STUDYING THE PHYSICAL DIVERSITY OF LATE-M DWARFS WITH DYNAMICAL MASSES^*,^†,^‡

We have monitored LP 349 − 25AB, LHS 1901AB, and Gl 569Bab with the AO system at the Keck II Telescope on Mauna Kea, Hawaii, using the facility NIR camera NIRC2 in its narrow field-of-view mode. At each epoch, we obtained data in one or more filters covering the standard atmospheric windows from the Mauna Kea Observatories (MKO) filter consortium (Simons & Tokunaga 2002; Tokunaga et al. 2002). For LP 349 − 25AB, we used LGS AO (Wizinowich et al. 2006; van Dam et al. 2006) when observing conditions allowed, and NGS AO otherwise (see Table 1). The LGS brightness, as measured by the flux incident on the AO wavefront sensor, was equivalent to a V ≈ 9.5–10.4 mag star. The tip-tilt correction and quasi-static changes in the image of the LGS as seen by the wavefront sensor were measured contemporaneously by a second, lower bandwidth wavefront sensor monitoring LP 349 − 25, which saw the equivalent of an R ≈ 14.3–14.6 mag star. For LHS 1901AB, we used NGS AO (Wizinowich et al. 2000; van Dam et al. 2004), and the incident flux on the wavefront sensor from LHS 1901 was equivalent to a V ≈ 13.0–13.4 mag star. For Gl 569Bab, the primary star Gl 569A (R = 9.4 mag) located 50 from the science target provided the NGS AO correction.

Our procedure for obtaining, reducing, and analyzing our images is described in detail in our previous work (e.g., Dupuy et al. 2009b, 2009c). Table 1 summarizes our observations of LP 349 − 25AB, LHS 1901AB, and Gl 569Bab. The binary separation, position angle (P.A.), and flux ratio were determined using the same three-component Gaussian representation of the point-spread function (PSF) as described in Dupuy et al. (2009c). At epochs where the binary was sufficiently well separated, we were also able to use the StarFinder software package (Diolaiti et al. 2000) to simultaneously solve for the PSF and binary parameters. As described in Dupuy et al. (2009c), we assessed systematic errors in both PSF-fitting procedures by applying them to artificial binary images constructed from images of PSF reference stars with similar FWHM and Strehl. We found good agreement between both methods, with StarFinder typically giving equivalent or smaller errors. We adopted the astrometric calibration of Ghez et al. (2008), with a pixel scale of 9.963 ± 0.005 mas pixel⁻¹ and an orientation for the detector's +y-axis of +013 ± 002 east of north. We applied the distortion correction developed by B. Cameron (2007, private communication), which changed our astrometry below the 1σ level. The resulting relative astrometry and flux ratios for LP 349 − 25AB, LHS 1901AB, and Gl 569Bab are given in Table 2.

For Gl 569Bab, we also used our Keck images to measure relative photometry between the primary star Gl 569A and Gl 569Bab at JHK, as there is no photometry published in the MKO system. We summed the flux in circular apertures with radii of 03–05. We used NIRC2 in its subarray mode to reduce the minimum allowed exposure time and thus avoid saturating the primary, which limited the size of the largest aperture we could use. However, in experimenting with even smaller apertures we found the same relative photometry to within 1σ. We used a portion of the array minimally affected by light from either the bright primary star or the binary to measure the median sky level, which was subtracted from our summed aperture fluxes. The relative flux of the binary in integrated light compared to Gl 569A was ΔJ = 4.15 ± 0.05 mag, ΔH = 4.14 ± 0.03 mag, and ΔK = 3.86 ± 0.03 mag. To compute absolute photometry for Gl 569B we applied these flux ratios to MKO photometry for Gl 569A, which was derived by converting its Two Micron All Sky Survey (2MASS) photometry to the MKO system using offsets computed from synthetic photometry of a SpeX prism spectrum of Gl 569A (A. Burgasser 2010, private communication). The conversions from 2MASS to MKO for J, H, and K were −0.03 mag, +0.02 mag, and −0.01 mag, respectively (all ⩽1.3σ compared to the 2MASS errors). Thus, the final MKO integrated-light photometry for Gl 569B was J = 10.75 ± 0.06 mag, H = 10.15 ± 0.04 mag, and K = 9.62 ± 0.03 mag.

Gl 569Bab was observed by HST/STIS on 2002 June 26 UT as part of a program to obtain resolved optical spectroscopy of ultracool binaries (GO-9499; PI: Martín). During acquisition, the STIS CCD imager took two images with the long-pass filter F28X50LP in which the binary is well detected and the primary star Gl 569A is saturated.⁶ We analyzed these images using our PSF-fitting routine based on the TinyTim model of the HST PSF (Krist 1995), as described in our previous work (e.g., Liu et al. 2008; Dupuy et al. 2009a). We adopted the pixel scale and distortion solution from the STIS Instrument Science Report 2001-02 (Walsh et al. 2001, 50.725 ± 0.056 mas pixel⁻¹).

We tested for systematic errors in our best-fit binary parameters by applying our PSF-fitting routine to artificial binary images created from STIS CCD images of single stars from HST calibration programs in Cycles 8 and 10 (CAL/STIS-8422 and 8924). To preserve the undersampled nature of the PSF, we created only artificial binaries separated by an integer number of pixels. The separation and instrumental P.A. of Gl 569Bab in the STIS images were 1.92 pixels and 31, so artificial binaries with Δ(x, y) = (0, 2) were an excellent representation of the science data. The single stars were ≈10× brighter in the STIS images than Gl 569Ba, so we scaled them to match the science data and then injected them into the actual science image to accurately simulate the noise. The binary images were injected at a distance of 5'' from Gl 569A, chosen to be comparable to Gl 569B's separation. For the final adopted errors we used the larger of the rms from the artificial binaries or the rms of the best-fit parameters to the science data. From our artificial binary tests, we found systematic offsets in separation (3.0 mas, 2.3σ), P.A. (02, 0.2σ), and flux ratio (0.15 mag, 5σ), which we applied to our best-fit binary parameters for Gl 569Bab. The final separation, P.A., and flux ratio we derived were 97.3 ± 1.3 mas, 940 ± 09, and 0.99 ± 0.03 mag (Table 2).

We retrieved archival images of LP 349 − 25AB obtained with the Very Large Telescope (VLT) at Paranal Observatory on five epochs spanning six months in 2006. These data were taken with the NACO AO system (Lenzen et al. 2003; Rousset et al. 2003) using the N90C10 dichroic and S13 camera. We adopt the pixel scale of 13.221 ± 0.017 mas pixel⁻¹ derived by B. Sicardy (2008, private communication)⁷ from observations of Pluto's motion compared to its known ephemeris and an orientation of the detector of 00 ± 01 (Forveille et al. 2005). We followed the same procedure for analyzing these data as in our previous work with VLT images (Dupuy et al. 2009a, 2009c). We registered, sky-subtracted, and performed cosmic-ray rejection on the raw archival images. We used the same analytic PSF-fitting routine as was used for the Keck data to fit the VLT images, with uncertainties determined from the standard deviation of measurements from individual dithers. The resulting best-fit parameters are summarized in Table 2.

