THE DISCOVERY OF Y DWARFS USING DATA FROM THE WIDE-FIELD INFRARED SURVEY EXPLORER (WISE)

WISEP J1541−2250 was observed on the night of 2011 April 17 (UT) with the NOAO Extremely Wide Field Infrared Imager (NEWFIRM) mounted on the Cerro Tololo Inter-American Observatory (CTIO) Victor M. Blanco 4 m Telescope. A description of the instrument, observing strategy, and data reduction can be found in Kirkpatrick et al. (2011). The resultant J- and H-band photometry is presented in Table 2.

Near-infrared images of WISEP J0410+1502, WISEPC J1405+5534, WISEP J1738+2732, and WISEPC J2056+1459 were obtained using the Wide-field Infrared Camera (WIRC; Wilson et al. 2003) on the 200 inch Hale Telescope at Palomar Observatory. A description of the instrument, observing strategy, and data reduction can be found in Kirkpatrick et al. (2011). The magnitudes and/or limits for each brown dwarf are given in Table 2.

WISEPC J0148−7202 was observed on the night of 2010 August 1 (UT) with the now decommissioned Persson's Auxiliary Nasmyth Infrared Camera (PANIC; Martini et al. 2004) on the east Nasmyth platform at the Magellan 6.5 m Baade Telescope. A description of the instrument, observing strategy, and data reduction can be found in Kirkpatrick et al. (2011). The J- and H-band magnitudes of WISEPC J0148−7202 are given in Table 2.

High-resolution observations of WISEP J1828+2650 and WISEPC J2056+1459 were obtained with NIRC2 behind the Keck II LGS-AO system (Wizinowich et al. 2006; van Dam et al. 2006) on the night of 2010 July 1 (UT). A description of the instrument, observing strategy, and data reduction can be found in Kirkpatrick et al. (2011). The J- and H-band magnitudes are given in Table 2.

A 0.9–2.5 μm, low-resolution (R ≡ λ/Δλ ≈ 150) spectrum of UGPS 0722−05 was obtained with SpeX (Rayner et al. 2003) on the 3 m NASA Infrared Telescope Facility (IRTF) on 2011 January 26 (UT). A description of the instrument, observing strategy, and data reduction can be found in Kirkpatrick et al. (2011). The spectrum, which is shown in Figure 2, has a high signal-to-noise ratio (S/N), reaching >50 at the peaks of the Y, J, and H bands.

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Low-resolution (R = 250–350), 1–2.4 μm spectra of WISEPC J0148−7202, WISEP J0410+1502, and WISEP J1541−2250 were obtained with the Folded-port InfraRed Echellette (FIRE; Simcoe et al. 2008, 2010) mounted at the auxiliary Nasmyth focus of the Magellan 6.5 m Baade Telescope. A description of the instrument, observing strategy, and data reduction can be found in Kirkpatrick et al. (2011). The spectra are shown in Figure 2.

WISEPC J2056+1459 was observed using the Near-Infrared Spectrometer (NIRSPEC; McLean et al. 1998, 2000) located on one of the Nasmyth platforms of the 10 m Keck II telescope on Mauna Kea, Hawaii. The 038-wide slit in the low-resolution mode provides a resolving power of R = 2500. WISEPC J2056+1459 was observed with the N3 order sorting filter (1.143–1.375 μm) on the night of 2010 October 21 (UT) and with the N5 order sorting filter (1.431–1.808 μm) on the night of 2010 November 22 (UT).

A series of 300 s exposures was obtained at two different positions along the 42'' long slit. An A0 V star was observed after each series of science exposures for telluric correction and flux calibration purposes. Calibration frames consisting of neon and argon arc lamps, dark frames, and flat-field lamps were also taken following the science exposures. The data were reduced in a standard fashion using the IDL-based REDSPEC¹⁴ reduction package as described in McLean et al. (2003). Since REDSPEC does not produce uncertainty arrays, we generated them as follows. First, we performed a simple sum extraction using the rectified, pair-subtracted images generated by REDSPEC. We then scaled the spectra to a common flux level and computed the average spectrum. The uncertainty at each wavelength is given by the standard error on the mean. The average spectrum is then corrected for telluric absorption and flux calibrated using the calibration spectrum generated by REDSPEC. Since the difference between the spectra produced by REDSPEC and our spectra was negligible, we used our spectrum for our analysis. Finally, the N3- and N5-band spectra were absolutely flux calibrated using the WIRC photometry (see Table 2) as described in Cushing et al. (2005) and merged to produce a 1.15–1.80 μm spectrum. The final spectrum, which is shown in Figure 2, has a peak S/N of 8 and 6 in the J and H bands, respectively.

