Keck Laser Guide Star Adaptive Optics Monitoring of 2MASS J15342952AB: First Dynamical Mass Determination of a Binary T Dwarf
Abstract
We present multiepoch, nearinfrared imaging of the binary T5.0+T5.5 dwarf 2MASS J153449842952274AB obtained with the Keck laser guide star adaptive optics system. Our Keck data achieve submilliarcsecond relative astrometry and combined with an extensive (re)analysis of archival HST imaging, the total dataset spans 50% the orbital period. We use a Markov Chain Monte Carlo analysis to determine an orbital period of 15.1 yr and a semimajor axis of 2.3 AU. We measure a total mass of ( ), where the largest uncertainty arises from the parallax. This is the first field binary for which both components are confirmed to be substellar. This is also the coolest and lowest mass binary with a dynamical mass determination to date. Using evolutionary models and accounting for the measurement covariances, we derive an age of 0.780.09 Gyr and a mass ratio of . The relatively youthful age is consistent with the low tangential velocity of this system. For the individual components, we find K and K, and (cgs), and masses of ( ) and ( ). These precise values generally agree with previous studies of T dwarfs and affirm current theoretical models. However, (1) the temperatures are about 100 K cooler than derived for similar field objects and suggest that the representative ages of field brown dwarfs may be overestimated. Similarly, (2) the HR diagram positions are discrepant with current model predictions and taken at face value would overestimate the masses. While this may arise from large errors in the luminosities and/or radii predicted by evolutionary models, the likely cause is a modest (100 K) overestimate in temperature of T dwarfs determined from model atmospheres. We elucidate future tests of theory as the sample of substellar dynamical masses increases. In particular, we suggest that field brown dwarf binaries with dynamical masses (“mass benchmarks”) can serve as reference points for and and thereby constrain ultracool atmosphere models, as good as or even better than single brown dwarfs with age estimates (“age benchmarks”).
1 Introduction
Over about the past decade, the parameter space of traditional stellar astrophysics has been greatly expanded with the discovery and characterization of brown dwarfs, objects that for most of their lifetimes are colder and less luminous than mainsequence stars. Despite ample progress in finding and characterizing brown dwarfs, very few direct measurements of their physical properties have been made so far. In particular, dynamical masses for brown dwarfs are sorely needed to test the theoretical models over a wide range of parameter space. In comparison to the 100 binary stars with direct mass determinations, dynamical masses have been measured for only a handful of objects clearly below the stellar/substellar boundary:

the very young (Myr) eclipsing M6.5+M6.5 binary brown dwarf 2MASS J053521840546085 (Stassun et al., 2006);
In addition, GJ 569Ba itself may be a unresolved binary brown dwarf (Simon et al., 2006), and the secondary component of the L0+L1.5 binary 2MASSW J0746425+2000321AB, which appears to be an old (1 Gyr) field system, has a mass near the stellar/substellar boundary (Reid et al., 2001; Bouy et al., 2004; Gizis & Reid, 2006).
About 100 ultracool visual binaries are known,
The subject of this paper is the T dwarf 2MASS J153449842952274AB,
hereinafter 2MASS J15342952AB, which has an integratedlight infrared
spectral type of T5 (Burgasser et al., 2002, 2006b).
Laser guide star (LGS) AO provides a powerful tool for high angular resolution studies of brown dwarf binaries. Through resonant scattering off the sodium layer at 90 km altitude in the Earth’s atmosphere, sodium LGS systems create an artificial star bright enough to serve as a wavefront reference for AO correction (Foy & Labeyrie, 1985; Thompson & Gardner, 1987; Happer et al., 1994). Thus, most of the sky can be made accessible to near diffractionlimited IR imaging from the largest existing groundbased telescopes. We have previously used Keck LGS AO to discover that the nearby L dwarf Kelu1 is a binary system (Liu & Leggett, 2005) and to identify the novel L+T binary SDSS J1534+1615AB (Liu et al., 2006b). In regards to dynamical mass determinations, groundbased telescopes equipped with LGS AO can provide the necessary longterm platforms for synoptic monitoring of visual binaries, especially where the required amount of observing time at each epoch is relatively modest but many epochs are needed, in contrast to HST where target acquistion can be slow and monitoring a populous sample over many epochs is quite telescope timeintensive.
We present here the results of multiepoch imaging of 2MASS J15342952AB, observed as part of our ongoing high angular resolution study of ultracool binaries using LGS AO. § 2 presents our Keck LGS AO observations and (re)analysis of archival HST imaging. § 3 presents the resolved photometric properties of the binary and fitting of the orbit using a Markov Chain Monte Carlo method. § 4 compares the resulting total mass against evolutionary models, and § 5 summarizes our findings. Those readers interested solely in the results can focus on § 4 and § 5.
2 Observations
2.1 Keck LGS AO
We imaged 2MASS J15342952AB from 2005–2008 using the sodium LGS AO system of the 10meter Keck II Telescope on Mauna Kea, Hawaii (Wizinowich et al., 2006; van Dam et al., 2006). Conditions were photometric for all the runs. We used the facility IR camera NIRC2 with its narrow fieldofview camera, which produces a field of view. Setup times for the telescope to slew to the science targets and for the LGS AO system to be fully operational ranged from 7–20 min, with an average of 12 min (e.g. Liu, 2006).
The LGS provided the wavefront reference source for AO correction, with the exception of tiptilt motion. The LGS brightness, as measured by the flux incident on the AO wavefront sensor, was equivalent to a mag star. Tiptilt aberrations and quasistatic changes in the image of the LGS as seen by the wavefront sensor were measured contemporaneously with a second, lowerbandwidth wavefront sensor monitoring the mag field star USNOB1.0 06010344964 (Monet et al., 2003), located 31″ away from 2MASS J15342952AB.
At each epoch, 2MASS J15342952AB was imaged in filters covering the standard 2.2 µm atmospheric window from the the Mauna Kea Observatories (MKO) filter consortium (Simons & Tokunaga, 2002; Tokunaga et al., 2002). Our initial observations in April 2005 were carried out with the (2.12 µm) filter to minimize the thermal background from the AO system, which is kept at ambient temperature. Subsequent runs employed the (2.20 µm) or (2.15 µm) filters. Hereinafter, for brevity we refer to all these data simply as band observations.
On each observing run, we typically obtained a series of dithered band images, offsetting the telescope by a few arcseconds between each 1–2 images. The sodium laser beam was pointed at the center of the NIRC2 fieldofview for all observations. In April 2005, we also obtained images with the MKO (1.25 µm) and (1.64 µm) filters. In April 2008, we also obtained images with the filter, which has a central wavelength of 1.592 µm and a width of 0.126 µm; this filter is positioned around the band flux peak in the spectra of mid/lateT dwarfs.
The images were reduced in a standard fashion. We constructed flat fields from the differences of images of the telescope dome interior with and without continuum lamp illumination. Then we created a master sky frame from the median average of the biassubtracted, flatfielded images and subtracted it from the individual images. Images were registered and stacked to form a final mosaic, though all the results described here were based on analysis of the individual images. Outlier images with much poorer FWHM and/or Strehl ratios were excluded from the analysis. Instrumental optical distortion was corrected based on analysis by B. Cameron (priv. comm.) of images of a precisely machined pinhole grid located at the first focal plane of NIRC2. The 1 residuals of the pinhole images after applying this distortion correction are at the 0.6 mas level over the detector field of view. Since the binary separation and the imaging dither steps are small, the effect of the distortion correction is minor, smaller than our final measurement errors.
Table 1 compiles the details of our observations, and Figure 1 presents our Keck LGS data. Full widths at half maxima (FWHM) and Strehl ratios were determined from two field stars located 5–6″ from 2MASS J15342952AB. The tabulated errors on the FWHM and Strehl ratios are the standard deviation of these quantities as measured from the individual images.
To measure the flux ratios and relative positions of 2MASS J15342952AB’s two components, we mostly used the two aforementioned nearby field stars, observed simultaneously with 2MASS J15342952AB on NIRC2. These stars provided an excellent measurement of the instantaneous PSF. We empirically modeled the PSF using the Starfinder software package (Diolaiti et al., 2000), which is designed for analysis of blended AO images. For the Jan 2008 data, we employed a different procedure, fitting analytic PSFs comprising multiple elliptical gaussians to model the binary images. These data were taken at much higher airmass than all the other data. Because of the larger atmospheric dispersion and the different colors of the field stars relative to 2MASS J15342952AB, PSF fitting produced less accurate results than the analytic approach, as determined by the artificial binary tests described below. For every image, we fitted for the fluxes and positions of the two components and then computed the flux ratio, separation, and position angle (PA) of the binary. The averages of the results were adopted as the final measurements. Overall, our PSF fitting produced very high quality relative measurements, with errors of order 1% for the flux ratios, 0.05 pixels for the binary separation, and 0.2 for the PA. Note that these latter two values account only for the internal instrumental measurements and do not include the errors on the astrometric calibration of NIRC2, which we include below.
