CFBDSIR J1458+1013B: A VERY COLD (>T10) BROWN DWARF IN A BINARY SYSTEM^*,^†,^†

We imaged CFBDSIR J1458+1013 on UT 2010 May 22 and 2010 July 8 using the sodium LGS AO system of the 10 m Keck II Telescope on Mauna Kea, HI (Wizinowich et al. 2006; van Dam et al. 2006). We used the facility IR camera NIRC2 with its narrow field-of-view camera, which produces a 102 × 102 field of view. Conditions were photometric for both runs with excellent seeing: 05–06 and 03–05 FWHM in May and July, respectively, as measured by a differential image motion monitor located at the nearby Canada–France–Hawaii Telescope (CFHT). The LGS provided the wavefront reference source for AO correction, with the tip-tilt motion measured contemporaneously from the R = 15.5 mag field star USNO-B1.0 1002–0236935 (Monet et al. 2003) located 55'' away from CFBDSIR J1458+1013. The LGS brightness, as measured by the flux incident on the AO wavefront sensor, was equivalent to a V ≈ 9.6 and 10.3 mag star in May and July, respectively.

At each epoch, we obtained a series of dithered images by offsetting the telescope by a few arcseconds between each 1–2 images. The sodium laser beam was pointed at the center of the NIRC2 field of view for all observations. In 2010 May, we successfully resolved CFBDSIR J1458+1013 into a tight binary using the moderate-band CH₄s filter, which has a central wavelength of 1.592 μm and a width of 0.126 μm. In 2010 July, we obtained images with the J (1.25 μm), H (1.64 μm), and K (2.20 μm) filters from the Mauna Kea Observatories (MKO) filter consortium (Simons & Tokunaga 2002; Tokunaga et al. 2002).

The images were analyzed in a similar fashion as our previous LGS papers (e.g., Liu et al. 2006, 2008). The raw images were reduced using standard methods of flat fielding and sky subtraction. After rejecting individual images of poor quality, we registered and stacked the data into a final mosaic. The binary's flux ratios and relative astrometry were derived by fitting an analytic model of the point-spread function as the sum of two elliptical Gaussians to the images of the binary in the mosaics. We did not correct the relative astrometry for instrumental optical distortion, as the size of the effect as predicted from a distortion solution by B. Cameron (2007, private communication) is insignificant compared to our measurements uncertainties. We adopted a pixel scale of 9.963 ± 0.005 mas pixel⁻¹ and an orientation for the detector's +y-axis of +013 ± 007 for NIRC2 (Ghez et al. 2008).

To validate our measurements, we created myriad artificial binary stars from the science data themselves; given the large flux ratio of the binary, a scaled and shifted version of the primary star provides an excellent simulation of the data (e.g., Dupuy et al. 2009c). For each filter, our fitting code was applied to artificial binaries with similar separations and flux ratios as CFBDSIR J1458+1013AB over a range of position angles (P.A.s). The rms scatter of the simulations was adopted as our measurement error; the results also showed that any systematic offsets are small. The exceptions to this were the J- and H-band separation measurements, where the average systematic offset from the simulations was slightly larger than the rms scatter, and for these data sets we adopted the offset as the uncertainty. Table 1 presents our final Keck LGS measurements, and Figure 1 shows our Keck LGS images.

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We use our measured flux ratios and the published JHK_S photometry from Delorme et al. (2010) to derive resolved IR colors and magnitudes for CFBDSIR J1458+1013AB on the MKO system. Delorme et al. report data using the K_S-band filter while our Keck LGS imaging used the K-band filter; to compute resolved K-band photometry, we synthesize an integrated-light color of $(K-\mbox{$K_S$}) = -0.17\pm 0.02$ mag from the published spectra of ULAS J1238+09 (T8.5), Wolf 940B (T8.5), ULAS J0034−00 (T9), CFBDS J0059−01 (T9), and ULAS J1335+11 (T9) (Burningham et al. 2008, 2009; Warren et al. 2007; Delorme et al. 2008a). This is consistent with the color synthesized from the CFBDSIR J1458+1013AB spectrum itself (Section 2.3), but the signal-to-noise (S/N) in the K-band spectrum is quite low, so we use the average from the known T8.5 and T9 objects. To obtain the resolved CH₄s photometry from the published H-band data, we synthesizes a color (CH₄s − H) = −0.47 ± 0.03 mag directly from the integrated-light spectrum of CFBDSIR J1458+1013AB. Table 3 presents the resolved photometry.

To determine the distance to CFBDSIR J1458+1013AB, we acquired seven epochs of J-band imaging in 2009 and 2010 spanning 1.07 years using the CFHT 3.6 m telescope on Mauna Kea, HI. We used the facility wide-field near-IR camera WIRCam (Puget et al. 2004), which has four 2048 × 2048 Hawaii-2RG detectors, each with an approximate field of view of 10' × 10'. At each epoch, we placed the target near the center of the northeast detector. The data were taken with slightly different observing procedures as they originated from two independent programs: at three of the epochs, images of 60 s × 6 co-adds were obtained at 10 dither positions, and at the other four epochs, single 60 s images were obtained at 11 dither positions. The median FWHM of the data was 073 (min/max of 055/080). The target was always observed near transit, with a maximum deviation in airmass of 0.03. This reduces any systematic offsets in the target's astrometry from the differential chromatic refraction between the late-T dwarf science target and the background stars to <1 mas (T. J. Dupuy & M. C. Liu 2011, in preparation), well below the measurement noise.