WISEPC J1405+5534, WISEP J1738+2732, and WISEP J1828+2650 were observed with the infrared channel of the Wide Field Camera 3 (WFC3; Kimble et al. 2008) on-board the Hubble Space Telescope (HST) as a part of a Cycle 18 program (GO-12330, PI: J. D. Kirkpatrick). The WFC3 uses a 1024 × 1024 HgCdTe detector with a plate scale of 013 pixel⁻¹ which results in a field of view of 123×126 arcsec. The G141 grism was used to perform slitless spectroscopy of each brown dwarf covering the 1.07–1.70 μm wavelength range at a resolving power of R ≈ 130. For each brown dwarf, we first obtained four direct images through the F140W filter (λ_p = 1392.3 nm) in the MULTIACCUM mode with the SPARS25 sampling sequence. Between each exposure, the telescope was offset slightly. We then obtained four images with the G141 grism at the same positions as the direct images. The spectroscopic observations were also obtained in the MUTLIACCUM mode but using the SPARS50 sequence.

The raw images were first processed using the CALWFC3 pipeline (ver. 2.3) which not only subtracts the bias level and dark current but also flat fields the direct images (the grism images are flat fielded during the extraction process described below). The spectra were then extracted using the aXe software (Kümmel et al. 2009), which is a suite of PyRAF/IRAF packages designed to extract spectra from the slitless modes of both WFC3 and the Advanced Camera for Surveys (ACS). aXe requires knowledge of both the position and brightness of the objects in the field of view. We therefore combined the four direct images using MULTIDRIZZLE (Koekemoer et al. 2002) and the latest Instrument Distortion Coefficient Table (IDCTAB). A catalog of the objects in the field was then constructed using SExtractor (Bertin & Arnouts 1996). For each object in the source catalog, two-dimensional (2D) subimages centered on the first-order spectra of each object were then combined using the task AXEDRIZZLE to produce a high S/N 2D spectral image. One-dimensional, flux-calibrated spectra and their associated uncertainties are then extracted from the 2D drizzle subimages.

Since the G141 grism mode is slitless, spectral contamination from nearby sources is not uncommon. The aXe software (using the Gaussian emission model) estimates the level of contamination for each object using the positions and magnitudes of all the objects in the field of view. The spectrum of one of the brown dwarfs, WISEP J1828+2650, exhibits moderate contamination that increases in intensity toward shorter wavelengths (see Figure 3). The aXe software does not actually correct for this contamination so we attempted to do so using the contamination image generated by aXe. Unfortunately, the contamination-corrected spectrum exhibits negative flux values which suggests that aXe is overestimating the contamination level. We will therefore use the contaminated spectrum and consider it an upper limit to the actual spectrum. This issue will be discussed in more detail in Section 4.1.1.

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The lower panel of Figure 4 shows the 1.15–1.70 μm spectrum of WISEP J1828+2650 along with the spectrum of UGPS 0722−05. The spectrum of WISEP J1828+2650, while dominated by the same CH₄ and H₂O absorption bands present in T dwarf spectra, has a feature not seen in any T dwarf: the J- and H-band peaks, when plotted in units of f_λ, are essentially the same height. As discussed in Section 3.2.4, the spectrum of WISEP J1828+2650 is contaminated by light from nearby stars. This contamination, which is not removed by the aXe software, becomes progressively worse at shorter wavelengths (see Figure 3) such that the true spectrum will have an even more extreme J- to H-band peak flux ratio.

