FIRE SPECTROSCOPY OF THE ULTRA-COOL BROWN DWARF, UGPS J072227.51−054031.2: KINEMATICS, ROTATION AND ATMOSPHERIC PARAMETERS^*

Since the FIRE spectrum of UGPS 0722−05 is the highest resolution observation of one of the coolest BDs, we compiled the most recent laboratory line lists for H₂O, CH₄, and NH₃ to identify absorption features (Barber et al. 2006; Nassar & Bernath 2003; Yurchenko et al. 2011, respectively). The HITRAN 2008 database was also used to supplement the line lists (Rothman et al. 2009). Prior to comparing to the FIRE spectrum of UGPS 0722−05, each line list was cropped to 0.8–2.5 μm and smoothed with a 50 km s⁻¹ Gaussian kernel, which corresponds to one FIRE resolution element. The absorption intensities for each line list (in units of cm molecule⁻¹) were scaled by the relative molecular abundances shown in Figure 3 of Saumon et al. (2006) for T_eff = 500 K. The non-equilibrium abundances were assumed for NH₃. The scaled values were then plotted along with the UGPS 0722−05 spectrum, and molecular features were manually identified. An example of our line list comparisons is shown in Figure 2.

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In Figure 3, we plot expanded views of the UGPS 0722−05 spectrum in the y, J, H, and K bands. Prominent absorption features are labeled in each panel. Of note in Figure 3 is the significant number of absorption features throughout the spectrum that are attributed to H₂O, CH₄, and NH₃. There are a large number of blends between the molecular features, especially with H₂O, but some isolated absorption bands do exist. We confirm the tentative identification of NH₃ by Lucas et al. (2010) near 1.514 μm. Additional isolated NH₃ absorption features can be found near 1.234, 1.244, 1.52, 1.526, 1.542, 1.56, 1.566, 1.568, and 1.574 μm. This suggests that observations spanning 1.5–1.6 μm present the best chance at directly detecting NH₃ at these temperatures. While the detection of NH₃ has been suggested as the hallmark of the Y spectral class (i.e., Leggett et al. 2007), these weak features are consistent with the end of the T dwarf sequence as advocated by Cushing et al. (2011).

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CH₄ exhibits prominent absorption bands near 1.6 and 2.15 μm. The structure seen in the UGPS 0722−05 spectrum is usually not detected at lower resolutions. These features may be used to derive spectral indices and provide isolated regions of the spectrum to derive atmospheric parameters (see Section 3.4).

The resolution of FIRE's echelle mode permits the measurement of UGPS 0722−05's radial velocity (RV) with a precision of a few km s⁻¹. We cross-correlated the spectrum of UGPS 0722−05 against other T dwarfs observed with FIRE and model atmosphere predictions. The T dwarf RV standards (Table 2) were taken from Zapatero Osorio et al. (2007) and were observed with a similar setup on FIRE as part of a larger effort to quantify BD kinematics (A. J. Burgasser et al. 2011, in preparation). We also employed the T = 400 K, 500 K, 600 K, and 700 K models (with log g = 5.0, [m/H] = 0.0) from the BT-Settl grid (Allard et al. 2010). The 1.27–1.31 μm spectral region in the J band contains many strong molecular features, making it ideal for cross-correlation. The models were smoothed to match the resolution of the FIRE observations. Cross-correlations were computed using the xcorl IDL routine (Basri & Martín 1999; Mohanty & Basri 2003; West & Basri 2009). The reported RV and uncertainty were computed by taking the unweighted mean and the standard deviation of the individual RV measurements, respectively. The measured RV and uncertainty for UGPS 0722−05 is 46.9 ± 2.5 km s⁻¹.