In order to gauge the accuracy of our measurements, we created myriad
artificial binary stars from images of the two PSF stars. One PSF
star was used to create artificial binaries, and the other was used as
the single PSF for fitting the components. For data at each epoch,
Starfinder was applied to the artificial binaries with similar
separations and flux ratios as 2MASS J15342952AB. These simulations showed
that any systematic offsets in our fitting code are very small, well
below the random errors, and that the random errors are accurate. In
cases where the RMS measurement errors from the artificial binaries
were larger than those from the 2MASS J15342952AB measurements, we
conservatively adopted the larger errors.
To convert the instrumental measurements of the binary separation and PA into celestial units, we used a weighted average of the calibration from Pravdo et al. (2006), with a pixel scale of mas/pixel and an orientation for the detector’s +y axis of east of north. These values agree well with Keck Observatory’s notional calibration of mas/pixel and , as well as the mas/pixel and reported by Konopacky et al. (2007). Also, comparison of NIRC2 images of M92 to astrometrically calibrated HST/ACS WideField Camera images gives a pixel scale for NIRC2 that agrees to better than 1 part in 10 with our values (J. Anderson, priv. comm.).
Finally, we must consider the effect of atmospheric refraction.
Because of the southern declination of 2MASS J15342952AB, all of our Keck
observations were necessarily undertaken at significant airmass
(1.55). Because the two components of the binary do not have
exactly the same spectral types (§ 3.1), the observed
positions on the sky are subject to slightly different amounts of
differential chromatic refraction (DCR). We computed the expected
shift in the relative astrometry at each epoch using the prescriptions
of Monet et al. (1992) for the DCR offset and
Stone (1984) for the refractive index of dry air. We
assumed a fiducial temperature of 275 K and pressure of 608 millibars
for conditions on Mauna Kea (Cohen & Cromer, 1988). We computed
the effective wavelengths for spectral types of T5.0 and T5.5 for the
two components using using all available spectra of these subclasses
contained in the SpeX Prism Spectral Library (from
Burgasser et al., 2004; Chiu et al., 2006, and
Looper et al., 2007) and the appropriate filter response
curve.
Table 1 presents the final resulting measurements from our Keck LGS data. For the April 2005 dataset, all three filters give astrometry consistent within the measurement errors; we use only the band results in the orbit fitting discussed below. In the Table and in our orbit fitting (§ 3.3), we take care to discriminate between the instrumental errors (namely those that arise solely from fitting the binary images) and the overall astrometric calibration of NIRC2, and thus any future refinements in the latter can be readily applied to our measurements.
2.2 Hst
WFPC2 Planetary Camera
The two components of 2MASS J15342952AB are only barely resolved in the HST/WFPC2 discovery images from August 2000. Therefore, to determine their relative positions and fluxes, we must model the images using the sum of two blended PSFs. The PSF of WFPC2’s Planetary Camera (PC) is undersampled (FWHM = 1.7 pix for ); this makes any empirical determination of the PSF difficult without PSFs sampled at many subpixel locations. Moreover, Anderson & King (2003) found that the WFPC2 PSF varies significantly over the detector due to geometric distortion, making it impossible to construct a reliable empirical PSF from other stars in the same image, even if there are enough to sample many subpixel locations. The original analysis by Burgasser et al. (2003b) employed a hybrid gaussian/empirical PSF to fit for the binary parameters with resulting uncertainties of 7 mas in separation and 9 in PA. The astrometry from the WFPC2 discovery epoch is obviously very important to the orbit determination, so we undertook our own analysis with a more accurate PSF model to improve the precision of the binary parameters.
We used the TinyTim software package (Krist 1995) to create model PSFs
for the WFPC2 images. We generated 5 supersampled PSFs that
included the effects of (1) variation with position on the detector;
(2) broadband wavelength dependence, by taking into account the
filter response curve and the spectrum of the source (using the
Keck/LRIS optical spectrum of the T4.5 dwarf 2MASS J055919141404488
from Burgasser et al. (2003) as the template for the individual
components of 2MASS J15342952AB), (3) telescope jitter (0 to 20 mas of
gaussian jitter), and (4) telescope defocus (10 m) to
account for HST breathing effects. Because the geometrical
distortion is locationdependent, we used TinyTim model PSFs generated
for the nearest integer pixel location to the centroid of the binary
or single T dwarf. Also, we used the template spectrum closest to the
spectral type of the T dwarf with sufficient wavelength coverage
(0.70–0.96 m) from S. K. Leggett’s spectral
library.
These TinyTim model PSFs were used to fit simultaneously for (1) the location of the primary, (2) the location of the secondary, (3) the normalization of the model PSF to the primary, and (4) the flux ratio of the two components. When fitting positions, the supersampled TinyTim PSF was interpolated using cubic convolution to the appropriate subpixel location. The best fit values were found using the amoeba alogorithm (e.g., Press et al., 1992) to find the minimum value of a 1.1”1.1” subimage centered on the binary. The image was cleaned using the IDL routine CR_REJECT in the Goddard IDL library to identify and mask the numerous cosmic rays in the undithered WFPC2 image pair. Masked pixels were excluded from the computation of the value. The noise in each pixel was determined from the biassubtracted raw WFPC2 image, assuming a read noise of 5.3 e/pix and a gain given by the header keyword ATODGAIN. A grid of PSFs in telescope jitter and defocus were tried, and the fit corresponding to the jitter and defocus combination yielding the lowest was chosen. For images of 2MASS J15342952AB we found that our PSFfitting routine yielded residuals of 2% of the peak value in 90% of pixels with .
Due to the optical distortion and “34th row” defect present in the
WFPC2 (Anderson & King 1999, 2003), the bestfit pixel locations of
each binary component do not exactly correspond to their locations in
an undistorted celestial reference frame. To remove these effects, we
applied the corrections of Anderson & King (2003), using a pixel scale
of mas/pix.
With only two undithered WFPC2 images of 2MASS J15342952AB, it is challenging to quantify the measurement uncertainties, and it is impossible to completely quantify the systematic errors, which arise from an imperfect PSF model and also probably depend on the subpixel positions of the two components given the undersampled nature of the data. Using only the RMS scatter of the two measurements, the inferred random errors in separation, PA, and flux ratio are 0.9 mas, 0.07, and 0.03 mag, respectively. To derive more robust random errors and to investigate the systematic errors, we conducted an extensive Monte Carlo simulation of our fitting routine.
We used WFPC2 images of seven other T dwarfs from the same
HST program, all apparently single, to create artificial binaries
which we then modeled using our PSFfitting routine.
The images of the single T dwarfs span a range in from about 1.5 mag brighter to 1.3 mag fainter than the primary component of 2MASS J15342952AB. We used these images at their native when simulating the primary component. To simulate the secondary component, we degraded the of the images assuming a flux ratio of 0.30 mag. We also tried flux ratios of 0.25 mag and 0.35 mag to explore the possibility that the uncertainties depend on the assumed flux ratio, but we found that this had an insignificant effect on our predicted uncertainties (, where and is the number of simulations). Signaltonoise degradation of an image was done by a multiplicative scaling followed by the addition of normally distributed random noise to each pixel, according to the same WFPC2 noise model we used to determine in the PSFfitting procedure. In fact, by running simulations where the primary images were degraded to much lower , we found that all of the single T dwarfs are in a high regime in which systematic errors (PSF model imperfections) dominate, not random errors (photon noise) — our simulations showed no dependence between the of the T dwarf used to construct artificial binaries and the resulting astrometric uncertainties. Therefore, we used the RMS of the results from all simulated binaries in order to determine the final uncertainties for 2MASS J15342952AB. As expected, the uncertainties in separation, PA, and flux ratio from our simulations were somewhat larger than those derived from the standard deviation of the measurements from the two 2MASS J15342952AB images, since both random and systematic errors have been evaluated in the simulations. In fact, the larger uncertainties are not simply due to averaging over, for example, the many subpixel locations of the single T dwarfs used in the Monte Carlo, because the simulated measurements for each single T dwarf show scatter consistent with the final derived uncertainties.
Table 2 presents our final results for the WFPC2 images,
with systematic offsets from the Monte Carlo simulations applied. Our
astrometry agrees well (better than 1) with the original
results of Burgasser et al. (2003b), though our measurement errors
are a factor of 8 smaller. Part of this improvement comes from our
use of TinyTimcomputed PSFs, as opposed to the simpler Burgasser
et al. PSF model of a gaussian plus empirical residuals. We also used
all possible single PSFs in our artificialbinary simulations, whereas
Burgasser et al. used only WFPC2 images of 2MASS J05591404, a
source that is suspected to be an unresolved
binary.
Our improvement to the WFPC2 astrometry was essential in our early attempts to fit the orbit based on Keck data obtained in 2005–2007. However, with the addition of data in 2008, the final HST+Keck dataset has sufficent time baseline and astrometric quality that the choice of WFPC2 astrometry does not highly impact the final orbit fitting results (§ 3.3.3).