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The roughly equal-intensity J and H flux peaks are also confirmed by our ground-based, near-infrared photometry, which gives J − H = 0.72  ±  0.42 mag. Model atmospheres of cool brown dwarfs predict that the near-infrared colors, which are blue for the hotter T dwarfs, turn back to the red at effective temperatures between 300 and 400 K as the Wien tail of the spectral energy distribution collapses. This turn to the red was proposed as one of the triggers that might force the creation of a Y spectral class (Burrows et al. 2003; Kirkpatrick 2008).

Further underscoring the extreme nature of WISEP J1828+2650 is its J–W2 color of 9.29 ± 0.35 which is over 2 mag redder than the WISEP J1541−2250, the second reddest brown dwarf in our sample at J–W2 = 7.18 ± 0.38 (Kirkpatrick et al. 2011). WISEP J1828+2650 is also the reddest brown dwarf in our sample in H–W2, J–[4.5], and H–[4.5], where [4.5] represents the Spitzer Space Telescope (Werner et al. 2004) Infrared Array Camera (IRAC; Fazio et al. 2004) channel 2 magnitude. Given the extreme nature of both its near-infrared spectrum and near- to mid-infrared colors, we identify WISEP J1828+2650 as the archetypal member of the Y spectral class.

The 1.15–1.70 μm spectra of WISEPC J1405+5534 and WISEP J1738+2732 are very similar and yet both are distinct from UGPS 0722−05, albeit in less extreme ways than the spectrum of WISEP J1828+2650 (see middle and upper panels of Figure 4). Although the relative heights of the J- and H-band peaks are similar to those of UGPS 0722−05, their widths are narrower. The narrowing of the H-band peaks is asymmetric, however, as most of the change is a result of enhanced absorption on the blue wings from 1.51 to 1.58 μm. What is the underlying cause of this absorption?

The H-band spectra of T dwarfs are shaped by CH₄ (and to a lesser extent H₂O) longward of 1.6 μm and by H₂O at wavelengths shortward of 1.6 μm. As the effective temperature falls, the opacity of the near-infrared overtone and combination bands of NH₃ becomes important since NH₃/N₂ > 1 for T ≲ 700 K at P = 1 bar (Lodders & Fegley 2002). The emergence of these NH₃ bands has long been suggested as the trigger for a new spectral class (Burrows et al. 2003; Kirkpatrick 2008; Leggett et al. 2007a) but identifying them has proven difficult because they overlap with the strong H₂O bands and because the abundance of NH₃ can be reduced by an order of magnitude due to vertical mixing in the atmospheres of brown dwarfs (Saumon et al. 2003, 2006; Hubeny & Burrows 2007).

Figure 5 shows the H-band spectra of the T4, T6, and T8 spectral standards, UGPS 0722−05, and WISEP J1738+2732 as well as the opacities for H₂O (Freedman et al. 2008), NH₃ (Yurchenko et al. 2011), and CH₄ (Freedman et al. 2008) at T = 600 K and P = 1 bar generated by one of us (R.S.F.). With increasing spectral type, the blue wing of the H-band peak becomes progressively suppressed. Delorme et al. (2008a) tentatively identified NH₃ absorption on the blue wing of the H-band spectrum of CFBDS J0059−0114, a T dwarf with a spectral type earlier than UGPS 0722−05. However, the change in the shape of the blue wing of the H-band peak from T6 to UGPS 0722−05 appears smooth, suggesting a common absorber or set of absorbers. It seems unlikely that NH₃ dominates given that it has not been identified in the spectra of mid-type T dwarf (T_eff ∼ 1200 K). A similar conclusion to ours is reached by Burningham et al. (2010) using spectral indices.

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In contrast, the H-band spectrum of WISEP J1738+2732 stands out in the sequence in that it exhibits additional absorption from 1.53 to 1.58 μm. This absorption broadly matches the position of the ν₁ + ν₃ absorption band of NH₃ centered at 1.49 μm suggesting that NH₃ is the cause of this absorption. However, we cannot conclusively identify NH₃ as the carrier given the low spectral resolution of the data and the fact that the absorption lies on the steep wing of the H₂O band. For example, water ice also has an absorption band centered at ∼1.5 μm (Warren & Brandt 2008) that could potentially produce such absorption if the abundance of water ice is high enough. One potential avenue for confirming that NH₃ is indeed the carrier would be to acquire higher spectral resolution data to search for individual NH₃ features (e.g., Saumon et al. 2000; Warren et al. 2007).