Forveille et al. (2005) published two epochs of astrometry for LP 349 − 25AB, and we investigated the possibility of improving the precision of their measurements by applying our PSF-fitting procedure to their data, which is in public archives. The CFHT observations of LP 349 − 25AB on 2004 July 3 UT were not available in the CFHT archive because they were obtained during engineering time (T. Forveille 2010, private communication), but the VLT/NACO observations from 2004 September 24 UT are in the VLT archive. We measured a separation of 111.2 ± 0.3 mas, a P.A. of 566 ± 012, and a flux ratio at H band of 0.40  ±   0.03 mag. Our flux ratio and separation are in good agreement with those measured by Forveille et al. (2005), 0.38 ± 0.05 mag and 107 ± 10 mas, while our P.A. of 566 ± 012 is somewhat inconsistent with their 71 ± 05 (at 2.8σ). We tried using each of these measurements to fit the orbit and found that they gave consistent dynamical masses with a very similar χ² for the best-fit. Our higher precision measurement would enable the uncertainty in some of the orbital parameters to be improved by up to a factor of ≈2. However, we conservatively chose to use the published astrometry of Forveille et al. (2005) as their larger errors and P.A. offset may result from analysis of astrometric calibration data unavailable to us that was taken along with their observations.

Montagnier et al. (2006) published three epochs of astrometry for LHS 1901ABand the first two data sets are available in the CFHT archive. Unfortunately, not all of the astrometric calibration data were available in the archive, so independent measurements from these data cannot be used in the orbit fit because, e.g., the orientation of the detector at the time of those observations is not accurately known. Montagnier et al. (2006) found uncertainties of 5 mas and 05 for all three data sets. The rms scatter of our PSF-fitting measurements is comparable or slightly lower (3–4 mas and 04–06), and thus even with the needed calibration data a drastic improvement in precision seems unlikely. Thus, we use the published astrometry of Montagnier et al. (2006) when fitting the orbit of LHS 1901AB (Table 2).

For Gl 569Bab, we do not use any of the previously published astrometry. We performed our own analysis on the original Keck/NIRC2 images from Simon et al. (2006) following the method described in Section 2.1. Konopacky et al. (2010) published one epoch of astrometry for Gl 569Bab which is contemporaneous with our 2009 May data; we conservatively choose to exclude their data from our orbit fit, although it is consistent with our best-fit orbit. We do not include any of the Keck/KCAM or SCAM astrometry published by Lane et al. (2001) or Zapatero Osorio et al. (2004), as those cameras have not been rigorously astrometrically calibrated, unlike NIRC2 and the STIS CCD.

In addition to astrometry, which we use to determine orbits and thus dynamical masses, we have also obtained NIR spectra to perform tests of model atmospheres, as discussed in Sections 3 and 4. Using the NASA Infrared Telescope Facility (IRTF) spectrograph SpeX (Rayner et al. 2003), we obtained spectra of LP 349 − 25, LHS 1901, and Gl 569B on 2008 July 6, 2010 January 30, and 2010 March 3 UT, respectively. We used SpeX in cross-dispersed (SXD) mode, with five orders spanning 0.81–2.42 μm. For LP 349 − 25 we used a 05 slit (R = 1200), and for LHS 1901 and Gl 569B we used a 03 slit (R = 2000). We calibrated, extracted, and telluric-corrected the data using the SpeXtool software package (Vacca et al. 2003; Cushing et al. 2004). We used integrated-light photometry from 2MASS to flux-calibrate our spectra of LP 349 − 25 and LHS 1901. For Gl 569B, we used our own integrated-light photometry derived from our Keck images (Section 2.1) to flux calibrate its spectrum. We used the mean of the JHK scaling factors computed for each bandpass to place our spectra on an absolute flux scale.

Combining our Keck AO monitoring with published discovery data, we have observations spanning 5.9 yr for LP 349 − 25AB, 5.9 yr for LHS 1901AB, and 7.9 yr for Gl 569Bab. Following our previous studies, we have determined the orbital parameters and their uncertainties using both a Markov Chain Monte Carlo (MCMC) approach, described in detail by Liu et al. (2008), as well as the least-squares minimization routine ORBIT (Forveille et al. 1999). In addition, we have developed our own visual binary orbit fitting routine that utilizes the Levenberg–Marquardt algorithm as implemented in the MPFIT routine for IDL (Markwardt 2009). To determine uncertainties on the best-fit parameters from this routine, we have performed Monte Carlo simulations in which Gaussian noise is added to the data corresponding to their measurement uncertainties. We used the resulting distributions to determine the medians and standard deviations of the best-fit parameters. When multiple astrometric measurements were available from different bandpasses at a single epoch, we used the highest precision measurement in the orbit fit (see Table 2). The best-fit orbits are shown in Figures 1 and 2.

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We found essentially symmetric uncertainties in the MCMC-derived orbital parameters for LP 349 − 25AB. These parameters agreed to within <0.5% of those derived by our custom fitting routine and the errors agreed to within <15%. As an additional test of our Levenberg–Marquardt fitting routine, we found that the best-fit parameters from ORBIT also agreed to within <1%, and the errors derived from our Monte Carlo approach agreed to within <10% of the errors computed from the full covariance matrix in ORBIT. The orbital parameters and errors derived by our MCMC analysis and custom fitting routine are given in Table 3.

We experimented with including the five epochs of relative astrometry from Konopacky et al. (2010) when fitting the orbit of LP 349 − 25AB. If all of their data are included, the χ² becomes unrealistically large: χ² of 58.2 for 31 degrees of freedom (dof). This large χ² value is due to the fact that two of their measurements from 2007 December and 2008 May are extreme outliers from the best-fit orbit. (Indeed, their own orbit fit is inconsistent with these data as the Konopacky et al. 2010 orbit has a reduced χ² of 2.15, which is unrealistically large.) By excluding their most discrepant epoch (2008 May 30 UT), we were able to achieve a reasonable χ² (33.1 for 29 dof). Neither the orbital parameters nor their uncertainties change significantly after including the Konopacky et al. (2010) data. This is because their astrometry does not offer additional unique constraints on the orbit, as it was obtained contemporaneously with ours and is of lower precision by a factor of ≈4–10. Thus, we conservatively choose to exclude the Konopacky et al. (2010) astrometry from our analysis. Our best-fit total mass (M_tot) for LP 349 − 25AB is 0.1205  ±   0.0007 M_☉ (0.6%), and after including the 2.1% error in the parallax this becomes 0.120^+0.008_−0.007 M_☉ (6%).

