https://orcid.org/0000-0003-0489-1528
Abstract
We present the detection of [3.6 μm] photometric variability in two young, L/T transition brown dwarfs, WISE J004701.06+680352.1 (W0047) and 2MASS J2244316+204343 (2M2244) using the Spitzer Space Telescope. We find a period of 16.4 ± 0.2 h and a peak-to-peak amplitude of 1.07 ± 0.04 per cent for W0047, and a period of 11 ± 2 h and amplitude of 0.8 ± 0.2 per cent for 2M2244. This period is significantly longer than that measured previously during a shorter observation. We additionally detect significant J-band variability in 2M2244 using the Wide-Field Camera on UKIRT. We determine the radial and rotational velocities of both objects using Keck NIRSPEC data. We find a radial velocity of |$-16.0_{-0.9}^{+0.8}$| km s−1 for 2M2244, and confirm it as a bona fide member of the AB Doradus moving group. We find rotational velocities of v sin i = 9.8 ± 0.3 and |$14.3^{+1.4}_{-1.5}$| km s−1 for W0047 and 2M2244, respectively. With inclination angles of |$85 ^{+5\circ }_{-9}$| and |$76 ^{+14\circ }_{-20}$|, W0047 and 2M2244 are viewed roughly equator-on. Their remarkably similar colours, spectra and inclinations are consistent with the possibility that viewing angle may influence atmospheric appearance. We additionally present Spitzer [4.5 μm] monitoring of the young, T5.5 object SDSS111010+011613 (SDSS1110) where we detect no variability. For periods <18 h, we place an upper limit of 1.25 per cent on the peak-to-peak variability amplitude of SDSS1110.
1 INTRODUCTION
The growing number of young exoplanets that have been directly imaged in the infrared (Marois et al. 2008; Lagrange et al. 2010; Macintosh et al. 2015) have revealed some unexpected results. With comparable temperatures but lower masses, the young directly imaged planets were expected to share similar atmospheric properties to the well-studied population of brown dwarfs. However most young directly imaged planets appear much redder in the near-IR than their higher mass field counterparts with similar spectral types. Fortunately, young brown dwarfs may still provide an excellent analogue to directly imaged planets, and we now have a significant population of young brown dwarfs with colours and magnitudes similar to directly imaged exoplanets, many of which have estimated masses in the planetary-mass regime (see the compilation of young, red M and L dwarfs made by Faherty et al. (2016), Liu, Dupuy & Allers (2016), and references therein). Three such objects are WISEP J004701.06+680352.1 (W0047), 2MASS J2244316+204343 (2M2244) and SDSS J111010+011613 (SDSS1110) (Gizis et al. 2012; Knapp et al. 2004; Gagné et al. 2015). W0047 and SDSS1110 are kinematically confirmed members of the 150-Myr-old AB Doradus moving group (Bell, Mamajek & Naylor 2015). 2M2244 is assigned a membership probability of 99.6 per cent for the same group based on its proper motion and distance (Gagné et al. 2014b, 2015; Gizis et al. 2015; Liu et al. 2016), but a radial velocity measurement is necessary to confirm moving group membership. We measure its radial velocity in this paper (Section 2.2) and confirm it as a member of the AB Doradus moving group. W0047 is classified as an L7 INT-G brown dwarf and 2M2244 is classified as an L6 VL-G object (Allers & Liu 2013; Gizis et al. 2015). W0047 and 2M2244 are a particularly interesting pair of young, low-gravity objects, with 0.65–2.5 μm spectra that are remarkably similar (Gizis et al. 2015). There are no other free-floating L/T transition dwarfs known to be both coeval and spectrally similar that are bright enough for detailed characterization (though see Best et al. 2015 for more candidates). SDSS1110 is a T5.5 10–12 MJup (Gagné et al. 2015) object, and is one of very few young, age-calibrated T dwarfs known to date. W0047, 2M2244 and SDSS1110 are the lowest mass confirmed members of the AB Doradus moving group (Liu et al. 2016), and can thus provide powerful insights into the atmospheres of the directly imaged planets.
A key probe of brown dwarf atmospheres is time-resolved photometric monitoring, which is sensitive to the spatial distribution of surface inhomogeneities as objects rotate. Large-scale field brown dwarf surveys have revealed ubiquitous variability across the entire L-T spectral range (Buenzli et al. 2014; Radigan et al. 2014; Wilson, Rajan & Patience 2014; Metchev et al. 2015). Due to their lower gravity, young brown dwarfs exhibit atmospheric scale heights and time-scales different from old field brown dwarfs (Freytag et al. 2010; Marley, Saumon & Goldblatt 2010; Marley et al. 2012). Thus, studying their variability provides valuable information on atmospheric structure in brown dwarfs and exoplanet atmospheres as a function of surface gravity. Because of their more recent formation, young brown dwarfs and exoplanets have inflated radii compared to the field brown dwarfs. Hence, they are expected to rotate more slowly than their older counterparts due to conservation of angular momentum. However, the planetary mass objects β Pic b, PSO-318.5-22 and 2M1207b all have rotation periods of 6–11 h (Snellen et al. 2014; Biller et al. 2015; Zhou et al. 2016; Allers et al. 2016), similar to higher mass brown dwarfs (Zapatero Osorio et al. 2006).
To date, the observed variability has been interpreted as evidence for condensate clouds, which are required by the majority of brown dwarf and exoplanet models (Marley et al. 2010; Morley et al. 2014). Magnetic phenomena, such as starspots, have also been suggested as a driver of photometric variability. While some L-T type brown dwarfs have been found to possess strong magnetic fields (Kao et al. 2015; Pineda et al. 2016), Miles-Páez et al. (2017) report no correlation between magnetic activity and photometric variability in a sample of L0-T8 brown dwarfs. Recently, Tremblin et al. (2016) proposed cloud-free models, suggesting that the observed variability is due to differing CO abundances or temperature fluctuations. Further work is required to establish which scenario is appropriate for these objects.
W0047 and 2M2244 present the unique opportunity to explore the effects of both viewing angle and age on observed variability. For an equator-on object (with an inclination angle, i ∼ 90°) we measure the full variability amplitude via photometric monitoring. In contrast, lower variability amplitudes are measured for objects that are close to pole-on (Vos, Allers & Biller 2017). Determining the variability amplitude and inclination angle of each object allows us to disentangle the effects of viewing angle on the observed variability.
