THE PROPERTIES OF THE 500 K DWARF UGPS J072227.51−054031.2 AND A STUDY OF THE FAR-RED FLUX OF COLD BROWN DWARFS^*

Optical spectra were obtained with the Gemini Multi-Object Spectrograph (GMOS; Hook et al. 2004) of the T8 dwarf 2MASSI J0415195−093506 (hereafter 2MASS 0415−09; Burgasser et al. 2002a) and of the T10 dwarf UGPS 0722−05 (Lucas et al. 2010). These objects were chosen as they are cool while covering a range in T_eff and being bright enough to make the observation feasible on an 8 m telescope. 2MASS 0415−09 has T_eff = 750 K (Saumon et al. 2007) and UGPS 0722−05 has T_eff ≈ 500 K (Lucas et al. 2010; Section 3).

GMOS at Gemini North was used, through queue time granted under program GN-2010B-Q-59. The R400 grating was used with the OG515 blocking filter. The central wavelength was 840 nm, with wavelength coverage of 620–1010 nm. Detector fringing affected the spectra longward of about 800 nm, which was mitigated by co-adding spatially offset sky-subtracted spectral images. The 05 slit was used with 2 × 2 binning, and the resulting resolution was 3.5 Å as determined from the arc images. An observing log is given in Table 1.

Flat fielding and wavelength calibration were achieved using the quartz halogen and CuAr lamps in the on-telescope calibration unit. The spectrophotometric standard EG 131 was used to determine the instrument response curve and to flux calibrate the spectra. The data were reduced using routines supplied in the IRAF Gemini package. Figure 1 shows the GMOS spectra; the signal-to-noise ratio is typically around 10 at the fainter blue end of each dwarf's spectrum, and around 20 or 30 at the brighter red end for the 2MASS 0415−09 spectrum and the UGPS 0722−05 spectrum, respectively.

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Photometry was obtained for a sample of T dwarfs using the GMOS instruments at both Gemini North and South, through queue time granted under programs GN-2010A-Q-81 and GS-2010B-Q-39. Objects were chosen that were bright enough to make i-band photometry (where there is very little flux) feasible on an 8 m telescope, and that provided (when combined with published data) adequate sampling of the spectral type versus i − z relationship. Photometry was also obtained for one L dwarf companion to a T dwarf, and for T dwarfs with SDSS photometry, in order to determine the transformation between the GMOS and SDSS systems. A total of 25 T dwarfs and 1 L dwarf were observed.

The sample is listed in the observing log given in Table 2. Exposure times are also given in Table 2; the targets were observed in a multi-position offset pattern and fringe frames for subtraction were created for each target in each filter using these multiple images. Twilight flats were used for flat fielding, and Landolt (1992) or SDSS photometric standard fields (Smith et al. 2002; http://www-star.fnal.gov/Southern_ugriz/www/Fieldindex.html) were used for calibration. The extinction coefficients for each filter at each site given on the Gemini GMOS calibration Web site were adopted: for Gemini North 0.10 and 0.05 mag airmass⁻¹, for Gemini South 0.08 and 0.05 mag airmass⁻¹, at i and z, respectively. Color terms are small and were not used. Photometry was derived using apertures with radii 6 or 10 pixels, or diameters 17 and 28. The data were reduced using routines supplied in the IRAF Gemini package.

Table 2 gives the derived i and z photometry in the GMOS-North and GMOS-South natural systems (see Section 2.2.1).

2.2.1. iz Photometric Systems

T Dwarfs and Photometric Systems. The extremely structured nature of the energy distribution of T dwarfs leads to large differences in the photometry obtained with different photometric systems. Stephens & Leggett (2004) demonstrate this for near-infrared filter sets. In the far-red, the very rapidly rising flux to the red, combined with the fact that the red edge of the z bandpass is usually defined by the detector cutoff, adds significant complications. Spectra for the very late type T dwarfs 2MASS 0415−09 and UGPS 0722−05 are shown in Figure 1, along with filter bandpasses.

We have synthesized i and z photometry for a sample of L and T dwarfs using flux-calibrated red and infrared spectra that span the filter bandpasses. We find that the synthesized SDSS- and GMOS-system values differ from the measured values by 10%–20%, which can be accounted for by small discrepancies in the red cutoffs of the filters.

GMOS North and GMOS South. The GMOS-North and GMOS-South systems are very similar—the filters are designed to be identical, but the E2V detector responses are slightly different (see Figure 1). Because of the difficulty in synthesizing the photometry, we use the repeat measurements of three brown dwarfs to determine the offset between the two systems. Table 2 shows that, for the T0, T4.5, and T8 dwarfs observed at both sites, the values obtained in the South are 0.05 ± 0.04 mag fainter than in the North. We convert the South to the North system by subtracting 0.05 mag from the i and z values measured with GMOS South.