From our MCMC analysis of LHS 1901AB, we found significant asymmetries in the posterior probability density distributions of the orbital period, semimajor axis, and eccentricity. The confidence limits on all orbital parameters are given in Table 3 and the distributions of these three parameters are shown in Figure 3. The orbital period and semimajor axis display a high degree of covariance as expected (e.g., see Section 3.2 of Dupuy et al. 2009b). There appear to be two slightly degenerate solutions, with one having a shorter period, lower eccentricity, and higher mass than the other. Our MCMC analysis enables us to treat this degeneracy properly by accounting for it in the confidence limits of these orbital parameters and the resulting dynamical mass. The difference in mass between these two solutions is very small (about 1.6%), insignificant compared to the 12% error contributed by the distance uncertainty. Our best-fit total mass for LHS 1901AB is 0.1944 ± 0.0028 M_☉ (1.4%), and after including the ^+4.0_−3.7% error in the parallax this becomes 0.194^+0.025_−0.021 M_☉ (12%).

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The orbital parameters we find from Gl 569Bab are all consistent with previously published orbits, with a singular exception. The semimajor axis we find (95.6^+1.1_−1.0 mas) is 4.3σ higher than the value of 90.4 ± 0.7 mas derived by Simon et al. (2006), and the Zapatero Osorio et al. (2004) and Konopacky et al. (2010) values are similarly discrepant (by 1.6σ and 3.7σ, respectively). Since all orbit determinations to date have been dominated by the nine epochs of astrometry from Keck KCAM and SCAM, the semimajor axis discrepancy implies that the pixel scale of one or both of these instruments was underestimated by ≈5%, resulting in systematically low semimajor axes. This is supported by the fact that the previously published NIRC2 astrometry from Simon et al. (2006) and Konopacky et al. (2010) is in good agreement with our best-fit orbit. Also, the HST/STIS measurement would be highly inconsistent with a value for the semimajor axis as low as previously found, showing that our semimajor axis is not simply due to a problem with the NIRC2 calibration.⁸ Since we find the same orbital period as in the previous work but a semimajor axis that is 5.4% larger, our dynamical total mass is significantly higher than previously found. This would be a 16% effect, but it is moderated somewhat by the revised Hipparcos parallax that is 1.6% (about 1σ) higher than the original value, which brings the mass down by 4.8% for a net change of 11%. Our best-fit total mass for Gl 569Bab is 0.140^+0.005_−0.004 M_☉and after accounting for the 1.6% parallax error this becomes 0.140^+0.009_−0.008 M_☉. Our MCMC analysis also reveals a slightly degenerate orbit solution with double-peaked distributions for the argument of periastron (ω) and P.A. of the ascending node (Ω) as shown in Figure 3. The degeneracy in these values is apparently not correlated with any other orbital parameters.

Gizis et al. (2000) used the integrated-light optical spectrum of LP 349 − 25 to derive a spectral type of M8.0 ± 0.5. Comparing our near-infrared spectrum of LP 349 − 25 to spectra of M dwarf standards from the IRTF Spectral Library (Cushing et al. 2005; Rayner et al. 2009), we find an infrared spectral type of M8. Without resolved spectroscopy of the binary, we cannot directly determine the spectral types of the individual components. However, we have used our photometry and the empirical SpT–absolute magnitude relations of Cruz et al. (2003, J band only) and Golimowski et al. (2004, L' band only) to estimate spectral types. We used the method described by Dupuy et al. (2009c), which accounts for both the measurement uncertainties and the intrinsic scatter in the empirical absolute magnitude relations. We found that the range of J-band absolute magnitudes allowed by our measurement errors exceeded the bounds of the Cruz et al. (2003) relation, and thus we base our estimates only on the L'-band relation. We estimate spectral types of M7.5 ± 1.0 for the primary and M8.0^+1.5_−1.0 for the secondary, which are consistent with the published integrated-light spectral type.

Reid et al. (2003) measured the integrated-light spectral type of LHS 1901 to be M6.5 and Lépine et al. (2009) measured M7.0. Our near-infrared spectrum is better matched by the M dwarf standard vB 8 (M7) than GJ 1111 (M6.5), thus we find an infrared type of M7 for LHS 1901. Using the method described above, the J-band absolute magnitudes of the individual components provide an estimated spectral type of M6.5^+1.0_−0.5 for both the primary and the secondary, consistent with measured integrated-light spectral types. The difference of zero subtype between the components is also consistent with our measured flux ratios and late-M dwarfs with known parallaxes. For example, the rms scatter among K-band absolute magnitudes for M6.5 dwarfs is 0.12 mag (cf. ΔK = 0.107 ± 0.007 mag for LHS 1901AB).

For Gl 569Bab, we adopt the spectral types of M8.5 ± 0.5 and M9.0 ± 0.5 derived by Lane et al. (2001). They used their resolved near-infrared spectra of the individual components to compute spectral indices and compared these values to field dwarfs of known spectral type. They found a difference of 0.5 subtypes between the two components and assigned the integrated-light spectral type of M8.5 from Henry & Kirkpatrick (1990) to the primary, resulting in a type of M9.0 for the secondary. These spectral types are consistent with those found by Martín et al. (2006, M9+M9) using resolved optical spectroscopy of Gl 569Bab from HST/STIS.

We computed the total bolometric luminosities (L_bol) of our sample binaries from their integrated-light spectra and photometry. In addition to our SpeX spectra, we used the L'- and M'-band photometry from Golimowski et al. (2004) and the 24 μm Spitzer photometry from Gautier et al. (2007) for LP 349 − 25, and we used the L'-band photometry from Forrest et al. (1988) for Gl 569B. For LHS 1901, we estimated a K − L' color of 0.56 ± 0.07 mag from the empirical relation of Dupuy et al. (2009a) to extend its spectral energy distribution (SED) to longer wavelengths. To accurately account for the SED at shorter wavelengths, we appended optical spectra, using the overlapping region of our SpeX spectra to determine the flux scaling. For LP 349 − 25 and Gl 569B, we used optical spectra from Reid et al. (2003) and Henry & Kirkpatrick (1990), respectively. For LHS 1901, we used the optical spectrum of the M7 standard vB 8 (Henry & Kirkpatrick 1990). We numerically integrated the spectra and photometry points, interpolating between the gaps in the data, extrapolating to zero flux at zero wavelength, and assuming a Rayleigh–Jeans tail beyond the last photometric point. We accounted for errors as described in Dupuy et al. (2009a), finding a total log(L_bol/L_☉) of −2.804^+0.026_−0.019 dex for LP 349 − 25, −2.67^+0.04_−0.03 dex for LHS 1901, and −3.212 ± 0.018 dex for Gl 569B.