Metchev et al. (2015) find evidence for higher variability amplitudes for young L3-L5.5 objects. This is unexpected because atmospheric models for young objects typically require very thick clouds (Madhusudhan, Burrows & Currie 2011) and variability studies have suggested that older objects with patchy coverage of thinner and thicker clouds tend to have the highest variability amplitudes (Apai et al. 2013; Buenzli et al. 2015). 2M2244, W0047 and SDSS1110 provide three valuable data points to further explore this trend beyond the early L-type dwarfs.
Periodic variability has previously been detected in W0047 and 2M2244. Lew et al. (2016) report variability with a peak-to-peak J-band amplitude of 8 per cent for W0047 during a 9 h observation, determining a period of 13.2 ± 0.14 h. Morales-Calderon et al. (2006) obtained Spitzer [4.5 μm] time-resolved photometry of 2M2244 and report variability with a period of 4.6 h and a peak-to-peak amplitude of 8 mmag during a 5.7-h observation. SDSS1110 has no previous variability detections in the literature. We have obtained Spitzer photometric monitoring for W0047, 2M2244 and SDSS1110 and J-band monitoring of 2M2244 taken with WFCAM at UKIRT, as well as high dispersion NIRSPEC spectra of W0047 and 2M2244. The spectrum of W0047 was first presented by Gizis et al. (2015), and we use the same data set in this paper. The paper is organized as follows. In Section 2, we discuss the analysis and results of our Keck NIRSPEC high-resolution spectra of 2M2244 and W0047. In Section 3, we present the light curves of our three targets 2M2244, W0047 and SDSS1110. In Section 4, we calculate the inclination angles of W0047 and 2M2244.
2 KECK NIRSPEC HIGH DISPERSION SPECTROSCOPY
We obtained high dispersion NIRSPEC spectra for W0047 from the Keck Observatory Archive (Prog ID: U055NS, PI: Burgasser) and observed 2M2244 as part of a larger programme (Prog ID: N160NS, PI: Allers). NIRSPEC is a near-infrared echelle spectrograph on the Keck II 10 m telescope on Mauna Kea, Hawaii. The NIRSPEC detector is a 1024 × 1024 pixel ALADDIN InSb array. Observations were carried out using the NIRSPEC-7 (1.839 − 2.630 μm) passband in echelle mode using the 3 pixel slit (0.432″), echelle angles of 62|$_{.}^{\circ}$|68 − 62|$_{.}^{\circ}$|97, and grating angles of 35|$_{.}^{\circ}$|42 − 35|$_{.}^{\circ}$|51. Observations of targets were gathered in nod pairs, allowing for the removal of sky emission lines through the subtraction of consecutive images. Arc lamps were observed for wavelength calibration. 5 − 10 flat-field and dark images were taken for each target to account for variations in sensitivity and dark current on the detector. W0047 was observed on 2013 September 17 with 2 × 1200 s exposures at an airmass of 1.5 and a mean DIMM seeing of 1.0 arcsec. 2M2244 was observed on 2013 July 6 with 4 × 240 s exposures at an airmass of 1.0 and a mean DIMM seeing of 0.5 arcsec.
We focus our analysis on order 33 (2.286–2.326 μm) since this part of the spectrum contains a good blend of sky lines and brown dwarf lines, allowing for an accurate fit. This spectral region is rich in CO features, as well as H2O and CH4 features. These features are discussed in detail by Blake, Charbonneau & White (2010). Order 33 is also commonly used in the literature for NIRSPEC high dispersion N-7 spectra (Blake et al. 2010; Gizis et al. 2013). We additionally look at orders 32 (2.364–2.398 μm) (for W0047) and 38 (1.987–2.016 μm) (for both W0047 and 2M2244) to check for consistency. Data were reduced using a modified version of the REDSPEC reduction package to spatially and spectrally rectify each exposure. The NIRSPEC Echelle Arc Lamp Tool was used to identify the wavelengths of lines in our arc lamp spectrum. After nod-subtracting pairs of exposures, we create a spatial profile which is the median intensity across all wavelengths at each position along the slit. We use Poisson statistics to determine the noise per pixel at each wavelength. We extract the flux within an aperture in each nod-subtracted image to produce two spectra of our source. The extracted spectra are combined using a robust weighted mean with the xcombspec procedure from the spextool package (Cushing, Vacca & Rayner 2004).
2.1 Determining radial and rotational velocities
We use the approach outlined in Allers et al. (2016) to determine the radial and rotational velocities of W0047 and 2M2244. We employ forward modelling to simultaneously fit the wavelength solution of our spectrum, the rotational and radial velocities, the scaling of telluric line depths, and the FWHM of the instrumental line spread function (LSF). We use the BT-Settl model atmospheres (Allard, Homeier & Freytag 2012) as the intrinsic spectrum for each of our targets. In total, the forward model has nine free parameters: the Teff and log (g) of the atmosphere model, the vr and v sin i of the brown dwarf, τ for the telluric spectrum, the LSF FWHM, and the wavelengths of the first, middle and last pixels. The forward model is compared to our observed spectrum, and the parameters used to create the forward model are adjusted to achieve the best fit.
To determine the best-fitting parameters of our forward model as well as their posterior distributions, we use a Markov Chain Monte Carlo (MCMC) approach. This involves creating forward models that allow for a continuous distribution of Teff and log(g) by linearly interpolating between atmosphere grid models. We employ the DREAM(ZS) algorithm (Ter Braak & Vrugt 2008), which uses an adaptive stepper, updating model parameters based on chain histories. To ensure that the median absolute residual of the fit agrees with the median uncertainty of our spectrum, we include a systematic uncertainty of 1.4 per cent in the spectrum of W0047.We plot our spectra and best-fitting models along with the residuals in Fig. 1. Final values for v sin i and radial velocities (RV) are shown in Table 2. Their 1σ uncertainties are determined from their marginalized distributions obtained from our MCMC method. Although we obtain values for Teff and log (g), these derived values should not be considered physical since we are using a narrow wavelength range in K band. Furthermore, atmospheric models are known to be unreliable for young L/T transition objects, even if J-band data are included (Liu et al. 2013; Allers et al. 2016). These parameters are more reliably determined from evolutionary models, as is done in Section 2.3. The results for both 2M2244 and W0047 are consistent across orders 32, 33 and 38 at the 2σ level. The mean and standard deviation of the LSF FWHM is 0.08 ± 0.01 and 0.081 ± 0.002 nm for 2M2244 and W0047, respectively, resulting in a resolution R = λ/Δλ ≃ 29 000 for both objects. The precision of our wavelength solution is determined to be 0.0025 and 0.0124 nm for 2M2244 and W0047.