ACS High Resolution Camera
The 2MASS J15342952AB system was observed on 2006 January 19 and 2006 April 11 (UT) with the High Resolution Camera (HRC) of HST’s Advanced Camera for Surveys (ACS) by program GO10559 (PI H. Bouy). The binary is much more widely separated at these epochs than in the WFPC2 observations, but the PSFs of the two components are still blended. We have therefore applied the same TinyTim PSFfitting technique described in the previous section to derive the relative astrometry from the ACS images. The primary differences between the WFPC2 and ACS datasets are: (1) ACS has much more severe geometric distortion than WFPC2, which changes the shape of the PSF and complicates astrometry because the pixels projected on the sky are not square, and (2) the ACS data are of much lower , with a total exposure time of only 50 sec for each cosmicray rejected, combined dithered image (cf., 1300 sec for a single WFPC2 image). Because of the lower , we found it unwarranted to fit the ACS images for telescope jitter and defocus as adding these free parameters did not improve the quality of the fits (as verified in the Monte Carlo simulations discussed below). Also, we found that the 25 lower of these data almost exactly negates any improvement to the astrometry that might be expected given the larger binary separation at these epochs.
We used distorted model PSFs generated by TinyTim to fit for the
position and flux of each binary component in images that had been
cosmicray cleaned (CRSPLIT=4) by the latest HST pipeline.
Bestfit pixel locations were corrected for geometric distortion using
the solution of Anderson & King (2004; Instrument Science Report
0415), and we used their measured ACS pixel scale, which was derived
by comparing commanded (POSTARG) offsets of HST in
arcseconds to the resulting pixel offsets. They derived two such
pixel scales for two epochs of observations of 47 Tuc, and we adopt the
mean and standard deviation of these two:
mas/pix.
Again, to investigate the measurement errors thoroughly, we performed Monte Carlo simulations of our fitting routine. We used images of single brown dwarfs to construct artificial binaries in configurations resembling 2MASS J15342952AB. At both ACS epochs, the binary is well represented by integerpixel shifts on a grid where and . There have been no HST/ACS science programs dedicated to studying single brown dwarfs; however, ACS images of the single brown dwarfs 2MASS J003616171821104 (L3.5; Kirkpatrick et al., 2000) and 2MASS J055919141404488 (T4.5; Burgasser et al., 2006b) were obtained for calibration purposes and are available in the HST Archive (CAL/ACS10374, PI Giavalisco). We found that despite the large difference in spectral types, any corresponding difference in the PSF does not alter the results of the Monte Carlo simulations. The of each of these single objects is much higher than that of 2MASS J15342952AB, so we degraded the of the single brown dwarfs for the artificial binary simulations. In fact, by varying the of the simulations, we found that the ACS data for 2MASS J15342952AB are well in the regime dominated by random photon noise, while the images of the single objects are in a high regime dominated by systematic errors (akin to the WFPC2 images of 2MASS J15342952AB). Therefore, given that we have four images, we divide the RMS of the Monte Carlo results by to represent the final uncertainties.
Table 2 contains our final ACS results.
2.3 IRTF/SpeX Spectroscopy
We obtained lowresolution (150) integratedlight spectra of 2MASS J15342952AB on 2008 May 16 UT from NASA’s Infrared Telescope Facility (IRTF) located on Mauna Kea, Hawaii. Conditions were photometric with seeing of about 0.7″ FWHM near the target. We used the facility nearIR spectrograph Spex (Rayner et al., 1998) in prism mode, obtaining 0.8–2.5 µm spectra in a single order. We used the 0.5″ wide slit, oriented at the parallactic angle to minimize the effect of atmospheric dispersion. 2MASS J15342952AB was nodded along the slit in an ABBA pattern, with individual exposure times of 180 sec, and observed over an airmass range of 1.64–1.60 as it rose. The telescope was guided during the exposures using images obtained with the nearIR slitviewing camera. The total onsource exposure time was 720 sec. We observed the A0 V star HD 142851 contemporaneously for flux and telluric calibration. All spectra were reduced using version 3.4 of the SpeXtool software package (Vacca et al., 2003; Cushing et al., 2004). The reduced IRTF/Spex spectrum is plotted in Figure 2 and compared to T dwarf spectral standards from Burgasser et al. (2006b). Visual examination shows an excellent match to the T5 spectral standard 2MASS J1503+2525, as does measurement of the Burgasser et al. (2006b) spectral indicies for 2MASS J15342952AB: HO– = 0.271 (T4.8), CH– = 0.420 (T4.8), HO– = 0.345 (T5.0), CH– = 0.430 (T5.0), and CH– = 0.224 (T5.1), with spectral type estimates based on the polynomial fits to the indices from Burgasser (2007a).
3 Results
3.1 Resolved Photometry and Spectral Types
We use our measured flux ratios and the published photometry from Knapp et al. (2004) to derive resolved IR colors and magnitudes for 2MASS J15342952AB on the MKO system. We use the HST photometry from Burgasser et al. (2003b) in determining the resolved magnitudes. Then to infer spectral types for the individual components, we compare these to magnitudes and colors of ultracool dwarfs from Knapp et al. (2004) and Chiu et al. (2006), excluding known binaries. We use nearIR spectral classfications from the Burgasser et al. (2006b) scheme. We assume that the components of 2MASS J15342952AB are themselves single, not unresolved binaries.
Figure 3 shows that component A has IR colors most typical of T4.5–T5 dwarfs, and component B is most similar to T5–T6 dwarfs. The individual absolute IR magnitudes (given in Table 3) give similar results. The “faint” polynomial fits for absolute magnitude as a function of spectral type from Liu et al. (2006b) give ) = {14.5, 14.6, 14.7, 14.9, 15.2} mag, = {14.6, 14.8, 15.0, 15.2, 15.5} mag, and = {14.7, 14.9, 15.1, 15.4, 15.7} mag for nearIR spectral types of T4.5, T5, T5.5, T6, and T6.5, respectively. Averaging the same data for each individual subclass gives = {13.90.6, 14.1, 14.40.4, 15.00.5, 15.10.5} mag, = {14.00.6, 14.2, 14.60.4, 15.30.4, 15.40.5} mag, and = {14.00.5, 14.3, 14.60.4, 15.50.7, 15.60.9} mag, where the uncertainties are the RMS of the photometry for each subclass (and no listed uncertainties for subclasses with only one object). Altogether, the absolute magnitudes suggest types of T5–T5.5 for component A and T5.5–T6 for component B.
The resolved colors provides a third means to estimate the spectral types, as these track the band methane absorption, which correlates well with overall nearIR spectral type (e.g., Figure 2 of Tinney et al., 2005). First, we compute individual magnitudes for 2MASS J15342952AB using the flux ratio from our LGS images, the integratedlight photometry of mag from Knapp et al. (2004), and an integratedlight color of mag synthesized from the nearIR spectrum of Burgasser et al. (2006b). Including the measurement errors in the flux ratios and band photometry, we find and mag and and mag for components A and B, respectively. Note that the relative color of the two components is known to higher precision, since the above computed colors for the two components contain the same 0.03 mag error that originates from the integratedlight band photometry. (In other words, the 0.05 mag uncertainties in the colors of the two components are not independent, but correlated.) Removing this effect gives a relative color of mag between A and B, i.e., greater methane absorption in component B is detected.
To determine the behavior of with nearIR spectral type,
we synthesized colors from the Spex Prism Spectral Library collection,
which contains lowresolution spectra of 68 T dwarfs after removing
spectrally peculiar objects and known binaries.
(1)  
(2) 
where for T0, = 21 for T1, etc. The RMS scatter about the fits are 0.02 mag and 0.3 subclasses, respectively. Using these polynomial relations, the observed ) colors give spectral types of T4.5 0.7 and T5.6 0.6 for components A and B, respectively, where the spectral type uncertainties come from formal propagation of the uncertainty in the colors. In addition, just as the relative color of the two components are known more accurately than the absolute colors, we compute a relative spectral type of subclasses between components A and B.
Combining the inferences from the colors, the absolute magnitudes, and the colors, we adopt spectral type estimates of T5 0.5 and T5.5 0.5 for the two components. The relative color favors a slightly larger spectral type difference than the absolute magnitudes but consistent with the adopted uncertainty. (Also the difference of the two components computed in § 4.3 favors a 0.5 subclass difference.)
Higherorder multiple systems are very rare among ultracool binaries, with an estimated frequency of (Burgasser et al., 2006d), and thus a priori we do not expect 2MASS J15342952AB to fall into this category. The colors and magnitudes are consistent with the system being composed of only two components, and not being a partially resolved higher order multiple system. If component B was actually an equalmass binary, the absolute magnitudes of its components would be 0.75 mag fainter than the integratedlight of B, meaning mags. This would suggest a spectral type around T7, based on the polynomial relations in Liu et al. (2006b), which is clearly too latetype compared to the integratedlight spectrum and the observed nearIR colors of B.