3.2.1. Galactic Orbit

To frame the kinematics of UGPS 0722−05 in a Galactic context, we computed its orbit using its measured velocity and position as initial conditions. Using the distance, position, proper motion, and RV reported in Table 1, we computed the cylindrical velocity vector [V_R, V_ϕ, V_Z] where the local standard of rest is [0, 220, 0] km s⁻¹ (Kerr & Lynden-Bell 1986), the solar motion is [11.1, 12.24, 7.25] km s⁻¹ (Schönrich et al. 2010), and the RV component V_R increases in the direction of the Galactic center (Johnson & Soderblom 1987). The Sun's radial position (X) was taken to be 8.5 kpc away from the Galactic center (Kerr & Lynden-Bell 1986) and 27 pc above the plane (Z; Chen et al. 2001; Jurić et al. 2008). Note that we are reporting velocities in a Galactocentric frame, rather than the traditional heliocentric UVW frame. While the effect is negligible for UGPS 0722−05, using UVW rather than a Galactic frame can introduce errors of a few km s⁻¹ for distances ≳100 pc. Employing a Galactocentric velocity frame will be important as more distant dwarfs are discovered in the next generation of surveys (i.e., the Large Synoptic Survey Telescope).

The orbit was integrated assuming a set of static, spherically symmetric oblate Plummer's sphere potentials for the Galactic halo, bulge, and disk, using the forms described in Kuzmin (1956) and Miyamoto & Nagai (1975) and with parameters from Dauphole & Colin (1995). A Runge–Kutta integrator was used to calculate the orbit over a period of ±250 Myr with a 10 kyr time step, and both energy and the Z-component of angular momentum were conserved to better than one part in 10³. To sample measurement uncertainties in the distance and velocity of UGPS 0722−05 relative to the Sun, we computed 100 realizations of the orbit through the Monte Carlo method, varying the starting conditions assuming normal distributions with means and widths given by the values in Table 1.

The baseline calculation is shown in Figure 4, revealing a flat orbit with small eccentricity (e). The maximum vertical displacement of the source from the Galactic plane never exceeds Z ∼ 60 pc, with radial excursions between 7 kpc <R < 9.5 kpc, and e = 0.11 ± 0.02. This orbit is consistent with membership in the Galactic thin disk population (Bochanski et al. 2007) suggesting that UGPS 0722−05 is a relatively young BD. However, we strongly caution the use of kinematic properties as an age discriminant, as they should only be considered in a statistical manner. Computing orbits for larger samples of MLTY dwarfs will help place the orbit of UGPS 0722−05 in a broader context.

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The rotational velocity of UGPS 0722−05 was also measured with a technique used by a number of previous studies (e.g., Reid & Mahoney 2000; Mohanty & Basri 2003; West & Basri 2009). Briefly, the science object (UGPS 0722−05) is cross-correlated with a rotationally unbroadened template (the T = 500 K, log g = 5.0 model, [m/H] = 0.0 from BT-Settl; Allard et al. 2010). The model is convolved with a Gaussian of 50 km s⁻¹ to approximate the effects of FIRE's line-spread function. This cross-correlation function (CCF) is compared to the CCFs derived from correlating the unbroadened template to rotationally broadened versions of itself. We constructed a series of rotating templates ranging in vsin i from 10 to 120 km s⁻¹, in steps of 10 km s⁻¹ using the technique described in Gray (1992). In Figure 5, we compare the autocorrelation of the template against the CCFs of the vsin i = 30, 40, and 60 km s⁻¹ templates and the CCF of UGPS 0722−05 over the same wavelength range described in Section 3.2. While vsin i = 40 km s⁻¹ was the closest match to the CCF of UGPS 0722−05, the vsin i = 30 and 50 km s⁻¹ were good fits to most of the CCF trough (see Figure 5). Thus, we report a vsin i for UGPS 0722−05 is 40 ± 10 km s⁻¹.