Left: The observed spectrum of W0047 (black) compared to our best-fitting forward model (red). Residuals are plotted in the bottom panel. Right: The observed and best-fitting forward model of 2M2244.
Our v sin i measurement of 9.8 ± 0.3 km s−1for W0047 is higher than both previous measurements by Gizis et al. (2015) (4.3 ± 2.2 km s−1) and Lew et al. (2016) (|$6.7^{+0.7}_{-1.4}$| km s−1), despite all three measurements using the same data set. The model atmosphere for W0047 used by Gizis et al. (2015) has Teff = 2300 and log (g) = 5.5 while evolutionary models predict Teff = 1270 and log (g) = 4.5 (Gizis et al. 2015). Our model (with Teff = 1670 and log (g) = 5.2) is in better agreement with the evolutionary model. Higher effective temperature and surface gravity results in more pressure broadening, producing a lower value of v sin i. Lew et al. (2016) do not provide details on the atmospheric model used. Again, the consistency between orders 32, 33 and 38 further supports our results.
2.2 2M2244+20 Membership in AB Doradus
A radial velocity measurement is required to confirm moving group membership. Using Bayesian analysis to assess the membership of >M5 brown dwarfs, Gagné et al. (2014a) find a 99.6 per cent probability that 2M2244 is a member of the AB Doradus moving group, predicting a radial velocity of −15.5 ± 1.7 km s−1. Our measured radial velocity of −16.0 ± 0.9 km s−1 is consistent with the predicted radial velocity. Including the measured radial velocity, along with parallax and proper motion measurements from Liu et al. (2016), and using the banyan-ii web tool (Gagné et al. 2014a; Malo et al. 2013), the probability of AB Doradus membership increases to 99.96 per cent. Thus, our radial velocity measurement confirms 2M2244 as a member of the AB Doradus moving group.
2.3 The physical properties of W0047 and 2M2244
Filippazzo et al. (2015) provide radius, log (g), Teff and mass estimates from evolutionary models for W0047 and 2M2244; however, the estimated age range used in this analysis of 50–110 Myr for AB Doradus is systematically younger than current estimates. Barenfeld et al. (2013) place a strong lower limit of 110 Myr and Luhman, Stauffer & Mamajek (2005) provides an upper limit of 150 Myr on the age of AB Doradus. Furthermore, Filippazzo et al. (2015) use a kinematic distance to determine the luminosity of 2M2244 while Liu et al. (2016) has since measured its parallax. We use these measured parallaxes to update the luminosities of 2M2244 and W0047. The errors on the updated luminosities are slightly overestimated, since the bolometric magnitudes and errors are not given in Filippazzo et al. (2015). For a uniformly distributed age of 110–150 Myr and normally distributed luminosities, we determine the physical properties of 2M2244 and W0047 using model isochrones (final parameters shown in Table 1). W0047 and 2M2244 both exhibit extremely red J − K colours, indicating a dusty atmosphere. Thus, we use the Saumon & Marley (2008) solar metallicity fsed = 2 models. The older age of the AB Doradus moving group that is used in this analysis pushes both masses above the deuterium burning limit, and above the masses presented in Filippazzo et al. (2015). The revised radii are consistent with those reported by Filippazzo et al. (2015).
Physical properties of W0047 and 2M2244 from the Saumon & Marley (2008) fsed = 2 evolutionary model.
| W0047 | 2M2244 | |
|---|---|---|
| log (L/L○) | −4.44 ± 0.04 | −4.48 ± 0.02 |
| Mass (MJup) | |$19.5^{+1.6}_{-1.7}$| | |$19.0^{+1.4}_{-1.5}$| |
| Teff | |$1250^{+20}_{-30}$| | |$1230^{+16}_{-15}$| |
| Radius (RJup) | 1.28 ± 0.02 | 1.28 ± 0.02 |
| log (g) (dex) | 4.49 ± 0.05 | |$4.48^{+0.04}_{-0.05}$| |
| W0047 | 2M2244 | |
|---|---|---|
| log (L/L○) | −4.44 ± 0.04 | −4.48 ± 0.02 |
| Mass (MJup) | |$19.5^{+1.6}_{-1.7}$| | |$19.0^{+1.4}_{-1.5}$| |
| Teff | |$1250^{+20}_{-30}$| | |$1230^{+16}_{-15}$| |
| Radius (RJup) | 1.28 ± 0.02 | 1.28 ± 0.02 |
| log (g) (dex) | 4.49 ± 0.05 | |$4.48^{+0.04}_{-0.05}$| |
Physical properties of W0047 and 2M2244 from the Saumon & Marley (2008) fsed = 2 evolutionary model.
| W0047 | 2M2244 | |
|---|---|---|
| log (L/L○) | −4.44 ± 0.04 | −4.48 ± 0.02 |
| Mass (MJup) | |$19.5^{+1.6}_{-1.7}$| | |$19.0^{+1.4}_{-1.5}$| |
| Teff | |$1250^{+20}_{-30}$| | |$1230^{+16}_{-15}$| |
| Radius (RJup) | 1.28 ± 0.02 | 1.28 ± 0.02 |
| log (g) (dex) | 4.49 ± 0.05 | |$4.48^{+0.04}_{-0.05}$| |
| W0047 | 2M2244 | |
|---|---|---|
| log (L/L○) | −4.44 ± 0.04 | −4.48 ± 0.02 |
| Mass (MJup) | |$19.5^{+1.6}_{-1.7}$| | |$19.0^{+1.4}_{-1.5}$| |
| Teff | |$1250^{+20}_{-30}$| | |$1230^{+16}_{-15}$| |
| Radius (RJup) | 1.28 ± 0.02 | 1.28 ± 0.02 |
| log (g) (dex) | 4.49 ± 0.05 | |$4.48^{+0.04}_{-0.05}$| |
3 SPITZER AND WFCAM PHOTOMETRY
For our Spitzer observations of W0047, 2M2244 and SDSS1110 we followed standard observing practices for obtaining precise, stable, and nearly photon limited performance. We employed ‘staring mode’ AORs in which the object did not move on the chip throughout the entire observation, with a long exposure time (Metchev et al. 2015). W0047 and 2M2244 were observed for 18.7 and 8.8 h on 2016 January 9 and September 15, respectively, in the Spitzer [3.6 μm] band with an exposure time of 30 s and a pixel scale of 1.221 arcsec. SDSS1110 was observed for 9.0 h on 2016 April 5 in the Spitzer [4.5 μm] band with an exposure time of 100 s and a pixel scale of 1.231 arcsec. Additionally, we include Spitzer [4.5 μm] archival data of 2M2244 (Program ID: 20079, PI: Stauffer) published in Morales-Calderon et al. (2006) for re-analysis.