Our WIRCam astrometry pipeline is described in detail by Dupuy (2010) and T. J. Dupuy & M. C. Liu (2011, in preparation) and successfully generates parallaxes that are in accord with previously published results for L and T dwarfs. We use SExtractor (Bertin & Arnouts 1996) to generate an astrometric catalog of all the sources in every individual image. We then cross-match detections across dithered images and use the mean and rms of each source to determine its final position and error at that epoch; we exclude any source that has fewer than seven detections or an S/N less than 7. We then cross-match these positions across different epochs, allowing for a full linear transformation in the astrometry to account for scale and orientation changes in the instrument. (WIRCam is installed and removed from the telescope for each observing run.) After an initial iteration, we remove any stars with large proper motions (>50 mas yr⁻¹) or parallaxes (>3σ) from the epoch-matching fit. Finally, we absolutely calibrate our astrometry by matching to 2MASS to determine the overall scale, orientation, and shear. For this target, 8 of our 72 reference stars were well detected in 2MASS and had sufficiently low proper motion (<30 mas yr⁻¹) to be used for absolute calibration.

We then fit for the proper motion and parallax of every source in the field. We measured a proper motion of 432 ± 6 mas yr⁻¹ at a P.A. of $154.2\pm 0.7\deg$ for CFBDSIR J1458+1013, in good agreement with the Delorme et al. (2010) measurement of 444 ± 16 mas yr⁻¹ and 1575 ± 21 from seeing-limited images. CFBDSIR J1458+1013 was the only object we measured in the field with a significant parallax (Figure 3), 42.4 ± 4.5 mas relative to the reference stars. (To our knowledge, this is the faintest object outside the solar system with an optical or IR parallax measurement; cf., Marocco et al. 2010.) To account for the mean parallax of our reference stars, we used the Besançon model of the Galaxy (Robin et al. 2003) to simulate the distance distribution of sources in the direction of CFBDSIR J1458+1013 within the magnitude range of our images (15.1 mag <J < 20.1 mag). We find a mean parallax of 0.9 ± 0.1 mas from the Galaxy model, with the error accounting for the sampling variance due to the finite number of reference stars. This results in an absolute parallax of 43.3 ± 4.5 mas for CFBDSIR J1458+1013 (23.1 ± 2.4 pc), in good agreement with the original 23 pc photometric estimate by Delorme et al. (2010). The resulting tangential velocity (47 ± 5 km s⁻¹) is higher than the median for field T dwarfs, but not extraordinary given the observed velocity dispersion of the field objects (e.g., Vrba et al. 2004; Faherty et al. 2009). Table 2 contains our astrometry results.

Table 3. Properties of CFBDSIR J1458+1013AB

Property	Component A	Components A + B	Component B
Integrated-light spectral type		T9.5
d (pc)		23.1 ± 2.4
Projected separation (AU)		2.6 ± 0.3
vtan (km s−1)		47 ± 5
J (mag)	19.86 ± 0.07		21.66 ± 0.34
CH4s (mag)	19.73 ± 0.10		21.90 ± 0.15
H (mag)	20.18 ± 0.10		22.51 ± 0.16
K (mag)	20.63 ± 0.24		22.83 ± 0.30
J − H (mag)	−0.32 ± 0.12		−0.85 ± 0.37
J − K (mag)	−0.78 ± 0.25		−1.18 ± 0.45
CH4s − H (mag)	−0.45 ± 0.14		−0.61 ± 0.22
H − K (mag)	−0.45 ± 0.26		−0.32 ± 0.34
M(J) (mag)	18.04 ± 0.23		19.84 ± 0.40
M(CH4s) (mag)	17.91 ± 0.24		20.08 ± 0.27
M(H) (mag)	18.36 ± 0.24		20.69 ± 0.27
M(K) (mag)	18.82 ± 0.33		21.02 ± 0.37
Near-IR spectral type	T9.5		>T10
$\log (\mbox{$L_{\rm bol}$}/\mbox{$L_{\odot }$})$ (dex)	−6.02 ± 0.14		−6.74 ± 0.19
Evolutionary Model Results for 1.0 and 5.0 Gyr: Lyon/COND Models and Lbol
Mass (MJup)	12.1 ± 1.9, 31 ± 4		5.8 ± 1.3, 14 ± 3
Total mass (MJup)		18 ± 2, 45 ± 5
q (≡ MB/MA)		0.48 ± 0.14, 0.45 ± 0.12
Teff(K)	556 ± 48, 605 ± 55		360 ± 40, 380 ± 50
log (g) (cgs)	4.45 ± 0.07, 5.00 ± 0.08		4.10 ± 0.10, 4.58 ± 0.11
Orbital period (yr)		35+28− 10, 22+18− 6
Evolutionary Model Results for 1.0 and 5.0 Gyr: Burrows et al. (1997) Models and Lbol
Mass (MJup)	13 ± 2, 36 ± 4		6.8 ± 1.5, 17 ± 4
Total mass (MJup)		20 ± 3, 53 ± 6
q (≡ MB/MA)		0.53 ± 0.15, 0.47 ± 0.13
Teff(K)	550 ± 50, 600 ± 60		350 ± 40, 380 ± 50
log (g) (cgs)	4.47 ± 0.07, 5.06 ± 0.07		4.14 ± 0.10, 4.65 ± 0.12
Orbital period (yr)		33+27− 9, 20+17− 6
Evolutionary Model Results for 1.0 and 5.0 Gyr: Burrows et al. (2003) Models and M(J)
Mass (MJup)	11.1 ± 0.7, >25		7.6 ± 0.6, 18.8 ± 1.3
Total mass (MJup)		18.7 ± 0.9, >44
q (≡ MB/MA)		0.68 ± 0.07, <0.75
Teff(K)	479 ± 20, >483		386 ± 15, 407 ± 15
log (g) (cgs)	4.37 ± 0.03, >4.85		4.19 ± 0.04, 4.69 ± 0.03
Orbital period (yr)		34+28− 10, <22