GMOS North and SDSS. There are significant differences between the GMOS and SDSS i and z bandpasses (see Figure 1). Differences at the red end of each filter will be especially important due to the rapidly increasing flux to the red. Of the 26 objects in Table 1, 11 have SDSS (Data Release 8, DR8; Aihara et al. 2011) i-band measurements and 13 have SDSS z-band measurements. Brown dwarfs with SDSS data were deliberately observed in order to determine the photometric transformations.

Figure 2 plots the difference between the SDSS and GMOS-North i and z values, as a function of i − z (as measured on GMOS North). Weighted (by the inverse of the square of the uncertainty) fits give

$$\begin{equation*} i_{{\rm SDSS}} - i_{{\rm GMOS}} = 0.723 - 0.0521\times (i - z)_{{\rm GMOS}} \end{equation*}$$

$$\begin{equation*} z_{{\rm SDSS}} - z_{{\rm GMOS}} = 0.221 - 0.0712\times (i - z)_{{\rm GMOS}} \end{equation*}$$

for 1.9 < (i − z)_GMOS < 4.0. Similarly, Figure 2 also shows δz as a function of z_GMOS − J_MKO. A weighted fit gives

$$\begin{eqnarray*} &&z_{{\rm SDSS}} - z_{{\rm GMOS}} = 0.318 - 0.0924\times (z_{{\rm GMOS}} - J_{{\rm MKO}}) \end{eqnarray*}$$

for 2.7 < z_GMOS − J_MKO < 4.3. Omitting four i band data points with σ(δi) ⩾ 0.5, the rms scatter around the i_SDSS − i_GMOS fit is 0.06 mag. Omitting four z-band data points with σ(δz) ⩾ 0.1, the rms scatter around the z_SDSS − z_GMOS fit, as a function of i − z, is 0.08 mag, and as a function of z − J it is 0.10 mag. Tests of the transformations for z using both i − z and z − J show that the difference in the derived z_SDSS is around 0.03 mag. We adopt an estimated uncertainty in the GMOS-North to SDSS system transformations of 8%.

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Table 3 lists the transformed GMOS photometry, together with SDSS DR8 photometry where available (note that there can be significant differences in the photometry between SDSS Data Releases and it is advisable to use the latest release). An 8% error has been added in quadrature to the measurement error to allow for the uncertainty in the GMOS to SDSS transformation, and an additional 4% is added in quadrature for measurements made using GMOS-South. The z − J relationship has been used to transform the z magnitudes as opposed to the i − z relationship, due to the smaller uncertainties in the J magnitudes. The difference between the z values determined from the two transformations is small: 0.01 ± 0.03 mag.

Table 3. GMOS i and z Photometry for L and T dwarfs Transformed to the SDSS System

Name	Spectral	i(err)	z(err)	i(err)	z(err)
R.A./Decl.	Type			SDSS DR8	SDSS DR8
2MASSI J0415195−093506	T8	23.45(0.09)	19.40(0.09)
SDSSp J042348.57−041403.5	T0	20.14(0.08)	17.31(0.08)	20.19(0.04)	17.29(0.01)
2MASS J05591914−1404488	T4.5	21.35(0.09)	17.22(0.08)
UGPS J072227.51−054031.2	T10	24.32(0.12)	20.52(0.10)
2MASS J07290002−3954043	T8	24.18(0.13)	19.67(0.09)
SDSS J075840.33+324723.4	T2	21.86(0.09)	18.07(0.08)	21.93(0.13)	17.96(0.02)
SDSS J083048.80+012831.1	T4.5	24.13(0.16)	19.58(0.10)		19.40(0.07)
SDSSp J083717.22−000018.3	T1	23.79(0.13)	20.02(0.11)	23.48(0.50)	19.83(0.10)
ULAS J092624.76+071140.7	T3.5	25.03(0.18)	20.83(0.12)
2MASSI J0937347+293142	T6	22.53(0.09)	18.01(0.08)
ULAS J095047.28+011734.30	T8	25.91(0.21)	21.93(0.11)
2MASSI J1047538+212423	T6.5	23.52(0.11)	18.95(0.09)
SDSS J104829.21+091937.8	T2.5	23.53(0.11)	19.66(0.10)	24.20(0.73)	19.52(0.08)
SDSSp J111010.01+011613.1	T5.5	24.26(0.17)	19.83(0.10)	23.92(0.78)	19.67(0.10)
2MASS J11145133−2618235	T7.5	23.69(0.13)	19.49(0.10)
ULAS J115759.04+092200.7	T2.5	24.19(0.13)	20.18(0.11)		19.92(0.15)
2MASS J12314753+0847331	T5.5	22.75(0.10)	18.74(0.10)	22.76(0.29)	18.91(0.04)
ULAS J130041.73+122114.7	T8.5	24.78(0.11)	20.29(0.09)	23.28(0.57)	20.04(0.16)
SDSS J141624.08+134826.7A	L7	18.39(0.08)	15.86(0.08)	18.38(0.01)	15.91(0.01)
SDSS J141623.94+134836.3B	T7.5	25.21(0.26)	20.87(0.09)
Gliese 570D (2MASS J14571496−2121477)	T7.5	23.08(0.09)	18.90(0.09)
SDSSp J162414.37+002915.6	T6	22.95(0.09)	18.89(0.08)	22.82(0.27)	19.07(0.04)
SDSSp J175032.96+175903.0	T3.5	23.73(0.10)	19.46(0.09)	23.76(0.44)	19.59(0.06)
Wolf 940B (ULAS J214638.83−001038.7)	T8.5		21.88(0.14)
2MASSI J2339101+135230	T5	23.38(0.10)	19.50(0.09)	23.41(0.45)	19.42(0.07)
2MASSI J2356547−155310	T5.5	22.92(0.10)	19.27(0.09)