3.2 Bolometric Luminosities
To measure the for the system, we combine our SpeX
0.9–2.4 µm spectrum with the published integratedlight
, band, and Spitzer/IRAC thermalIR photometry and
uncertainties (Burgasser et al., 2003b; Knapp et al., 2004; Golimowski et al., 2004a; Patten et al., 2006).
We then integrated the SED, using a Monte Carlo approach to account for all the measurement errors. We find dex for the system, with the uncertainty increasing to 0.018 dex after including the uncertainty in the distance. (As discussed in § 4, we keep track of these independent uncertainties in our calculations.) The largest uncertainty in the integration arises from the 0.03 mag uncertainty in the integratedlight photometry used to normalize the SpeX spectrum. We crosschecked our method using the same data for the T4.5 dwarf 2MASS J05591404 and found excellent agreement with the measured by Cushing et al. (2006) using absolutely fluxcalibrated spectra from 0.6–15 µm.
The computed total agrees well with that inferred from using the band bolometric corrections () from Golimowski et al. (2004), namely using the resolved band absolute magnitudes and the estimated spectral types, which would give and dex for the individual components and thus dex for the total system. However, the uncertainties are larger when using to derive , since this incorporates the uncertainties arising from the 0.5 subclass uncertainty (0.06 mag in bolometric magnitude) and the intrinsic scatter in the Golimowski et al. relation (0.13 mag). In short, direct integration of the observed SED is more accurate.
To apportion the observed total into the individual components, we assume the observed band flux ratio of the system represents the luminosity ratio. This would be exactly correct if the two components had identical spectral types (and neglecting photometric variability). To account for the difference in spectral types, we generate a Monte Carlo distribution of values for each component using the Golimowski et al. polynomial fit as a function of spectral type subject to the following rules: the spectral type of component A is uniformly distributed from T4.5–T5.5; the spectral type of component B is no later than T6; and the difference in their spectral types is at least 0.5 subclasses. This produces an average difference in between the two components of 0.09 mags and an RMS of 0.03 mags. Thus, we find and dex for the two components, including the uncertainty in the distance.
3.3 Dynamical Mass Determination
Orbit Fitting using Markov Chain Monte Carlo
We have data at 9 independent epochs, which is formally sufficient to determine the 7 parameters of a visual binary orbit given our measurements (9 positions + 9 times). However, two pairs of measurements are separated by only one month (April/May 2006 and March/April 2007), and the cadence of the orbital phase covered is limited, with the HST/WFPC2 datum being taken almost 5 years before the next epoch. While standard gradientdescent (LevenbergMarquardt) leastsquares techniques would be sufficient to derive an orbit (§ 3.3.2), we also would like to accurately determine the probability distribution of the orbit parameters (which may not be normally distributed) and the associated degeneracies. For epochs with Keck data taken in multiple filters, we choose the filter with the smallest astrometry errors.
Thus, we first used a combination of gradientdescent techniques from random starting points and simulatedannealing techniques to isolate the class of potential orbital solutions near a reduced chisquared () of 1. Then, to fully explore this class of solutions, we used a Markov Chain Monte Carlo (MCMC) approach (e.g. Bremaud, 1999). MCMC provides a means to explore the multidimensional parameter space inherent in fitting visual orbits that is computationally efficient, able to discern the degeneracies and nongaussian uncertainites in the fit, and allows for incorporation of a priori knowledge. In short, the MCMC approach is distinct from ordinary Monte Carlo methods in that instead of a completely random steps through the model parameter space, the steps are chosen such that the resulting number of samples (the “chain”) is asymptotically equivalent to the posterior probability distribution of the parameters being sought. (See Tegmark et al., 2004, Ford, 2005, and Gregory, 2005 for explications of applying MCMC to astronomical data.)
We parameterized the binary’s orbit using the standard 7 parameters:
period (), semimajor axis (), inclination (), epoch of
periastron (), PA of the ascending node ()
By making steps of the same size in the positive and negative
directions for these parameters in constructing the Markov chain, we
would implicitly assume that our prior knowledge of these parameters
is a uniform distribution. This is not an accurate representation of
our prior knowledge since, for example, binaries with periods between
and years are not 10 times more common than binaries
with periods between 10 and years. We therefore applied a
prior to the likelihood function in the MCMC fitting where and
are distributed evenly in logarithm and that the parameters
and are uniformly distributed, rather
than and , to save the algorithm from unnaturally
preferring circular solutions. This is equivalent to the
distribution as discussed by, e.g., Duquennoy & Mayor (1991). The
very small effect of the choice of prior is discussed
below.
As a consistency check, we also ran our MCMC fitting code on the astrometric data for the binary L dwarf 2MASSW J0746+2000AB from Bouy et al. (2004). We found excellent agreement between the orbital parameters derived by us (using MCMC) and by Bouy et al. (using a variety of chisquare minimization approaches). Not only do the results agree to within the quoted errors, there is better than 1% agreement on the bestfit results and better than 20% agreement on the 95% confidence intervals.
Fitting Results
Figures 5 show the resulting probability distributions for the orbital parameters from the MCMC chain. The probability distributions are clearly not gaussian. For a given parameter, we adopt the median as the result and describe a confidence limit of % as simply the bounds of the sorted sample. At 68(95)% confidence, we find a modest eccentricity of 0.25, an orbital period of 15.1 yr and a semimajor axis of 171 mas (2.3 AU including the uncertainties in the plate scale and parallax). Two of the orbital angles are very wellconstrained, the inclination deg (nearly edgeon) and the PA of the ascending node deg. The final results are summarized in Table 4.
Figure 6 shows the strong correlation between the
determination of the orbital period and the eccentricity. It
illustrates that there are two classes of possible orbits: one branch
having shorter periods and smaller semimajor axes and the other
branch having longer periods and larger semimajor axes.
Figure 7 shows that the short branch orbits
have just passed apoastron (, ). This is the favored solution, with 98% of the steps in
the MCMC chain residing in this branch (using as the dividing
criteria in the plane). However, a nearly circular orbit means
it can be difficult to clearly distinguish whether the system has just
passed apoastron or periastron, and thus a minority of the MCMC steps
(2%) fall into the longperiod branch.
The MCMC fitting provides probability distributions for the orbital parameters, but does not provide a single bestfitting orbit per se, since a range of possible orbits fit the data with similar values. One illustration of this is the result for = 179 deg, where the 95% confidence limits are broad enough to span both the shortperiod and longperiod solution branches. Thus to plot orbits on the sky, we employ gradientdescent methods to find the bestfitting orbit with the MCMCderived values as the starting point. Figures 9 and 10 shows the resulting orbit, which has a period of 15.2 yr, a total mass of 0.0556 and . To illustrate how the uncertainty in the orbital period impacts the orbit, we also show the bestfitting orbits found when fixing the period to 12 and 20 yr, which have total masses of 0.0523 and 0.0590 and of 1.1 and 1.0, respectively. All three orbits reside in the shortperiod branch and show that the projected separation is now rapidly decreasing. The system is expected to be wellresolved again in the year 2011.
Applying Kepler’s Third Law to the period and semimajor axis distributions gives the posterior probability distribution for the total mass of the binary, with median of 0.0556 , a standard deviation of 0.0018 (3.2%), and a 68(95)% confidence range of about 0.0018(0.0037) (Figure 11). However, the MCMC probability distribution does not include the uncertainties in the parallax (1.6%) and the NIRC2 pixel scale (0.11%). By Kepler’s Third Law, the quadrature sum of these errors amounts to an additional 4.9% uncertainty on the derived total mass. Since the MCMCderived mass distribution is asymmetric, we account for this additional error in a Monte Carlo fashion; for each step in the chain, we draw a value for the pixel scale and parallax from a normal distribution and then compute the total mass. The resulting mass distribution is essentially gaussian (Figure 11). Our final determination of the total mass is at 68(95)% confidence. Thus, the total mass of this system is wellmeasured, with the parallax error being the dominant uncertainty. This is the coolest and lowest mass binary with a dynamical mass determination to date.
Alternative Orbit Fits
The WPFC2 discovery epoch in 2000 is obviously a key component to fitting the orbit. As described in § 2.2.1, we independently analyzed this dataset and greatly reduced the measurement errors compared those reported by Burgasser et al. (2003b). To examine the impact of this improvement, we also tried fitting the orbit using the original Burgasser et al. astrometry. Without the 2008 Keck data, our improved WFPC2 astrometry is essential for a wellconstrained fit. However, with the complete dataset, the fitted orbital parameters and the total mass are insensitive to the specific choice of WFPC2 astrometry, changing by less than 1.
Also, to check the effect of our assumed prior on the MCMC fitting (flat in and ), we tried three alternative priors from the literature:

Solartype stars: Duquennoy & Mayor (1991) analyzed a welldefined sample of 164 nearby solartype stars (spectal type F7 to G9) and found a lognormal distribution in orbital period:
(3) where is the period in days and .

