Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://www.stsci.edu/~golim/papers/saumon2007.pdf Äàòà èçìåíåíèÿ: Tue Feb 20 21:36:09 2007 Äàòà èíäåêñèðîâàíèÿ: Tue Oct 2 11:19:21 2012 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: earth's atmosphere

The Astrophysical Journal, 656:1136 ­ 1149, 2007 February 20
# 2007. The American Astronomical Society. All rights reserved. Printed in U.S.A.

A

PHYSICAL PARAMETERS OF TWO VERY COOL T DWARFS
D. Saumon
Los Alamos National Laboratory, Los Alamos, NM; dsaumon@lanl.gov

M. S. Marley
NASA Ames Research Center, Moffett Field, CA

S. K. Leggett and T. R. Geballe
Gemini Observatory, Hilo, HI

D. Stephens and D. A. Golimowski
Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD

M. C. Cushing1 and X. Fan
Steward Observatory, Tucson, AZ

J. T. Rayner
Institute for Astronomy, University of Hawaii, Honolulu, HI

K. Lodders
Department of Earth and Planetary Science, Washington University, St. Louis, MO

and R. S. Freedman
SETI Institute, NASA Ames Research Center, Moffett Field, CA Received 2006 September 30; accepted 2006 November 1

ABSTRACT We present new infrared spectra of the T8 brown dwarf 2MASS J04151954 þ0935066: 2.9 ­ 4.1 m spectra obtained with the Infrared Camera and Spectrograph on the Subaru Telescope, and 5.2 ­ 14.5 m spectra obtained with the Infrared Spectrograph on the Spitzer Space Telescope. We use these data and models to determine an accurate bolometric luminosity of log Lbol /L ¼ þ5:67 and to constrain the effective temperature, gravity, mass, and age to 725 ­ 775 K, log g ¼ 5:00 5:37, M ¼ 33 58 MJup , and age ¼ 3 10 Gyr. We perform the same analysis using published 0.6 ­ 15 m spectra for the T7.5 dwarf 2MASS J12171110þ0311131, for which we find a metal-rich composition (½ Fe / H $ 0:3), and log Lbol /L ¼ þ5:31, TeA ¼ 850 950 K, log g ¼ 4:80 5:42, M ¼ 25 66 MJup , and age ¼ 1 10 Gyr. These luminosities and effective temperatures straddle those determined with the same method and models for Gl 570D by Saumon et al. and make 2MASS J04151954þ0935066 the coolest and least luminous T dwarf with well-determined properties. We find that synthetic spectra generated by the models reproduce the observed red through mid-infrared spectra of 2MASS J04151954þ0935066 and 2MASS J12171110þ0311131 very well, except for known discrepancies that are most likely due to the incomplete CH4 opacities. Both objects show evidence of departures from strict chemical equilibrium, and we discuss this result in the context of other late T dwarfs in which disequilibrium phenomena have been observed. Subject headings: stars: individual (2MASS J04151954þ0935066, 2MASS J12171110þ0311131, Gl 570D) -- stars: low-mass, brown dwarfs Online material: color figures

1. INTRODUCTION The Sloan Digital Sky Survey (SDSS; York et al. 2000) and the Two Micron All Sky Survey (2MASS; Beichman et al. 1998; Skrutskie et al. 2006) have revealed large numbers of ultracool low-mass field dwarfs, known as L and T dwarfs. The effective temperatures (TeA ) of L dwarfs are $1450 ­ 2200 K, and those of currently known T dwarfs are $700 ­ 1450 K (Golimowski et al. 2004; Vrba et al. 2004). T dwarfs are identified by the presence of CH4 absorption features in both the H and K near-infrared bands, the 2 2 × 3 and 2 3 features at 1.63 and 1.67 m, the P-branch of the 2 × 3 band at 2.20 m, and the 3 × 4 and 1 × 4 bands at 2.32 and 2.37 m. Spectral classification schemes using
1

Spitzer Fellow.

near-infrared spectra have been presented for T dwarfs by Burgasser et al. (2002) and Geballe et al. (2002). These similar schemes, using primarily the strengths of the H2O and CH4 absorption features at 1 ­ 2.5 m, were recently merged by Burgasser et al. (2006b). Currently, there are six dwarfs known that are classified as later than T7. Five of these were discovered in the 2MASS database: 2MASS J04151954þ0935066, 2MASS J09393548þ 2448279, 2MASS J11145133þ2618235, 2MASS J12171110þ 0311131, and 2MASS J14571496þ2121477 ( Burgasser et al. 1999, 2000, 2002; Tinney et al. 2005). The sixth, HD 3651B, was recently discovered through searches for wide companions to stars known to host extrasolar planets ( Mugrauer et al. 2006; Luhman et al. 2007 ). Trigonometric parallaxes have been published for four of these dwarfs, and Table 1 lists these four objects. Full 2MASS 1136


TABLE 1 Published Astrometric and Photospheric Data for t he T7.5 ­ T 8 Dwarfs w ith Measured P ar allax Teff (K) Name HD 3651B ........................................................... 2MASS J04151954þ0935066 ............................ 2MASS J12171110þ0311131 ............................ 2MASS J14571496þ2121477(Gl 570D) .............
a c b

log g (cm sþ 2) Lum. 780 600 725 800 ­ ­ ­ ­
d

References
e

Spectral Type T7.5 T8 T7.5 T7.5

a

Parallax (error) (mas) 90.03(0.72) 174.34(2.76) 93.2(2.06) 170.16(1.45)

Vtan (error) (km sþ1) 31.0(1.2) 61.4(1.0) 53.5(1.2) 56.4(0.9)

log (Lbol /L) (error) þ5.60(0.05) þ5.73(0.05) þ5.32(0.05) þ5.53(0.05)

b

Spec. 760 740 860 780 ­ ­ ­ ­

c

Spec.

c

Col./ Lum. 5.1 ­ 5.0 ô 4.5 ô 5.09 ­

Disc. 1, 2 4 6 8

Astr. 3 5 5, 7 3, 9

920 760 880 820

840 750 975 820

4.7 ­ 5.1 4.9 ­ 5.0 4.7 ­ 4.9 5.1

5.5 0.25 0.25 5.23

Spectral types are based on the near-infrared classification scheme for T dwarfs by Burgasser et al. (2006b). Bolometric luminosities from Golimowski et al. (2004) and Luhman et al. (2007). Derived from the near-infrared spectral ratio technique of Burgasser et al. (2006a) and Burgasser (2007). d Derived from observed luminosity by Golimowski et al. (2004), Liu et al. (2007), and S06. e Derived from near-infrared colors by Knapp et al. (2004), or from luminosity by Liu et al. (2007) and S06. References.-- (1) Mugrauer et al. 2006; (2) Luhman et al. 2007; (3) ESA 1997; (4) Burgasser et al. 2002; (5) Vrba et al. 2004; (6) Burgasser et al. 1999; (7) Tinney et al. 2003; (8) Burgasser et al. 2000; (9) van Altena et al. 1995.


1138

SAUMON ET AL.