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Other iz Systems. Additional z-band photometry is available for 52 T dwarfs identified in the UKIDSS database. These data were obtained using the European Southern Observatory (ESO) Multi-Mode Instrument (EMMI) mounted on the New Technology Telescope (NTT) at La Silla, Chile, and are published in Warren et al. (2007), Lodieu et al. (2007), Pinfield et al. (2008), and Burningham et al. (2008, 2010). Warren et al. use spectrophotometry for a set of T dwarfs to calculate z_SDSS = z_EMMI + 0.2, and this offset has been applied in the UKIDSS publications.

z-band photometry is also available for three T dwarfs identified in the CFBDS data set. These data were obtained using MegaCam on the CFHT and are published in Delorme et al. (2008, 2010). Reyle et al. (2010) synthesize i and z photometry for L and T dwarfs using flux-calibrated spectra. Comparison of these values to measured SDSS values suggests a large difference between the systems of ∼0.3 mag, where the MegaCam values are fainter. We have synthesized CFHT and SDSS z magnitudes using the files available for the MegaCam optics, filters, and detector, as well as the telescope optics, available from the CFHT Web sites,¹² and find a smaller difference. Synthesizing SDSS and MegaCam values indicates that z_SDSS = z_MegaCam − C, where C = 0.1 for early-type T dwarfs and C = 0.2 for late-type T dwarfs. We have applied this smaller correction to the photometry for the three CFBDS dwarfs.

A 2.8–4.2 μm spectrum was obtained for UGPS 0722−05 using the Infrared Camera and Spectrograph (IRCS; Kobayashi et al. 2000) on the Subaru telescope. UGPS 0722-05 was observed on the nights of 2011 January 23 and 24 with the L-band grism, using a 09 slit; the spectral resolution is R ≈ 180. The total integration time was 120 minutes, made up of 48 minutes from January 23 and 72 minutes from January 24. Observations were made in an ABBA pattern with 60 s integrations and a 6'' nod.

The spectrum was extracted in IRAF using a 075 aperture. Since no suitable arc lamp is available, a linear solution was adopted for the wavelength calibration, based on two widely spaced telluric features, following the procedure described in the IRCS data reduction cookbook (http://www.subarutelescope.org/Observing/DataReduction/index.html). The estimated accuracy in the wavelength calibration is ∼1 nm.

Two A- to F-type stars were observed as telluric standards on each night, before and after the observation of UGPS 0722-05. The extracted telluric-calibrated spectra from January 23 and January 24 were found to be very similar, with the exception of a slight disagreement in the slope of the continuum at the longest wavelengths (4.00–4.18 μm). The spectrum was flux calibrated using IRAC [3.6] photometry, which has an uncertainty of 5% (Section 3.2, Table 4).