Notes. All infrared photometry on the MKO photometric system. For the 5 Gyr Burrows et al. (2003) evolutionary model fits, component A is brighter in M(J) than the model grid, so its derived physical parameters are listed as limits.

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We obtained integrated-light near-IR spectra of CFBDSIR J1458+1013AB with the X-Shooter spectrograph on VLT-UT2 (Program 085.C-0805). The observations were carried out in four 1 hr observing blocks (hereafter OB) from 2010 May 5 to July 9, achieving a total exposure time on target of 11700 s, split into eight A–B nods on the slit of 2 × 732 s each. The slit width was 12, and the seeing varied between 08 and 10. We chose a large slit size, because direct acquisition of the target was impossible and we had to acquire using a blind offset from a reference source.

The spectra for each OB were reduced using the standard ESO X-Shooter pipeline (Modigliani et al. 2010), which produced a two-dimensional, curvature-corrected spectrum of the NIR arm of X-Shooter (1.0–2.5 μm). No signal was detected in the UVB and visible arm of the instrument. The trace was extracted using our own IDL procedures, using Gaussian boxes in the spatial dimension at each wavelength. A similar Gaussian extraction box was used at about five times the FWHM of the trace to obtain the noise spectrum of the sky. The resulting one-dimensional spectrum from each science target OB was then divided by the spectra of telluric stars observed just before or after, reduced and extracted using the same pipelines.

The resulting four spectra from all the OBs were then median combined to produce the final science spectrum. Since the resulting spectrum (with R ≡ λ/Δλ ≈ 4300) has low S/N and most analyses of late-T dwarfs have used much lower resolution spectra, we smoothed the spectra using a weighted average over 50 pixels in the wavelength dimension (corresponding to 3 and 5 nm at J-band and K-band, respectively), weighting by the inverse variance of the extracted sky spectrum. This approach uses the full spectral resolution of X-Shooter to give a much lower weight to wavelengths affected by telluric emission lines, thus improving the S/N with respect to simple unweighted binning using the average or median.

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Given the large wavelength range covered by X-Shooter, seeing variation in the spectral direction can led to wavelength-dependent slit losses. Therefore, we flux-calibrated the spectrum using JHK_S photometry of CFBDSIR J1458+1013 from Delorme et al. (2010) and Y-band data from the UKIDSS Data Release 8 (Y = 20.58 ± 0.21 mag, on the Vega system). Following Delorme et al. (2008b), we applied small scaling factors to each of the broadband wavelength ranges so that the magnitudes derived from the CFBDSIR J1458+1013 spectrum matched the photometry. The final spectrum is shown in Figure 4.

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Examination of the Digitized Sky Survey images shows no plausible optical counterpart if component B were a background object. Similarly, the z-band imaging from 2004 July presented in Delorme et al. (2010) shows no star to a depth of z ∼24 mag, 2–3 mag deeper than expected for a background M star if it had the near-IR magnitude of component B. In fact, the high proper motion of the source means that our two Keck epochs separated by 1.5 months are sufficient to confirm the two components are physically associated. (For the 2010 July epoch, we choose the Keck H-band astrometry, which has the smallest errors.) Figure 2 shows the large expected motion for component B if it were an object at infinite distance, given our measured proper motion and parallax for CFBDSIR J1458+1013. (The proper motion dominates over the parallax.) In contrast, the relative positions of the two components do not change between our observations. The length of the vector between the observed and predicted change is non-zero at 9.1σ. Thus, we conclude the two components are physically associated.

3.2.1. Comparison with Known Late-T Dwarfs

3.2.2. Spectral Index Analysis with Solar-metallicity Models

To quantify the absorption features of CH₄, H₂O, CIA H₂, and possibly NH₃, we calculated spectral indices previously used for T dwarfs (Burgasser et al. 2006b; Warren et al. 2007; Delorme et al. 2008a). The measurements (Table 4) indicate that CFBDSIR J1458+1013A has some of the strongest absorption features seen in the near-IR spectra of late-T dwarfs, exceeded by only UGPS J0722−05 for the W_J and NH₃-H indices. Given the ≈2 mag flux difference between components A and B, it is reasonable to consider the integrated spectrum is dominated by the primary (as discussed below).