Ultracool visual binaries: Allen (2007) conducted a detailed analysis of published imaging surveys of 361 ultracool field objects to model the separation distribution as a lognormal distribution:
(4) where is the semimajor axis in AU and .
^{25} 
Ultracool visual and spectroscopic binaries: Maxted & Jeffries (2005) analyzed a sample of 47 ultracool binaries with multiple radial velocity measurements and adopted a lognormal distribution truncated at large separations to match the known visual ultracool binaries:
(5) where is the semimajor axis in AU, , and for AU.
Figure 12 shows the posterior probability distributions for the total mass from the different priors. Overall, the choice of prior has very little effect on the mass determination. The Allen (2007) distribution favors slightly higher masses, but its results are consistent with the other priors.
As a final independent check, we also fit our astrometry using the linearized leastsquares fitting routine ORBIT (Forveille et al., 1999), using the MCMCderived parameters as the starting guess. The ORBIT results are given in Table 4, with a resulting , and show excellent agreement with the MCMC results.
4 Discussion
A primary goal of measuring fundamental properties for ultracool binaries is to compare the measurements against theoretical models of their physical properties. A number of studies have been published for the previous ultracool visual binaries with dynamical masses (§ 1), with subtle and/or overt differences in the ways that observations are compared to models. In the analysis that follows, we strive to clearly elucidate the comparison of our 2MASS J15342952AB observations to the models, both in terms of its approach and limitations. From the standpoint of the observations, we have high quality measurements of (1) the total mass of the system and (2) the individual absolute magnitudes, with (3) the individual bolometric luminosities only slightly less reliable. (We have not measured the complete spectral energy distribution but have accounted for this uncertainty in computing in § 3.2). We now examine what can be learned from these data in concert with evolutionary models and theoretical atmospheres.
4.1 Substellarity
The most immediate result from our measurement is that 2MASS J15342952AB is a bona fide brown dwarf binary. The total mass of is below the solarmetallicity stellar/substellar boundary of 0.070–0.074 (e.g. Hayashi & Nakano, 1963; Kumar, 1963; Burrows et al., 2001), with the boundary increasing to higher masses for lower metallicities (Saumon et al., 1994) — therefore, the individual components are clearly substellar. This is the second binary where both components are directly confirmed to be brown dwarfs, after the young eclipsing M6.5+M6.5 binary 2MASS J053505 (Stassun et al., 2006), and is the first such field binary in this category.
4.2 Age
Brown dwarfs follow a massluminosityage relation. We have measured two of these quantities, the (total) mass and the luminosity, and by using evolutionary tracks we can determine the third quantity, the age of the system. We use models from the Tucson group (Burrows et al., 1997), which provide predictions for , and the “COND” models from the Lyon group (Baraffe et al., 2003), which predict both and absolute magnitudes. We conservatively assume the system is coeval and that the system is a true binary, not a partially (un)resolved higher order multiple system (§ 3.1).
For each tabulated model age, we use the individual absolute magnitudes and/or bolometric luminosities to calculate the mass of the components and then sum the masses. We then apply the observed total mass to determine the age range of the system. All measurement errors in and the total mass are accounted for in a Monte Carlo fashion, namely we repeat the model calculations over multiple realizations for the and the total mass values. We take great care to account for the covariance between the relevant quantities in the calculation. For instance, the total mass of the system and the luminosity both depend on the parallax, and thus their errors are positively correlated; we therefore draw the parallax values from a normal distribution and incorporate these in determining the Monte Carlo distribution of total masses and luminosities, which themselveed are then propagated in the modelbased calculations. This approach results in a probability distribution for the system’s age (as well as the other resulting parameters discussed below), which we summarize with the median value and confidence limits.
Figure 13 shows the results of these calculations to determine the age of the system. For a consistent comparison between the Lyon and Tucson models, we use only the results derived from the measurements. However, the Figure also shows that using the absolute magnitudes predicted by the Lyon models would give similar results.
We determine an age of Gyr from the Burrows models and Gyr from the Baraffe models at 68(95)% confidence. To construct a representatve “average” of the model results, we merge the results of the individual Monte Carlo calculations into a single distribution and compute its confidence limits. Thus, we assign an age of Gyr (Table 5). This is relatively youthful compared to the mainsequence stars in the solar neighborhood, e.g., 95% of nearby solartype stars have age estimates of 1 Gyr (Nordström et al., 2004). However, the mean age of T dwarfs is expected to be younger than for field stars, since the known census is magnitudelimited and younger objects are brighter. The age distribution of field ultracool dwarfs has been modeled by Burgasser (2004) and Allen et al. (2005); they generally find that field T dwarfs can span younger ages than for lowmass stars, though the predicted age distributions for both types of objects have large spreads.
Kinematics provide an independent (albeit indirect) indicator of age, as older objects are expected to generally show larger space motions due to their accumulated history of dynamical interactions (e.g. Wielen, 1977). The tangential velocity of 2MASS J15342952AB () is the second smallest measured for T dwarfs, with only the T5.5 dwarf 2MASS 15463325 being smaller (; Tinney et al., 2003). This is generally in accord with the Gyr inferred from the evolutionary models, namely that 2MASS J15342952AB is among the youngest members of the nearby field population. However, since the measured distribution of field T dwarfs is quite broad, with an unweighted average of 38.4 km s and a standard deviation of 20.4 km s among the 21 unique objects in the Tinney et al. (2003) and Vrba et al. (2004) parallax samples, 2MASS J15342952AB does not appear to be anomalously young for a field object. A radial velocity measurement is needed to determine the binary’s space motion and thus better constrain its kinematics.
4.3 Temperatures and Surface Gravities
With the age of the system determined above, the combination of the
observations and the evolutionary models provide highly precise values
for the remaining physical parameters. The results derived from the
two sets of evolutionary tracks are given in
Table 5 and are computed from the same Monte
Carlo approach that accounts for the covariance in the measurements.
The Tucson and Lyon models give consistent values, with the Tucson
models giving slightly larger radii and thus slightly cooler
temperatures. Again, to compute a representative “average” for each
parameter, we merge the Monte Carlo distributions computed from each
set of models and compute confidence limits for the aggregate. This
is not intended to be physically meaningful, but rather is a
quantitative representation of the results that accounts for
nongaussian and/or inconsistent distributions from the two sets of
models.
We thus find radii of and
, effective temperatures of
K and K, and surface gravities of and for components A and B,
respectively.
To reiterate, these properties are derived using only the measured total mass and resolved magnitudes/luminosities, along with the assumption that the system is coeval and composed of two components. No additional assumptions have been made to determine the individual masses. We also have avoided using spectral types and/or effective temperatures in this aspect of our analysis (contrary to some previous studies), as these quantities can introduce additional systematic errors and/or circular reasoning. For instance, it would be incorrect to employ the relations between spectral type and from Golimowski et al. (2004a) or Vrba et al. (2004) to determine for the two components and then compare to evolutionary tracks, as the Vrba et al. and Golimowski et al. relations are derived from the radii of field brown dwarfs predicted by the evolutionary tracks themselves. Likewise, it is not necessary to use determinations from atmospheric models to determine the age of the system or the physical properties of the individual components in our approach. (See also § 4.5.)
As already noted above, our Monte Carlo calculations account for the covariance in the measurements. One important effect is that the uncertainties derived from the resolved magnitudes and luminosities of the two components are correlated, since they all depend on the measurement uncertainties in the integratedlight photometry of the system. As a consequence, the relative temperture difference between the two components ( K) can be calculated to higher precision than would be indicated by the uncertainties in the individual determinations ( K = 24 K). This agrees with the 70 K difference expected from the Golimowski et al. (2004a) polynomial fits for the 0.5 subclass difference between the two components. (The from the Golimowski et al. fits would be about twice as large for a 1 subclass difference.)
The physical parameters for 2MASS J15342952A and B are in general agreement with previous determinations for the properties of field T dwarfs. However, our values have much higher precision, because the accurate total mass measurement leads to a small age range, which leads to strong constraints on the radii and thus small uncertainties on the derived and values. (We discuss this further in § 4.5.) T dwarf surface gravities have been inferred to be by comparing theoretical model atmospheres to optical spectra (Burrows et al., 2002), nearIR colors and line strengths (Knapp et al., 2004), and lowresolution nearIR/midIR spectra (Burgasser et al., 2006a; Saumon et al., 2006; Leggett et al., 2007a; Cushing et al., 2007). This range encompasses our determinations for 2MASS J15342952AB.
On the other hand, our very precise temperatures for the two components of 2MASS J15342952AB are discrepant with previous studies of T dwarfs: the ’s of 2MASS J15342952AB appear to be cooler than determined previously for midT dwarfs. These discrepancies occur for two separate comparisons.