With WISEP J1828+2650 classified as the prototypical Y dwarf, we can now investigate the transition between the T and Y spectral classes. T dwarfs are classified at near-infrared wavelengths using the Burgasser et al. (2006) scheme, wherein nine T dwarf spectral standards with subtypes ranging from T0 to T8 are used for direct spectral comparisons. Burgasser et al. also defined five spectral indices that measure the depths of the CH₄ and H₂O bands which can be used as a proxy for direct comparisons. With the discovery of brown dwarfs with spectral types later than T8, the question of how to extend the Burgasser et al. scheme beyond T8 naturally arises.

The first >T8 dwarf to be identified was ULAS J003402.77−005206.7 (ULAS J0034−0052; Warren et al. 2007). Based on a direct comparison to the spectrum of the T8 spectral standard and the values of the Burgasser et al. spectral indices, Warren et al. adopted a spectral type of T8.5. A second >T8 dwarf soon followed with the discovery of CFBDS J0059−0114 by Delorme et al. (2008a). They used the W_J index which measures the half-width of the J-band peak (Warren et al. 2007) and the NH₃–H index which measures the half-width of the H-band peak (i.e., the depth of the putative NH₃ absorption), to classify both CFBDS J0059−0114 and ULAS J0034−0052 as T9 dwarfs. Burningham et al. (2008) added two T dwarfs to the tally of >T8 dwarfs with the discovery of ULAS J133553.45+113005.2 (ULAS J1335+1130) and ULAS J123828.51+095351.3 (ULAS J1238+0953). Using both direct spectral comparison and spectral indices, they classified them as T8.5 and T9, respectively. Burningham et al. also proposed extending the Burgasser et al. scheme to T9 by assigning ULAS J1335+1130 as the T9 spectral standard. Additional T dwarfs with spectral types later than T8 have since been discovered (see Table 4), but to date, the latest-type T dwarf currently known is UGPS 0722−05 (Lucas et al. 2010) which has been classified as T10 via a combination of spectral indices and direct comparisons to the T9 dwarfs.

Figure 6 shows the 1.15–1.70 μm spectra of the T6, T7, T8 spectral standards, UGPS 0722−05, and WISEP J1738+2732. The spectra show smooth changes in their spectral morphology with increasing spectral type including progressively deeper absorption bands centered at 1.15, 1.45, and 1.65 μm and progressively narrower J- and H-band peaks. However, UGPS 0722−05 does not appear to be two subtypes later than T8 as required by its T10 spectral type. Rather, the changes in spectral morphology from T6 to UGPS 0722−05 suggest that UGPS 0722−05 is more naturally classified as a T9. Given its brightness (J = 16.5, 1.5 mag brighter than ULAS J1335+1130) and position near the celestial equator, UGPS 0722−05 also makes an ideal spectral standard. We therefore define it to be the T9 spectral standard.

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WISEP J1738+2732 is clearly of later type than UGPS 0722−05 but should it be classified as a T dwarf or a Y dwarf? As noted in the previous section, WISEP J1738+2732 exhibits excess absorption from 1.53 to 1.58 μm that we have tentatively ascribed to NH₃. This absorption becomes even more apparent when the spectrum is placed in sequence with the T6 to T9 spectral standards (lower right panel of Figure 6). Given the smooth change in width of the J-band peak and the rapid fall in the flux of the blue wing of the H band between UGPS 0722−05 and WISEP J1738+2732 (which suggests the emergence of a new absorption band), we classify WISEP J1738+2732 as a Y dwarf and assign it a spectral type of Y0. Additionally, we tentatively identify it as Y0 spectral standard.

With the T9 and Y0 spectral standards defined, we can return to the question of classifying the other new WISE discoveries. The J- and H-band peaks of WISEPC J0148−7202 are slightly narrower than UGPS 0722−05 and slightly wider than WISEP J1738+2732 so we classify this dwarf as T9.5. The spectrum of WISEPC J1405+5534 is very similar to that of WISEP J1738+2732 (see Figure 4). However, we note that the wavelength at which the peak H-band flux is reached is shifted ∼60 Å to the red relative to UGPS 0722−05 (see Figure 4) and the other late-type T dwarfs which suggests that WISEPC J1405+5534 may be peculiar. We therefore classify it as Y0 (pec?). Interestingly, a similar, albeit larger, shift of 200 Å is seen in the spectrum of Jupiter.