Vol. 656

Fig. 1.-- Ground-based red and near-infrared spectra of three of the six known T dwarfs later than T7: 2MASS J0415þ0935, 2MASS J1217þ0311, and Gl 570D. Broad and strong absorption features are identified. The spectra are normalized to the peak flux and offset; dashed lines indicate the zero flux level. Data sources are Burgasser et al. (2003), Geballe et al. (2001, 2002), and Knapp et al. (2004).

names are given in the table, but in the rest of this paper we use abbreviated names in the form 2MASS JHHMMôDDMM, except for 2MASS J14571496þ2121477, to which we refer by its more commonly used name, Gl 570D. Table 1 lists published values of trigonometric parallax, tangential velocity, bolometric luminosity, TeA , and surface gravity ( g). Three of the very late T dwarfs, 2MASS J0415þ0935, 2MASS J1217þ0311, and Gl 570D, have been observed spectroscopically in the mid-infrared, and they form the sample for this paper. Only near-infrared spectra are available for the other three known T7.5 ­ T8 dwarfs, and these will be discussed in a future publi-

cation. Figure 1 plots the red and near-infrared spectra for the three dwarfs in our sample. It can be seen that the bands of H2O and CH4 are extremely strong, as is the K i 0.77 m doublet. Narrow peaks of flux emerge from between these bands. In this paper we present new 2.9 ­ 4.1 and 5.5 ­ 15 m lowresolution spectra of one of our sample, 2MASS J0415þ0935 ( T8). The former were obtained using the Infrared Camera and Spectrograph ( IRCS; Kobayashi et al. 2000) on the Subaru Telescope on Mauna Kea, and the latter using the Infrared Spectrograph ( IRS; Houck et al. 2004) on the Spitzer Space Telescope (Werner et al. 2004). We use these data, together with previously published


No. 2, 2007

PHYSICAL PARAMETERS OF TWO VERY COOL T DWARFS

1139

red and near-infrared spectra and trigonometric parallaxes, and grids of evolutionary and atmospheric models, to determine accurate values of Lbol , TeA , and log g for this dwarf. We carry out the same analysis for a second member of the sample, 2MASS J1217þ 0311 ( T7.5), using published IRS data, and compare these parameters to those derived in the same way for the third member, Gl 570D ( T7.5) by Saumon et al. (2006, hereafter S06). Matches between the data and synthetic spectra generated from the atmospheric models are examined. 2. OBSERVATIONS 2.1. Published Observational Data Near-infrared spectroscopy and 2MASS photometry for 2MASS J0415þ0935, 2MASS J1217þ0311, and Gl 570D can be found in the discovery papers ( Table 1; Burgasser et al. 1999, 2000, 2002). Red spectra are presented by Burgasser et al. (2003). Near-infrared spectra are also presented by Geballe et al. (2001, 2002) for Gl 570D and 2MASS J1217þ0311, and by Knapp et al. (2004) for 2MASS J0415þ0935. Near-infrared spectral indices and the implied spectral types can be found for them in Burgasser et al. (2006b). Near-infrared photometry on the Mauna Kea Observatory ( MKO) system ( Tokunaga et al. 2002) is available for Gl 570D (Geballe et al. 2001), 2MASS J1217þ0311 ( Leggett et al. 2002), and 2MASS J0415þ0935 ( Knapp et al. 2004). Longer wavelength data are also available for our sample. 0 Golimowski et al. (2004) presented LMKO photometry for all three 0 dwarfs and MMKO photometry for 2MASS J0415þ0935. Patten et al. (2006) gave Spitzer 's Infrared Array Camera ( IRAC; Fazio et al. 2004) photometry at 3.55, 4.49, 5.73, and 7.87 mfor the three dwarfs. IRS 5.2 ­ 14.5 m spectra have been published for Gl 570D (S06) and 2MASS J1217þ0311 (Cushing et al. 2006). 2.2. New 2.9 ­ 4.1 m IRCS Data 2MASS J0415þ0935 was observed on the night of 2002 December 12 with the Infrared Camera and Spectrograph ( IRCS; Kobayashi et al. 2000) mounted on the 8.2 m Subaru Telescope. We used the L-band grism with a slit width of 0.600 , which resulted in a spectrum covering 2.90 ­ 4.16 m at a resolving power of R $ 210. A series of forty 35 s exposures were taken in pairs, with the target at two different positions along the 2000 slit. A nearby A0 V star, HD 29573, was also observed to correct for absorption due to the Earth's atmosphere and the instrument throughput, and a series of flat-field exposures and dark frames were taken at the end of the night. The spectra were extracted using a modified version of the Spextool data reduction package (Cushing et al. 2004). Each pair of exposures was subtracted and then flat fielded. The spectra were then extracted and wavelength calibrated using sky emission features. The target spectra were corrected for telluric absorption and the instrument throughput by dividing by the spectrum of HD 29573 and multiplying by a Planck function for a temperature of 9500 K, as appropriate for an A0 V star. The spectrum was rebinned to have 1 pixel per resolution element. The final signalto-noise ratio (S/ N ) of the spectrum ranges from 4 to 10 per binned resolution element. Flux calibration was obtained by scal0 ing the spectrum to match the LMKO magnitude. 2.3. New 5.2 ­ 14.5 m IRS Data 2MASS J0415þ0935 was observed with the Infrared Spectrograph ( IRS; Houck et al. 2004) on 2005 September 6, using the Spitzer Space Telescope as part of our General Observer cycle 1

campaign to obtain mid-infrared spectra for a number of late-L and T dwarfs. The Short-Low (SL) module was used to obtain both second-order (5.2 ­ 7.7 m) and first-order (7.4 ­ 14.5 m) spectra in staring mode. Two first-order and one second-order sequences were acquired. Each sequence consisted of 18 observations taken at one position along either the first-order or secondorder slit, followed by a nod to a second position on the slit for an additional 18 observations. The data were processed using version 13.2.0 of the IRS pipeline, which removed all of the ``Spitzerspecific'' effects and produced a basic calibrated data ( BCD) image for each observation. The BCD images were reduced using various scripts and contributed IDL software. First, a mask identifying bad pixels was created by flagging those pixels that were variable with time, unstable, or ``not-a-number '' ( NAN ) during the course of observations. The images and mask were then run through version 1.5 of the IRSCLEAN _ MASK routine (available from the Spitzer Science Center) to correct the bad pixels. The sky background in each image was removed by combining all of the data in the same order, but other nod position, using a median rejection algorithm, and subtracting the resulting sky frame. The residual background in each subtracted image was removed by taking the median value of the background on a row-by-row basis and then subtracting the value for each row. After a final visual inspection of the images, the data were loaded into the Spectroscopic Modeling Analysis and Reduction Tool (SMART; Higdon et al. 2004) for extraction and wavelength calibration, using a fixed width aperture of 3 pixels. All of the spectra taken in the same order and nod position were combined using a mean clipping algorithm. IRS observations of the standard star HR 6348, taken on 2005 September 9 and 14, were similarly combined and extracted, and a spectral template provided by G. C. Sloan was used to determine the relative spectral response for each order and nod position. These response functions were used to correct for the instrumental response and to produce an initial flux calibration for the 2MASS J0415þ0935 spectra. The spectra in each order were combined, and the two orders merged to produce a single spectrum from 5.2 to 14.5 m. IRAC channel 4 photometry from Patten et al. (2006) was used to produce a final flux calibration-- the spectra were scaled by a constant to produce a match to the photometry. The new IRS spectrum of 2MASS J0415þ0935 and the published spectra for Gl 570D and 2MASS J1217þ0311 are shown in Figure 2, with the principal absorbing species identified. Note that 2MASS J1217þ0311 is located in a part of the sky having a high mid-infrared background, leading to a somewhat noisier spectrum than the other two T dwarfs. 3. EVOLUTION OF BROWN DWARFS: AGE, MASS, GRAVITY, AND LUMINOSITY Brown dwarfs cool as they age with a cooling rate dependent on the mass. Hence both mass and age are fundamental parameters for these objects. For field brown dwarfs, such as those in Table 1, constraining the age is a challenge. In contrast, HD 3651B and Gl 570D are companions to K-type main-sequence stars, which allows age to be constrained based on kinematics, X-ray luminosity, H , and Ca ii H and K emission. Liu et al. (2007) showed that HD 3651B is aged 3 ­ 12 Gyr, and Gl 570D is aged 1 ­ 5 Gyr. Only kinematic information is available for 2MASS J0415þ0935 and 2MASS J1217þ0311. These dwarfs have Vtan $ 50 60 km sþ1, suggesting that their ages lie in the range 1 ­ 10 Gyr, and that neither is very young, nor are they likely to be halo members (see, for example, the discussion of kinematics in the solar region by Eggen [1998] and references therein).


1140

SAUMON ET AL.

Vol. 656

Fig. 2.-- Spitzer IRS spectra of 2MASS J0415þ0935, 2MASS J1217þ0311, and Gl 570D. Broad and strong absorption features are identified. The spectra are normalized to the peak flux and offset; dashed lines indicate the zero flux level. Data sources are Cushing et al. (2006), S06, and this work.