We apportioned these total bolometric fluxes to the individual components by using the measured K-band flux ratio and the bolometric correction–SpT relation derived by Golimowski et al. (2004), properly accounting for uncertainties in the component spectral type estimates. The resulting individual luminosities are given in Table 4. For the components of Gl 569Bab, our L_bol values are in good agreement with the estimates from Lane et al. (2001). As in our previous work, we correctly account for the covariance between the individual luminosities (via the flux ratio) in the following analysis, allowing more precise determinations of relative quantities (e.g., ΔT_eff and the mass ratio).

Table 4. Measured Properties of Target Binaries^a

Property	LP 349 − 25			LHS 1901			Gl 569B
	A	B	Ref.	A	B	Ref.	Ba	Bb	Ref.
Mtot (M☉)	0.120+0.008−0.007		1, 2	0.194+0.025−0.021		1, 3	0.140+0.009−0.008		1, 4
Semimajor axis (AU)	1.94 ± 0.04		1, 2	3.70 ± 0.16		1, 3	0.923 ± 0.018		1, 4
d (pc)	13.2 ± 0.3		2	12.9 ± 0.5		3	9.65 ± 0.16		4
Spectral type	M7.5 ± 1.0	M8.0+1.5−1.0	1	M6.5+1.0−0.5	M6.5+1.0−0.5	1	M8.5 ± 0.5	M9.0 ± 0.5	5, 6
J (mag)	11.154 ± 0.025	11.506 ± 0.028	1, 7	10.631 ± 0.020	10.743 ± 0.020	1, 7	11.27 ± 0.06	11.78 ± 0.06	1
H (mag)	10.606 ± 0.023	10.932 ± 0.023	1, 7	10.197 ± 0.016	10.312 ± 0.016	1, 7	10.67 ± 0.04	11.21 ± 0.04	1
K (mag)	10.151 ± 0.018	10.458 ± 0.018	1, 7	9.796 ± 0.019	9.904 ± 0.019	1, 7	10.16 ± 0.03	10.64 ± 0.03	1
L' (mag)	9.80 ± 0.07	10.02 ± 0.07	1, 8	...	...		9.46 ± 0.10	9.95 ± 0.10	1, 9
J − K (mag)	1.00 ± 0.03	1.05 ± 0.03	1, 7	0.83 ± 0.03	0.84 ± 0.03	1, 7	1.11 ± 0.07	1.15 ± 0.07	1
H − K (mag)	0.46 ± 0.03	0.47 ± 0.03	1, 7	0.40 ± 0.02	0.41 ± 0.03	1, 7	0.50 ± 0.05	0.57 ± 0.05	1
J − H (mag)	0.55 ± 0.03	0.57 ± 0.04	1, 7	0.43 ± 0.03	0.43 ± 0.03	1, 7	0.61 ± 0.07	0.58 ± 0.07	1
K − L' (mag)	0.35 ± 0.07	0.44 ± 0.07	1, 7, 8	...	...		0.70 ± 0.10	0.68 ± 0.11	1, 9
MJ (mag)	10.55 ± 0.05	10.90 ± 0.05	1, 2, 7	10.09 ± 0.09	10.20 ± 0.09	1, 3, 7	11.35 ± 0.07	11.86 ± 0.07	1, 4
MH (mag)	10.01 ± 0.05	10.33 ± 0.05	1, 2, 7	9.65 ± 0.09	9.77 ± 0.09	1, 3, 7	10.74 ± 0.06	11.28 ± 0.05	1, 4
MK (mag)	9.55 ± 0.05	9.86 ± 0.05	1, 2, 7	9.25 ± 0.09	9.36 ± 0.09	1, 3, 7	10.24 ± 0.05	10.71 ± 0.05	1, 4
$M_{L^{\prime }}$ (mag)	9.20 ± 0.08	9.42 ± 0.08	1, 2, 8	...	...		9.54 ± 0.10	10.03 ± 0.11	1, 4, 9
log (Lbol/L☉)	−3.041 ± 0.024	−3.175 ± 0.026	1	−2.95 ± 0.04	−2.99 ± 0.04	1	−3.424 ± 0.019	−3.623 ± 0.020	1
Δlog (Lbol)	0.133 ± 0.019		1	0.044 ± 0.015		1	0.199 ± 0.016		1

Notes. ^aAll near-infrared photometry on the MKO system. References. (1) This work; (2) Gatewood & Coban 2009; (3) Lépine et al. 2009; (4) van Leeuwen 2007; (5) Henry & Kirkpatrick 1990; (6) Zapatero Osorio et al. 2004; (7) Cutri et al. 2003; (8) Golimowski et al. 2004; (9) Forrest et al. 1988.

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We used a variety of solar-metallicity model atmosphere grids to fit our integrated-light IRTF/SpeX spectra, summarized in Table 5. The two publicly available grids we used are Ames-Dusty (Allard et al. 2001) and PHOENIX-Gaia (Brott & Hauschildt 2005). We also used an improved version of Ames-Dusty that employs the same treatment of dust but with updated line lists for some important opacity sources such as FeH, CrH, and H₂O (see Section 3.2 of Rice et al. 2010); this "Gaia-Dusty" model grid is the same as that employed by Konopacky et al. (2010). Our fourth model grid Drift-PHOENIX (Witte et al. 2009) relies on yet another gas opacity data set and, more importantly, features improved dust opacities. The model treats the dynamics of the dust in a presently unrivaled level of detail by calculating the rate of seed formation and solving an actual growth rate equation system for gravitational settling of composite grains (Woitke & Helling 2003; Helling & Woitke 2006; Helling et al. 2008).

We fit model atmospheres to our spectra using the procedure outlined by Bowler et al. (2009). For every model spectrum, we found the optimal scaling factor to match the observed spectrum by minimizing the χ² statistic. The model spectrum with the lowest resulting χ² value gives the best-fit parameters for T_eff and log(g). For each spectrum, we fit individual wavelength ranges corresponding to the standard near-infrared bandpasses (YJHK). We also performed fits to the entire SED, both with and without the segment of the spectrum between 0.81 and 0.95 μm. This region of the spectrum is often excluded when fitting models to L and T dwarfs (e.g., Cushing et al. 2008) because it is strongly affected by the broad wings of the resonant K i doublet at 0.77 μm, which have long been difficult to model (e.g., Burrows & Volobuyev 2003) and can be impacted by dust modeling (Johnas et al. 2008). Such alkali lines are present but weaker in late-M dwarfs, and they may contribute to observed discrepancies with models between ≈0.7 and 0.9 μm for objects as early as L0 (Reiners et al. 2007).