The spectra of the remaining brown dwarfs, WISEPC J2056+1459, WISEP J0410+1502, and WISEP J1541−2250, do not have sufficient S/N to convincingly show the excess absorption from 1.53 to 1.58 μm. However, the J-band peaks of these three brown dwarfs are all narrower than UGPS 0722−05. Indeed, the spectra of all of them are a better match to the spectral morphology of WISEP J1738+2732 than UGPS 0722−05 so we classify these brown dwarfs as Y0 as well. In addition, the peak Y-band fluxes of WISEP J0410+1502 and WISEP J1541−2250 are slightly higher than in the spectrum of UGPS 0722−05. This is consistent with the blueward trend in the Y−J color of late-type T dwarfs (Leggett et al. 2010; Burningham et al. 2010) which Burningham et al. (2010) ascribed to the weakening of the strong resonance K i doublet (7665, 7699 Å) as K condenses into KCl. Finally, since the spectrum of WISEP J1828+2650 is distinct from both UGPS 0722−05 and WISEP J1738+2732, we classify it as >Y0. A more precise subtype will require the discovery of additional Y dwarfs to bridge the gap in spectral morphology between WISEP J1738+2732 and WISEP J1828+2650.

There are also 12 T dwarfs with spectral types later than T8 currently in the literature (see Table 4). Since we have reclassified UGPS 0722−05 as a T9 dwarf, we must also reclassify the other 11 dwarfs using this new system. To accomplish this, we have smoothed the published spectra to a resolving power of R = 150 and resampled them onto the same wavelength scale as the IRTF/SpeX spectrum of UGPS 0722−05. This ensures that differences in resolving power and wavelength sampling between the late-type T dwarfs and the Burgasser et al. IRTF/SpeX spectra of the T dwarf spectral standards do not adversely affect our classification. Table 4 gives the revised spectral types derived from direct comparison for the 12 T dwarfs with published spectral types later than T8. When the J- and H-band regions gave conflicting spectral types, we used the typed inferred from the J band.

Although the primary (and preferred) method of assigning a spectral type is to compare the spectrum of a brown dwarf against that of the spectral standards, the use of spectral indices remains popular in the literature. We have therefore computed the H₂O–J, CH₄–J, H₂O–H, CH₄–H (Burgasser et al. 2006), W_J (Warren et al. 2007), and NH₃–H (Delorme et al. 2008a) indices of the new WISE brown dwarfs and as well as UGPS 0722−05. Figure 7 illustrates the positions of the indices' flux windows relative to the spectrum of UGPS 0722−05. The index values are computed in a Monte Carlo fashion whereby 5000 realizations of each spectrum are generated by randomly drawing from normal distributions with means given by the flux densities at each wavelength and standard deviations given by the uncertainty in the flux densities. The values of the indices and their uncertainties are given by the mean and standard deviation of the distribution of index values computed from the 5000 realizations and are listed in Table 5.

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Figure 8 shows the values of the six indices as a function of spectral type. Also shown are the index values of the T6−T8 spectral standards, a sample of T5−T8 dwarfs from the SpeX Prism Spectral Library, and the 12 T dwarfs with previously published spectral types later than T8. The classification of WISEP J1738+2732 as a Y dwarf is bolstered by the distinctive break in the trend of the NH₃–H values with spectral type which suggests that a new absorption band has indeed emerged at the T/Y dwarf transition. The remaining spectral indices do not show a break at the T/Y transition, but the CH₄–J, H₂O–H, and W_J indices do show a smooth trend with spectral type down to Y0 indicating that they can still be used as proxies for direct spectral comparisons. Indeed, the value of the W_J spectral index for WISEP J1738+2732 is far from saturated so we support the suggestion by Burningham et al. (2008) that this index can be used as a proxy for direct comparison for late-type T dwarfs and early-type Y dwarfs. However, the CH₄–H index is clearly beginning to saturate at T9 and the H₂O–J index may even reverse at Y0 rendering these indices less useful for classification purposes. Finally, although there is scatter due to the very low S/N of some of the spectra, the new WISE brown dwarfs are clearly distinct from the previous ⩾T8.5 dwarfs and cluster around the Y0 spectral standard.