We use the solar-abundance BT-Settl-2009 models (Allard & Freytag 2010) to estimate T_eff and log (g) for component A from the index measurements. We compensate for the systematic errors of the models (e.g., Leggett et al. 2007; Liu et al. 2008) by scaling their index predictions to match those measured for the T8.5 benchmark Wolf 940B (Burningham et al. 2009). Its high-quality spectrophotometry, parallax, and age estimate from its primary star enable a precise estimate of its properties using evolutionary models (T_eff = 575 K; log (g) = 4.75, [M/H] = 0 from Burningham et al. 2009; see also Leggett et al. 2010b). With this approach, the temperatures and gravities for the >T8 dwarfs derived from an index–index plot broadly agree with the values derived from the analysis of their full near-IR spectra (Burgasser et al. 2006a; Warren et al. 2007; Delorme et al. 2008a; Burningham et al. 2008; Lucas et al. 2010).

Since the systematic errors in the models in this low-temperature regime are likely much larger than the measurement errors, we use the model grid only for relative estimates of temperature and gravity differences among the late-T dwarfs, not absolute measurements. Figure 5 indicates that CFBDSIR J1458+1013A is as cool as UGPS J0722−05 and ≳50 K or more cooler than the other >T8 dwarfs. (The caveat is that the model analysis assumes a single metallicity for all the objects, consistent with the similarity in Y-band shapes discussed above.) The plot also puts CFBDSIR J1458+1013A at a higher (≳0.5 dex) surface gravity than the other objects, as expected from the highly suppressed K-band flux. The higher gravity suggests that CFBDSIR J1458+1013A is older and higher mass than UGPS J0722−05, consistent with their relative tangential velocities (47 ± 5 km s⁻¹ and 19 ± 3 km s⁻¹, respectively). Of course, tangential velocities are only a statistical proxy for age so this comparison should be treated accordingly.

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To assess the impact of component B on the integrated-light spectrum, we used the BT-Settl-2009 model atmospheres to create composite spectra. We chose models with 600–700 K for the primary and 400–500 K for the secondary, matching pairs of models with 200–250 K temperature differences and the same surface gravity. The pairs of spectra were scaled to agree with the observed J-band or H-band flux ratio and summed to form artificial composites. We then added noise based on the measured S/N of the VLT spectrum and measured the same indices. We found that the blended composites had very similar index values as the input primary spectrum alone, with systematic effects at the 5%–20% level, typically 10%. Such amplitudes are not sufficient to affect the interpretation of Figure 5.

3.2.3. Model Atmosphere Fitting

To further place CFBDSIR J1458+1013AB in context, we perform a homogeneous comparison of the near-IR spectra of very late T dwarfs to low-temperature atmospheric models. We restrict our analysis to ⩾T8 dwarfs with parallaxes, excluding the aforementioned possible binary T8 dwarf 2MASS J0939−24, but also include two benchmark T7.5 dwarfs (Table 5). We use the published J-band photometry to establish the absolute flux calibration of the spectra, again assuming the primary dominates the integrated-light spectrum. For CFBDSIR J1458+1013AB, we again assumed that the integrated-light spectrum is dominated by component A and normalized it using the resolved J-band photometry of component A.

Table 5. Atmospheric Model Fits to Late-T Dwarfs with Parallaxes

Name		Ames-Cond					BSL03					BT-Settl-2009
		Teff	log g	Ra	dspec (σmc, σtot)b		Teff	log g	Rc	dspec (σmc, σtot)b		Teff	log g	Rc	dspec (σmc, σtot)b	dπ (σπ)
	Ref	(K)	(cgs)	(RJup)	(pc)		(K)	(cgs)	(RJup)	(pc)		(K)	(cgs)	(RJup)	(pc)	(pc)	π Ref
Gl 570D (T7.5)	1	800	4.5	1.06	6.8 (0.1, 1.4)		797d	4.80d	0.996	14.8 (0.2, 2.6)		900	5.0	0.903	7.9 (0.2, 1.4)	5.84 (0.03)e	13
HD 3651B (T7.5)	2, 3	800	4.5	1.06	13.1 (0.2, 2.5)		797d	4.80d	0.996	14.1 (0.2, 2.1)		850	4.5	1.07	15.8 (0.2, 2.3)	11.06 (0.04)	13
2MASS J0415−09 (T8)	4	800	5.0	0.89	6.29 (0.09, 2.4)		703	4.07	1.33	6.50 (0.1, 2.9)		600	5.5	...  f	...  f	5.65 (0.09)	14
Ross 458C (T8.5)	5, 6	900	4.0	1.24	23.1 (0.09, 3.2)		859d	4.24d	1.27	24.2 (0.1, 2.5)		850	4.5	1.07	17.8 (0.1, 2.6)	11.7 (0.2)	13
Wolf 940B (T8.5)	7	800	4.5	1.06	30.4 (0.3, 5.5)		483d	4.85d	0.924	8.37 (0.07, 2.9)		650	5.0	0.874	15.5 (0.1, 3.7)	12.5 (0.7)	15
CFBDS J0059−01 (T9)	8	700	4.5	1.04	20.2 (0.3, 4.1)		483d	4.85d	0.924	8.01 (0.1, 2.7)		600	5.0	0.879	11.5 (0.2, 3.3)	9.2 (0.4)	16
ULAS J0034−00 (T9)	9	800	4.5	1.06	30.5 (0.5, 5.8)		686	4.66	1.04	24.7 (0.4, 5.8)		750d	4.0d	1.17	30.7 (0.5, 4.5)	12.8 (0.6)	16, 17
ULAS J1335+11 (T9)	10	800	4.5	1.06	26.4 (0.2, 5.2)		686	4.66	1.04	20.6 (0.1, 5.0)		800d	4.0d	1.21	29.9 (0.1, 4.6)	10.3 (0.3)	16
CFBDSIR J1458+1013AB (T9.5)g	11	700	4.5	1.04	46.8 (1.0, 10)		555d	4.83d	0.946	27.2 (0.9, 7.6)		700	5.0	0.880	40.0 (0.8, 9.3)	23.1 (2.4)	18
UGPS J0722−05 (T10)	12	700	4.5	1.04	9.9 (0.1, 2.0)		421d	4.72d	0.961	2.62 (0.02, 1.4)		600	5.0	0.879	5.6 (0.1, 1.6)	4.1 (0.5)	12