The results of our model atmosphere fitting procedure are given in Table 6. We report fits both for our full wavelength range (0.81–2.42 μm) and for the NIR only (0.95–2.42 μm). We prefer the NIR SED fits for the following reasons: (1) the NIR SED fits are more consistent with the individual YJHK band fits (typically within one model grid step of 100 K, 0.5 dex in log(g)); (2) the full SED fits are systematically cooler by ≈100 K compared to the individual band fits, implying that the lowest signal-to-noise (S/N) portion of the spectrum from 0.81 to 0.95 μm has a disproportionate influence on the results; and (3) by adopting a 0.95 μm cutoff here, our results will be directly comparable to future work on L and T dwarfs that require such a cutoff because of the problems with K i lines.

Figure 4 shows the χ² contours of the fits to our observed NIR SEDs using all model spectra. The elongation of the contours in the log(g) direction indicates that gravity is less well constrained by our fits than effective temperature. We also note that there are occasionally local χ² minima in these plots that correspond to physically implausible parameters. For Drift-PHOENIX, the deviant χ² minimum occurs at very low temperatures (2000 K) and high gravities (log(g) = 6.0, which for masses of <0.08 M_☉ correspond to radii of <0.045 R_☉, more than a factor of 2 lower than evolutionary model predicted radii). For the other three model grids, χ² minima extend to higher temperatures (≈3300 K) and extremely low gravities (log(g) = 3.5, which for masses of >0.06 M_☉ correspond to radii of >0.7 R_☉). In the rare cases when the global minimum is found in one of these physically implausible regions (≈3% of fits; see Table 6), we select the second best-fitting model instead, and this always results in best-fit parameters from the prevailing solutions of T_eff = 2700–3000 K.

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The different grids of model atmospheres generally give very similar best-fit parameters despite their significantly different input assumptions. For example, the treatment of dust in the Drift-PHOENIX models is much more realistic than in other models, yet for our sample it yields the same T_eff values as other grids. Thus, it appears that the effects of dust at the warm temperatures of late-M dwarfs only subtly impact the resultant model spectra for our purposes. In fact, for the NIR SED fits (0.95–2.42 μm), all four sets of models give exactly the same T_eff.

Finally, we investigated how binarity impacts the atmospheric parameters derived from integrated-light spectra. We constructed artificial binary integrated-light spectra by summing individual IRTF/SpeX SXD spectra, both from our own spectra (e.g., summing the spectra of LP 349 − 25 and Gl 569B) and from publicly available spectra of the M7, M8, and M9 spectral standards vB 8, vB 10, and LHS 2924 (Cushing et al. 2005; Rayner et al. 2009). We fit these spectra both individually and summed, after scaling down the later type spectrum to best match the measured JHK flux ratios of LP 349 − 25AB and Gl 569Bab.⁹ Comparing the summed and input "primary" spectrum fits, we found that the best-fit values from individual bands were nearly identical (at most different by one grid step of 100 K or 0.5 dex). In some cases, we found that the summed spectra gave systematically lower temperatures of 100 K as compared to the input "primary" spectrum. However, this was not the case when the input spectra had JHK colors comparable to the components of LP 349 − 25AB and Gl 569Bab. We note that within each binary the components have very similar JHK colors, so we might expect that simulated component and summed spectra would give the same results. For example, the integrated-light J − K color of LP 349 − 25 is 1.02 mag, and its components are only different by ≈0.03 mag (J − K = 1.00 mag and 1.05 mag) despite the binary flux ratio of ≈0.3 mag (the H − K and J − H colors are even closer, Δcolor ≈ 0.01 mag).

In summary, our simulations show that the individual band fits should be unaffected by contamination from the spectrum of the secondaries in our sample binaries, and even if the SED fits are affected they will give T_eff values systematically lower by only 100 K. Given that our best-fit values of the NIR SEDs show no such systematic offsets from the band fits, we conclude that our fits to the integrated-light spectra accurately find the best-fit parameters of the primary component's spectrum.

We have considered whether the space motion and activity of our sample binaries can provide useful constraints on their ages. For LP 349 − 25, there are two discrepant measurements of its radial velocity (RV) in the literature: (1) Reiners & Basri (2009) derived −16.8 ± 2.0 km s⁻¹ from cross-correlation of their Keck/HIRES spectrum with the RV standard Gl 406 (M6) and (2) Konopacky et al. (2010) found a center-of-mass velocity of −8.0 ± 0.5 km s⁻¹ by fitting an orbit to their multi-epoch near-infrared RVs.¹⁰ Combining these RVs with the parallax and proper motion measured by Gatewood & Coban (2009; assuming 4 mas and 4° errors in their proper motion amplitude and P.A., respectively), we derive heliocentric velocities for LP 349 − 25 of (U, V, W) = (+4.8 ± 0.8, −17.2 ± 1.4, +5.2 ± 1.3) km s⁻¹ and (+1.9 ± 0.4, −11.2 ± 0.4, −0.5 ± 0.4) km s⁻¹, respectively. We adopted the sign convention for U that is positive toward the Galactic center and accounted for the errors in the parallax, proper motion, and RV in a Monte Carlo fashion. These space motions place LP 349 − 25 only 0.7σ or 0.9σ away from the mean of the ellipsoid defined by all other ultracool dwarfs with UVW measurements. (This sample is described in detail in Section 3.4 of Dupuy et al. 2009c.) Using the same method as in our previous work, we have also assessed LP 349 − 25's membership in the Galactic thin and thick disk populations using the Besançon model of the Galaxy (Robin et al. 2003), finding at most a 0.3% probability of thick disk membership using the Reiners & Basri (2009) RV and <0.1% for the Konopacky et al. (2010) RV. Thus, although the derived space motions are different, the conclusion that LP 349 − 25 is a normal thin disk member is unaffected. As a likely thin disk member, the age of LP 349 − 25 is essentially unconstrained by its kinematics. Finally, the fact that LP 349 − 25 is chromospherically active (log(L_Hα/L_bol) = −4.52; Gizis et al. 2000) could potentially provide an age constraint, as the activity of M dwarfs changes with age. However, the long lifetime of activity in such late-M dwarfs found by West et al. (2008) places only a weak constraint of ≲9 Gyr for the age of the LP 349 − 25AB system. Given the measured mass and luminosities of LP 349 − 25AB, it is in fact likely to be much younger, as discussed in detail in the following sections.

For LHS 1901, there is no published radial velocity, precluding the kinematic analysis described above. The proper motion and parallax of Lépine et al. (2009) provide a measurement of its tangential velocity (V_tan = 41.1 ± 1.6 km s⁻¹), indicating that LHS 1901 is typical of late-M dwarfs within 20 pc (V_tan = 29 ± 21 km s⁻¹; Faherty et al. 2009) and not likely to be a member of the thick disk or halo populations. Both Reid et al. (2003) and Lépine et al. (2009) have shown that LHS 1901 is not active, which is uncommon for nearby, late-M dwarfs. West et al. (2008) found that activity lifetime increases monotonically with M dwarf spectral type, and for M6 and M7 dwarfs these lifetimes are 7.0 ± 0.5 Gyr and 8.0^+0.5_−1.0 Gyr, respectively. Thus, the lack of activity seen in LHS 1901 (M6.5) indicates that its age is likely to be at least as old as 6 Gyr, the 2σ lower limit for the activity lifetime of M6 and M7 dwarfs.