A convenient feature of brown dwarfs is that the mass-radius relation shows a broad maximum at $4 MJup , and that their radii are within ô30% of the radius of Jupiter for masses 0.3 ­ 70 MJup and ages k200 Myr ( Fig. 3 of Burrows et al. 2001). This peak results from the balance between electron degeneracy pressure, which dominates in the more massive brown dwarfs, and electrostatic repulsion of atoms and molecules, which dominates at the lower masses. With a nearly constant radius over more than a 2 order-of-magnitude variation in mass, the gravity of a brown dwarf is closely correlated to its mass and is approximately in-

dependent of age for older brown dwarfs such as those in our sample ( Fig. 3). S06 used the observed integrated flux and atmospheric and evolutionary models to derive log g ¼ 5:09 5:23 for Gl 570D, corresponding to a mass of 38 ­ 47 MJup . Burgasser et al. (2006a) used measured and modeled near-infrared spectral indices to determine TeA and log g for a sample of T dwarfs, using the well-determined values for Gl 570D as calibration of the method; their values are given in Table 1. The value for Gl 570D agrees with that determined by S06, as would be expected. Applying the


No. 2, 2007

PHYSICAL PARAMETERS OF TWO VERY COOL T DWARFS

1141

Fig. 3.-- Plot of effective temperature vs. surface gravity showing brown dwarf evolution with ½ Fe / H ¼ 0. The allowed (TeA , log g) values for 2MASS J0415þ0935, Gl 570D, and 2MASS J1217þ0311 fall along the nearly vertical lines from left to right, respectively; Lbol is very nearly constant along each curve. The thick portion of each curve shows the restricted range of the most likely solutions based on considerations of age and fitting the spectrum and photometry of each object. Our brown dwarf evolutionary tracks are shown by thick, nearly horizontal lines labeled with the mass in solar masses. Dotted lines are isochrones for 0.3, 1, 3, and 10 Gyr ( from right to left ). Filled circles show the three models for 2MASS J0415þ0935 and the three models for 2MASS J1217þ0311 specified in Tables 2 and 3. [See the electronic edition of the Journal for a color version of this figure.]

spectral indices technique to HD 3651B, Burgasser (2007) derived log g ¼ 4:7 5:1 and mass 20 ­ 40 MJup , whereas luminosity arguments ( Luhman et al. 2007; Liu et al. 2007) imply log g ¼ 5:1 5:5 and mass 40 ­ 70 MJup . The values of log g derived by Burgasser et al. (2006a) for 2MASS J1217þ0311 and 2MASS J0415þ0935 are consistent with the estimates made by Knapp et al. (2004) based on HþK color (also shown in Table 1), and suggest masses of 20 ­ 30 MJup and 25 ­ 35 MJup , respectively. Here we analyze the brown dwarfs 2MASS J1217þ0311 and 2MASS J0415þ0935 with the same method as described in S06 for Gl 570D, which is based on the integrated observed flux. The model atmospheres, spectra, and evolutionary sequences that are the basis for our analysis of the spectroscopic and photometric data are described briefly in x 4. Section 5 presents the values of TeA , log g, luminosity, mass, radius, and age we have obtained for 2MASS J1217þ0311 and 2MASS J0415þ0935, along with the values for Gl 570D from S06. In x 6 we perform fits of the spectroscopic and photometric data to further constrain the range of acceptable parameters, including metallicity, and explore the possibility of nonequilibrium chemistry in their atmospheres. 4. MODELS: EVOLUTION AND SPECTRA To constrain the properties of the T dwarfs in our sample with known parallax and mid-infrared spectra, we follow the procedure detailed in S06, Geballe et al. (2001), and Saumon et al. (2000). The method uses synthetic spectra to fill in gaps in the spectral coverage and complement the data at long wavelengths, in order to obtain a bolometric correction. For objects with measured parallax, this bolometric correction is computed self-consistently

with evolutionary models, which give the radius and the bolometric luminosity of the brown dwarf. There are no assumptions beyond those that are implicit in the computation of the atmosphere models, synthetic spectra, and evolution. Because we are studying late T dwarfs, the entire analysis is based on cloudless model atmospheres. For solar metallicity, the models used here are the same as those used for Gl 570D by S06. The chemical equilibrium calculations for the atmosphere models are described in Lodders & Fegley (2002) and use the solar abundances of Lodders (2003). In addition, we have computed a grid of atmosphere models and associated evolutionary tracks for a nonsolar metallicity of ½ Fe / H ¼ ×0:3. The nonsolar sequences use exactly the same interior physics as the solar sequence; only the surface boundary condition, which is extracted from the model atmospheres, is different. There is growing evidence that the abundances of NH3 and CO in the atmospheres of late T dwarfs can differ substantially from those expected from chemical equilibrium. The observed abundances for these two species can be simply explained as departures from chemical equilibrium driven by vertical mixing in the atmospheres ( Fegley & Lodders 1996; Lodders & Fegley 2002; Griffith & Yelle 1999; Noll et al. 1997; Saumon et al. 2000, 2003; S06 ), a phenomenon that has been recognized in giant planets for some time now ( Prinn & Barshay 1977; Fegley & Lodders ´ 1994; Bezard et al. 2002). In the lower atmosphere, which is convective, the mixing timescale over 1 pressure scale height Hp is very short (mix ¼ Hp /vconv $ 1 s), where vconv is the convective velocity computed from the mixing-length theory of convection. Thus, the mixing timescale in the convection zone comes from the mixing-length formalism, and it is not adjustable. In the overlying radiative zone, the physical cause for the mixing is presently unknown and could arise from the turbulent dissipation of waves generated at the convective/radiative boundary, meridional circulation, or differential rotation, for example. Such processes are expected to mix the radiative atmosphere on much longer timescales than convection. For modeling purposes, we treat the mixing timescale in the radiative zone as a free parameter, parameterized by the coefficient of eddy diffusivity, Kzz . We consider values in the range log Kzz (cm2 sþ1) ¼ 2 ­ 6, which corresponds to mix ¼ 2 Hp /Kzz $ 10 yr to $1 hr, respectively, in the atmospheres of late T dwarfs. For comparison, Kzz would have to be of order 107 ­ 109 cm2 sþ1 to get mixing timescales as short as those found in the convection zone. Since the IRS spectra and 4 ­ 5 m photometry probe a band of NH3 and a band of CO, respectively, we consider departures from chemical equilibrium caused by vertical mixing in comparing our models with the data. 5. DETERMINATION OF THE PHYSICAL PARAMETERS OF 2MASS J0415þ0935 AND 2MASS J1217þ0311 Bolometric luminosities have previously been determined for Gl 570D, 2MASS J1217þ0311, and 2MASS J0415þ0935 by Geballe et al. (2001) and Golimowski et al. (2004). These authors used the measured parallaxes for these dwarfs and the observed red through 5 m spectral energy distributions (SEDs), with an extrapolation to longer wavelengths, to obtain the emitted flux. The validity of the long-wavelength extrapolation has been verified by Cushing et al. (2006), who combined Spitzer mid-infrared data with shorter wavelength data to determine bolometric luminosities for a sample of M1 ­ T5 dwarfs. Their luminosities agree with those of Golimowski et al. (2004) within the latter's $10% uncertainties. Also, S06 repeated the Geballe et al. (2001) study of Gl 570D, adding mid-infrared spectra, and found good agreement with the earlier study.


1142
TABLE 2 Rang e o f Physical Parameters o f 2MASS J0415þ0 935 Teff (K) log g (cm sþ2) Mass (MJup) Radius (R)

SAUMON ET AL.

Vol. 656
TABLE 3 Ra ng e o f P hy s ic a l P a ra met e rs o f 2 MAS S J1 217þ0311

Model

log (Lbol /L) [ Fe/ H ] = 0

Age (Gyr)

Model

Teff (K)

log g (cm sþ2)

log (Lbol /L) [ Fe/ H ] = 0

Mass (MJup)

Radius (R)

Age (Gyr)

A.................. B .................. C ..................