Photometry was obtained from the corrected Basic Calibrated Data images, provided by the Spitzer Science Center after processing through irac pipeline version 19.2.0. The centroids of the target and a number of reference stars are found using box_centroider.pro. We perform aperture photometry on these centroids, using various aperture sizes and choosing the aperture size that produces light curves with the lowest RMS (3.0, 3.5 and 3.5 pixels for 2M2244, W0047 and SDSS1110, respectively). Outliers are identified and rejected from the raw light curves using a 6σ clip, removing ∼5–45 points in each light curve.
The light curves are then corrected for intrapixel sensitivity variations, the so-called ‘pixel phase effect’. This is the slight variation in flux depending on where a point source falls with respect to the centre of a pixel. The pixel phase response is modelled as a ‘double-Gaussian’, a summation of Gaussians in the orthogonal pixel directions. We correct for the pixel phase effect using the pixel_phase_correct_gauss.pro routine from the Spitzer IRAC website. The pixel phase corrected flux is then binned into ∼5 minute bins using a weighted average, followed by a final 3σ clip to produce the final light curves. The photometric noise of our normalized and corrected light curves is calculated following Radigan et al. (2014). While the standard deviation produces a measurement of noise for flat curves, in the case of variable light curves the standard deviation measures both noise and intrinsic variations. We therefore use the point-to-point noise to measure the photometric noise. This is the standard deviation of the light curve subtracted from a shifted version of itself, divided by |$\sqrt{2}$|. This measure of photometric noise is not sensitive to low frequency trends and thus provides a better estimate of the noise for variable light curves.
We also include an observation of 2M2244 taken with the infrared Wide-Field Camera (WFCAM; Casali et al. 2007) on 2016 July 21 ut as part of a larger survey for variability on free-floating low-mass objects. This is a wide-field imager on the 3.8 m UK Infrared Telescope on Mauna Kea, with a pixel scale of 0.4 arcsec. The observation was carried out with the J-band filter and seeing of ∼1.1 arcsec during the 4 h sequence. The target was observed using an ABBA nod pattern, with three exposures of 40 s at each position. The frames were reduced using the WFCAM reduction pipeline (Irwin et al. 2004; Hodgkin et al. 2009) by the Cambridge Astronomical Survey Unit. Aperture photometry is performed on the target as well as on a large number of reference stars in the field using an aperture size of 3.5 pixels. Raw light curves obtained from aperture photometry display brightness fluctuations due to changes in seeing, airmass and residual instrumental effects. To a very good approximation, these changes are common to all stars in the field of view and can be removed via division of a calibration curve calculated from a set of iteratively chosen, well-behaved reference stars (Radigan et al. 2012). For each star, a calibration curve is created by median combining all other reference stars (excluding that of the target and of the star itself). The standard deviation and linear slope for each light curve are calculated and stars with a standard deviation or slope 1.2 times greater than that of the target are discarded. This process is iterated a number of times, until a set of well-behaved reference stars is chosen. Reference stars are also examined by eye to check for any residual trends. Final detrended light curves are obtained by dividing the raw curve for each star by its calibration curve.
3.1 Identification of variables
We plot the periodogram of the target as well as a number of reference stars in the field to identify periodic variability in our targets. For each periodogram, the 1 per cent false-alarm probability (FAP) is calculated from 1000 simulated light curves. These light curves are produced by randomly permuting the indices of reference star light curves (Radigan et al. 2014). This produces light curves with Gaussian-distributed noise. The 1 per cent FAP is plotted in blue in each periodogram. The rotational periods and peak-to-peak variability amplitudes of targets showing periodic variability are determined by fitting an appropriate function to the data using mpfit.pro. This is an implementation of the Levenberg–Marquardt least-squares minimization algorithm which provides the best-fitting periods and variability amplitudes with their 1σ uncertainties. Finding that the least-squares method can be sensitive to initial parameter guesses, we also use the MCMC algorithm emcee (Foreman-Mackey et al. 2013) to fully explore the posterior probability distributions of our model parameters.
Aperiodic or stochastic variations are not easily detectable from Lomb–Scargle periodograms so we additionally check for stochastic variability by comparing the photometric standard deviation of our target with the mean standard deviation of comparison stars of similar brightness. If the standard deviation of the target is considerably larger than the mean standard deviation of the comparison stars this suggests stochastic variability in the target.
3.2 W0047
The light curve of W0047 (Fig. 2) appears sinusoidal over an entire period. The periodogram displays a strong peak at ∼16 h that is well above the 1 per cent FAP value. The least-squares best-fitting sinusoidal function gives a period of 16.3 ± 0.3 h and an amplitude of 1.08 ± 0.04 per cent. We also use the emcee package (Foreman-Mackey et al. 2013) to obtain the full posterior probability distribution for each parameter of the sinusoidal model. We use 1000 walkers with 7500 steps (after discarding the initial burn-in sample) in the four-dimensional parameter space to model the light curve. Fig. 3 shows the posterior probability distributions of the amplitude, period, phase and constant parameters of the fit. Each parameter is well constrained, and the MCMC method gives a period of 16.4 ± 0.2 h and a peak-to-peak amplitude of 1.07 ± 0.04 per cent.
Top panel shows the normalized, pixel phase corrected light curve of W0047 with best-fitting sinusoidal function overplotted in red. The best-fitting function gives a period of 16.3 ± 0.2 h and an amplitude of 1.08 ± 0.04 per cent. The middle panel shows the best fitting function injected into a simulated light curve. The bottom panel shows the periodogram of the target and the simulated curve, as well as the periodogram of several reference stars in the field. The blue dashed line shows the 1 per cent false-alarm probability.
Posterior distributions of parameters of the Spitzer light curve of W0047 (shown in Fig. 2) The middle dashed line is the median, the two outer vertical dashed lines represent the 68 per cent confidence interval. The contours show the 1σ, 1.5σ and 2σ levels.