The age of the M2.5 primary star in the Gl 569 triple system has been discussed extensively in the literature. Zapatero Osorio et al. (2004) find that the space motion of Gl 569A places it close to, but is not likely a member of, the Ursa Major moving group (300 Myr; Soderblom et al. 1993). However, they suggest that it may be a member of a stream of young A and F stars identified by Chereul et al. (1999), which have ages of 300–800 Myr as derived from Strömgren photometry. Simon et al. (2006) prefer a younger age of 100–125 Myr because Gl 569A seems to lie on the Pleiades sequence in the color–magnitude diagram of Luhman et al. (2005). We have considered whether the X-ray emission from Gl 569A may also place an independent constraint on the age of the system. We computed the X-ray flux of Gl 569A from its ROSAT count rate, using the Schmitt et al. (1995) conversion factor, finding F_X = (3.03 ± 0.30) × 10⁻¹² erg cm⁻² s⁻¹ (log L_X = 28.54). This lies between the median values of L_X for M dwarfs in the Pleiades (125 Myr) and Hyades (625 Myr) as determined by Preibisch & Feigelson (2005). The X-ray luminosity of Gl 569A is higher than ≈75% of Hyades objects and is fainter than ≈70% of Pleiades objects. This suggests an intermediate age of ∼300–450 Myr for the Gl 569 system, although its X-ray luminosity is consistent with the full range of ∼125–625 Myr at 1σ.

As described in detail by Liu et al. (2008) and Dupuy et al. (2009b), the total mass of a binary along with its individual component luminosities can be used to estimate the age of the system from evolutionary models. This age estimate can be quite precise (≈10%) when both components are substellar, since the luminosities of brown dwarfs depend very sensitively on age. This is the case for LP 349 − 25AB: the Lyon and Tucson models give consistent ages of 0.127^+0.021_−0.017 Gyr and 0.141^+0.023_−0.019 Gyr, respectively (Figure 5 and Table 7). The model-derived age of the system is consistent with its kinematics (Section 3.5) and the implications of such a young age for the LP 349 − 25AB system are addressed in detail in Section 5.

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Because LHS 1901AB is composed of two very low mass stars whose luminosities remain essentially constant over their main-sequence lifetime, the model-derived age for this system is not very precise. Lyon and Tucson models give consistent ages of 0.28^+9.72_−0.08 Gyr and 0.37^+9.63_−0.15 Gyr, respectively (Table 8). The large upper limits to the age distributions are set by the oldest age for which the model grids are computed (10 Gyr). These broad age distributions are consistent with the age constraint that comes from the lack of chromospheric activity in LHS 1901 (>6 Gyr; Section 3.5). Because the median model-derived ages are quite young, they would be inconsistent with an age as old as 6 Gyr, but a more precise parallax measurement is needed to test this. For example, if we fix the parallax at its presently measured value but improve its precision from 3.0 mas to 1.0 mas, an attainable goal with seeing-limited astrometry, this age discrepancy would rise to >2σ significance for the Lyon models.

Gl 569Bab has a higher mass than LP 349 − 25AB but lower component luminosities, and thus the Lyon and Tucson models give older ages of 0.46^+0.11_−0.07 Gyr and 0.51^+0.13_−0.08 Gyr, respectively (Figure 5 and Table 9). These are consistent with the age constraints from Gl 569A discussed in Section 3.5, with the exception of the age of 100–125 Myr proposed by Simon et al. (2006) based on its position on the color–magnitude diagram. Given the unavailability of such data for M dwarfs at ∼500 Myr, we suggest that Gl 569A may well be consistent with such an older age. Our model-derived age for the Gl 569Bab system is also in agreement with the age estimates from Lane et al. (2001) and Zapatero Osorio et al. (2004).

All of our target binaries have flux ratios near unity, thus enabling robust individual mass estimates with only a very weak dependence on model assumptions. For LHS 1901AB, the Lyon and Tucson models give mass ratios (q ≡ M_B/M_A) of 0.958^+0.015_−0.014 and 0.966^+0.011_−0.016, respectively. Thus, the model-derived individual masses (listed in Table 8) are nearly identical and their precision is dominated by the ⁺¹³₋₁₁% uncertainty in M_tot.

Because the model-derived ages for LP 349 − 25AB are quite young, the inferred mass ratios are somewhat further from unity than they would otherwise be for the measured 0.133 ± 0.019 dex luminosity ratio. The Lyon and Tucson models give consistent mass ratios of 0.872^+0.014_−0.018 and 0.863^+0.013_−0.019, respectively. This results in individual masses of 0.064^+0.005_−0.004 M_☉ and 0.056 ± 0.004 M_☉ for the components of LP 349 − 25AB (Lyon), placing both below the substellar boundary (∼0.070 M_☉; Chabrier et al. 2000) and LP 349 − 25B likely below the lithium depletion boundary (≈0.055–0.065 M_☉; Chabrier & Baraffe 1997). Konopacky et al. (2010) reported resolved RV measurements for LP 349 − 25AB and, combined with their astrometric orbit, found q = 2.0^+3.0_−0.7. This is nominally inconsistent with our model-derived mass ratio at 1.6σ, with their value corresponding to the secondary being more massive than the primary. In Figure 6, we show their measurements along with the RV curve predicted for mass ratios of 0.87 and 2.0, assuming their best-fit center-of-mass velocity of −8.0 ± 0.5 km s⁻¹. Fixing the orbital elements to the values from the astrometric orbit, we find χ² values for the RV measurements that are unreasonably small for both values of q (χ² = 0.5 for q = 2.0 and χ² = 1.7 for q = 0.87; 6 dof). This implies that the errors on the RV measurements are overestimated, and within these large errors both values of the mass ratio (0.87 and 2.0) are acceptable. We discuss the plausibility of these different mass ratios in detail in Section 5.

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For Gl 569Bab, the Lyon and Tucson models give consistent mass ratios of 0.866^+0.019_−0.014 and 0.886^+0.021_−0.017, respectively. This agrees with the spectroscopically determined mass ratio of 0.71^+0.19_−0.13 from Konopacky et al. (2010). Our slightly higher model-derived mass ratio results in somewhat more similar masses (0.075 ± 0.004 and 0.065^+0.005_−0.004 M_☉, Lyon) than implied by the directly measured mass ratio (0.082^+0.008_−0.009 and 0.059^+0.009_−0.007 M_☉). In both cases however, Gl 569Bb is expected to lie near the mass limit for lithium burning, which can be tested directly in the future with resolved optical spectroscopy of the Li i doublet at 6708 Å. In addition, absolute astrometric monitoring of the 2.4 yr orbital period binary can readily yield a refined measurement of the mass ratio: 1 mas astrometry would give a 5% mass ratio error, ∼4× better than spectroscopy.