690 730 775

4.68 5.04 5.37

þ5.66 þ5.67 þ5.68 [ Fe/ H ] = +0.3

19.5 34.6 57.9

0.104 0.091 0.080

1 3.2 10

D................. E ................. F .................

860 910 965

4.84 5.14 5.44

þ5.30 þ5.31 þ5.31 [ Fe/ H ] = +0.3

26.4 42.2 66.2

0.100 0.089 0.079

1 2.7 10

A0 ................. B0 ................. C0 .................

685 725 767

4.63 5.00 5.34

þ5.66 þ5.67 þ5.68

18.3 33.4 55.6

0.106 0.093 0.082

1 3.2 10

D0 ................ E0 ................ F0 ................

850 910 950

4.80 5.17 5.42

þ5.31 þ5.31 þ5.32

25.3 44.7 65.3

0.102 0.089 0.080

1 3.2 10

Note.--Uncertainties are ô0.02 dex in Lbol , which translates to ô9 K in TeA (at fixed g) and ô0.07 dex on log g (at fixed TeA , or ô0.01 dex at a fixed age).

Note.-- Uncertainties are ô0.03 dex in Lbol , which translates to $ô25 K in TeA (at fixed g) and ô0.09 dex on log g (at fixed TeA , or ô0.03 dex at a fixed age).

Here we rederive Lbol , TeA , and log g for 2MASS J0415þ 0935 and 2MASS J1217þ0311 using the method developed in Saumon et al. (2000) for Gl 229B, which has also been applied to Gl 570D (Geballe et al. 2001; S06). The method can be applied to brown dwarfs of known parallax and is not sensitive to systematic problems present in the synthetic spectra, as opposed to direct fitting of the observed spectra that would be affected by such problems. For brown dwarfs with a well-sampled SED ( >50% of the flux), the method has been shown to be very robust. We have first summed the observed fluxes using red spectra ( Burgasser et al. 2003), near-infrared spectra (Geballe et al. 2002; Knapp et al. 2004), 3 m spectra where available (this work), and IRS spectra (this work and Cushing et al. 2006). The 1 ­ 4 m spectra are flux calibrated using accurate MKO system JHKL 0 photometry from Leggett et al. (2002), Golimowski et al. (2004), and Knapp et al. (2004). The IRS spectra are flux calibrated using the IRAC channel 4 photometry from Patten et al. (2006). The uncertainties in the integrated observed flux are dominated by the flux calibration uncertainties. For 2MASS J0415þ0935 they are 5% at all wavelengths except for the 1 ­ 2.5 m spectrum, which has a 3% uncertainty. For 2MASS J1217þ0311 they are 5% in the red, 3% in the near-infrared, and 18% at IRS wavelengths. The integrated fluxes at Earth over the observed spectral regions are 1:532 ô 0:057 ; 10þ12 ergs sþ1 cmþ2 for 2MASS J0415þ 0935 and 9:67 ô 0:55 ; 10þ13 ergs sþ1 cmþ2 for 2MASS J1217þ 0311, which in each case represents $75% of the bolometric flux. The above uncertainties are the sum of the uncertainties in each integrated segment, and thus are conservative. Among all possible values of TeA and log g, only a small subset will give a bolometric flux correction to the above values that makes Lbol consistent with the evolution (mass and age) and the known parallax. In the fTeA ;gg space, this subset forms a onedimensional curve. The location along the curve can be parameterized with the mass, age, gravity, effective temperature, luminosity, or radius. So far, only age constraints and detailed spectral fitting have been used to further limit the allowed range of the solution along the one-dimensional curve. For Gl 570D, with an age of 2 ­ 5 Gyr and detailed fits of the IRS spectrum, S06 obtained TeA ¼ 800 820 K, log g ¼ 5:09 5:23 cm sþ2 , and mass 38 ­ 47 MJup .2
Table 1 of S06 gives erroneous values of Lbol for two of the models. The correct values are log Lbol /L ¼ þ5:521 for model A and þ5.528 for model C.
2

Applying the same technique of S06, we derive the possible solutions in log g and TeA for 2MASS J0415þ0935 and 2MASS J1217þ0311, shown as curves in Figure 3. These objects' kinematics constrain their ages to be in the range 1 ­ 10 Gyr. Tables 2 and 3 give a set of specific values along each curve for TeA, log g, luminosity, mass, radius, and age for these dwarfs for both ½ Fe / H ¼ 0 and +0.3. Note that the tabulated solutions have nearly constant Lbol . This is not an assumption of the method but a consequence of the very weak dependence of the calculated bolometric correction on TeA of the atmosphere models when the bolometric flux correction is <30%. Our values of Lbol agree with those of Golimowski et al. (2004) within the quoted uncertainties for both objects. For a given object, the solutions for ½ Fe / H ¼ 0 and +0.3 are very close to each other, which shows that this method of determination of (TeA ;g) is quite robust, given a good sampling of the SED. These models are also indicated in Figure 3 for solar composition. The points chosen along each curve correspond to ages of 1 Gyr (models A and D), $3 Gyr (models B and E), and 10 Gyr (models C and F ). Atmospheric models and synthetic spectra were generated for these parameters and are compared to the observed spectra and photometry in x 6 to determine the optimum range of parameters for each dwarf. 6. COMPARISON OF OBSERVED AND SYNTHETIC SPECTRA AND PHOTOMETRY With the values of TeA and g constrained to lie along the curves shown in Figure 3 and between the ages of 1 and 10 Gyr, we now seek to further constrain the allowed range by optimizing the fits of the corresponding synthetic spectra to the observations. For this purpose, we have three parameters at our disposal. One is the location along the solution curve, which for convenience we parameterize with the gravity (mass, radius, age, and TeA are other possible choices); the metallicity of the atmosphere, for which we consider values of ½ Fe / H ¼ 0 and +0.3; and the timescale of mixing in the radiative part of the atmosphere, parameterized by the eddy diffusion coefficient with values of Kzz ¼ 0, 10 2, 10 4, and 106 cm2 sþ1. Values of Kzz increasing from zero will give increasingly vigorous mixing and larger departures from chemical equilibrium. The introduction of vertical mixing and its associated parameter is motivated by strong evidence of departures from chemical equilibrium in late T dwarfs, which can be well modeled by this process ( Noll et al. 1997; Saumon et al. 2000; S06; Golimowski et al. 2004); we explore whether this is also the case for 2MASS J0415þ0935 and 2MASS J1217þ0311. By


No. 2, 2007

PHYSICAL PARAMETERS OF TWO VERY COOL T DWARFS

1143

Fig. 4.-- Comparison of the optical through near-infrared spectrum of 2MASS J0415þ0935 with models of different metallicities. The lower thin curve is the best-fitting model with ½ Fe / H ¼ 0 (model C ), and the upper thin curve is the best-fitting model with ½ Fe / H ¼ ×0:3 (model C0 ). Both models assume chemical equilibrium (Kzz ¼ 0). The model fluxes have not been normalized to the data but have been smoothed to a resolving power of k /à k ¼ 500 to approximate that of the data. The data are shown by the thick line. [See the electronic edition of the Journal for a color version of this figure.]

combining the radius, R(TeA ;g), from the evolution calculations and the parallax, we compute fluxes at Earth from the models and compare them directly with the observed fluxes, without any arbitrary normalization, except where indicated otherwise. In the following comparison of the models with the spectroscopic and photometric data, we first discuss the near-infrared spectrum, which provides the best constraint on the metallicity through the K-band peak, followed by the mid-infrared spectrum, where NH3 bands are indicators of the presence of departures from chemical equilibrium. Finally, 3 ­ 4 m spectroscopy and photometry provide a consistency check on the previous determinations, and 4­5 m photometry gives a measure of the mixing timescale in the radiative region of the atmosphere through the strength of the 4.7 m band of CO. 6.1. 2MASS J0415þ0935
6.1.1. 0.7 ­ 2.5 m Spectrum

Fig. 5.-- Fits of the IRS spectrum of 2MASS J0415þ0935 showing the difference between a model in chemical equilibrium and a model that includes vertical transport that drives the nitrogen and carbon chemistry out of equilibrium. The lower thin curve is the best-fitting model in chemical equilibrium (model A from Table 2, with Kzz ¼ 0), and the upper thin curve is the best-fitting nonequilibrium model (model B, with Kzz ¼ 106 cm2 sþ1). The data and the noise spectrum are shown by the histograms. The uncertainty on the flux calibration of the IRS spectrum is ô5%. The model fluxes, which have not been normalized to the data, are shown at the resolving power of the IRS spectrum (k /àk ¼ 90). [See the electronic edition of the Journal for a color version of this figure.]

