably between the –0.5 and –1.0 dexmetallicity tracks, which is in precise agreement with themetallicity of –0.70 dex of the primary star. Previouslywe showed that the synthetic spectra from the atmo-spheric models did a poor job of reproducing the correctphysical parameters of HD 114762B from the best-fittingmodels. Nevertheless, the color-absolute magnitude dia-gram, which crudely measures the synthetic spectral en-ergy distributions of the models, appears to well-matchthe observations. This suggests that the shape of themodels at lower metallicities is accurate, but that the de-tailed treatment of opacity sources in the near-infraredstill needs improvement.To obtain a sense of the relative metallicities of othermetal-poor low-mass objects, we also plot all currentlyknown ultracool subdwarfs with parallax measurementsin the M K S vs J – K S CMD in Figure 19. Parallaxesare from Schilbach et al. (2009) and Monet et al. (1992,for LHS 377). Spectroscopically-classified mild subd-warfs fall in the expected mild-metallicity regions of theBCAH97/98 evolutionary tracks, and objects classifiedas subdwarfs are located between the [M/H] = –1.0 to–2.0 metallicity tracks. The M, L, and T spectral typesappear to follow an increasing absolute magnitude trendwith later spectral type, an expected feature for progres-sively later-type and lower-luminosity objects. The loca-tions of ultracool subdwarfs in the M K S vs J – K S CMDhe Benchmark Companion HD 114762B 19
HD 114762B
Fig. 19.— M K S vs J – K S color-absolute magnitude diagram showing the positions of ultracool subdwarfs with parallaxes. The [M/H]= { } evolutionary tracks are from BCAH98 and the [M/H] = { –1.0, –1.3, –1.5, –2.0 } tracks are from BCAH97 (10 Gyr models forboth). The evolutionary tracks were converted from the CIT photometric system to the 2MASS system using the relations in Carpenter(2001). Parallaxes are from Schilbach et al. (2009) and Monet et al. (1992). See Figure 1 of Schilbach et al. (2009) for the identificationof the other ultracool subdwarfs in this diagram. The position of HD 114762B in this diagram is shown as a yellow star. Its predictedmetallicity from the color-magnitude diagram is consistent with the value of –0.70 dex for the primary star HD 114762A. therefore supports the current extension of the opticalspectral classification scheme to lower metallicities. Nev-ertheless, the development of a rigorous spectral classifi-cation scheme will be needed with the discovery of largenumbers of ultracool subdwarfs.Based on the correct metallicity prediction forHD 114762B, we suspect that the accuracy of theBCAH97/98 evolutionary models is greater for ultracoolsubdwarfs than for their solar-metallicity counterparts,for which the inclusion of clouds in the atmosphericmodels is necessary to reproduce their observed J – K S colors. In the low-mass metal-poor regime,continuum CIA H is the dominant opacity source inthe near-infrared, so dust-free model atmospheres like N extGen probably do a reasonable job of reproducingthe color-magnitude relations of ultracool subdwarfs.The discovery of additional benchmark companions overa large range of metallicities will be necessary for thisclaim to be properly verified.
Spectroscopic Parallaxes
Spectroscopic Parallax to HD 114762B
Since the factor C k used to scale the model atmo-spheres to the flux calibrated spectra is equal to R /d ,in principle accurate radius values could be used to de-rive the distance without knowing the parallax, assum- Fig. 20.—
Surface gravity as a function of effective tempera-ture for different values of radius and metallicity from the 10 Gyrevolutionary models of Chabrier & Baraffe (1997). The modelsare interpolated over radius and metallicity. The gray shaded re-gion shows the range of T eff from fitting synthetic spectra to theOSIRIS data (2800 ±
100 K). The red tracks show the metallicityrange from the atmospheric model fitting (–0.5 ± C k (= R /d ), can be used to estimatethe distance to HD 114762B without knowing the parallax or thebolometric flux and assuming the object is not a binary. J -band region. Knowing a pos-teriori that this fitting technique is acceptable, we canuse the resulting effective temperature and metallicity toderive a radius from the evolutionary models and thena distance from C k (equal to R /d ). This method isparticularly well suited for observations of ultracool sub-dwarfs, which have ages that can be constrained fromtheir kinematic properties. We refer to the distances es-timated using this method as “spectroscopic parallaxes.”The best-fitting model to our OSIRIS spectrum is [–0.5/2800/5.5] (Table 3), where, for this analysis, we as-sume errors of 0.5 dex for the metallicity, 100 K for theeffective temperature, and 0.5 dex for the surface grav-ity. For ultracool objects, the evolutionary models pro-vide tighter constraints on the surface gravity than theatmospheric models do, so the surface gravity is ignoredfor our estimate of the radius. The evolutionary modelspredict the radius to be between ∼ R ⊙ foran effective temperature of 2800 ±