Effective temperature (T_eff) is one of the most difficult properties to measure directly, as it requires a direct measurement of the radius and luminosity. To date, radius measurements remain elusive for very low mass stars and brown dwarfs in the field. Thus, when testing model predictions we are restricted to consistency checks between different methods of estimating T_eff. In Section 3.4, we estimated the temperatures of the primary components of our sample binaries by fitting their integrated-light spectra with atmospheric models. The best-fit Drift-PHOENIX and Gaia-Dusty model spectra are shown in Figure 7 plotted over the observed spectra. Evolutionary models provide a nearly independent temperature estimate by providing a prediction of the radius, which yields T_eff when combined with the measured L_bol.¹¹

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For LHS 1901A and LHS 1901B, Lyon evolutionary models give effective temperatures of 2860 ± 50 K and 2820⁺⁵⁰₋₄₀ K, respectively, and the Tucson evolutionary models give 100 K warmer temperatures of 2960 ± 30 K and 2930⁺³⁰₋₄₀ K. Both sets of models give consistent surface gravities of log(g)= 5.2 (cgs) for both components. All NIR atmospheric model fits gave systematically higher temperatures of 3000–3100 K and surface gravities near the predicted value (5.0 ± 0.5 dex). Given the nominal uncertainty (i.e., the model atmosphere grid step) of 100 K in the best-fit T_eff values, the largest discrepancy of ≈150 K with the Lyon evolutionary models is marginally significant. To provide an additional point of comparison for the T_eff estimates, we compiled all M6.5 and M7 dwarfs with effective temperatures derived by Gautier et al. (2007) using the nearly model-independent infrared flux method (Blackwell & Shallis 1977). We found a mean and standard deviation of 2710 ± 30 K for these objects, which is lower than T_eff estimates from both classes of models by 140–290 K, agreeing somewhat better with evolutionary models.

For LP 349 − 25A and LP 349 − 25B, Lyon models give effective temperatures of 2660 ± 30 K and 2520 ± 30 K, respectively, and the Tucson models give 120 K warmer temperatures of 2780 ± 30 K and 2640 ± 30 K. Lyon models predict surface gravities of about 4.9 (cgs) for both components, and Tucson models predict 5.0 (cgs). In comparison, atmospheric model fits of LP 349 − 25A gave 2800–3000 K and surface gravities near the predicted value (5.0 ± 0.5 dex).¹² Again, the Tucson evolutionary model T_eff is consistent with that derived from atmospheric models, while the Lyon evolutionary models are lower by ≈150 K.

For Gl 569Ba and Gl 569Bb, Lyon models give effective temperatures of 2430 ± 30 K and 2210 ± 30 K, respectively, and the Tucson models give 100 K warmer temperatures of 2530 ± 30 K and 2300 ± 30 K. Lyon models predict surface gravities of about 5.2 (cgs) for both components and Tucson models predict 5.3 (cgs). In comparison, atmospheric model fits of Gl 569Ba gave 2700–2900 K, with a wide range of surface gravities (log(g) = 4.5–6.0). These T_eff values are much higher than evolutionary models by 150–250 K and the broad range of surface gravities is in reasonable agreement.

In order to understand why temperature estimates from the two classes of models typically do not agree, we show our observed spectra in Figure 8 plotted with Drift-PHOENIX and Gaia-Dusty model spectra that have T_eff and log(g) values closest to the Lyon Dusty evolutionary model-derived values. This enables us to assess what spectral features prevented our fitting procedure from selecting these model spectra, which are very similar to the spectra used for the atmospheric boundary condition in the Lyon models.¹³ The NIR SED fits do not seem to be significantly affected by broadband colors (e.g., the better fitting models do not necessarily have J − K colors closer to what is observed). Rather, the shapes of the spectra, which are sculpted by broad molecular absorption bands, seem to determine the best-fit models.

• 1.  
  The disagreement in shape is most pronounced at the H band, where the observed spectrum is much flatter than the low-T_eff, low-gravity model spectra that would better correspond to evolutionary model-derived properties. This could be due partly to missing FeH opacity in the models between ∼1.5 and 1.7 μm (Reid et al. 2001; Wallace & Hinkle 2001; Cushing et al. 2003).
• 2.  
  The observed K-band shape is also flatter (i.e., the band peak at 2.2 μm is more suppressed) than in the low-T_eff, low-gravity model spectra.
• 3.  
  In the J band, the fit seems to be driven by the deep H₂O absorption band at 1.33 μm, which is too deep in the low-T_eff, low-gravity model spectra.
• 4.  
  In the Y band, the FeH 0 − 0 bandhead at 0.99 μm is too strong in the spectra corresponding to evolutionary model-derived properties. This could alternatively be interpreted as the overall continuum at the Y band being too high in the atmospheric models (e.g., missing opacity from wings of resonant alkali lines such as K i).

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In general, we have found that atmospheric models predict systematically higher effective temperatures than evolutionary models.¹⁴ This pattern is illustrated in Figure 9, which shows the T_eff estimates from each class of models plotted against each other. A systematic shift of ≈250 K would bring the models into agreement, with either the atmospheric model estimates being too warm or the evolutionary model estimates too cool (i.e., model radii too large by 15%–20%).¹⁵ We note that the observed discrepancy cannot simply be due to the fact that our method relies on fitting the integrated-light spectra of binaries. As discussed in Section 3.4, if the secondary component's flux impacted the best-fit model it would have the effect of lowering the derived T_eff, whereas we find temperatures that are too warm. This means that the discrepancy could only be larger than we observe. In addition, even a significant nonsolar metallicity for our binaries could not explain the observed temperature offset, as Bowler et al. (2009) showed that models of varying metallicity gave the same best-fit T_eff to within the model grid step of 100 K for the ultracool subdwarf HD 114762B (d/sdM9).