The best synthetic near-infrared spectra are model C for ½Fe / H ¼ 0 and model C0 for ½ Fe / H ¼ ×0:3. As can be seen from Figure 4, neither value of the metallicity provides a better fit to the optical and near-infrared spectrum. No improvement would come from an intermediate value of [ Fe/ H ] either. The high end of the allowed gravity range is somewhat preferred, as it provides a slightly better match to the Y-band peak.
6.1.2. 5 ­ 15 m Spectrum

The synthetic spectra of each of the triplets of models ( Table 2) are very similar to each other in the near-infrared, because the effect of increasing the gravity is partially canceled by the accompanying increase in effective temperature from models A to C. The (P; T ) structures of these three models are almost identical, with deviations of less than 0.14 dex in pressure at a given temperature. The general agreement of the synthetic spectra with the data is very good ( Fig. 4), although there are some systematic deviations. For example, (1) the 1.6 m band of CH4 is too weak in the models, (2) the J-band peak is too broad, and (3) the shape of the Y-band peak is incorrect. The first is due to incompleteness of the CH4 line list at temperatures above 300 K, and the other two to the absence of CH4 opacity in our model spectra below 1.50 m. The known bands of CH4 at shorter wavelengths (Strong et al. 1993) have no corresponding line list, but they are located such as to increase the opacity on both sides of the J-band peak ( Fig. 1), making it narrower, and to cut into the blue side of the Y-band peak. The latter may also be affected by the profile we have adopted for the far red wing of the K i resonance doublet ( Burrows et al. 2000). As S06 found for Gl 570D, the solar metallicity models all underestimate the K-band flux of 2MASS J0415þ0935, which suggests that it may be enriched in metals. Spectra with ½ Fe / H ¼ ×0:3 (models A0 ,B0 , and C0 in Table 2) reproduce the K-band peak very well, but the J peak becomes much too strong.

The mid-infrared spectrum covers strong bands of NH3, a tracer of nonequilibrium chemistry that can reduce the NH3 abundance in the atmosphere by a factor of $10 (S06). In this spectral range, the average flux level decreases noticeably as the gravity increases along the sequence of models in Table 2. We follow the approach of S06 by computing the 2 between the synthetic spectra and the observed spectrum beyond 9 m for each triplet of models, four values of Kzz , and both metallicities. In all cases, the best nonequilibrium model (Kzz > 0) provides a much better match than the best equilibrium model, at a very high level of significance (>50 ). If we allow for arbitrary normalization of the flux rather than considering the absolute fluxes, we find that the equilibrium abundance of NH3 is still ruled out at the 22 level. Therefore both the average flux level and the detailed shape of the spectrum give a NH3 abundance that is well below that predicted by equilibrium chemistry. Other explanations (e.g., low intrinsic nitrogen abundance) were ruled out in S06. For ½ Fe / H ¼ 0, the best equilibrium model (Kzz ¼ 0) is clearly A. The best nonequilibrium model is B, with Kzz ¼ 104 106 cm2 sþ1. These spectra are shown in Figure 5. For ½ Fe / H ¼ ×0:3, model A0 is the best equilibrium model, and the best match with nonequilibrium chemistry is obtained with model C0 and Kzz ¼ 106 cm2 sþ1. Nonequilibrium, solar metallicity models give significantly better fits, however.
6.1.3. 2.9 ­ 4.1 m Spectrum

The 3 ­ 4 m spectrum shows a very strong and very broad 3.3 mCH4 band, which is saturated at the center ( Fig. 6). Only the 3.9 ­ 4.1 m region is sensitive to the CH4 abundance, which depends on the metallicity and potential departures from chemical


1144

SAUMON ET AL.

Vol. 656

equilibrium. The latter act to reduce the CH4 abundance in the upper atmosphere. The three solar metallicity models reproduce the spectrum well but underestimate the 3 m bump by about 2 .Nonequilibrium chemistry raises the flux in the 3 m bump and brings it in excellent agreement with the data ( Fig. 6). It also raises the flux longward of 3.9 m to a level generally higher than the data, but within the 1 error bars. The metal-rich model spectra are quite similar, but their higher abundance of CH4 results in somewhat lower fluxes in the 3.9 ­ 4.1 m region than those of the solar metallicity spectra. This can be compensated by a higher value of Kzz , however. The 2.9 ­ 4.1 mspectrumhas aS/ N $6 ­ 7, which is not sufficient to discriminate between our different model spectra. All of them are in fair agreement with the data; nonequilibrium models (with any Kzz ) fit the 3 m bump better, however.
Fig. 6.-- Comparison of the 2.9 ­ 4.1 m spectrum of 2MASS J0415þ0935 with representative models in and out of chemical equilibrium. The dotted curve is model B with Kzz ¼ 0 (chemical equilibrium), and the thin solid curve is model B with Kzz ¼ 104 cm2 sþ1. The appearance of the 4.7 m band of CO due to nonequilibrium chemistry can be seen in the models between 4.4 and 4.9 m. The data are shown by the histogram. The model fluxes have not been normalized to the data and are shown at a resolving power of k /àk ¼ 200. [See the electronic edition of the Journal for a color version of this figure.]

6.1.4. Photometry

Figure 7 shows the synthetic photometry in the MKO L 0 and M bands and the IRAC bands [3.55] and [4.49], along with the observed values. The M 0 and [4.49] bands both probe the 4.7 m band of CO, a sensitive tracer of nonequilibrium chemistry, which can dramatically enhance the CO abundance ( Fig. 6). The synthetic L 0 magnitude is a weak function of gravity, metallicity, and Kzz , with all models giving values that agree to within ô0.25 mag. With solar metallicity models, the L 0 magnitude is
0

Fig. 7.--MKO and IRAC photometry of 2MASS J0415þ0935 as a function of the coefficient of eddy diffusion for a range of models. Observed are shown by the horizontal lines. Synthetic photometry for each of the models in Table 2 is shown by the various curves: Dotted lines,models A and models B and B0 ; dashed lines,models C andC0 . Upper curves are for ½ Fe / H ¼ 0, and lower curves are for ½ Fe / H ¼ ×0:3; the latter are always below t given pair of models. The filled circles show the values for a representative best-fit model (see Fig. 8). Models with Kzz ¼ 0 (in chemical equilibrium log Kzz ¼ þ1. [See the electronic edition of the Journal for a color version of this figure.]

values (ô1 ) A0 ; solid lines, he former for a ) are plotted at


No. 2, 2007

PHYSICAL PARAMETERS OF TWO VERY COOL T DWARFS

1145

Fig. 9.-- Comparison of the optical through near-infrared spectrum of 2MASS J1217þ0311 with models of different metallicities. The lower thin curve is the best-fitting model with ½ Fe / H ¼ 0 (model D), and the upper thin curve is the best-fitting model with ½ Fe / H ¼ ×0:3 (model E0 ). Both models assume chemical equilibrium (Kzz ¼ 0). The model fluxes have not been normalized to the data but have been smoothed to a resolving power of k /àk ¼ 500 to approximate that of the data. The data are shown by the thick line. [See the electronic edition of the Journal for a color version of this figure.]