100 K, a metallicityof –0.5 ± ± × − for C k based on the best-fitting model to the flux-calibratedOSIRIS data ( § ± R ⊙ ,the distance estimate is 42 ± § ± ∼ g - T eff space so that a small changein temperature produces a small change in radius in thislow-temperature regime (Figure 20). At hotter tempera-tures, however, a small change in temperature produces alarge change in radius; the uncertainty in radius is there-fore impractically large for T eff & ±
100 K instead of 2800 K ± § ∼ ± ± ± < σ . Spectroscopic Parallaxes to Other Ultracool Subdwarfs
We applied this same spectroscopic parallax techniqueto four ultracool subdwarfs with parallaxes previouslydiscussed in § TABLE 8Spectroscopic Parallaxes for Ultracool Subdwarfs C k ( × − ) d esta d π b π Object { = R /d } (pc) (pc) Ref.LHS 377 3.6 ± ±
30 35 ± ± ±
10 46 ± ± ± ± ± ± ± References . — (1) Monet et al. (1992), (2) Schilbach et al. (2009) a Spectroscopic parallax. See § b Parallactic distance. Upper and lower limits on the distance errorsare averaged for clarity. –2.0 dex (which encompasses the moderately metal-poor“sd” class of ultracool subdwarfs), ages of ∼
10 Gyr, anderrors of ±
100 K for the effective temperatures. Usingthe effective temperatures from the atmospheric modelfits (Table 6), we obtained radii estimates of 0.16 ± R ⊙ , 0.12 ± R ⊙ , 0.100 ± R ⊙ , and 0.090 ± R ⊙ for LHS 377, LSR 2036+5059, SSSPM 1013–1356, and 2MASS 1626+3945, respectively. The result-ing distance estimates are listed in Table 8 along withthe parallactic distances. The estimates from spectro-scopic parallaxes are surprisingly accurate, although lessso at higher effective temperatures ( & .Our spectroscopic parallax technique can be comparedto the conventional photometric distance estimates whichrely on empirical relations between spectral type andabsolute magnitude. Polynomial fits to spectral type-absolute magnitude data for late-type objects typicallyproduce rms errors of ∼ ∼ ∼
10% agreement with published parallaxes), al-though this method has only been tested on a small sam-ple of subdwarfs. Extending this approach to a broaderrange of objects and wavelength ranges may be fruitful. SUMMARY AND CONCLUSION
We have presented a near-infrared spectroscopic anal-ysis of HD 114762B, the first benchmark ultracool sub-dwarf companion. The metallicity of HD 114762B is in-ferred from the primary star, which has a mean metal-licity of [Fe/H] = –0.71 based on independent estimatesfrom the literature. The spectral characteristics of HD114762B include suppressed H and K -band continuumas well as deeper 1.4 and 1.9 µ m H O bands comparedto solar-metallicity M dwarfs. The SpeX 1.00–2.35 µ m We note that Leggett et al. (2000) obtained an effective tem-perature of 2900 ±
100 K for LHS 377 using T eff -( V – I )-[M/H]relations from evolutionary models. A visual inspection of the best-fitting GAIA model shows poor agreement between the LHS 377spectrum and the model, so our value of 3200 K from the best-fitting
GAIA model may be overestimated. A reduced T eff forLHS 377 would lower the radius obtained from the evolutionarymodels, which would place the estimated distance closer to the ac-tual value. This may suggest that GAIA model fits to earlier-typeultracool subdwarfs are not reliable, although we have shown thatconsistent values were obtained for objects near d/sdM8-d/sdM9types ( § he Benchmark Companion HD 114762B 21spectrum does not, however, exhibit the extreme CIA H which is characteristic of the “sd” class of ultracool sub-dwarfs. In this respect, HD 114762B is more similar tomild subdwarfs, which are believed to have an intermedi-ate metallicity between dwarfs and subdwarfs. We assignit a spectral type of d/sdM9 ± µ m. Aspectral type later than sdM7.5 can also be inferred fromthe strength of the K I lines and the strength of the 1.4 µ m H O band compared to M-type subdwarf spectra.The measured luminosity places HD 114762B just abovethe hydrogen-burning minimum mass based on the evo-lutionary models of CB97.We use this unique benchmark object to test low-massmetal-poor atmospheric and evolutionary models. Thebest-fitting PHOENIX/
GAIA synthetic spectrum to ourOSIRIS J -band data has physical parameters that areconsistent with both the metallicity of the primary starand the high surface gravity of late-type objects. Fits tothe SpeX 1.00–2.35 µ m spectrum, however, yield physicalparameters that are inconsistent with these values. Wealso fit the models to low-resolution spectra of other late-type mild ultracool subdwarfs with similar spectral typesto HD 114762B. The best-fitting models’ surface gravityand metallicity are mutually inconsistent among the fourobjects and were likewise inconsistent for fits to differ-ent regions of the same spectrum. Fits to HD 114762B,however, yield consistent effective temperatures between2500-2800 K. We conclude that the metallicities and sur-face gravities derived from fitting atmospheric modelsto low-resolution near-infrared spectra of ultracool sub-dwarfs are not trustworthy, but that the effective tem-peratures are probably more reliable.Problems with atmospheric models at low masses andlow metallicities have already been noted in the litera-ture; only moderately good matches have resulted fromfits to the red-optical spectral regions of ultracool sub-dwarfs, even when applied over relatively short wave-length ranges (Schweitzer et al. 1999; L´epine et al. 2004;Burgasser et al. 2007). These same studies held themodel