Figure 3 shows the final reduced spectrum. The error spectrum is also shown, which is based on the difference between the two subsets of data. The signal-to-noise ratio varies across the spectrum and is around 5–15 from 3.7 μm to 4.1 μm, the wavelength region less impacted by strong CH₄ absorption. The spectrum has significant structure around 3.8 μm: there are absorption features at 3.71–3.74 μm, 3.77–3.79 μm, and 3.83–3.86 μm. The Saumon & Marley models show that all the structure in this region is due to absorption by CH₄, and the models reproduce the observations quite well (Section 3.4). These models show the absorption bands around 3.8 μm strengthening with decreasing temperature, with the features at 3.72 μm and 3.84 μm only being apparent for T_eff ≲ 800 K, depending on resolution. There is possibly a hint of the structure in the R ≈ 600 spectrum of the 900–1000 K dwarf Indi Bb presented by King et al. (2010), but the R ≈ 100 AKARI spectrum of the 750 K dwarf 2MASS 0415−09 presented by Yamamura et al. (2010) is too coarse to show these features.

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In Lucas et al. (2010), we found a parallax for UGPS 0722−05 of 237 ± 41 mas based on seven UKIRT observations from 2006 to 2010; adding a very low signal-to-noise 2MASS detection gave a value of 246 ± 33 mas. The UKIRT observations for this object have continued, and we now have 23 observations covering a period from 2006 November to 2011 April. Following the procedures for observing, image treatment, and astrometric reduction described in Marocco et al. (2010), we determine parallax and proper motions that are very similar in value to those presented in Lucas et al. but with much smaller, <1%, errors. The revised values are given in Table 4.

Incorporating the 2MASS observation did not improve the precision of our result. Also, the UKIRT observations provide fainter reference objects, therefore the correction from relative to absolute parallax is smaller and more accurate. The high precision found for this object is consistent with that found in Marocco et al. (2010) for targets of similar brightness with similar temporal baselines.

In this section, we perform an analysis of the spectral energy distribution of UGPS 0722−05 in order to constrain T_eff, gravity (g), mass, and age for the object. Lucas et al. (2010) classify the dwarf as T10 and find T_eff = 520 ± 40 K based on its luminosity. Cushing et al. (2011) reclassify the dwarf as T9 and estimate T_eff = 650 K based on a fit of synthetic spectra to the near-infrared spectrum. Bochanski et al. (2011) present high-resolution near-infrared spectra for UGPS 0722−05 and find that synthetic near-infrared spectra indicate T_eff = 500–600 K (a 100 K warmer temperature is found if the luminosity constraint is neglected), although the fit is poor. Lucas et al. and Bochanski et al. use the BT-SETTL models of Allard et al. (2007a), while Cushing et al. (and this work) use the models of Saumon & Marley (2008). Note that at these low temperatures the near-infrared spectrum makes up <30% of the total flux from the brown dwarf. Also, the opacity line lists for important molecules are known to be incomplete in the near-infrared and thus all models are subject to systematic errors. Hence the temperatures found by Bochanski et al. and Cushing et al., based on near-infrared data alone, are prone to potentially significant error. In fact, Cushing et al. find that the near-infrared spectroscopic temperatures imply distances to the dwarfs that can be very different from photometric or trigonometric parallax solutions. In this work, we incorporate mid-infrared data and a new parallax to reduce the uncertainty in the derived properties of the brown dwarf.

The difference in spectral type assigned by Lucas et al. and Cushing et al. of T10 cf. T9 is important to note. A definitive spectral-type determination for UGPS 0722−05 is beyond the scope of this paper. The T10 classification is based on a comparison of the dwarf's spectral indices to those of the T8 and T9 dwarfs, where the T9 dwarfs are classified based on the extension of the Burgasser et al. (2006) scheme by Burningham et al. (2008). However, Cushing et al. propose that UGPS 0722−05 is T9 based on a comparison of 1.1–1.7 μm spectra for the T6, T7, and T8 spectral standards of Burgasser et al. (2006). The definition of the end of the T sequence and the start of the Y sequence is likely to change as more dwarfs are identified with 300 ⩽ T_eff (K) ⩽600; in the meantime, we adopt a spectral type of T10 for UGPS 0722−05, as found by Lucas et al.

In this analysis, we use the near-infrared spectrum and near- and mid-infrared photometry given by Lucas et al. (2010), together with the new optical and L-band spectra presented here. To these data, we add the WISE mid-infrared photometry given by Kirkpatrick et al. (2011) for UGPS 0722−05. The optical, near-infrared, and L-band spectra are flux-calibrated using the GMOS z photometry presented here, the JHK photometry presented in Lucas et al., and the IRAC [3.6] photometry presented in Lucas et al., respectively.