Notes. Best-fitting Ames-Cond (Allard et al. 2001), BSL03 (Burrows et al. 2003), and BT-Settl-2009 (Allard & Freytag 2010) model spectra to the combined 1.15–1.35 μm, 1.45–1.6 μm, and 1.95–2.25 μm regions of the observed spectra. ^aRadius derived from an interpolated grid of Lyon/Cond evolutionary models. This value corresponds to the best-fitting T_eff and log g Ames-Cond atmospheric model. ^bModel-derived spectroscopic distance estimate based on the method of Bowler et al. (2009). σ_mc denotes the Monte Carlo derived distance error associated with the best-fitting atmospheric model and incorporates measurement and flux-calibration errors. σ_tot is the Monte Carlo derived total measurement error in the distance, based on the measurement errors and assuming 1σ uncertainties of 50 K and 0.25 dex in T_eff and log g in the model atmosphere fits. ^cRadius computed using the best-fitting T_eff and log g and the power-law fit to R(T_eff, log g) from Equation (1) of Burrows et al. (2003). ^dBest-fit model is at the edge of the model grid. ^eDistance to the primary Gl 570 A. ^fThe best-fitting model atmosphere parameters are outside the grid of evolutionary models, so there is no corresponding radius or distance estimate. ^gIntegrated light spectrum. References. (1) Burgasser et al. 2000; (2) Mugrauer et al. 2006; (3) Luhman et al. 2007; (4) Burgasser et al. 2002; (5) Goldman et al. 2010; (6) Scholz 2010b; (7) Burningham et al. 2009; (8) Delorme et al. 2008a; (9) Warren et al. 2007; (10) Burningham et al. 2008; (11) Delorme et al. 2010; (12) Lucas et al. 2010; (13) van Leeuwen 2007; (14) Vrba et al. 2004 (15) Harrington & Dahn 1980 (16) Marocco et al. 2010; (17) Smart et al. 2010; (18) this work.

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We fit three grids of atmospheric models: (1) the Ames-Cond models (Allard et al. 2001) spanning $\mbox{$T_{\rm eff}$}= 400\hbox{--}1200$ K ($\Delta \mbox{$T_{\rm eff}$}=100$ K) and $\mbox{$\log (g)$}\ = 4.0\hbox{--}6.0$ ($\Delta \mbox{$\log (g)$}\ = 0.5$), (2) the Tucson models (Burrows et al. 2003, hereafter BSL03), which are irregularly gridded between $\mbox{$T_{\rm eff}$}\approx 150\hbox{--}850$ K and $\mbox{$\log (g)$}\approx 3.3\hbox{--}4.8$ (cgs), and (3) the aforementioned BT-Settl-2009 models spanning 400–1200 K and log (g) =4.0–6.0 dex ($\Delta \mbox{$T_{\rm eff}$}=50$ K above 600 K and 100 K below 600 K). All grids are for solar metallicity compositions and chemical equilibrium. The models were Gaussian smoothed to the resolution of the data and interpolated onto the wavelength grid of the observed spectrum.

The atmospheric models have known systematic errors, particularly in the Y band and the red side of the H band as a result of imperfect modeling of the pressure-broadened K i doublet in the far-red and the incomplete list of CH₄ lines, respectively. We therefore restrict our fits to the 1.15–1.35 μm, 1.45–1.6 μm, and 1.95–2.25 μm spectral regions. The model emergent spectra are scaled to the flux-calibrated spectra by minimizing the χ² statistic (e.g., Equations (5) and (6) of Bowler et al. 2009). For observed spectra without measurement errors (CFBDS J0059−01 and UGPS J0722−05), we perform a least-squares fit to the data (Equation (1) of Stephens et al. 2009 with w_i = 1, and the scaling factor is solved for by equating the derivative of G₁ with zero).