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This rotation velocity is similar to those of late L and T dwarfs (e.g., Zapatero Osorio et al. 2006; Reiners & Basri 2008). Of the nine T dwarfs observed by Zapatero Osorio et al. (2006), only one BD (SDSSJ134646.45−003150.4) had a vsin i under 20 km s⁻¹ and the authors speculated that this may be due to inclination.¹⁰ The remaining eight T dwarfs demonstrated rotational velocities between 20 and 40 km s⁻¹ and this distribution does not vary significantly from the observed rotation velocities of L dwarfs (Reiners & Basri 2008). The vsin i of UGPS 0722−05 reinforces the findings of previous studies suggesting that T dwarfs are inefficient at rotational braking. In solar-type stars, magnetic fields power two sources of angular momentum loss: disk braking and flaring events (Skumanich 1972; Bouvier et al. 1997). Large-scale magnetic fields can form in convective, rotating low-mass objects (i.e., Browning 2008) and have been observed in some late M and L dwarfs (Reiners & Basri 2008; Hallinan et al. 2008), but remain undetected in T dwarfs (Berger 2006). This may indicate the lack of magnetic fields in T dwarfs, or alternatively, a weak coupling between the fields and the predominately neutral atmosphere. This de-coupling would reduce disk braking and flare frequency (due to reconnection events), which would decrease angular momentum loss in T dwarfs compared to solar-type stars.

To examine the physical properties of UGPS 0722−05, we compared its FIRE spectrum to the BT-Settl models of Allard et al. (2010). These models are based on the PHOENIX code (Hauschildt et al. 1999), and reflect an update to the original Settl models of Allard et al. (2003) with a microturbulence velocity field determined from two-dimensional hydrodynamic models (Freytag et al. 2010) and updated solar abundances from Asplund et al. (2009). We adopted a set of solar–metallicity ([m/H] = 0.0) models sampling T_eff = 400–900 K in 100 K steps, and log g = 3.5–5.5 cm s⁻² in 0.5 cm s⁻² steps, with the exceptions that violate evolutionary parameters (e.g., T_eff ⩽ 700 K and log g = 5.5).

Our fitting procedure was based on the formalism developed by Cushing et al. (2008), Bowler et al. (2009) and Burgasser et al. (2010). Model surface fluxes (in f_λ units) were smoothed to a common resolution of λ/Δλ = 6000 using a Gaussian kernel, and both models and FIRE data were interpolated onto a common wavelength grid spanning 0.9–2.4 μm. The FIRE data were also scaled to the observed J magnitude of UGPS 0722−05. We then performed eight separate fits to the data, encompassing the full spectral range (excluding regions of strong telluric absorption), the yJHK spectral peaks, and three "narrow" regions (0.04–0.12 μm in width) sampling strong molecular absorption (Table 3). Data and models were compared using a χ² statistic, with the degrees of freedom equal to the number of resolution elements sampled. The optimal scaling factor minimizing χ² was computed following Cushing et al. (2008) and is equivalent to (R/d)², where R is the radius of the BD and d its distance from the Sun (Bowler et al. 2009). Two sets of fits were done, one in which the distance was treated as a free parameter and one in which the model-derived distance must agree with the parallax measurement of Lucas et al. (2010) to within 5σ. We also allowed for variations in the radial (±50 km s⁻¹ in steps of 1.25 km s⁻¹ about the reported value) and rotational velocities (0–100 km s⁻¹ in steps of 3 km s⁻¹) of the model templates to find a χ² minimum. Means and uncertainties in the atmospheric parameters (T_eff, log g) and associated physical parameters (mass, age, and radius based on the evolutionary models of Baraffe et al. 2003) were determined using the F-test probability distribution function as a weighting factor, as described in Burgasser et al. (2010). We also propagated sampling uncertainties of 50 K and 0.25 dex for T_eff and log g, respectively.