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In order to investigate the atmospheric properties (e.g., T_eff, log g) of the brown dwarfs, we have compared their near-infrared spectra to a new preliminary grid of model spectra generated with the model atmospheres of Marley & Saumon. A detailed description of the basic models can be found in Marley et al. (2002), Saumon & Marley (2008), Cushing et al. (2008), and Stephens et al. (2009). This preliminary grid includes a new NH₃ line list (Yurchenko et al. 2011) and a new prescription for the collision induced opacity for H₂ (D. Saumon et al. 2011, in preparation). A more detailed study that compares the model spectra to the near-infrared spectra, and WISE and Spitzer photometry is in preparation.

The grid consists of solar metallicity, cloudless models with the following parameters: T_eff = 200–1000 K in steps of 50 K, log g = 3.75 − 5 in steps of 0.25 (cm s⁻²), and K_zz = 0, 10⁴ cm² s⁻¹. Although the opacities of the condensate clouds are not included in the atmospheric models, i.e., they are cloudless, the effects on the atmospheric chemistry due to the rainout of the condensates is accounted for in the models. This assumption is reasonable for the silicate and liquid iron clouds since they form well below the observable photosphere (see however, Burgasser et al. 2010) but may not be valid if, as expected, H₂O clouds form high in the atmosphere of the coldest models. The eddy diffusion coefficient, K_zz, parameterizes the vigor of mixing in the radiative layers of the atmosphere. A value of K_zz > 0 cm² s⁻¹ results in mixing that can prevent the abundances of CO and CH₄ (the dominant carbon-bearing species) from coming into chemical equilibrium because the mixing timescales become shorter than the timescales of key chemical reactions involved in the conversion of CO to CH₄ (Lodders & Fegley 2002; Saumon et al. 2003; Hubeny & Burrows 2007). Typical values of K_zz in the stratospheres of giant planets are 10²–10⁵ cm² s⁻¹ (Saumon et al. 2006). The abundances of N₂ and NH₃ (the dominant nitrogen-bearing species) are also kept from coming into chemical equilibrium by mixing, but in this case the mixing timescales are set in the convective layers of the atmosphere by the mixing length theory. As a result, the final non-equilibrium abundances of N₂ and NH₃ are not sensitive to variations in the eddy diffusion coefficient K_zz. However by convention, models with K_zz = 0 cm² s⁻¹ are in full chemical equilibrium (i.e., the effect of convective mixing on the nitrogen chemistry is ignored) and models with K_zz ≠ 0 cm² s⁻¹ exhibit both carbon and nitrogen non-equilibrium chemistry.

The best-fitting models are identified using the goodness-of-fit statistic, $G_k= \sum _{i=1}^n w_i (\frac{f_i - C_k\mathcal {F}_{k,i}}{\sigma _i} )^2$, where n is the number of data pixels, w_i is the weight for the ith wavelength (set to unity in this case), f_i and F_{k, i} are the flux densities of the data and model k, respectively, σ_i are the errors in the observed flux densities, and C_k is an unknown multiplicative constant equal to (R/d)², where R is the radius of the star and d is the distance to the star (Cushing et al. 2008). In order to increase the S/N of the data, we first smoothed the higher resolution spectra to R = 200. The model spectra were also smoothed to the same resolving power and linearly interpolated onto the wavelength scale of the data. For each model, we compute the scale factor C_k by minimizing G_k with respect to C_k and identify the best-fitting model as having the global minimum G_k value. To estimate the range of models that fits the data well, we run a Monte Carlo simulation that uses the uncertainties in the individual spectral points and the uncertainties in the absolute flux calibration of the spectra to generate 10⁴ simulated noisy spectra. The fitting process is repeated on each simulated spectrum and models that are consistent with the best-fitting model at the 3σ level are considered equally good representations of the data. We did not attempt to fit the spectrum of WISEP J1828+2650 because it is contaminated with light from other stars in the WFC3 field of view (see Sections 3.2.4 and 4.1.1). After discussing the results of the fits to the spectra of the other brown dwarfs, we return to estimate an approximate effective temperature for WISEP J1828+2650.