We also use the new values for the trigonometric parallax and proper motions presented here. We combine these data with the radial velocity determined by Bochanski et al. (2011) to determine UVW velocities for UGPS 0722−05. We find that the kinematics of this brown dwarf are typical of thin disk objects, in agreement with Bochanski et al. (see, e.g., Figure 21 of Kilic et al. 2010, which is based on thick disk and halo velocities from Chiba & Beers 2000, and thin disk kinematics from Soubiran et al. 2003). Bochanski et al. find that UGPS 0722−05 has a rotational velocity of 40 ± 10 km s⁻¹, which is rapid, but similar to the values found for other T dwarfs (e.g., Zapatero Osorio et al. 2006). Note that the velocity is computed by comparison to a model spectrum and is thus sensitive to the treatment of line broadening.

Table 4 lists the available observational data for UGPS 0722−05.

We compare the optical to 4 μm spectrum of UGPS 0722−05 to solar-metallicity cloudless models described in Saumon & Marley (2008), with updated H₂ collision-induced absorption and the new NH₃ line list of Yurchenko et al. (2011). These new models are described in Saumon et al. (2012). Currently, only solar-metallicity models are available for this new grid, however the photometric colors of UGPS 0722−05 imply that it has a metallicity close to solar (Lucas et al. 2010) and brown dwarf evolution is insensitive to small deviations from solar metallicity (e.g., Saumon & Marley 2008; Leggett et al. 2010b; Burrows et al. 2011).

The inclusion of the 4 μm flux peak is useful for covering the spectral energy distribution, and we find that the spectral data (the far-red spectrum and the 3–4 μm spectrum presented here, together with the near-infrared spectrum of Lucas et al. 2010) sample 30%–40% of the derived bolometric flux (see below). For each model, defined by T_eff and gravity, there is an associated radius determined by evolutionary models (Saumon & Marley 2008). The analysis follows the self-consistent luminosity method described in Leggett et al. (2010b) and Saumon et al. (2006, 2007). Briefly, the observed spectrum is integrated to give an observed flux (5.17 ± 0.13 × 10⁻¹³ erg s⁻¹cm⁻²), and synthetic spectra are used to determine a bolometric correction. A family of (T_eff, g) values are derived that provide bolometric luminosity (L_bol) values consistent with both the synthesized bolometric correction and the luminosity implied by evolutionary models. The L_bol values vary slightly due to the differences between the models used for the unmeasured parts of the spectral energy distribution. We limit the allowed age range for the dwarf to between 40 Myr (defined by assuming it will be more massive than 2 M_Jupiter) and 7 Gyr (the thin disk kinematics suggest the dwarf is younger than 10 Gyr). We show below in Section 3.5 that the warmer effective temperatures associated with ages greater than 7 Gyr do not fit the mid-infrared photometry and are less likely.

Figure 4 shows a plot of T_eff against log g and illustrates the solutions that we obtain with our luminosity method, superimposed on the cloudless cooling tracks of Saumon & Marley (2008). Table 5 lists three representative solutions (shown as solid dots in Figure 4) for T_eff, log g, log L_bol, mass, and radius, which span the adopted range in age. The uncertainty in log L_bol is dominated by the uncertainty in the flux calibration of the spectrum (2.6% overall) and is ±0.014 dex, or ±4 K in T_eff, for a fixed gravity. These are formal uncertainties based on those for the flux calibration and the parallax and do not take into account systematic biases in the models. Our luminosity range of 6.8 × 10⁻⁷ to 8.9 × 10⁻⁷ L_☉ is consistent with the lower range of the values found by Lucas et al. (determined by combining the near-infrared spectrum with mid-infrared photometry).

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Figure 5 shows the observed optical through near-infrared and L-band spectrum, and the synthetic spectra for the three Saumon & Marley models of Table 5. These model spectra include departures from chemical equilibrium caused by vertical mixing, parameterized with an eddy diffusion coefficient of K_zz = 10^5.5 cm² s⁻¹. At these wavelengths, mixing does not significantly impact the spectra; however, we find in Section 3.5 that rapid mixing is needed to reproduce the 4.5 μm photometry. In Figure 5, the synthetic spectra have not been scaled to fit, but are calibrated by the measured distance to the object and the radius implied by evolutionary models for each (T_eff, g) value. None of the models fit the 1.0–1.3 μm region well, although the highest temperature and highest gravity model (with less flux at 1.0–1.3 μm) would be favored, with T_eff = 550 K.