Assuming rigid rotation, we use our measured v sin i and a radius estimate of 1.28 ± 0.02 RJup, which allow us to place an upper limit of |$16.3^{+0.8}_{-1.4}$| h on the rotational period of W0047. We can therefore discount the possibility of a double-peaked light curve with a longer rotational period. The measured period is significantly longer than the previously measured 13.2 ± 0.14 h (Lew et al. 2016), however this initial period was determined from an ∼9-h observation that did not cover a full rotation. The photometric noise of our target is similar to that measured for comparison stars in the field of similar brightness; thus we find no evidence for aperiodic variability.
With a peak-to-peak amplitude of 1.07 ± 0.04 per cent, this is among the highest Spitzer [3.6 μm] variability amplitudes detected. Metchev et al. (2015) notes a tentative correlation between low-gravity and high-amplitude variability among a sample of eight L3-L5.5 dwarfs. The variability detection measured here adds to a growing number of young, L objects that display high-amplitude variability, suggesting that this correlation may extend into the late-L spectral types (Biller et al. 2015; Metchev et al. 2015; Lew et al. 2016).
3.3 2M2244
3.3.1 Spitzer [3.6 μm] monitoring
Same as Fig. 2, but for 2M2244 data taken on 2016 September 15. Here we consider a two-term Fourier series to model the variability. The Fourier function gives a period of 10 ± 2.4 h with a peak to trough amplitude of 0.8 ± 0.2 per cent. The bottom panel shows that the Fourier-term fit matches the target periodogram well, reproducing both the minor smaller peak at ∼4 h and the large peak at ∼10 h.
After experimentation with different starting parameters for the least-squares fit, we find that the results are not consistent across different initial guesses for the model parameters. Using the Morales-Calderon et al. (2006) measurement of 4.6 h as an initial guess on the period of 2M2244, the best-fitting solution gives a period of ∼4 h. In contrast, using the peak of our periodogram (∼10 h) as an initial guess on the period, we obtain a best-fitting period of 10 h for the Fourier model. In fact, any initial guess >5 h yields a best-fitting period of 10 h. It is clear that the least-squares fitting procedure cannot locate global minima, and is over-dependent on initial guesses. Hence, we use the emcee algorithm to explore the posterior distribution of the model parameters using the two-term Fourier model. We use 1000 walkers with 7500 steps (after discarding the initial burn-in sample) to model the light curve. Our measured v sin i value of |$14.3^{+1.3}_{-1.5}$| km s−1 and estimated radius of 1.28 ± 0.02 RJup allow us to place an upper limit of |$11.1^{+1.9}_{-1.2}$| h on the period of 2M2244, hence we use an upper limit of 13 h as a prior in our MCMC analysis. The posterior distributions of the parameters for the Fourier model are shown in Fig. 5. This model favours a period of |$11.1^{+1.4}_{-2.0}$| h and this value is insensitive to the initial parameter guesses.
Posterior distributions of parameters of the Fourier model fit to the Spitzer light curve of 2M2244 (shown in Fig. 4). The middle dashed line is the median, the two outer vertical dashed lines represent the 68 per cent confidence interval. We have placed an upper limit on the period of 13 h using our radius estimate from Table 1 and v sin i measurement from Table 2. The contours show the 1σ, 1.5σ and 2σ levels.
3.3.2 Spitzer [4.5 μm] monitoring
Our measured period is inconsistent with that of Morales-Calderon et al. (2006) who find a period of 4.6 h during a ∼6 h observation in the Spitzer [4.5 μm] band. We downloaded these data from the Spitzer Heritage Archive. The reduced light curve and periodogram are shown in Fig. 6. The periodogram peaks at 4.6 h, as reported by Morales-Calderon et al. (2006). The curve appears sinusoidal over the observation period but we investigate the possibility of a double-peaked light curve. Fitting a pure sinusoid to the data gives a period of 4.6 ± 0.2 h while fitting a two-term truncated Fourier series gives a period of 10 ± 3 h; however, the functions are indistinguishable from each other over this observation. Injecting the 4.6 h sinusoid fit and the 10 h truncated Fourier fit into simulated light curves and reference stars produces the same periodogram shape as the target, seen in the bottom panel of Fig. 6. We use the MCMC method to explore the parameter posterior distributions for both the sinusoid model and the Fourier model. Again we use an upper limit of 13 h as a prior on the period. The posteriors are shown in Figs 7 and 8. Again, both models fit the light curve well, with the sinusoidal model giving a period of |$4.8^{+0.3}_{-0.2}$| h and the Fourier series model giving a period of |$12.01^{+0.7}_{-1.4}$| h. Thus, we conclude that the original observation is too short to rule out a double-peaked light curve with the ∼11 h period of the Spitzer [3.6 μm] data set, and from this data set either scenario is possible.
![Same as Fig. 2, but for the Morales-Calderon et al. (2006) [4.5 μm] observation of 2M2244, taken on 2005 November 27. The best-fitting sinusoidal function gives a period of 4.6 ± 0.2 h while the double-peaked Fourier function gives a period of 10 ± 3 h. Injecting both functions into simulated light curves and reference stars gives a periodogram shape similar to the observed light curve's periodogram. The functions are indistinguishable from each other over this observation.](https://cdn.statically.io/img/oup.silverchair-cdn.com/oup/backfile/Content_public/Journal/mnras/474/1/10.1093_mnras_stx2752/2/m_stx2752fig6.jpeg?Expires=1723644425&Signature=TIZ05nPPWAz3Iu4Bh8UU27KQTfTnGmJxmu7My-pwxplbcSCz7GeqMLSkM2pRyx9p6wt4MbJTWfVT78r4gqk-FNoNNVB1Tlobfu54DumvqaYyHGTEfzOuFSGQ-2Yiq5OWMNqW8B20s8S-c4rUvxxQ2pf~dXd7DgucYGhVAhtNakKkH4aS9Gw7MM0ZY~C7RHuWkY62rctPfELjIZWhruI9iXmoNjcCv8VhKM7EDpFwFn7eONyvRN1~Jlz0ZsTe-UQbDLlbwBAetZBWCZ2e0LOxRlxFk-ZGr-c8j03I33QxaiKgfi6pPB~QOZRa4xKqYcTxWj~vzE7Uc8JGoMrpxaV0Hg__&Key-Pair-Id=APKAIE5G5CRDK6RD3PGA)
Same as Fig. 2, but for the Morales-Calderon et al. (2006) [4.5 μm] observation of 2M2244, taken on 2005 November 27. The best-fitting sinusoidal function gives a period of 4.6 ± 0.2 h while the double-peaked Fourier function gives a period of 10 ± 3 h. Injecting both functions into simulated light curves and reference stars gives a periodogram shape similar to the observed light curve's periodogram. The functions are indistinguishable from each other over this observation.