Temperature discrepancy with evolutionary models
Temperatures for field T dwarfs have been inferred by combining accurate determinations with radius predictions from evolutionary tracks. This approach is expected to be reasonably accurate, since the radii of brown dwarfs older than 100 Myr are predicted to vary by 30%. Golimowski et al. (2004a) adopt a typical age of 3 Gyr and a plausible range of 0.1–10 Gyr in computing from , and Vrba et al. (2004) adopt a radius range of predicted by Burgasser (2002) simulations of the solar neighborhood assuming a constant star formation history. (Both studies use the Tucson evolutionary tracks.) There are 8 T4.5–T6.5 dwarfs in these studies (after updating the spectral types to the latest classification by Burgasser et al. (2006b)), and all of these appear to be single based on high angular resolution imaging (Burgasser et al., 2003b, 2006c; Liu et al., in prep). We compute the average and standard deviation of both studies to obtain K for T4.5 (2 objects), 1146 K for T5.0 (interpolated), 1077 K for T5.5 (1 object), K for T6.0 (3 objects), and K for T6.5 (3 objects). We have excluded the T6+T8 binary 2MASS J12252739AB and the peculiar T6 dwarf 2MASS J0937+2931, and we have assumed the T4.5 dwarf 2MASS J05591404 is an equalmagnitude unresolved binary based on its pronounced overluminosity (e.g., Figure 3 of Burgasser, 2007a). Neither sample contains any T5.0 objects, but the 4 other subclasses almost exactly follow a straight line, so we linearly interpolate to find for T5.0.
In comparison to the field objects, the components of 2MASS J15342952AB appear to have 100 K cooler temperatures relative to their spectral subclass ( K for the primary and K for the secondary, where we have adopted a 30 K uncertainty for the T5 and T5.5 field objects based on the other subclasses with more than one object). The disagreement is modest, and a more definitive comparison is hampered by the few determinations (i.e., parallaxes) for T4.5–T6.5 dwarfs. Nevertheless, the result is potentially intriguing.
In particular, Metchev & Hillenbrand (2006) have noted perhaps a similar effect for the three known lateL (L7–L8) dwarf companions to field stars. More precise estimates can be obtained from evolutionary models for these companions than for field objects by incorporating the age estimates of their primary stars. (See § 4.5 for details.) Metchev & Hillenbrand find that the L dwarf companions appear to be 100–200 K cooler than single field lateL dwarfs. They raise the possibility that the modelderived radii are at fault, either due to incorrect cooling rates or systematic overestimate of the field dwarf ages. However, they prefer the hypothesis that the discrepancy is a manifestation of an unanticipated surface gravity dependence of the L/T transition, causing younger L/T transition objects to have cooler temperatures than older ones. This is motivated by their analysis of the young (0.1–0.4 Gyr) L7.5 companion HD 203030B and apparently supported by the young (0.1–0.5 Gyr) T2.5 companion HN Peg B, which also appears to be 200 K cooler than field objects of the same spectral type (Luhman et al., 2007; Leggett et al., 2008).
We find that the T5.0 and T5.5 components of 2MASS J15342952AB may also be 100 K cooler than comparable field objects. Since these two components are latertype than the L/T transition (e.g., their positions in IR colormagnitude diagrams is coincident with the locus of mid/lateT dwarfs with blue nearIR colors), this may suggest that the discrepancy might not be solely associated with the L/T transition. Instead, 2MASS J15342952AB and the aforementioned L/T companions may indicate that a systematic error in the estimated ages and radii of field lateL and T dwarfs is the culprit.
The 10% temperature discrepancy for 2MASS J15342952AB amounts a 20% underestimate of the radii. For a fixed value of (which is the appropriate constraint here), the Burrows et al. (2001) scaling relations give
(6) 
where is the age and is the radius. This agrees well with
the exponent value of 8.2–8.4 extracted from the Tucson models for
sources of to . Propagating the
uncertainties in the disagreement, the implied age
overestimate is a factor of , meaning implied ages of
0.3–1.0 Gyr for the field population.
The same discrepancy can be seen in an alternate fashion, namely by comparing the luminosities for the same T4.5–T6.5 field objects: for T4.5, for T5.0 (interpolated), for T5.5, for T6.0, and for T6.5. The luminosities of 2MASS J15342952AB are comparable to the field objects of similar type ( for T5.0 component A and for T5.5 component B). Thus, in order for all the objects to have similar temperatures and , they must have about the same radius and thus about the same age as 2MASS J15342952AB. In other words, the measured total mass of 2MASS J15342952AB is too small (by a factor of 2) compared to the mass expected from the evolutionary models for 3 Gyr objects with .
A representative age of 0.5 Gyr for the field population is not ruled out given the state of the observations. Though Golimowksi et al. did consider the range of 0.1–10 Gyr, they adopted a nominal age of 3 Gyr in determining for field dwarfs, based on the 2–4 Gyr age estimate from the tangential velocities of ultracool dwarfs by Dahn et al. (2002). A younger age could be accomodated, since the tangential velocity of a population is only an approximate statistical estimate of its age. Indeed, kinematic analysis of the space motions of L and T dwarfs suggests a younger age of 0.5–2 Gyr (Osorio et al., 2007). Similarly, the radii of adopted by Vrba et al. is based on a mass function where ; a somewhat steeper mass function would lead to younger typical ages (e.g., Figure 8 of Burgasser, 2004, though Metchev et al., 2007 suggest based on a small sample of T dwarfs). Thus, the discrepancy of evolutionary modelderived temperatures between objects of known mass/age and the field population can be plausibly explained by a modest overestimate of the ages of the field population. A larger sample of ultracool dwarfs with known masses and/or ages is needed to better explore this issue (§ 4.5).
Temperature discrepancy with model atmospheres
The spectrum of 2MASS J15342952AB has not yet been fitted with model atmospheres due to its composite nature. In fact, the T dwarf class as a whole has not been extensively subjected to such comparisons. Burgasser et al. (2006a) determined for a sample of sixteen T5.5–T8 dwarfs by comparing nearIR spectral indices to condensate(dust)free atmosphere models from the Tucson group. They determined K for one T5.5 dwarf, and an unweighted linear fit of atmospherederived versus spectral type for their sample (excluding the peculiar T6 dwarf 2MASS J0937+2931) gives
(7) 
where for T5.5, for T6, etc. The RMS about the linear fit is 50 K, which we adopt as the uncertainty (a value somewhat larger than the 10 K to 40 K range computed for individual objects in their sample). Extrapolating the linear fit gives K for T5. This is obviously approximate, e.g., given the potential systematic effects in the models and the spectral classification scheme, though this value agrees with the K found by by fitting model atmospheres to the 0.95–14.5 µm spectrum of the T4.5 dwarf 2MASS J05591404 (Cushing et al., 2007).
Thus, model atmospheres indicate K and
K for 2MASS J15342952A and B, respectively. The
temperatures we find using evolutionary tracks appear to be cooler by
100 K at modest significance ( K for component A
and K for component B, if we assume that the errors add in
quadrature). We cannot objectively discern if the problem lies in the
evolutionary tracks, the model atmospheres, or both. However, the
evolutionary models are thought to be robust to the principal input
uncertainties (Chabrier et al., 2000). On the other hand, the
model atmospheres are quite uncertain. Even though the spectral
appearance of mid and lateT dwarfs is relatively simple —
dominated by collisioninduced H, HO, and CH in the
nearIR and the wings of the K i 0.77 µm resonance line
in the farred — the line lists for HO and CH are known to
be incomplete, and the input physics to the atmosphere models are
complex. Current atmospheres generally match the observed spectra of
lateT (T6–T8) dwarfs, but not exactly so
(e.g. Burrows et al., 2006; Burgasser et al., 2006a; Saumon et al., 2006; Leggett et al., 2007a).
4.4 ColorMagnitude and HertzsprungRussell Diagrams
We have directly measured the total mass of the 2MASS J15342952AB system. However, using the evolutionary tracks to determine the physical properties also implicitly determines the mass ratio, since the modelderived age and observed individual luminosities translate into individual masses (again with the assumption that the system is composed of only two components). We infer the mass ratio of the system from the ratio of the bolometric luminosities, as this is very robust. To illustrate this, consider the analytic scaling relation for solarmetallicity substellar objects from Burrows et al. (2001):
(8) 
where is the mass, is the age and is the Rosseland
mean opacity. We measure a dex difference in between the two components
We first compare the individual components against the COND evolutionary models of the Lyon group, which provide predictions for the absolute magnitudes and colors. The model predictions are generated for the CIT photometric system, so we transform our resolved MKO photometry for 2MASS J15342952AB to this system using the results of Stephens & Leggett (2004). Figure 14 shows that the models are somewhat too red compared to the data. This is not surprising, as model atmospheres for T dwarfs are known to be deficient in the CH and HO opacities relevant at these wavelengths (e.g. Leggett et al., 2007a). The plotted COND models are also computed only for solarmetallicity, and a nonsolar metallicity for 2MASS J15342952AB would impact the colors and magnitudes (e.g. Liu et al., 2006a; Burgasser, 2007b). Indeed, current models do not exactly match the observed colormagnitude loci for field T dwarfs (e.g., Figure 8 of Knapp et al., 2004 and Figure 7 of Burrows et al., 2006). Nevertheless, 2MASS J15342952AB will provide a strong test to for future models, since the components’ magnitudes, colors, and masses are very wellmeasured.