Fig. 8.-- Model spectrum representing a typical best fit of all the spectroscopic and photometric data for 2MASS J0415þ0935. The model parameters are ½ Fe / H ¼ 0, TeA ¼ 730 K, log g ¼ 5:035 (model B in Table 2), and an eddy diffusion coefficient of Kzz ¼ 106 cm2 sþ1. Model spectra are shown at a resolving power of k /àk ¼ 500 (top) and 90 (bottom) to approximately match that of the data. The model fluxes have not been normalized to the data (thick line). [See the electronic edition of the Journal for a color version of this figure.]

best reproduced with models A and B with Kzz ¼ 0, and increasing Kzz drives the synthetic L 0 steadily away from the observed values. At ½ Fe / H ¼ ×0:3, all three models provide a good match for Kzz $ 10 104 cm2 sþ1. The MKO L 0 filter measures the 3.45 ­ 4.1 m flux and discriminates better between the various models than our 2.9 ­ 4.1 m spectrum. Not surprisingly, the IRAC [3.55] magnitude behaves very much like L 0 , but models generally are fainter than the observed value. The latter can only be reproduced with model C (any Kzz )orwith any model (including both metallicities) if Kzz $ 106 cm2 sþ1. The MKO M 0 and IRAC [4.49] magnitudes behave similarly and give a consistent picture in which Kzz ¼ 0 is strongly excluded, and good matches can be obtained for any gravity if Kzz $ 105 106 cm2 sþ1 (solar metallicity) or Kzz $ 103 104 cm2 sþ1 (½ Fe / H ¼ ×0:3). This is strong evidence that the 4.7 m band of CO is deep in 2MASS J0415þ0935 and that the CO abundance is well above the chemical equilibrium value ( Fig. 6).
6.1.5. Optimum Models

In this analysis, we are not able to determine the metallicity of 2MASS J0415þ0935. Both ½ Fe / H ¼ 0and ½ Fe / H ¼ ×0:3 can give equally good agreements with each segment of spectrum and each magnitude (with different parameters, however). Overall, most aspects of the SED can be reproduced fairly well by models in the range between models B and C (or B0 and C0 for ½ Fe / H ¼ ×0:3) with a coefficient of eddy diffusion of Kzz > 104 cm2 sþ1. The parameters of 2MASS J0415þ0935 are thus: TeA ¼ 725 775 K, log g ¼ 5:00 5:37, log Lbol /L ¼ þ5:67, M ¼ 33 58 MJup , and age between 3 and 10 Gyr. This range of parameters is highlighted in Figure 3. An example of such a model is shown in Figure 8, and its corresponding synthetic magnitudes are shown in Figure 7. 2MASS J0415þ0935 is the least luminous T dwarf analyzed in details so far and is also the coolest ( Fig. 3). In comparison, the TeA and log g derived by Burgasser et al. (2006a, their Fig. 9) is about 40 K hotter than ours for their quoted range of gravity ( log g ¼ 4:9 5:0). Their parameters correspond to log Lbol /L ¼ þ5:59 ô 0:02, which is consistent with our model B within their quoted uncertainties. 6.2. 2MASS J1217þ0311
6.2.1. 0.7 ­ 2.5 m Spectrum

No single synthetic spectrum fits this extensive data set, but a clear picture emerges. The IRS spectrum, and the M 0 and [4.49] magnitudes all clearly indicate that NH3 is underabundant, and CO is overabundant compared to the values expected from chemical equilibrium. In 2MASS J0415þ0935, the chemistry of nitrogen is quenched in the convection zone where the mixing timescale is determined by the mixing-length theory of convection. The NH3 bands in the IRS spectrum are therefore good indicators of the presence of nonequilibrium chemistry but do not provide a handle on the value of the mixing timescale parameter in the radiative zone, Kzz . On the other hand, the carbon chemistry is quenched in the radiative zone and is quite sensitive to Kzz .

For 2MASS J1217þ0311 the near-infrared model spectra for both metallicities again give very nearly identical solutions for Lbol , TeA , and log g ( Table 3). And again, we find that the solar metallicity models underestimate the K-band flux significantly, although the agreement with the Y and J peaksisexcellent ( Fig.9). On the other hand, models with ½ Fe / H ¼ ×0:3give an excellent fit of the entire near-infrared SED, except for the usual problem with the 1.6 m band of CH4. The maximum J-band flux is less sensitive to [ Fe/ H ] at the higher TeA of 2MASS J1217þ0311 than it is for 2MASS J0415þ0935, allowing a good fit of the K-band peak at ½ Fe / H ¼ ×0:3 without compromising the good fit of the J-band peak. The width of the J-band peak is also much better reproduced than for 2MASS J0415þ0935, because the temperature where it is formed in the atmosphere is higher and the CH4 contribution to the opacity smaller than in 2MASS J0415þ0935. Water is now mostly responsible for shaping the J-band peak, and the omission of CH4 opacity in this wavelength range (x 6.1.1) is of lesser consequence. The best-fitting models with ½ Fe / H ¼ 0 a n d + 0. 3 a re s h ow n i n F i g u r e 9 . T h e q ua l i t y o f t h e fi t w i t h


1146

SAUMON ET AL.
6.2.4. Optimum Models

Vol. 656

Fig. 10.-- Fits of the IRS spectrum of 2MASS J1217þ0311 showing the difference between a model in chemical equilibrium and a model that includes vertical transport that drives the nitrogen and carbon chemistry out of equilibrium. The upper thin curve is the best-fitting model in chemical equilibrium (model E0 from Table 3, with Kzz ¼ 0), and the lower thin curve is a representative nonequilibrium model (model F0, with Kzz ¼ 102 cm2 sþ1). The data and the noise spectrum are shown by the histograms. The uncertainty on the flux calibration of the IRS spectrum is ô18%. The model fluxes, which have not been normalized to the data, are shown at the resolving power of the IRS spectrum (k /àk ¼ 90). [See the electronic edition of the Journal for a color version of this figure.]

The near-infrared spectrum of 2MASS J1217þ0311 indicates that it is metal-rich, with [ Fe/ H ] close to +0.3, which is consistent with the photometry shown in Figure 11. While the IRS spectrum shows prominent bands of NH3, it is too noisy to indicate whether the NH3 abundance departs from chemical equilibrium or even to constrain the gravity. The full range of TeA and log g of models D0 , E0 , and F0 ( Table 3 and highlighted in Fig. 3) remains plausible. Evidence for nonequilibrium chemistry comes solely from the IRAC [4.49] magnitude, which is 0.2 ­ 0.4 mag below that expected from chemical equilibrium. To summarize, 2MASS J1217þ0311 has ½ Fe / H $ ×0:3, TeA ¼ 850 950 K, log g ¼ 4:80 5:42, and log Lbol /L ¼ þ5:31, and we are unable to constrain the age to better than 1 ­ 10 Gyr. This implies a mass between 25 and 65 MJup . The values derived by Burgasser et al. (2006a) agree with our model D0 at the 1 level, based on their quoted uncertainty. On the basis of the IRAC [4.49] magnitude, it appears that CO is more abundant than expected from chemical equilibrium and that a coefficient of eddy diffusion Kzz > 102 cm2 sþ1 ( possibly as high as 106 cm2 sþ1) is appropriate to model this object. A model that represents a good compromise between all the constraints (model E0 in Table 3, with Kzz ¼ 102 cm2 sþ1 ) is compared to the spectrum in Figure 12, and the corresponding photometry is shown in Figure 11. 7. CONCLUSIONS The new 3­ 4 and 5­15 m spectra presented here for the T8 dwarf 2MASS J0415þ0935, together with its near-infrared spectrum and trigonometric parallax, allow a very accurate determination of its bolometric luminosity ( log Lbol /L ¼þ5:67 ô 0:02) and constrain the possible values of (TeA ;g). Although the age for this isolated disk dwarf is not known, comparisons of synthetic to observed red through mid-infrared spectra show that we can constrain it to 3 ­ 10 Gyr, with corresponding values of TeA ¼ 725 775 K, log g ¼ 5:00 5:37, and a mass between 33 and 58 MJup . These ranges are different from error bars in the sense that the values of TeA , log g, and M within the quoted intervals are correlated ( Fig. 3 and Table 2). The metallicity is likely between ½ Fe / H ¼ 0 and +0.3. Applying the same method of analysis, using published data, to the T7.5 dwarf 2MASS J1217þ0311, we find log Lbol /L ¼ þ5:31 ô 0:03 and an age of 1­ 10 Gyr. These correspond to TeA ¼ 850 950 K, log g ¼ 4:80 5:42, and a mass of 25­65 MJup .The metallicity of 2MASS J1217þ0311 is ½ Fe / H $ ×0:3, which indicates that it is very unlikely to be as old as 10 Gyr. The lower end of each of the parameter ranges given above is therefore more appropriate. In terms of TeA , 2MASS J1217þ0311 and 2MASS J0415þ 0935 straddle the value of 800 ­ 820 K derived for the T7.5 dwarf Gl 570D by S06. The spectral classifications are uncertain by half a subclass, but on face value the half-subclass difference between Gl 570D and 2MASS J0415þ0935 corresponds to a $60 K difference in TeA if both objects have the same gravity ( Fig. 3). Although 2MASS J1217þ0311 has the same spectral type as Gl 570D, it is warmer by 30 ­ 170 K, depending on the respective gravity of each object. At the low end, this difference is not significant, but a higher value would warrant a study of the effects of gravity and metallicity on the indices used to determine the spectral type of T dwarfs ( Burgasser et al. 2006b). As was found previously for Gl 229B ( Noll et al. 1997; Oppenheimer et al. 1998; Saumon et al. 2000) and Gl 570D (S06), we find evidence for departures from equilibrium chemistry in