Table 6 lists the best-fitting model parameters for each brown dwarf, as well as UGPS 0722−05. The derived effective temperatures of the WISE brown dwarfs are all cold, ranging from 350 to 500 K. Indeed all but one have estimated effective temperatures of less than 450 K making them the coldest spectroscopically confirmed brown dwarfs known. Five out of the six best-fitting models also have K_zz ≠ 0 which indicates that vertical mixing is present in the atmospheres of these cold brown dwarfs. This is not a surprising result given that strong evidence for vertical mixing in the atmospheres of brown dwarfs has been found at longer wavelengths (Saumon et al. 2006, 2007; Leggett et al. 2007b, 2009; Burgasser et al. 2008; Stephens et al. 2009; Geballe et al. 2009; Cushing et al. 2010). At such low temperatures, the effects of non-equilibrium chemistry on the J- and H-band spectra of brown dwarfs is limited to weakening the NH₃ absorption bands. The detection of mixing therefore underscores the fact that NH₃ is probably at least partially responsible for the absorption seen on the blue wing of the H-band peak of WISEPC J1405+5534 and WISEP J1738+2732.

Figure 9 shows the best-fitting model spectra overplotted on the data. Since this is the first time such cold model spectra have been compared to observed spectra, the agreement between the models and the data is encouraging. In particular, the height and width of the J-band peaks are well matched by the model spectra. Previous studies of hotter brown dwarfs fail to match both the peak and width of this peak (e.g., Leggett et al. 2009; Burgasser et al. 2011). The improved fits may be a result of the fact that we are fitting a smaller wavelength range (Cushing et al. 2008; Seifahrt et al. 2009) and/or because the high J vibration–rotation lines (the so-called hot lines), whose cross sections are less well known, become less important at such cold temperatures.

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The models do, however, provide a poor fit to the blue wing of the H-band peak of the spectra and fail to reproduce the heights of the Y-band peaks of WISEP J0410+1502 and WISEP J1541−2250. Note that the peak of the Y band is shaped by the 2ν₁ +2ν₄ band of NH₃ centered at about 1.03 μm and therefore Y-band spectra of cold brown dwarfs could provide the first clear detection of NH₃ at near-infrared wavelengths. In principle, the blue wing of the H-band model spectrum could be brought into better agreement with the data by further reducing the abundance of NH₃. However, as noted above, the abundance of NH₃ is insensitive to variations in K_zz because it is quenched in the convective region where the mixing timescale is set by the mixing length theory and not by the eddy diffusion coefficient. Therefore, the mismatch between the data and models is most likely a result of some other inadequacy in the model atmospheres.

Finally, although we cannot fit the models to the spectrum of WISEP J1828+2650, we can still estimate a rough effective temperature. The most salient feature of the spectrum is that the J- and H-band peaks are roughly the same height in flux density units of f_λ. Only model spectra with T_eff ⩽ 250 K have J-band peak fluxes that are equal to or less than the H-band peak fluxes. A second estimate of the effective temperature can be derived from the observed J–W2 color of 9.29 ± 0.35. We computed synthetic Mauna Kea Observatories Near-Infrared (MKO-NIR; Tokunaga et al. 2002) J and W2 magnitudes for each model in the grid and find that model spectra with T_eff = 275–300 K have J–W2 colors that fall within ±2σ of the observed color. Taken together, these estimates suggest that an appropriate upper limit to the effective temperature of WISEP J1828+2650 is ∼300 K which makes WISEP J1828+2650 the coolest spectroscopically confirmed brown dwarf known.

With estimates of the effective temperatures and surface gravities of the new brown dwarfs in hand, we can also estimate their radii (R) and masses (M) using evolutionary models. We used the cloudless structure models of Saumon & Marley (2008) because they used atmospheric models that are nearly identical to the ones we used in our analysis for boundary conditions. As a result, the derived T_eff, log g, R, and M estimates are all self-consistent. The radii and masses of the brown dwarfs are given in Table 6.