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In previous work, we have found, as we do here, that the models overpredict the flux at the 1.0 μm Y band and the 1.25 μm J band, for brown dwarfs cooler than ∼700 K (e.g., Leggett et al. 2009, 2010a, 2010b). It is known that the CH₄ opacity line list at these wavelengths is incomplete, and this is a possible explanation for the discrepancies seen in Figure 5 in the Y and J bands, although thin clouds may also affect the relative peak fluxes (e.g., Burgasser et al. 2011).

The models fit the 2.8–4.2 μm spectrum reasonably well, although they are too faint at 4.1 μm, which is probably due to the uncertain CH₄ absorption that still dominates in these models at 4.1 μm. Note that the models include the effects of vertical mixing on the CO abundance, which has a strong band for λ > 4.5 μm. The abundance of CO₂, which has a strong band centered at 4.23 μm, is also increased by vertical transport (Burningham et al. 2011) but this effect is not included here. An excess of CO₂ would further depress the modeled flux in the 4.2–4.4 μm region. The three model spectra are very similar in the L-band wavelength region and do not constrain our fit.

For brown dwarfs as cold as UGPS 0722-05, most of the flux is emitted in the mid-infrared and the models can be usefully constrained by the available photometry at 3–12 μm. Figure 6 shows a comparison of the synthetic photometry to the observed IRAC [3.6] and [4.5], L' and N magnitudes given by Lucas et al. (2010), and Figure 7 shows the comparison for the WISE W1(3.4), W2(4.6), W3(12), and W4(22) values given by Kirkpatrick et al. (2011). The apparent magnitudes are plotted as a function of the vertical mixing coefficient K_zz cm² s⁻¹. Generally, larger values of K_zz imply greater enhancement of CO over CH₄. Values of log K_zz = 2–6, corresponding to mixing timescales of ∼10 yr to ∼1 hr, respectively, reproduce the observations of T dwarfs (e.g., Saumon et al. 2007). Figures 6 and 7 show that the mixing strongly impacts the IRAC [4.5] and WISE W2 4.2–5.0 μm flux; rapid mixing enhances CO and CO₂ in this region, reducing the flux from the dwarf. These two data points constrain the mixing coefficient for UGPS 0722-05 to log K_zz ≈ 5.5–6.0. (The choice of mixing coefficient does not impact the physical parameters derived using our self-consistent luminosity method; see, e.g., Leggett et al. 2010b).

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The 8–16 μm flux (N, W3; Figures 6 and 7) constrains T_eff for UGPS 0722-05 to be between 492 K and 518 K; the warmest 550 K model is excluded. We find that a mixing coefficient of log K_zz ≈ 5.5–6.0 and T_eff ≈ 505 K fits all the photometry except W1(3.4) and [3.6] (the L'(3.8 μm) photometry is too uncertain to constrain the models). W1 and [3.6] effectively measure the same part of the spectrum, and Figure 5 shows that the Saumon & Marley models underestimate the flux at 3.5–4.2 μm. The discrepancy at 4.1 μm in particular has a strong impact on the photometry, given that this is the only region with significant flux within these particular passbands. Figures 6 and 7 show that the synthetic photometry is too faint by ∼20% in this region.

Although no mid-infrared spectra for UGPS 0722−05 exist, these models have been validated using spectral data for brown dwarfs with a similar T_eff. The models reproduce the 7.5–14.2 μm Spitzer spectra well for ULAS J003402.77005206.7 and ULAS J133553.45+113005.2 with T_eff = 550–600 K and 500–550 K, respectively (Leggett et al. 2009), as well as for Wolf 940 B with T_eff = 585–625 K (Leggett et al. 2010b). Thus, Figures 6 and 7 demonstrate that the models reproduce the spectral energy distribution at 4.2 ≲ λ (μm) ≲ 16 well, and that our L_bol determination is robust.

The 8–16 μm flux (N, W3; Figures 6 and 7) indicates that UGPS 0722−05 has T_eff mid-way between 492 K and 518 K, hence we adopt T_eff = 505 K, which implies log g = 4.00 (Table 5 and Figure 4). A significantly warmer temperature is excluded: higher values of T_eff result in too little flux at these wavelengths. The photometry derived from a model with T_eff = 505 K and log g = 4.00 is shown in Figures 6 and 7. This result is consistent with the young disk kinematics, as the high value of T_eff = 550 K corresponds to an age of 6.6 Gyr (Table 5), approaching the limit of what would be expected for the thin disk. However, the result does also mean that the models have an excess of flux at 1.0–1.3 μm (Figure 5). We estimate the uncertainty in T_eff to be 10 K, by allowing for ∼2σ variations in the W3 photometry and assuming a minimum mass of 2–3 M_Jupiter for this brown dwarf. This uncertainty does not include systematic errors due to the known inadequacies of our model atmospheres (and all currently available model atmospheres) caused by the incomplete opacities for atmospheres at these temperatures and pressures.