½ Fe / H ¼ ×0:3 suggests that 2MASS J1217þ0311 is likely a metal-rich brown dwarf.
6.2.2. 5 ­ 15 m Spectrum

The goodness of fit of the models to the IRS spectrum of 2MASS J1217þ0311, as measured by their 2, shows no statistically significant sensitivity to the choice of gravity or to the value of the coefficient of eddy diffusion, Kzz . It is not possible to distinguish between the solar metallicity models D, E, and F, or between the metal-rich models D0 , E0 , and F0 (Table 3), or to determine whether the chemistry departs from strict equilibrium (Kzz ¼ 0). This is largely due to the lower S/ N of the spectrum, which ranges from 3 to 12 for k ! 9 m, compared to $9­54 for the IRS spectrum of 2MASS J0415þ0935. Since the near-infrared spectrum strongly favors a metal-rich composition (½ Fe / H ¼ ×0:3), we show in Figure 10 the best-fitting metal-rich equilibrium model (model E0 , with Kzz ¼ 0) and the best-fitting nonequilibrium model (model F0 ) with Kzz arbitrarily set to 100 cm2 sþ1, since the 2 does not vary with Kzz in this case. The slope of the spectrum beyond 11 m appears to be steeper than in the models, which accounts partly for the inability to select among the various models considered on the basis of the 2 .The 4.7 mband of CO is predicted to be quite strong even for such a modest value of Kzz .
6.2.3. Photometry

In Figure 11, the MKO L 0 and the IRAC [3.55] and [4.49] magnitudes of 2MASS J1217þ0311 are compared to the synthetic magnitudes for all six models in Table 3, as the coefficient of eddy diffusion is varied from Kzz ¼ 0 to 106 cm2 sþ1. The metal-rich models generally fare better in all three bands. The L 0 magnitude favors low values of Kzz < 102 cm2 sþ1, while the IRAC [3.55] band is a rather poor match unless Kzz is high ($106 cm2 sþ1). The IRAC [4.49] band, which measures the nonequilibrium tracer CO, favors nonequilibrium models with Kzz > 102 cm2 sþ1 and more likely >104 cm2 sþ1. We cannot get a consistent fit for these three magnitudes, however, which most likely reflects a limitation of our models.


No. 2, 2007

PHYSICAL PARAMETERS OF TWO VERY COOL T DWARFS

1147

Fig. 11.-- MKO and IRAC photometry of 2MASS J1217þ0311 are shown by the horizontal lines. Synthetic photometry for each of models E and E0 ; dashed lines,models F andF0. Upper curves are for The filled circles show the values for a representative best-fit model electronic edition of the Journal for a color version of this figure.]

as a function of the coefficient of eddy diffusion for a range of models. Observed values (ô1 ) the models in Table 3 is shown by the various curves: Dotted lines, models D and D0 ; solid lines, ½ Fe / H ¼ 0, and lower curves are for ½Fe / H ¼ ×0:3; the latter are below the former for small Kzz . (see Fig. 11). Models with Kzz ¼ 0 (in chemical equilibrium) are plotted at log Kzz ¼ þ1. [See the

both objects studied here. Specifically, the mid-infrared band of NH3 in 2MASS J0415þ0935 is weaker than expected from chemical equilibrium models. The IRS spectrum can be fit very well if the NH3 abundance is decreased by a factor of 8 ­ 10. The MKO M 0 magnitude of 2MASS J0415þ0935 is $1 mag fainter than equilibrium models predict, a clear indication of a significant enhancement of the CO abundance. Similarly, the IRAC [4.55] magnitude of 2MASS J1217þ0311 is 0.2 ­ 0.4 mag fainter than expected, showing a more modest enhancement of CO than in 2MASS J0415þ0935, compared to the predictions of equilibrium models. Departures of the chemistry of carbon and nitrogen from chemical equilibrium is the consequence of a simple mechanism based on the kinetics of the relevant chemical reactions and the assumption that vertical mixing takes place. Unless the radiative zone is quiescent on timescales of years, nonequilibrium chemistry of carbon and nitrogen should be a common feature of all low-TeA brown dwarfs. These departures from chemical equilibrium can be modeled by considering vertical mixing in the atmosphere and the timescales of the reactions that are responsible for the chemistry of nitrogen and carbon. Deep in the atmosphere, the mixing timescale is determined by the properties of the convection zone, modeled with the mixing-length theory. In the radiative zone, mixing is caused by some undetermined physical

process on a longer, and a priori unknown, timescale. This timescale is the only free parameter of the nonequilibrium models. Until the physical processes that can cause mixing in the radiative zone of brown dwarf atmospheres are modeled, we have no indication as to the value of that mixing timescale. Fegley & Lodders (1994) showed that the nonequilibrium abundances of CO, HCN, GeH4, AsH3, and PH3 observed in Jupiter and Saturn can all be modeled very well with Kzz ¼ 107 109 cm2 sþ1 .However, all of these species are quenched deep in the convection zone, which is consistent with the high values of Kzz needed to reproduce their abundances.3 The value of Kzz in the radiative zones of brown dwarf atmospheres thus remains unconstrained, except for an upper limit provided by the mixing timescale in the convection zone. In this context, the successful modeling of the spectra of brown dwarfs with a simple, one-parameter model may provide guidance in determining the physical process(es) responsible for the mixing. As more objects are analyzed in detail, a pattern may emerge in the derived values of Kzz that can be compared
3 In our models, Kzz is used to parameterize the mixing timescale diative zone only, and the mixing timescale in the convection zone is with the mixing-length theory. In the planetary science literature, Kzz parameterize the mixing timescale regardless of whether the mixing a radiative or a convective zone.

in the racomputed is used to occurs in


1148

SAUMON ET AL.

Vol. 656

of Kzz . On the other hand, their carbon chemistry is quenched in the radiative zone, and the flux in the 4.7 m band of CO is very sensitive to the choice of Kzz . The values found so far for the coefficient of eddy diffusivity in the radiative zone are log Kzz ¼ 4 5 for Gl 229B ( based on the CO mole fraction determined by Saumon et al. [2000]) and $5 ­ 6 for 2MASS J0415þ0935. For 2MASS J1217þ0311, the three photometric measurements cannot be fit simultaneously, and we find a weak constraint of log Kzz > 2. If we (arbitrarily) ignore its L 0 magnitude, then log Kzz > 5 gives a very good fit to all the other data. The present analysis of 2MASS J0415þ0935 and of 2MASS J12170311 is based on fits of the low-resolution SED. Medium resolving power (k /àk > 2000) and especially high resolving power (k /àk > 20;000) near-infrared spectra open the possibility of constraining the gravity by fitting the fine structure of the spectrum, which should further limit the ranges of TeA and log g obtained here as well as the value of Kzz .Such ananalysis will be greatly simplified by the fact that the fitted model must lie on the curves shown in Figure 3, which reduces the fit from a three-dimensional parameter space (TeA ; log g; ½ Fe / H )to a twodimensional space ( log g; ½ Fe / H ).