Posterior distributions of parameters of the sinusoidal fit to the Morales-Calderon et al. (2006) Spitzer light curve of 2M2244 (shown in Fig. 6) The middle dashed line is the median, the two outer vertical dashed lines represent the 68 per cent confidence interval. We have placed an upper limit on the period of 13 h using our radius estimate from Table 1 and v sin i measurement from Table 2. The contours show the 1σ, 1.5σ and 2σ levels.
Posterior distributions of parameters of the Fourier model fit to the Morales-Calderon et al. (2006) Spitzer light curve of 2M2244 (shown in Fig. 6) The middle dashed line is the median, the two outer vertical dashed lines represent the 68 per cent confidence interval. We have placed an upper limit on the period of 13 h using our radius estimate from Table 1 and v sin i measurement from Table 2. The contours show the 1σ, 1.5σ and 2σ levels.
3.3.3 UKIRT WFCAM monitoring
The WFCAM photometry of 2M2244 is shown in Fig. 9. In this 4 h J-band observation we see evidence of significant ( ∼ 4 per cent) variability. The periodogram shows a highly significant peak that favours periodicities >5.5 h. This observation is too short to accurately measure the period, but it is consistent with an ∼11 h period. Since we have not covered a full period we cannot measure the full J −band variability amplitude, but can set a lower limit of ∼ 4 per cent.
Upper panel: UKIRT WFCAM photometry of 2M2244+20 taken on 2016-06-21. 2M2244+20 is shown in blue with a reference star shown in grey. Lower panel: Periodogram of 2M2244+20 as well as the periodograms of reference stars in the field. In this observation 2M2244+20 shows trends with periodicities <5.5 h.
3.3.4 The period of 2M2244
Considering all three epochs of data for 2M2244, we favour a longer period of 11 ± 2 h. We conclude that the initial Spitzer [4.5 μm] monitoring observation by Morales-Calderon et al. (2006) is too short to completely rule out a longer period. The light curve is most likely double-peaked in this epoch, due to two different atmospheric structures in either hemisphere. We see a very different shape in the 2016 September Spitzer [3.6 μm] light curve. This is plausibly due to evolution of the cloud structure in ∼10 years between epochs. This could also be due to the fact that we are probing different pressure levels in each Spitzer band; however, recent studies have found [3.6 μm] and [4.5 μm] light curves to have similar shape and phase (Metchev et al. 2015; Cushing et al. 2016). A recent paper by Apai et al. (2017) suggests another possible explanation for evolving light curves such as that observed for 2M2244. In this paper, the variability of three brown dwarfs is modelled by longitudinal bands with sinusoidal surface brightness modulations and an elliptical spot. When two bands have slightly different periods due to differing velocities or directions, they interfere to produce beat patterns. These beat patterns produce high amplitude variability when the waves are in phase and produce double-peaked variability when the phase shift between the waves is close to 90°. This model can explain light curves that are sometimes single peaked and other times double peaked as well as providing an explanation for the shape of the periodogram in the bottom panel of Fig. 4, where the higher frequency peak at ∼5 h may be explained by a beat pattern with wavenumber k = 2.
Both our periodogram and MCMC analysis of the new [3.6 μm] data set point to a period of ∼11.0 h. This period is also consistent with our UKIRT WFCAM J −band observation. As we still have not covered a full period for 2M2244, we combine the periods obtained from our MCMC Fourier models (shown in Fig. 5 and 8) to make a conservative estimate of 11 ± 2 h for 2M2244.
The observed peak-to-peak amplitude of 0.8 ± 0.2 per cent for the more recent Spitzer [3.6 μm] is comparable to the 1.0 ± 0.1 per cent modulation observed in the original Spitzer [4.5 μm] epoch of Morales-Calderon et al. (2006). The amplitude ratio, A[4.5]/A[3.6] of 1.25 ± 0.2 per cent is similar to the amplitude ratios found by Metchev et al. (2015).
3.4 SDSS1110
The light curve of SDSS1110 (top panel of Fig. 10) does not display any obvious trends, and our periodogram analysis (middle panel) confirms this. To determine the sensitivity of our observation, we inject simulated sinusoidal curves into random permutations of our SDSS1110 light curve. The simulated sine curves have peak-to-peak amplitudes ranging from 0.4 − 1.6 per cent and periods of 2 − 18 h, with randomly assigned phase shifts. Each simulated light curve is put through our periodogram analysis, which allows us to produce a sensitivity plot, shown in the bottom panel of Fig. 10. The blue region corresponds to periods and amplitudes detected with a FAP < 1 per cent, the white region corresponds to those detected with 1 per cent < FAP < 5 per cent, and the orange region corresponds to those with FAP > 5 per cent. For periods <18 h, an upper limit of 1.25 per cent is placed on the variability amplitude of SDSS1110. Considering only periods <10 h, as done by Metchev et al. (2015), we place an upper limit of 0.9 per cent on the variability amplitude. However, since we expect that young brown dwarfs will rotate more slowly due to conservation of angular momentum, the limit based on periods <18 h is more robust.
The top panel shows the normalized, pixel phase corrected light curve of SDSS1110. The middle panel shows the periodogram of SDSS1110 (thick black line) as well as the periodograms of several other reference stars in the field. The 1 per cent FAP value is plotted in blue. The bottom panel shows the sensitivity of the observation as a function of amplitude and period. The blue area represents amplitudes detectable by the pipeline as a function of period (FAP < 1 per cent), the white area shows amplitudes marginally detectable (1 per cent < FAP < 5 per cent), and the orange area shows amplitudes not detectable (FAP > 5 per cent). For periods <18 h, we place an upper limit of 1.25 per cent on the variability amplitude of SDSS1110.