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We have considered what systematic errors could contribute to this discrepancy between evolutionary and atmospheric models. Currently available evolutionary models use much older versions of model atmospheres as their boundary condition and this could potentially result in systematic errors in their output. Saumon & Marley (2008) calculated evolutionary models both with and without the effects of dust clouds in the atmosphere and found at worst 6% differences in the resulting radii, which is much lower than what is needed to account for our observed discrepancy. We can also estimate how other input assumptions impact the evolutionary model output simply by comparing the predictions of the Lyon and Tucson models, which use different helium abundances, model atmospheres, and dust treatment. These two sets of models predict radii different by 7%–10% and temperatures different by ≈100 K for the objects in our sample—more than a factor of 2 lower than what is needed to fully account for the observed discrepancy. Presently available model atmospheres are more advanced than evolutionary models, but as shown in Figure 7 they cannot completely match our observed near-infrared spectra. Therefore, the resulting temperature values must harbor systematic errors at some level. Thus, we conclude that the model atmospheres must be responsible for at least part of the observed 250 K discrepancy. In fact, we suggest that the atmospheric models are more likely than the evolutionary models to be the primary source of the discrepancy, since roughly the same T_eff offset is observed over a wide range of masses, ages, and activity levels but the same temperature range. This proposition will readily be testable with eclipsing binary measurements given the large implied radius difference between models (15%–20%).

We computed resolved photometry for our sample binaries in the MKO photometric system to compare to Lyon model predictions. For Gl 569Bab, we used our integrated-light MKO photometry described in Section 2.1 along with the best available flux ratios from Table 2. For LP 349 − 25 and LHS 1901, we first converted their integrated-light 2MASS photometry to the MKO system by deriving correction terms from our near-infrared spectra. The resulting component magnitudes for all three binaries are listed in Table 4. Near-infrared colors on the MKO photometric system were derived from the Lyon models in the same fashion as other properties (e.g., T_eff), and the results are listed in Tables 7, 8, and 9. In Figures 10 and 11, we show the photometry of LP 349 − 25AB and Gl 569Bab compared to Lyon mass tracks computed for the individual masses of both components. The observed JHK L' photometry is significantly discrepant with model tracks at all ages, with models typically predicting ≈0.1–0.2 mag bluer JHK colors than observed and ≈0.1–0.2 mag redder K − L' colors. For LHS 1901AB, the JHK colors predicted by models are in much better agreement with the observations. The most discrepant color is H − K, which is only 0.07 mag (2.3σ) redder than predicted, and this may be due to missing FeH opacity in the H band. (We do not show a corresponding figure for LHS 1901AB as its components are main-sequence stars that evolve at essentially constant color.)

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Konopacky et al. (2010) have recently described an approach to test models of ultracool dwarfs with dynamical mass measurements that is somewhat different from ours. They use the measured individual luminosities along with T_eff estimates for each component to derive any other property (e.g., M_tot or age) from evolutionary models. (Their T_eff estimates are derived by fitting model atmospheres to resolved broadband photometry of the binaries.) This approach is similar to ours in that it uses two quantities to determine a third from evolutionary models, which is necessary because brown dwarfs occupy a mass–L_bol–age (or T_eff–L_bol–age) relation instead of the simpler mass–L_bol relation for stars on the main sequence. In Liu et al. (2008), we considered in detail such model tests using different combinations of these fundamental parameters and we ultimately chose to use mass and L_bol to derive other properties as these are the most directly measured quantities. However, any discrepancies we have found in the models should also manifest themselves in the T_eff–L_bol approach that has been adopted by Konopacky et al. (2010). In this section, we examine the results of analyzing our late-M dwarf measurements using the Konopacky et al. (2010) approach.

We first interpolated the Lyon and Tucson model grids at individual (T_eff, L_bol) points in the same fashion as Konopacky et al. (2010), with our temperatures coming from the Gaia-Dusty atmospheric model fitting of the NIR SED as described in Section 3.4. (This is the exact same model atmosphere grid as used by Konopacky et al. 2010.) In order to compute uncertainties in the model-derived properties using this approach, we used 10³ luminosity and temperature values randomly drawn from normal distributions corresponding to the measurement errors. We assumed 100 K errors in T_eff, equal to the model atmosphere grid step. The resulting evolutionary model-derived masses are plotted in Figure 12 against those derived by Konopacky et al. (2010).

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Our masses are significantly higher than theirs by about a factor of ∼2–4 because our T_eff estimates are systematically higher, while their luminosity measurements are very similar to ours. In order for models to match our much higher temperatures at similar luminosities, the masses must be larger and the ages somewhat older. The best illustration of this disagreement is the case of 2MASS J2206 − 2047A, as Konopacky et al. (2010) used essentially identical luminosities and photometry as Dupuy et al. (2009a), and the component fluxes are nearly identical, removing any ambiguity in fitting its integrated-light spectrum. Konopacky et al. (2010) found 2350 ± 80 K from fitting its resolved broadband photometry, while our best-fit spectrum from the very same grid of model atmospheres has a temperature of 2900 ± 100 K. Therefore, despite the other similarities in our inputs, we found a primary mass of 0.090^+0.006_−0.006 M_☉ using the Lyon Dusty evolutionary models, while they found 0.047^+0.016_−0.012 M_☉. Neither of these masses agrees with the measured mass (0.077^+0.012_−0.017 M_☉; Table 7 of Dupuy et al. 2009a): our mass is higher, and the Konopacky et al. (2010) mass is much lower. The differences between our derived masses for LP 349 − 25A and Gl 569Ba are even larger, as Konopacky et al. (2010) found extremely low masses for these objects (0.02 ± 0.02 M_☉ and 0.02^+0.02_−0.01 M_☉, respectively).¹⁶

Fundamentally, both the Konopacky et al. (2010) approach and our standard method to test models provide similar information: a consistency check on the temperatures from atmospheric and evolutionary models. The comparison presented here highlights how the amplitude, and even the sign, of discrepancies found between measured and model-predicted masses depend strongly on the input temperature estimates. Using the exact same atmospheric model grids, but different methods, our two groups have arrived at values of T_eff different by ≈650 K. This is due to the fact that the fitting method of Konopacky et al. (2010) relies solely on the broadband colors of models, whereas our method is driven by the shape of specific spectral features. As shown in Figure 10 and in our previous work (Liu et al. 2008; Dupuy et al. 2009a, 2009b, 2009c), the broadband colors of models consistently disagree with observations of objects of known mass over a broad range of spectral types. We also note that a significant disadvantage of the Konopacky et al. (2010) L_bol–T_eff approach is that evolutionary models occupy a very thin strip in this parameter space as opposed to L_bol–M. This resulted in many of our randomly drawn (L_bol, T_eff) measurements falling outside the range predicted by models (from 1.2% to 99.8% in the worst case), and we simply excluded these points from the analysis.

Konopacky et al. (2010) interpreted their observed discrepancies with theory as an error in the evolutionary model cooling curves, i.e., a mass problem. Using their method, we find an opposite mass discrepancy because our T_eff estimates are ≈650 K higher than theirs, resulting in higher masses. We suggest that the strong sensitivity of this model-testing method to the input T_eff estimates means that any observed discrepancies more readily identify problems in the way T_eff is determined from atmospheric models (i.e., a temperature problem), rather than a problem with evolutionary models.