Fig. 12.-- Model spectrum representing a typical best fit of all the spectroscopic and photometric data for 2MASS J1217þ0311. The model parameters are ½ Fe / H ¼ ×0:3, TeA ¼ 910 K, log g ¼ 5:167 (model E0 in Table 3), and an eddy diffusion coefficient of Kzz ¼ 102 cm2 sþ1. Model spectra are shown at a resolving power of k /àk ¼ 500 (top) and 90 (bottom) to approximately match that of the data. The model fluxes have not been normalized to the data (thick curve). [See the electronic edition of the Journal for a color version of this figure.]

with the results of detailed modeling of mixing processes when it becomes available. The mixing timescale parameterized by Kzz also enters the modeling of clouds in L dwarfs (Ackerman & Marley 2001), and empirically determined values of Kzz in brown dwarfs allow for the development of a more consistent theory of vertical mixing and of the cloud model. Of the four brown dwarfs that have been studied in enough detail so far, three show clear evidence of nonequilibrium abundances for at least one of the two key tracers ( NH3 and CO): Gl 229B, Gl 570D, and 2MASS J0415þ0935. The fourth, 2MASS J1217þ0311, appears to have a nonequilibrium CO abundance. In all four objects, the nitrogen chemistry is quenched in the convection zone, where the mixing timescale is not adjustable. The depletion of NH3 that ensues depends very weakly on the value

This work is based in part on data collected at the Subaru Telescope, which is operated by the National Astronomical Observatory of Japan. This work is also based in part on observations made with the Spitzer Space Telescope, which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under a contract with NASA. Support for this work was provided by NASA through an award issued by JPL /Caltech. This work was also supported in part under the auspices of the US Department of Energy at Los Alamos National Laboratory under contract W-7405-ENG-36. M. C. C. acknowledges support from NASA through the Spitzer Space Telescope Fellowship Program, through a contract issued by JPL /Caltech. Work by K. L. is supported by NSF grant AST 04-06963. M. S. M. acknowledges the support of the NASA Office of Space Sciences. T. R. G. and S. K. L. are supported by the Gemini Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc. (AURA), under a cooperative agreement with the NSF on behalf of the Gemini partnership: the National Science Foundation ( United States), the Particle Physics and Astronomy Research Council ( United Kingdom), the National Research Council (Canada), CONICYT (Chile), the Australian Research Council, CNPq ( Brazil), and CONICET (Argentina).

REFERENCES Ackerman, A. S., & Marley, M. S. 2001, ApJ, 556, 872 ESA. 1997, The Hipparcos and Tycho Catalogues ( ESA SP-1200; Noordwijk: Beichman, C. A., Chester, T. J., Skrutskie, M., Low, F. J., & Gillett, F. 1998, ESA) PASP, 110, 480 Fazio, G., et al. 2004, ApJS, 154, 10 ´ Bezard, B., Lellouch, E., Strobel, D., Maillard, J.-P., & Drossart, P. 2002, Fegley, B., Jr., & Lodders, K. 1994, Icarus, 110, 117 Icarus, 159, 95 ------. 1996, ApJ, 472, L37 Burgasser, A. J. 2007, ApJ, in press (astro-ph /0611542) Geballe, T. R., Saumon, D., Leggett, S. K., Knapp, G. R., Marley, M. S., & Burgasser, A. J., Burrows, A., & Kirkpatrick, J. D. 2006a, ApJ, 639, 1095 Lodders, K. 2001, ApJ, 556, 373 Burgasser, A. J., Geballe, T. R., Leggett, S. K., Kirkpatrick, J. D., & Golimowski, Geballe, T. R., et al. 2002, ApJ, 564, 466 D. A. 2006b, ApJ, 637, 1067 Golimowski, D. A., et al. 2004, AJ, 127, 3516 Burgasser, A. J., Kirkpatrick, J. D., Liebert, J., & Burrows, A. 2003, ApJ, 594, 510 Griffith, C. A., & Yelle, R. V. 1999, ApJ, 519, L85 Burgasser, A. J., et al. 1999, ApJ, 522, L65 Higdon, S. J. U., et al. 2004, PASP, 116, 975 ------. 2000, ApJ, 531, L57 Houck, J., et al. 2004, ApJS, 154, 18 ------. 2002, ApJ, 564, 421 Knapp, G. R., et al. 2004, AJ, 127, 3553 Burrows, A., Hubbard, W. B., Lunine, J. I., & Liebert, J. 2001, Rev. Mod. Kobayashi, N., et al. 2000, Proc. SPIE, 4008, 1056 Phys., 73, 719 Leggett, S. K., et al. 2002, ApJ, 564, 452 Burrows, A., Marley, M. S., & Sharp, C. M. 2000, ApJ, 531, 438 Liu, M. C., Leggett, S. K., & Chiu, K. 2007, ApJ, in press Cushing, M. C., Vacca, W. D., & Rayner, J. T. 2004, PASP, 116, 362 Lodders, K. 2003, ApJ, 591, 1220 Cushing, M. C., et al. 2006, ApJ, 648, 614 Lodders, K., & Fegley, B., Jr. 2002, Icarus, 155, 393 Eggen, O. J. 1998, AJ, 115, 2397 Luhman, K. L., et al. 2007, ApJ, 654, 570


No. 2, 2007

PHYSICAL PARAMETERS OF TWO VERY COOL T DWARFS

1149

Mugrauer, M., Seifahrt, A., Neuhaeuser, R., & Mazeh, T. 2006, MNRAS, 373, L31 Noll, K. S., Geballe, T. R., & Marley, M. S. 1997, ApJ, 489, L87 Oppenheimer, B. O., Kulkarni, S. R., Matthews, K., & van Kerkwijk, M. H. 1998, ApJ, 502, 932 Patten, B. M., et al. 2006, ApJ, 651, 502 Prinn, R. G., & Barshay, S. S. 1977, Science, 198, 1031 Saumon, D., Geballe, T. R., Leggett, S. K., Marley, M. S., Freedman, R. S., Lodders, K., Fegley, B., Jr., & Sengupta, S. K. 2000, ApJ, 541, 374 Saumon, D., Marley, M. S., Cushing, M. C., Leggett, S. K., Roellig, T. L., Lodders, K., & Freedman, R. S. 2006, ApJ, 647, 552 (S06) Saumon, D., Marley, M. S., Lodders, K., & Freedman, R. S. 2003, in IAU Symp. 211, Brown Dwarfs, ed. E. L. Martin (San Francisco: ASP), 345 ´

Skrutskie, M. F., et al. 2006, AJ, 131, 1163 Strong, K., Taylor, F. W., Calcutt, S. B., Remedios, J. J., & Ballard, J. 1993, J. Quant. Spectrosc. Radiat. Transfer, 50, 363 Tinney, C. G., Burgasser, A. J., & Kirkpatrick, J. D. 2003, AJ, 126, 975 Tinney, C. G., Burgasser, A. J., Kirkpatrick, J. D., & McElwain, M. W. 2005, AJ, 130, 2326 Tokunaga, A. T., Simons, D. A., & Vacca, W. D. 2002, PASP, 114, 180 van Altena, W. F., Lee, J. T., & Hoffleit, E. D. 1995, The General Catalogue of Trigonometric Stellar Parallaxes (4th ed.; New Haven: Yale Univ. Obs.) Vrba, F. J., et al. 2004, AJ, 127, 2948 Werner, M., et al. 2004, ApJS, 154, 1 York, D. G., et al. 2000, AJ, 120, 1579