The best-fitting models are summarized in Table 5 and plotted in Figure 6. The Ames-Cond models yield effective temperatures between 700–800 K and a gravity of 4.5 dex for almost all objects; the temperatures for the latest-type objects are ≈100–200 K hotter than analyses from their discovery papers (which use variants of the BT-Settl models). The BSL03 models typically produce much cooler temperatures (420–800 K) and somewhat higher gravities (4.6–4.8 dex), with the results for the earlier-type objects often at the edge of the model grid, indicating a broader set of models is probably needed. The BT-Settl-2009 model results are usually intermediate between those from the other two models. The fits show that CFBDS J0059−01, CFBDSIR J1458+1013AB, and UGPS J0722−05 are the three coldest objects in the sample, with the Ames-Cond models indicating all have comparable temperatures while the BSL03 and BT-Settl-2009 models indicate that CFBDSIR J1458+1013AB is the warmest. (Note that in terms of the absolute values derived from the fitting, the analysis in the Appendix on the resulting spectroscopic distances suggests that the temperatures may be somewhat overestimated.)

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Again, to assess the effect of component B on the analysis of the integrated-light spectrum, we took the artificial noisy composite spectra described in Section 3.2.2 and applied the same model atmosphere fitting procedure. We found that the T_eff's determined for the composite spectra were at worst 50 K colder than those of the input primary spectrum alone, and often the same. The fitted surface gravities were the same for the composites and the primary spectrum. Thus, the blended light from the much fainter secondary appears to have little consequence for our analysis, as expected.

We also examine another method to derive physical properties from atmospheric models. Although the distance estimates using the scaling factor (R/d)² may differ substantially from the true distances, the known distance can be used in combination with the scaling factor, a grid of radii, and a likely age range to infer a temperature and mass range for the object. This is effectively using the scaling factor as a proxy for temperature, and it has the benefit of relying on the absolute level of the model emergent flux density rather than the detailed shape of the synthetic spectrum, which may have systematic errors. Using the results from Table 5, we compute the range of effective temperatures and masses for the three sets of models. The results are shown in Table 6 assuming an age range of 1–10 Gyr, except for Ross 458C where we assume an age of 0.1–1.0 Gyr (Goldman et al. 2010). The BSL03 models are limited at high gravities by an upper mass cutoff of 25 M_Jup so they only provide lower limits on T_eff and mass. The resulting range of temperatures and masses is similar to those estimated in previous work (Liu et al. 2007; Burningham et al. 2008; Delorme et al. 2008a). This analysis indicates that CFBDSIR J1458+1013A has a similar effective temperature (540–660 K) and mass (12–42 M_Jup) to the T9 dwarfs ULAS J0034−00 and ULAS J1335+11, with CFBDS J0059−01 and UGPS J0722−05 being perhaps slightly cooler, in accord with the relative ordering of their absolute magnitudes.

Table 6. Physical Properties Derived from Model Atmospheres and Parallactic Distances

Name	Ames-Cond				BSL03				BT-Settl-2009
	Teff	log g	M		Teff	log g	M		Teff	log g	M
	(K)	(cgs)	(MJup)		(K)	(cgs)	(MJup)		(K)	(cgs)	(MJup)
Gl 570D (T7.5)	780–880	4.7–5.4	21–54		>520	>4.4	>13		760–880	4.7–5.4	21–54
HD 3651B (T7.5)	780–880	4.7–5.4	21–54		>700	>4.6	>22		740–860	4.7–5.4	20–54
2MASS J0415−09 (T8)	790–800	4.7–5.3	23–53		>660	>4.6	>19		600–720	4.5–5.2	9–45
Ross 458C (T8.5)	690–760	4.0–4.7	6–20		>590	>3.9	>5		660–740	4.0–4.7	6–20
Wolf 940B (T8.5)	570–680	4.5–5.2	12–43		>500	>4.4	>12		560–640	4.4–5.2	12–42
CFBDS J0059−01 (T9)	520–600	4.4–5.2	10–35		>440	>4.3	>10		500–600	4.4–5.1	11–34
ULAS J0034−00 (T9)	560–680	4.5–5.2	12–43		>500	>4.4	>12		560–660	4.4–5.2	12–42
ULAS J1335+11 (T9)	560–660	4.4–5.2	12–42		>500	>4.4	>12		560–640	4.4–5.2	12–42
CFBDSIR J1458+1013AB (T9.5)a	520–640	4.4–5.2	11–42		>460	>4.3	>10		520–620	4.4–5.2	11–36
UGPS J0722−05 (T10)	480–600	4.4–5.1	10–35		>420	>4.3	>9		480–580	4.4–5.1	10–33

Note. ^aIntegrated light spectrum.

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In accord with the integrated-light spectrum, the near-IR colors of component A are similar to those of the known T8–T10 dwarfs, with its (H − K) color of −0.45 ± 0.26 mag being somewhat bluer than most objects, though the uncertainty is large. As discussed above, the bluer color is likely due to a higher surface gravity (i.e., an older age) compared to most other late-T dwarfs.