Table 3. Atmosphere Model Measurements

Parameter	Full Spectrum	y	J	Jr	H	Hr	K	Kr
Fit Ranges (μm)	0.9–2.35	0.9–1.15	1.15–1.35	1.27–1.31	1.45–1.8	1.50–1.57,	1.9–2.35	2.1–2.18
						1.63–1.75
dof	3409	982	743	182	1016	585	659	220
No distance restriction
Min χ2	87.4	19.0	66.3	62.7	107	35.4	10.9	7.5
Teff (K)	700 ± 50	750 ± 70	600 ± 50	620 ± 60	590 ± 60	500 ± 50	610 ± 60	630 ± 70
log g (cgs)	4.0 ± 0.3	3.5 ± 0.3	4.5 ± 0.3	4.5 ± 0.3	4.1 ± 0.4	4.4 ± 0.3	3.7 ± 0.4	3.8 ± 0.4
Mass (${\cal M}_{\odot }$)	0.005	0.003	0.012	0.012	0.008	0.011	0.004	0.004
Age (Gyr)	0.08	0.02	0.9	0.9	0.5	1.5	0.07	0.09
d (pc)	49	61	22	20	27	6.4	23	24
Distance restriction
Min χ2	118	74.3	196	90.6	118	35.4	20.9	12.1
Teff (K)	500 ± 50	500 ± 50	500 ± 50	600 ± 50	500 ± 50	500 ± 50	520 ± 70	510 ± 60
log g (cgs)	4.0 ± 0.3	4.0 ± 0.3	4.0 ± 0.3	5.0 ± 0.3	4.4 ± 0.3	4.4 ± 0.3	4.4 ± 0.5	4.2 ± 0.4
Mass (${\cal M}_{\odot }$)	0.005	0.005	0.005	0.029	0.010	0.011	0.013	0.009
Age (Gyr)	0.2	0.2	0.3	5.1	1.3	1.4	2.1	1.0
d (pc)	4.6	4.2	4.9	6.7	6.2	6.4	4.2	3.5

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The best-fit models and data are plotted in Figure 6. The upper panel displays the best fit to the entire spectrum, with the distance limit enforced. There are significant deviations between the model and data in the JHK bands, suggesting that there remain missing or incorrect molecular opacity in the BT-Settl model calculations. However, the agreement between the best-fit distance-restricted model and data improves in the "narrow" regions, as shown in Figure 6. Given the deviations between the models and data, caution is warranted in using the physical parameters listed in Table 3, however, some general trends do emerge. First, we examined the relative effect of the distance restriction. The distance-restricted fits prefer a cooler T_eff, ∼500 K instead of 700 K. The distance-restricted fits also suggest a higher surface gravity and older age, but there is no clear behavior in the mass determination. We also note that most of the fits with unrestricted distances prefer distances much larger than the measured parallax.

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We adopt the restricted distance and wavelength sets (J_r, H_r, and K_r) for further discussion. These clipped wavelength sets were chosen to sample strong molecular absorption, mostly due to CH₄. Agreement between the data and model within these windows indicates that the BT-Settl models may have the proper opacity included in these windows, but due to the dearth of benchmark BDs (Konopacky et al. 2010, and references therein), the physical parameters derived from these fits may have large systematic uncertainties. These fits suggest an object with T_eff ≃ 500–600 K, log g ≃ 4.2–5.0, mass ∼10–30 $\cal {M}_{\rm Jup}$, and an age of 1–5 Gyr. These parameters agree with the results of Lucas et al. (2010), who reported T_eff =480–560 K, log g =4.0–4.5, mass = 5–15 $\cal {M}_{\rm Jup}$, and an age of 0.2–2.0 Gyr. To examine the accuracy in other bandpasses, synthetic photometry was computed in the Infrared Array Camera and WISE bands reported in Table 1 using the T_eff = 500 K, log g = 4.0 model and reported parallax. In general, the synthetic photometry matched the reported values within <1 mag, and agreed within <0.05 mag for the W1 and W3 bandpasses, suggesting the calculated opacities in these filters may be correct. We note that the H_r region produced identical results with and without the distance restriction, suggesting that the BT-Settl models may perform well in this wavelength range. However, adopting the uncertainties from the physical parameters from only this range probably underestimates the systematic errors, especially since only one set of models was considered.