The photometric noise measured for SDSS1110 is comparable to the noise measured for comparison stars of similar brightness, and thus we do not find evidence for stochastic or aperiodic variability. We additionally check the periodogram of the unbinned light curve to search for evidence of very short period (<1 h) deuterium pulsations proposed by Palla & Baraffe (2005). The periodogram does not display significant peaks at these short periods. A photometric variability survey of late-M brown dwarfs with Teff > 2400 K and ages of 1 − 10 Myr concluded that pulsations cannot grow to observable amplitudes in these objects (Cody & Hillenbrand 2014). The absence of short period pulsations detected in the light curve of SDSS1110 suggests that this conclusion may extend to even cooler (Teff ∼ 900–1300 K) brown dwarfs, however a larger sample will be needed to robustly explore this possibility. Deuterium pulsations are not expected to occur in objects with masses over the deuterium burning limit at the age of AB Doradus so would not be expected to occur in W0047 and 2M2244.
4 THE INCLINATION ANGLES OF W0047 AND 2M2244
With measured values for v sin i and the rotation period, P, in hand, an assumption of radius allows us to determine the angle of inclination, i. We assume that the brown dwarf rotates as a rigid sphere. However, this is not strictly true. The rotational period of Jupiter, as measured by magnetic fields originating in the core is 9h55m403, whereas the period measured using features rotating along the equator is 9h50m30s, a difference of 5 min (Cox 2002). Since rotational periods as measured from photometric variability in general have much larger uncertainties, the rigid body assumption is reasonable for our analysis. Thus, the equatorial rotation velocity, v, is given by v = 2πR/P, where R is the radius of the brown dwarf and P is its rotation period. We use the radii calculated from evolutionary models in Section 2.3.
Monte Carlo analysis was used to determine the inclination, i, for each target, using the posterior v sin i distributions obtained from our MCMC analysis. For the period and radius we draw samples from a Gaussian distributed sample with a width given by the reported errors. The radius estimates, rotational and radial velocities, periods and resulting inclinations are shown in Table 2.
Calculated effective temperatures, log (g), rotational velocities, radial velocities, periods, [3.6 μm] peak-to-peak variability amplitudes and inclination angles for W0047 and 2M2244.
| Parameter | W0047 | 2M2244 |
|---|---|---|
| v sin i (km s−1) | 9.8 ± 0.3 | |$14.3_{-1.5}^{+1.3}$| |
| RV (km s−1) | |$-19.8 _{-0.2}^{+0.1}$| | |$-16.0_{-0.9}^{+0.8}$| |
| P (h) | 16.4 ± 0.2 | 11.0 ± 2.0 |
| [3.6 μm] Amp ( per cent) | 1.07 ± 0.04 | 0.8 ± 0.2 |
| R (RJup) | 1.3 ± 0.04 | 1.29 ± 0.03 |
| i | |$85 ^{+5\circ }_{-9}$| | |$76 ^{+14\circ }_{-20}$| |
| Parameter | W0047 | 2M2244 |
|---|---|---|
| v sin i (km s−1) | 9.8 ± 0.3 | |$14.3_{-1.5}^{+1.3}$| |
| RV (km s−1) | |$-19.8 _{-0.2}^{+0.1}$| | |$-16.0_{-0.9}^{+0.8}$| |
| P (h) | 16.4 ± 0.2 | 11.0 ± 2.0 |
| [3.6 μm] Amp ( per cent) | 1.07 ± 0.04 | 0.8 ± 0.2 |
| R (RJup) | 1.3 ± 0.04 | 1.29 ± 0.03 |
| i | |$85 ^{+5\circ }_{-9}$| | |$76 ^{+14\circ }_{-20}$| |
Calculated effective temperatures, log (g), rotational velocities, radial velocities, periods, [3.6 μm] peak-to-peak variability amplitudes and inclination angles for W0047 and 2M2244.
| Parameter | W0047 | 2M2244 |
|---|---|---|
| v sin i (km s−1) | 9.8 ± 0.3 | |$14.3_{-1.5}^{+1.3}$| |
| RV (km s−1) | |$-19.8 _{-0.2}^{+0.1}$| | |$-16.0_{-0.9}^{+0.8}$| |
| P (h) | 16.4 ± 0.2 | 11.0 ± 2.0 |
| [3.6 μm] Amp ( per cent) | 1.07 ± 0.04 | 0.8 ± 0.2 |
| R (RJup) | 1.3 ± 0.04 | 1.29 ± 0.03 |
| i | |$85 ^{+5\circ }_{-9}$| | |$76 ^{+14\circ }_{-20}$| |
| Parameter | W0047 | 2M2244 |
|---|---|---|
| v sin i (km s−1) | 9.8 ± 0.3 | |$14.3_{-1.5}^{+1.3}$| |
| RV (km s−1) | |$-19.8 _{-0.2}^{+0.1}$| | |$-16.0_{-0.9}^{+0.8}$| |
| P (h) | 16.4 ± 0.2 | 11.0 ± 2.0 |
| [3.6 μm] Amp ( per cent) | 1.07 ± 0.04 | 0.8 ± 0.2 |
| R (RJup) | 1.3 ± 0.04 | 1.29 ± 0.03 |
| i | |$85 ^{+5\circ }_{-9}$| | |$76 ^{+14\circ }_{-20}$| |
We find an inclination angle of |$85 ^{+5\circ }_{-9}$| for W0047, so this object is viewed nearly equator-on. This inclination is significantly larger than the |$33^{+5\circ }_{-8}$| calculated by Lew et al. (2016). This is as a result of both our longer period and larger v sin i measurements. The inclination angle of 2M2244 is found to be |$76 ^{+14\circ }_{-20}$|, which is similar to that of W0047. Considering their remarkably similar colours, spectra and inclination angles, the results are consistent with the idea that atmospheric appearance is influenced by viewing angle rather than rotation period or variability properties. Fig. 11 shows (J − KS)2MASS colour anomaly plotted against the inclination angle for variable brown dwarfs with our results for W0047 and 2M2244 overplotted (Vos et al. 2017). The colour anomaly of each object is defined as the median (J − KS)2MASS colour for the spectral type and gravity flag of that object subtracted from its (J − KS)2MASS colour. Thus, positive and negative values of colour anomaly refer to objects that are redder and bluer than the corresponding median colour for their spectral types and gravity flags. Median colours for L0-T6 field objects and their uncertainties were taken from Schmidt et al. (2010). Liu et al. (2016) provide linear relations between spectral type and absolute magnitude for VL-G and INT-G brown dwarfs, and these were used to calculate the median colours for the intermediate and low-gravity objects. Since W0047 and 2M2244 have nearly identical spectra (Gizis et al. 2015), we treat them both as L7 INT-G objects, and apply the same colour anomaly correction to both. The error bars for these objects are simply the J and KS magnitude uncertainties combined. Our estimate of the median colour of low-gravity objects is limited by the low number of such objects known. As more of these objects are discovered this median colour will become more accurate. Vos et al. (2017) find that the correlation between near-infrared colour anomaly and inclination angle of field brown dwarfs is statistically significant at the 99 per cent level. Variable brown dwarfs viewed equator-on appear redder than the median while objects closer to pole-on are bluer than the median. This figure is updated in Fig. 11. W0047, 2M2244 and the low-gravity objects 2M0103+19, 2M1615+49, PSO-318 and 2M2208+29 may follow this trend, although more inclination data for young dwarfs are needed to fully explore this possibility. This may be explained if clouds are inhomogeneously distributed in latitude or if grain size and cloud thickness vary in latitude. If thicker or large-grained clouds are situated predominantly at the equator, while thinner or small-grained clouds are situated at the poles then we would expect to observe objects with i ∼ 90° to be redder than the median and objects with lower inclination angles to be bluer than the median. The addition of more inclination data for brown dwarfs is likely to reveal the physical origin of the correlation seen in Fig. 11.