Our near-IR parallax for the system provides the absolute magnitudes for component B and reveals its extreme nature. Compared to the T10 dwarf UGPS J0722−05, CFBDSIR J1458+1013B is fainter by 1.4 ± 0.4, 1.9 ± 0.3, and 2.0 ± 0.4 mag in its JHK absolute magnitudes, respectively. Being significantly fainter than previously known brown dwarfs (Figure 7), the properties of CFBDSIR J1458+1013B provide a first look at the empirical trends beyond spectral type T10, especially enlightening given the uncertainties in model atmosphere predictions for such cold objects (e.g., Burrows et al. 2003). The very blue (CH₄s − H) color indicates strong CH₄ absorption persists at H band, comparable to the known T8–T9 dwarfs which have a (CH₄s − H) ≈ −0.5 to −0.6 mag (e.g., Figure 2 of Tinney et al. 2005 and Section 3.2 of Liu et al. 2008).

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The near-IR colors of CFBDSIR J1458+1013B are very blue (Figure 8), with its H − K color similar to and its J − K color slightly bluer than previously known T dwarfs (except for the T6p dwarf 2MASS 0937+29, which is suspected to have low metallicity; Burgasser et al. 2002). For its absolute magnitude, its J − K color is much redder than those predicted by the Lyon/Cond (Baraffe et al. 2003) and Saumon & Marley (2008, hereafter SM08) models, and to a lesser degree the BSL03 models as well. The most intriguing behavior is seen in J − H, where the blueward trend with spectral type among the T dwarfs appears to reach an inflection point with the T8–T10 dwarfs, and then CFBDSIR J1458+1013B continues to bluer colors.

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How much cooler is CFBDSIR J1458+1013B than previously known late-T dwarfs? Using its absolute magnitudes as a simple proxy for L_bol (i.e., assuming the same bolometric corrections as other T9–T10 objects), its L_bol is a factor of ≈4–6 times smaller. Old brown dwarfs have essentially constant radii, so this would correspond to an object that is a factor of ≈1.5 cooler. The T9–T10 objects have estimated T_eff of 500–600 K from model atmosphere fitting and their bolometric luminosities (Leggett et al. 2009, 2010b; Marocco et al. 2010; Lucas et al. 2010); simple scaling would then make CFBDSIR J1458+1013B ≈350–400 K.

With L_bol estimates for the individual components and an assumed age, evolutionary models can fully determine the remaining physical properties of the two components (e.g., Saumon et al. 2000). This approach is desirable as predictions of L_bol are less dependent on the assumed model atmospheres than predictions of the absolute magnitudes (Chabrier et al. 2000b; Saumon & Marley 2008). This approach has also been widely used for temperature determinations for field L and T dwarfs (e.g., Golimowski et al. 2004). Of course, such estimates should be treated with caution, since CFBDSIR J1458+1013B resides in a low-temperature, low-luminosity regime where the models have not been tested against any observations. (In the case of L dwarfs, Dupuy et al. 2009b have found that for a given luminosity and assumed age, the evolutionary models may overestimate the masses.)

To estimate L_bol, we adopt J-band bolometric corrections from the coolest T dwarfs with parallaxes: ULAS J0034−00 (T9; BC_J = 1.96 ± 0.11 mag), CFBDS J0059−01 (T9; 1.87 ± 0.21 mag), and ULAS J1335+11 (T9; 1.82 ± 0.09 mag) from Marocco et al. (2010), and UGPS J0722−05 (T10; 1.36 ± 0.21 mag) from Lucas et al. (2010). The unweighted average is 1.75 ± 0.27 mag, and we apply this to both components of CFBDSIR J1458+1013AB. The resulting values for L_bol/L_☉ are (1.1 ± 0.4) × 10⁻⁶ and (2.0 ± 0.9) × 10⁻⁷ for components A and B, respectively. In comparison, CFBDS J0059−0114 and UGPS J0722−05 have L_bol/L_☉= (7.2 ± 1.2) × 10⁻⁷ and (9.2 ± 3.1) × 10⁻⁷, respectively, making CFBDSIR J1458+1013B a factor of ≈4–5 less luminous than these two objects.

Table 3 presents the derived physical quantities for ages of 1.0 and 5.0 Gyr. The L_bol uncertainty is propagated into the calculations in a Monte Carlo fashion. The inferred temperature of component B is exceptionally low, 360–380 K from the Lyon/COND models and 350–380 K from the Burrows et al. (1997) ones. Including the random uncertainties from the Monte Carlo results, we adopt a final T_eff estimate of 370 ± 40 K. The model-derived mass is 6–14 (7–17) for the Lyon/COND (Burrows) models, possibly placing the object below the notional 13 M_Jup dividing line between planets and brown dwarfs based on the deuterium-burning limit. Overall, the physical properties of CFBDSIR J1458+1013B overlap those of the gas-giant planets found from radial velocity surveys. In fact, both components of CFBDSIR J1458+1013AB would reside in the planetary-mass regime and have retained their initial deuterium abundance for ages of ≲1 Gyr.