With the individual mass estimates and an independent determination of , it is possible to directly test different evolutionary tracks using the HertzsprungRussell (HR) diagram. We use the values of K and K for 2MASS J15342952A and B, derived in § 4.3 from model atmosphere studies. Figure 15 shows the individual components on the HR diagram and compares these to the Tucson and Lyon evolutionary tracks. The locations of the two components disagree with both sets of models (which agree very well between themselves).
The likely interpretation is that the temperatures from the model atmospheres place the components to the left of the evolutionary tracks, i.e., too warm. As discussed in § 4.3, the model atmospheres are a significant source of the uncertainty in placing the components on Figure 15. A possible systematic error of only 100 K would be sufficient to resolve the discrepancy with the data. Therefore, while acquiring resolved spectra of the two components could help refine the temperature determination, the systematic uncertainties in the atmosphere models will still hamper accurate placement on the HR diagram. We discuss this further in the next section.
The opposite interpretation is that the evolutionary models are
incorrect, leading to a 50% overprediction of the
luminosities and a 20% overprediction of the radii, given
the component masses. Equivalently, if one were simply to assume the
HR diagram positions are accurate, the evolutionary models would
suggest individual masses of around 0.05 and 0.06 from
the Lyon and Tucson models, respectively, i.e., nearly a factor of two
overestimate in the masses. While it may be that the evolutionary
models are so substantially incorrect, such a conclusion is not
compelling at this point, given the plausible errors in the determinations.
Direct mass determinations for the individual components from radial velocity monitoring and/or absolute orbital astrometry will help to further characterize the system. Such data will directly test the determined from the evolutionary tracks. The expected maximum radial velocity difference of the two components is only 4.6 km s. Since the two components are nearly equal mass and brightness, the orbital motion will be very difficult to detect in the integratedlight spectrum. Resolved AO spectroscopy will be required, and the small amplitude will make it a challenging measurement given the few km s accuracy that has been achieved for T dwarfs on the largest existing telescopes (Osorio et al., 2007).
Individual mass measurements can in principle also test the evolutionary tracks directly. One can estimate the age of each component from its mass and luminosity (as we have done using the total mass) and see if the ages indicate coevality for the system. However, given the nearequal flux ratio of this system (and most ultracool binaries), this coevality test is unlikely to be very discriminating. Moreover, individual masses cannot resolve the discrepancy seen in the HR diagram (Figure 15), which largely arises from the uncertainties in the model atmospheres.
4.5 Future Tests of Theory with Field Substellar Binaries
With the advent of LGS AO on the largest groundbased telescopes, we can expect an increasing number of dynamical masses for ultracool field dwarfs in the nearfuture. The most useful systems for testing theory will be those with both independent mass and age determinations, namely binaries that are associated with open clusters/groups and/or field stars of known age. The former will present a significant technical challenge, e.g., ultracool binaries in the Hyades ( pc; Perryman et al., 1998) and Pleiades ( pc; Soderblom et al., 2005) with suitably short orbital periods are unresolvable with current technology and thus none are currently known. Ultracool binary companions to field stars are extremely rare and thus while very valuable systems, these will only probe a very limited range of spectral type, age, and mass: only four systems are known with suitably short orbital periods ( yr) — the T1+T6 binary Ind Bab (McCaughrean et al., 2004), the L4+L4 binary HD 130948BC (Potter et al., 2002), the L4.5+L6 binary GJ 417BC (Bouy et al., 2003; Gizis et al., 2003), and the L4.5+L4.5 binary GJ 1001BC (Golimowski et al., 2004b). Therefore, there is significant motivation to develop analyses that employ masses derived from the much more numerous field binaries. In this regard and as illustrated by our analysis for 2MASS J15342952AB, one can identify two orthogonal pathways to confront theory: (1) comparison to evolutionary tracks and (2) comparison to atmospheric models.
Comparison to evolutionary tracks (“HR Diagram Test”)
Direct measurements of , , and mass (or age) for brown dwarfs enable use of the HR diagram, by comparing the observations to evolutionary tracks that correspond to the measured masses of the objects. As illustrated by Figure 15, the Lyon and Tucson tracks differ at the 5–10% level in mass, and thus mass determinations of 2–3% accuracy could discriminate between the two models, if and can be wellmeasured. (Improvements in the parallaxes of many ultracool binaries will also be needed to achieve such accurate masses.) Accurate measurements for are largely straightforward, as good as a few percent (e.g., § 3.2). However, direct determinations are extremely challenging, since radius measurements are needed. Brown dwarfs are too small and faint to be resolved with current or planned interferometers, and no eclipsing ultracool field binaries are yet known. Thus, must be derived from modeling the observed colors, magnitudes, and/or spectra; the approach currently suffers from uncertainties at the level of a few to several hundred Kelvin and systematic errors that are difficult to quantify (e.g. Cushing et al., 2007). In comparison, Figure 15 shows that determinations good to 30 K are needed. Therefore, decisive tests of evolutionary tracks using field binaries will be challenged by this uncertainty in , in the absence of direct radius measurements.
Comparison to atmospheric models (“Age/Mass Benchmark Test”)
Brown dwarfs obey a massluminosityage () relation, and for most field objects neither the mass nor the age is known. A commonly used approach to circumvent this limitation is to study brown dwarfs that are companions to mainsequence stars, where (indirect) age estimates are available from the primary star (e.g. Saumon et al., 2000; Geballe et al., 2001; McCaughrean et al., 2004; Metchev & Hillenbrand, 2006; Liu et al., 2006a; Burgasser, 2007b). This approach can also be applied to members of coeval clusters/groups and companions to postmainsequence stars of known age (e.g. Kirkpatrick et al., 1999; Pinfield et al., 2006). In these situations, and are known, and combined with evolutionary models, one can derive and consequently and . Then the observed colors, magnitudes, and spectra can test the accuracy of atmospheric models with the same and . Examination of the known “age benchmark” T dwarfs in this fashion finds that the properties deduced from atmospheric models are in good agreement with those from the evolutionary models, within the uncertainties in the ages and metallicities of the primary stars (Burgasser, 2007b; Leggett et al., 2007a, 2008).
We suggest that, in an analogous fashion, field binaries with known
masses can also serve as “benchmark” objects. In this case, and
are known, and combined with evolutionary models, one can
derive , as we have done in § 4.1. This provides and
and thereby allows tests of atmospheric models. The chain of
analysis is identical to brown dwarf companions of known age: given
independent knowledge of two quantities out of , use
evolutionary models to derive the third.
At face value, using objects that are age benchmarks or mass benchmarks is less fundamental than direct tests of the evolutionary models using the HR diagram. However, in practice the Benchmark Test is much more feasible to implement and subject to much smaller systematic errors. In the absence of direct radius measurements, the HR Diagram Test is held hostage to the systematic errors in the determination of from atmospheric models. In contrast, the Benchmark Test relies on the evolutionary models, which are thought to be more robust (e.g. Chabrier et al., 2000). In short, given the choice of relying on atmospheric models (HR Diagram Test) or evolutionary models (Benchmark Test), the evolutionary models are likely to be preferred.
To assess the relative utility of “age benchmarks” (brown dwarf companions to stars) compared to “mass benchmarks” (brown dwarfs with dynamical masses), we turn to Equation 8. For an object with a measured and ignoring the weak dependence on , given a measurement of or with accompanying uncertainty of or , the fractional error in the remaining quantity is related by:
(9) 
Typical uncertainties in the ages of mainsequence field stars are
about 50–100% (e.g. Kirkpatrick et al., 2001; Liu et al., 2006a; Metchev & Hillenbrand, 2006), and thus agebenchmark objects would have a
25–50% uncertainty in the mass inferred from evolutionary
models.
We can use the analytic fits to evolutionary models from Burrows et al. (2001) to gauge the relative accuracy on and derived from both types of benchmarks. Using standard error propagation and assuming uncorrelated errors, we find for mass benchmarks:
(10)  
(11) 
(12)  
(13) 
where and are the uncertainties in the temperture, mass, luminosity, and surface gravity, respectively. And then for age benchmarks, we find:
(14)  
(15) 
(16)  
(17) 
Thus with representative values for the fractional errors in age (50%), luminosity(10%), and mass (5%), we see that and are better constrained by a factor of 5 using mass benchmarks than age benchmarks. Figure 16 plots the derived analytic estimates for both types of benchmarks. These contour plots provide a convenient means to gauge the expected errors in and determinations from benchmarks. The morphology of the contours also illustrates whether the observational errors in the age, mass, and/or dominate the uncertainties in and . For the specific case of 2MASS J15342952AB, there is good agreement between the analytic estimates and the values derived directly from the actual evolutionary models (Table 5).