(J − KS)2MASS colour anomaly plotted against the inclination angle for variable brown dwarfs. Black insets denote low-gravity brown dwarfs. In addition to 2M2244 and W0047, the low-gravity variable objects shown in this plot are 2M0103+19 (L4), 2M1615+49 (L4), PSO-318 (L7.5) and 2M2208+29 (L3). Inclination data for 2M2244 and W0047 are calculated in this paper, inclination data for other objects are from Vos et al. (2017).
Vos et al. (2017) also find a relation between the colour anomaly of an object and its variability amplitude, where objects that are redder than the median for their spectral type and gravity class tend to have higher variability amplitudes. Fig. 12 shows an updated version of this plot, showing that W0047 and 2M2244 are also consistent with this trend.
![Spitzer [3.6 μm] variability amplitude plotted against (J − KS)2MASS colour anomaly for variable brown dwarfs. Data for 2M2244 and W0047 are presented in this paper, data for other objects are from Vos et al. (2017).](https://cdn.statically.io/img/oup.silverchair-cdn.com/oup/backfile/Content_public/Journal/mnras/474/1/10.1093_mnras_stx2752/2/m_stx2752fig12.jpeg?Expires=1723644425&Signature=sybVILym1jGd1w~FBnDI51lz3-eEOELrgpo4uV5~O4dDG8c9BEAbaN6Uouia3MGFPUIVhDFoTk3LLPmHopi8ekMlTQUGFQxnvWIwQjQubAa9-ro5~9~8H5YbSbkw9IMusk6HIrIznRoYXtsGopm-EKH2-ameGa6DoEsIRlfHglg7yRZtcStIVmCPrUcU7lqXL9y~sF1SrP2h5DV11FI5e3qTwsR9EiOi8cFAzwM1s3-Uom8qDPxGICKE9XvOL3gztr4lmyRRjxv3UwdfvrlZN31azt5vx~uAcurjrKJRksqS6Winc0~4Zu7VkBqqblVKOGDjQ1Q5ltNdNxDZHbzfvQ__&Key-Pair-Id=APKAIE5G5CRDK6RD3PGA)
Spitzer [3.6 μm] variability amplitude plotted against (J − KS)2MASS colour anomaly for variable brown dwarfs. Data for 2M2244 and W0047 are presented in this paper, data for other objects are from Vos et al. (2017).
5 CONCLUSIONS
We have obtained Spitzer [3.6 μm] photometric monitoring for two young free-floating objects, W0047, 2M2244, and Spitzer [4.5 μm] monitoring of SDSS1110 as well as J-band monitoring of 2M2244. Additionally, we obtain NIRSPEC N-7 spectra of W0047 and 2M2244. We detect variability in the two late-L, low-mass dwarfs, W0047 and 2M2244. MCMC analysis of the Spitzer [3.6 μm] light curve of 2M2244 gives a period of 11 ± 2 h and a peak to trough amplitude of 0.8 ± 0.2 per cent. We detect significant ( ∼ 3 per cent) J-band variability in 2M2244. We find a period of 16.4 ± 0.2 h for W0047 and an amplitude of 1.07 ± 0.04 per cent. Variability is not observed in the T5.5 object SDSS1110 during an 8.5-h observation. For periods <18 h, we place an upper limit of 1.25 per cent on the variability amplitude of SDSS1110.
With a peak to trough amplitude of 1.07 ± 0.04 per cent for W0047, this is among the highest Spitzer [3.6 μm] variability amplitudes detected. This variability detection adds to a growing number of young, L-type objects that display high amplitude variability, suggesting that this correlation may extend into the late-L spectral types (Metchev et al. 2015; Biller et al. 2015; Lew et al. 2016).
The v sin i of both targets is determined using NIRSPEC-7 high dispersion spectra, finding |$v \sin i = 14.3_{-1.5}^{+1.3}$| km s−1 for 2M2244 and v sin i = 9.8 ± 0.3 km s−1 for W0047. Assuming rigid sphere rotation and using expected radii from evolutionary models, we find that both objects are close to equator-on, with inclination angles of |$85 ^{+5\circ }_{-9}$| and |$76 ^{+14\circ }_{-21}$| for W0047 and 2M2244, respectively. Their remarkably similar colours, spectral appearance and inclination angles are consistent with the possibility that viewing angle shapes the observed spectrum of a brown dwarf or giant exoplanet.
ACKNOWLEDGEMENTS
JV acknowledges the support of the University of Edinburgh via the Principal's Career Development Scholarship. KA acknowledges support from the Isaac J. Tressler Fund for Astronomy at Bucknell University. BB gratefully acknowledges support from STFC grant ST/M001229/1. We thank Michael Kotson for assistance with the evolutionary models. This work is 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 supported by a NASA Keck PI Data Award, administered by the NASA Exoplanet Science Institute. Data presented herein were obtained at the W. M. Keck Observatory from telescope time allocated to the National Aeronautics and Space Administration through the agency's scientific partnership with the California Institute of Technology and the University of California. The Observatory was made possible by the generous financial support of the W. M. Keck Foundation. UKIRT is owned by the University of Hawaii (UH) and operated by the UH Institute for Astronomy; operations are enabled through the cooperation of the East Asian Observatory. When the data reported here were acquired, UKIRT was supported by NASA and operated under an agreement among the University of Hawaii, the University of Arizona, and Lockheed Martin Advanced Technology Center. The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Mauna Kea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain.
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