In summary, we find that UGPS 0722−05 has T_eff = 505 ± 10 K. This implies that the dwarf has a mass of 3–11 M_Jupiter and an age between 60 Myr and 1 Gyr (see Table 5). Figure 8 plots the entire spectral energy distribution for this solution, together with the observed spectra and observed and synthesized mid-infrared photometry.

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In the atmospheres of late-type T dwarfs, the refractory elements Mg, Al, Ca, and Ti have been removed by condensation at high temperatures in the deep atmosphere and the Cs, K, Li, Na, and Rb neutral alkalis are starting to be removed as they gradually turn into chloride gases and other halide or hydroxide gases. Note that the fundamental vibrational frequencies of alkali halides are in the mid- to far-infrared, between 20 and 50 μm, where the low flux from the brown dwarf and the limited sensitivity of the instrumentation make their detection extremely difficult.

Lodders (1999) gives a detailed description of the alkali chemistry in cool dwarf atmospheres, and here we summarize the major points that are important for understanding Rb and Cs chemistry. Rb and Cs lines, and the red wing of the strong 0.77 μm K i resonance doublet, are seen in our optical spectrum for the 500 K dwarf UGPS 0722−05 in Figure 1 (see also Figures 10 and 11 below). The trends in chemistry as function of pressure (P) and temperature (T) are shown in Figure 9, which also shows the P–T profiles for selected T dwarf atmosphere models, as indicated in the legends. Curves show where certain gases are equal in abundance—for example, Rb=RbCl, long-dashed curve, indicates that the abundance of monatomic Rb equals that of RbCl gas. Other (solid) curves indicate where certain elements begin to be stable in condensed form—for example Na₂S(s) for sodium sulfide solid. The curves showing chemistry of Rb or Cs are colored red and blue, respectively.

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The Saumon & Marley model atmospheres show that the Rb and Cs lines are formed in regions where the temperature is significantly warmer than the T_eff value, and that the Rb i lines, by virtue of being closer to the K i doublet, are formed on a higher background of opacity and so higher up in the atmosphere in a cooler region than the Cs i lines. For a brown dwarf with T_eff ≈ 1000 K, the Rb lines form at 930–1000 K and the Cs lines at 1130–1430 K. For T_eff ≈ 750 K these values become 880–1000 K and 1050–1230 K for Rb and Cs, respectively. For T_eff ≈ 500 K these values become 850–940 K and 940–1050 K for Rb and Cs, respectively. These zones are indicated along the P–T profiles in Figure 9. For a T_eff ≈ 500 K dwarf, such as UGPS 0722−05, we are just entering the temperature regime where the RbCl abundance is larger than the neutral Rb abundance; the abundance of CsCl should be significantly larger than the neutral Cs abundance.

For T_eff ≈ 500 K brown dwarfs, Figure 9 also indicates that Na₂S is condensing (the opacity of the solid is not currently included in the models). Removal of sodium from the gas reduces the abundances of monatomic Na and NaCl gas. Thus, there is more chlorine available to react with monatomic K and Rb gas to form KCl and RbCl gas and this accounts for the increase in KCl and RbCl only a few degrees below the onset of Na₂S condensation. With a further decrease in temperature, the partial pressures of the chloride gases increase and vapor saturation eventually sets in so that the K, Rb, and Cs chloride solid condensates become thermodynamically stable.

Figure 10 shows our observed red spectra of 2MASS 0415−09 and UGPS 0722−05; these dwarfs have T_eff ≈ 750 K and 500 K, and log g ≈ 5.2 and 4.0, respectively (Saumon et al. 2007; this work). The K i absorption at 0.770 μm remains significant for both T dwarfs, although the near-infrared 1.243/1.252 μm doublet becomes hard to detect for spectral types later than around T7 (e.g., McLean et al. 2003); the stronger 1.252 μm feature is marginally detected in 2MASS 0415−09 and UGPS 0722−05 (McLean et al. 2003; Bochanski et al. 2011). The near-infrared features arise from a lower level whose population is very sensitive to temperature and will disappear at warmer values than the optical feature. Neutral Cs and Rb are well detected in both objects, with similar line strengths in the two dwarfs, relative to the pseudo-continuum. Thus, although for Cs we are well into the regime where CsCl should be the dominant form, these lines are still seen in the far-red, where the atmosphere is relatively transparent.