To gauge the systematic effects, we also compute physical properties using the BSL03 models, which provide predictions for absolute magnitudes. (The Lyon/COND models also provide absolute magnitudes, but these disagree more strongly with the color–magnitude data in Figure 7.) We compare the BSL03 models to the J-band observations, as this bandpass represents the peak of the near-IR spectral energy distribution (SED). (Note that this is largely equivalent to using the BSL03 atmospheric models for their bolometric corrections.) The results are listed in Table 3 and agree reasonably well with those derived from L_bol and assuming the bolometric corrections from the known T9–T10 dwarfs.

Measuring the differential deuterium abundance would help constrain the age of the system, analogous to the binary lithium test proposed by Liu & Leggett (2005). The deuterium depletion timescales are long for such low-mass objects, so the exact age at which they become fully depleted is fuzzy. Using a finely interpolated version of the Lyon/COND models (Baraffe et al. 2003) and constrained by the observed luminosity of each component, we find that the full range of 99%–0% deuterium content for the primary is 0.5–1.3 Gyr, while the 99%–0% deuterium range for the secondary is 2.3–5.4 Gyr. Thus, for ages of <0.5 Gyr, both components retain their deuterium and would have masses of <9 and <4 M_Jup. Between 0.5 and 2 Gyr, the primary is depleted but the secondary retains its deuterium. And for ages older than 2 Gyr both components are depleted and are >20 and >10 M_Jup. (Allers et al. 2010 report the discovery of a young field L dwarf binary whose estimated luminosities and age indicate that the two components may be in the process of differential deuterium depletion.) Note that the deuterium abundance is expected to be difficult to measure (Chabrier et al. 2000a). An additional complication is the theoretical predictions for the D-burning limit depend on the metallicity, initial D and He abundances, and atmospheric boundary conditions and can range from ≈11 to 14 M_Jup (Spiegel et al. 2011).

To estimate the orbital period of the binary, we adopt the statistical conversion factor between projected separation and true semi-major axis from Dupuy & Liu (2011). They offer several choices, based on the underlying eccentricity distribution and degree of completeness to finding binaries by imaging ("discovery bias"). We adopt the eccentricity distribution from their compilation of ultracool visual binaries with high-quality orbits and assume their case of modest discovery bias, namely, that the smallest possible projected separation for detection is half the semi-major axis. This gives a multiplicative correction factor of 1.07^+0.42_{− 0.27} (68.3% confidence limits) for converting the projected separation into semi-major axis (compared to 1.10^+0.92_{− 0.35} for a uniform eccentricity distribution with no discovery bias). The resulting orbital period estimates range from 20 to 35 years for ages of 1.0–5.0 Gyr, albeit with significant uncertainties (Table 3). Dynamical masses for ultracool binaries may be realized from orbital monitoring covering ≳30% of the period (e.g., Bouy et al. 2004; Liu et al. 2008; Dupuy et al. 2009a). Thus, CFBDSIR J1458+1013AB warrants continued high angular resolution imaging to determine its visual orbit, which can then be combined with the parallax to directly measure its total mass.

Using the fitting results from Section 3.2.3, we can test the accuracy of atmospheric models by comparing the measured distances to model-derived spectroscopic distances following the method of Bowler et al. (2009). The scaling factor between the model emergent spectra and the observed spectra is equal to (R/d)², so if a radius is known (or assumed) then the distance can be computed. Bowler et al. estimated distances to four late-M and L subdwarfs using this method and found agreement to within ∼10% of published parallaxes. Several subsequent studies have used this technique to estimate distances for late-T dwarfs without parallaxes (e.g., Mainzer et al. 2011), but this method has yet to be tested for such objects. We do so now with the Ames-Cond, BSL03, and BT-Settl-2009 models.

To compute model-derived spectroscopic distances, for the Ames-Cond and BT-Settl-2009 atmospheric models we use radii from the companion grid of Lyon/Cond evolutionary models (Baraffe et al. 2003) interpolated across ages, effective temperatures, and surface gravities. For the BSL03 models, we use a power-law fit for the radius as a function of T_eff and log (g) from the Burrows et al. (1997) evolutionary models (Equation (1) of BSL03). We compute errors in the spectroscopic distances from two components. (1) Measurement uncertainties from the finite S/N of the spectra and the absolute flux calibration from the J-band photometry are accounted for in a Monte Carlo fashion. We adopt the median and rms of the resulting distributions as one version of the results. (2) In addition, we account for systematic uncertainties in the models by assuming normally distributed errors of 50 K and 0.25 dex in the fitted T_eff and log (g). The standard deviation of the resulting spectroscopic distance distribution is reported along with the uncertainty due to random errors.

Table 5 and Figure 9 summarize the results, with both sets of uncertainty calculations. The agreement between the spectroscopic distances and the parallactic distance range from ≈10% to about a factor of two, with no apparent trend in accuracy with distance, spectral type, or model grid. The large scatter likely arises from the sensitivity of the distance estimate to the best-fitting model T_eff. The typically larger spectroscopic distances compared to parallactic distances imply an overestimate of T_eff in the best-fitting model, because the scaling factor is highly sensitive to temperature (absolute flux level) and very weakly dependent on gravity.

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