surface gravity fixed at log g = 5.0 or 5.5 whileonly allowing the temperature and metallicity to vary.The models should, however, be able to predict all threeparameters with no a priori assumption about any par-ticular one. In addition, the models should be able topredict roughly the same parameters for objects of thesame spectral type as well as for different spectral regionsof the same object. We have shown that neither appearsto be true for the ultracool subdwarfs we studied, mak-ing the discovery of benchmark metallicity calibratorslike HD 114762B ever more important.Our results suggest that the best method to determinethe metallicity of field ultracool subdwarfs may be touse the medium-resolution J -band region. The 1.18-1.35 µ m range encompasses metal-sensitive atomic absorp-tion lines as well as the metal-sensitive 1.4 µ m steamband. An interesting line that may be important forvery metal-poor ultracool subdwarfs is the Fe I µ m feature, which the GAIA models predict to be es-sentially independent of temperature and gravity, butwhich is strongly dependent on metallicity for [M/H] . –1.0. We found that fitting the individual absorptionlines rather than the entire 1.18-1.35 µ m spectrum ofHD 114762B produced temperatures and gravities that were more consistent with the values derived from theCB97 evolutionary models. Nevertheless, fitting the en-tire J -band spectrum and the individual absorption fea-tures yielded metallicities consistent with the primarystar and surface gravities consistent with empirical val-ues of late-type objects.The location of HD 114762B in the BCAH97/98 M K S vs J – K S color-absolute magnitude diagram is consistentwith the metallicity of the primary star. The metallic-ity and surface gravity inferred from GAIA fits to low-resolution near-infrared spectra are not trustworthy, butthe results from the color-magnitude diagram suggestthat the overall shape of the synthetic spectra are infact reliable, at least for the mass ( ∼ M ⊙ ) andmetallicity ([Fe/H] = –0.71) of HD 114762B.Additionally, we calculated the bolometric luminositiesand bolometric corrections for four known ultracool sub-dwarfs (LHS 377, LSR 2036+5059, SSSPM 1013–1356,and 2MASS 1626+3945) with parallaxes and whose near-infrared spectra were available in the SpeX Prism Spec-tral Library. Ultracool subdwarfs have higher luminosi-ties and smaller bolometric corrections than do ultracooldwarfs in the same spectral subclass. While unresolvedbinarity is a possibility, a hotter effective temperaturescale and/or a larger radius is a more likely explanationfor the overluminosity.Finally, we have also developed a technique to estimatethe distances to ultracool subdwarfs based on the avail-able models and a single near-infrared spectrum. Usingthe effective temperature from the best-fitting syntheticspectrum and an assumed age ( ∼
10 Gyr for objects withthick disk or halo kinematics), a radius can be inferredfrom evolutionary models. The radius can then be usedalong with the model scaling factor C k (equal to R /d )to derive a distance estimate to the object. We appliedthis technique to five ultracool subdwarfs with trigono-metric distances and obtained distance estimates accu-rate to <
10% of the parallactic distances, or about 2times better than estimates based on photometry alone.This technique is particularly useful for ultracool subd-warfs, whose ages can be constrained by their kinematics.It will be worthwhile to study HD 114762B at otherwavelengths, including obtaining thermal infrared pho-tometry ( λ > µ m) to better constrain the long-wavelength end of the model-fitting, and, if possible,optical spectra, which would allow for an independentspectral classification of this object. The dominant errorin our luminosity determination originates from the er-rors in the photometry used to flux calibrate the spectra.Better near-infrared photometry would therefore enablemore a precise luminosity estimate and, by extension,more precise predictions from the evolutionary models.We thank the anonymous referee for helpful feedback.We also thank Adam Burgasser for maintaining the SpeXPrism Spectral Library, as well as Peter Hauschildt andthe entire PHOENIX group for making their models pub-licly available; likewise we thank Isabelle Baraffe, GillesChabrier, France Allard, and Peter Hauschildt for thepublic release of their evolutionary models. This re-search has made use of the SIMBAD database, oper-ated at CDS, Strasbourg, France. This publication alsomakes use of data products from the Two Micron All2Sky Survey, which is a joint project of the University ofMassachusetts and the Infrared Processing and AnalysisCenter/California Institute of Technology, funded by theNational Aeronautics and Space Administration and theNational Science Foundation. MCL and BPB acknowl-edge financial support from the Alfred P. Sloan ResearchFellowship, NSF grant AST-0507833. The authors wish to recognize and acknowledge the very significant cul-tural role and reverence that the summit of Mauna Keahas always had within the indigenous Hawaiian commu-nity. We are most fortunate to have the opportunity toconduct observations from this mountain. Facilities:
Keck: II (OSIRIS), IRTF (SpeX)
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