The persistence of Rb and Cs at lower temperature provides more evidence for the existence of a deep silicate cloud layer (Ackerman & Marley 2001; Burgasser et al. 2002b; Knapp et al. 2004; Marley et al. 2002, 2010). In strongly gravitationally bound atmospheres, condensates can settle into cloud layers below the cooler atmosphere, which then become depleted in the elements that are sequestered in the clouds. In brown dwarfs, removal of high-temperature condensates into clouds prevents secondary condensate formation and solid solution formation. Thus, the silicates albite (Na-feldspar, NaAlSi₃O₈) and orthoclase (K-feldspar, KAlSi₃O₈) do not form, since the silicates which would form these compounds are sequestered in a cloud layer below the atmospheric level at which this reaction would otherwise proceed (Rb and Cs can also substitute in the feldspar lattice at temperatures lower than required for Na and K dissolution). Instead, Na condenses as sulfide, and the other alkalis condense as chlorides.

Figure 11 compares the observed spectrum of UGPS 0722−05 to the spectrum generated by our T_eff = 505 K model. It can be seen that although the red wing of the K i doublet at 0.770 μm is incorrectly modeled, the models reproduce the Rb feature reasonably well, while the modeled Cs lines are stronger than observed. Now that brown dwarfs cooler than 500 K are being discovered (Cushing et al. 2011; Liu et al. 2011; Luhman et al. 2011), we can expect to see pronounced changes in the optical spectra of the coolest brown dwarfs, as the alkalis convert into chloride gases and also condense as salts.

Figures 12 and 13 show absolute z, Y, J, and H magnitudes and colors, with model sequences. The iz data are AB magnitudes on the SDSS system (see Section 2.2.1), and the YJH are Vega magnitudes on the Mauna Kea Observatories system (Tokunaga et al. 2002; Tokunaga & Vacca 2005). The photometry and parallaxes are taken from the literature, supplemented by the iz photometry presented here. A compilation of YJH data and parallaxes is available at http://www.gemini.edu/staff/sleggett, which is described in Leggett et al. (2010a) and references therein. Figures 12 and 13 include astrometry and photometry published after Leggett et al., in Marocco et al. (2010) and Burningham et al. (2010, 2011). Figures 12 and 13 also include the published z photometry described in Section 2.2.1 and SDSS iz photometry for the brighter L and T dwarfs presented in Geballe et al. (2002), Knapp et al. (2004), and Chiu et al. (2006).

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Figure 12 implies that the calculated i magnitude is too faint by ∼1 mag. This is consistent with the discrepancy between the models and observations shown in Figure 11, where the 0.770 μm K i line is shallower than modeled (i and z bandpasses are shown in Figure 1). Figure 12 also suggests that Y and J are too bright by ∼0.2–0.3 mag. The discrepancy at Y and J can be seen in Figure 5, where there is excess model flux at 1.0–1.3 μm, which we interpret as due to the incompleteness of the CH₄ line list and possibly the presence of thin clouds.

Marley et al. (2002; see also Burrows et al. 2000) point out that the i − z color is sensitive to pressure broadening of the K i doublet. The exceptionally strong pressure broadening affecting the 0.770 μm K i resonance doublet requires the application of a sophisticated line broadening theory. In the Saumon & Marley models, these lines are modeled with a Lorentzian core and a far wing exponential cutoff using a weakly constrained cutoff parameter. The modeled i − z color changes by as much as 0.4 mag when computed with the cutoff parameter changed by a factor of two. A much more accurate calculation of the pressure-broadened line profiles of alkali metals in brown dwarfs has been developed by Allard et al. (2003, 2005, 2007b) and Allard & Spiegelman (2006) and will be incorporated in the Saumon & Marley models. The BT-Settl models (Allard et al. 2003, 2007a; Freytag et al. 2010), which use these newer line profiles, do show a better match to the UGPS 0722-05 optical spectrum.

Symbols in Figures 12 and 13 indicate the metallicity and gravity of the dwarfs, where they can be constrained by a companion, by bolometric luminosity, or by their IRAC colors (Leggett et al. 2011). There are no clear trends with metallicity or gravity, although the measurement uncertainties and scatter are large. The model sequences suggest that the izYJ colors become more sensitive to metallicity and gravity for T_eff ⩽ 700 K, and trends may become clearer when more such objects, T9 and later-type dwarfs, are known. i − z and z − J are calculated to be predominantly sensitive to metallicity, while Y − J and z − Y are sensitive to gravity. The colors of the latest-type T dwarfs, T9–T10, are consistent with models with T_eff = 500–600 K.