5 Conclusions
We have determined the first dynamical mass for a binary T dwarf, the T5.0+T5.5 system 2MASS J15342952AB, by combining six epochs of Keck LGS AO imaging from 2005–2008 with three epochs of HST imaging obtained in 2000 and 2006. Both datasets achieve milliarcsecond accuracy or better for the relative astrometry of the two components and are validated through extensive testing with images of simulated binaries. We employ a Markov Chain Monte Carlo analysis to determine the orbital parameters and their uncertainties. The time baseline of our complete dataset covers about half of the total period. We find that the orbital motion of the binary is viewed in an almost edgeon orientation and has a modest eccentricity. Our determination of a yr orbital period is significantly longer than the original 4year estimate, as by chance the binary was at a very small projected separation when discovered in 2000.
The total mass of the system is ( ), including the uncertainty in the parallax. This is the second brown dwarf binary directly confirmed, the first among the field population. It is also the coolest and lowest mass binary with a dynamical mass determination to date.
With very accurate measurements of the total mass and the bolometric luminosity (), we use the Tucson and Lyon evolutionary tracks to determine the remaining physical properties for the system. The two sets of models give largely consistent results, which highlights the difficult of distinguishing between them even with such precise observational data. We average the model results to represent the final determinations. We find a relatively youthful age for the system of 0.790.09 Gyr (1), consistent with its low tangential velocity relative to other field T dwarfs. The remaining physical parameters of the individual components are then fully determined: radii of and , effective temperatures of K and K, surface gravities of and , and masses of () and () for components A and B, respectively. We take care to account for the covariances inherent in the measurement uncertainties, by using a Monte Carlo approach to derive these physical quantities from the evolutionary models. Our approach also assumes that the system is coeval and composed of only two components.
These precise determinations for 2MASS J15342952A and B are in general accord with the and values found previously for field T dwarfs based on model atmospheres and with the ages of T dwarfs predicted by Monte Carlo simulations of the solar neighborhood. However, upon closer scrutiny, there are two potential discrepancies with past studies. Both suggest that the temperatures of field T dwarfs may be overestimated by 100 K, though we stress that the two discrepancies must arise from independent effects. (1) The temperatures of 2MASS J15342952A and B appear to be cooler than field objects of comparable spectral type. This resembles discrepancies previously noted by Metchev & Hillenbrand (2006) and Luhman et al. (2007) for lateL/earlyT dwarfs that are companions to young mainsequence stars. They have hypothesized that the effect is due to the gravity sensitivity of the L/T transition. The fact that this discrepancy also occurs for 2MASS J15342952AB suggests instead that the problem may arise from a factor of overestimate in the adopted ages of field objects when determining their temperatures using evolutionary tracks. Ages of 0.3–1.0 Gyr are preferred based on this binary. (2) The temperatures of 2MASS J15342952A and B are slightly cooler than inferred for other midT dwarfs from model atmospheres. Detailed analysis of the system’s integratedlight and resolved spectra with model atmospheres is needed to directly assess the and of the two components and to refine the comparison with the values derived from evolutionary models.
The positions of the two components on the HR diagram are discrepant with theoretical evolutionary tracks corresponding to their individual masses. In fact, taken at face value, using the HR diagram positions to infer masses from the evolutionary tracks would lead to masses of 0.05–0.06 , about a factor of two larger than the actual measured masses. While this discrepancy could stem from large systematic errors in the luminosities (50% errors) and/or radii (20% errors) predicted by evolutionary models, the likely cause is that temperatures from model atmospheres are too warm by 100 K for midT dwarfs. This highlights the need for continued improvements to the model atmospheres.
Future monitoring of 2MASS J15342952AB will help to refine its orbit and its dynamical mass. The orbital separation of the system is now rapidly decreasing and will not be readily resolvable again until around 2011. At the same time, an improved parallax for the system will be required — the uncertainty in the total mass from the orbit fitting is 3%, compared to the 5% that arises from the uncertainty in the parallax. Radial velocity monitoring and/or absolute astrometry will directly determine the individual masses and test if the system is a higher order multiple. However, given the very similar fluxes of the two components (implying nearly equal mass), individual mass measurements are unlikely to resolve the discordant HR diagram position of the two components relative to evolutionary tracks. This problem is likely driven by the systematic uncertainties in current model atmospheres for T dwarfs.
The fundamental characteristic of the field population is that it
spans a range of (largely unknown) ages. However despite this
uncertainty, field brown dwarf binaries can strongly test theoretical
models, if analyzed appropriately. These systems will be especially
valuable in light of the current paucity of eclipsing field ultracool
binaries and resolvable, shortperiod ultracool binaries in open
clusters/groups.
Date  Filter 
Airmass  FWHM  Strehl ratio  Separation 
Position angle 
mag 

(UT)  (mas)  (mas)  (deg)  
2005May01  1.66  102 12  0.020 0.002  211.3 1.5 (1.5)  14.1 0.3 (0.3)  0.163 0.014  
1.63  86 6  0.047 0.006  211.7 0.8 (0.8)  13.86 0.15 (0.13)  0.286 0.011  
1.61  88 6  0.101 0.012  212.4 1.1 (1.0)  14.0 0.2 (0.2)  0.278 0.021  
2006May05  1.56  64 3  0.210 0.014  190.6 0.3 (0.2)  15.43 0.12 (0.09)  0.282 0.010  
2007Mar26  1.56  82 3  0.151 0.016  158.0 0.6 (0.6)  17.5 0.2 (0.19)  0.287 0.012  
2007Apr22  1.57  67 5  0.20 0.03  153.7 0.4 (0.3)  17.53 0.13 (0.10)  0.269 0.010  
2008Jan15  2.05  100 3  0.074 0.002  114.4 1.1 (1.1)  21.5 0.9 (0.9)  0.27 0.06  
2008Apr01  1.55  87 4  0.095 0.018  102.5 0.7 (0.7)  21.1 0.7 (0.7)  0.25 0.04  
1.58  78 7  0.048 0.018  102.0 0.4 (0.4)  20.4 1.5 (1.5)  0.21 0.04 
Date  Instrument  Filter  Separation 
Position angle 
mag 

(UT)  (mas)  (mas)  
2000Aug18  WFPC2  62.8 1.2  357.1 0.8  0.30 0.05  
2006Jan19  ACS  199.0 1.1  14.5 0.6  0.28 0.06  
2006Apr11  ACS  191.2 1.1  15.5 0.4  0.30 0.04 
Property  2MASS J15342952A  2MASS J15342952B 

(mags)  4.95 0.04  5.10 0.04 
(mags)  0.08 0.04  0.21 0.04 
(mags) 
0.30 0.05  0.37 0.05 
(mags)  0.17 0.04  0.17 0.04 
(mags)  0.25 0.04  0.38 0.04 
(mags)  19.57 0.04  19.87 0.05 
(mags)  14.61 0.05  14.77 0.05 
(mags)  14.69 0.05  14.98 0.05 
(mags)  14.86 0.05  15.15 0.05 
Estimated spectral type 
T5.0 0.5  T5.5 0.5 

MCMC  ORBIT  

Median  68.3% c.l.  95.5% c.l.  
Time of periastron (MJD)  55960 
240, 210  740, 450  56024 347 
Orbital period (yr)  15.1  1.6, 2.3  3.1, 5.1  15.2 2.6 
Semimajor axis (mas)  171  13, 19  27, 41  172 22 
Semimajor axis (AU) 
2.3  0.2, 0.3  0.4, 0.6  2.3 0.3 
Inclination ()  84.3  0.6, 0.6  1.7, 1.0  84.3 0.8 
Eccentricity  0.25  0.13, 0.11  0.20, 0.25  0.24 0.16 
PA of the ascending node ()  13.0  0.3, 0.3  0.9, 0.5  13.0 0.4 
Argument of periastron ()  179  14, 6  83, 11  178 10 
Total mass (): fitted  0.0556  0.0017, 0.0019  0.004, 0.004  0.056 0.004 
Total mass (): final  0.056  0.003, 0.003  0.006, 0.007  0.056 0.005 
Note. – Median values and confidence limits for orbital parameters derived from our default MCMC fitting, which uses a prior distribution flat in and . The “fitted total mass” represents the direct MCMC results from fitting the observed orbital motion of the two components. The “final total mass” includes the additional 4.9% error from the uncertainties in the parallax and the Keck/NIRC2 pixel scale; the former is 15 larger than the latter. The final mass distribution is essentially gaussian. The rightmost column gives the results from the ORBIT routine by Forveille et al. (1999). (See § 3.3.2.)
Property  Tucson models  Lyon models  “Average”  

Component A  Component B  Component A  Component B  Component A  Component B  
log(age)  
Radius ()  
(K)  
(cgs)  
(K) 