HIGH RESOLUTION IMAGING OF VERY LOW MASS SPECTRAL BINARIES: THREE RESOLVED SYSTEMS AND DETECTION OF ORBITAL MOTION IN AN L/T TRANSITION BINARY^*

The 43 sources observed in our study (Table 1) were selected from known late-M, L and T dwarfs in the vicinity of the Sun with a suitable tip-tilt star for LGS-AO correction. These include 33 M9-T3 dwarfs initially classified as spectral binaries by visual inspection, before the B10 and BG14 selection criteria had been defined. We re-examined their binary candidacy by dividing them into two groups according to spectral type: 15 objects in the M9–L7 range analyzed with the BG14 method, and 22 objects in the L5–T3 range, analyzed with the B10 method. The four objects overlapping in these spectral type ranges were analyzed by both methods. Ten other low mass stars and brown dwarfs were also observed as back-up targets, but were excluded from the analysis because visual inspection rejected them as spectral binary candidates.

Indices were measured from low resolution (λ/Δλ = 75–120), near-infrared IRTF/SpeX spectra (Rayner et al. 2003) covering 0.9–2.4 μm, accessed from the SpeX Prism Libraries (Burgasser 2014). One of our targets, 2MASS J2126+7617, has a declination outside the observable range of SpeX/IRTF (−50° < δ < + 67°), so a smoothed Keck/NIRSPEC spectrum was used instead (Kirkpatrick et al. 2010). Spectral indices given in B10 and BG14 were calculated for each spectrum, and regions of interest (ROI) in index-index spaces were delineated using confirmed binaries. Slight modifications to the limits of some ROIs in both B10 and BG14 were made to include known binaries WISEP J0720–0846 and 2MASS J1209–1004 (Burgasser et al. 2015a; Liu et al. 2010, respectively), which had not been detected at the time the index selection criteria were defined. Table 2 shows the updated limits of the index selection ROIs for both sets of criteria. Strong and weak candidates are selected by the number of times they fall within the ROIs, as described in B10 and BG14.

Table 2.  Updated Index Selection Criteria for B10 and BG14

x	y	Limits
Burgasser et al. (2010)
H2O-J	H2O-K	0.325 < x < 0.65 and y > 0.615x + 0.300
CH4-H	CH4-K	0.6 < x < 1.0 and y > 1.063x − 0.288
CH4-H	K/J	0.65 < x < 1.00 and y > 0.471x − 0.096
H2O-H	H-dip	0.44 < x < 0.68 and y < 0.49
SpT	H2O-J/H2O-H	L8.5 < x < T3.5, y < 0.925 and y < −0.037x + 2.106
SpT	H2O-J/CH4-K	L8 < x < T4.5 and y < 0.041x − 0.517
Bardalez Gagliuffi et al. (2014)
SpT	CH4-H	M7.5 < x < L8 and $y\lt -4.3\times {10}^{-4}{x}^{2}+0.0253x+0.6824$
H2O-J	CH4-H	0.60 < x < 0.92 and y < −0.094x + 1.096
H2O-J	H-bump	0.65 < x < 0.90 and y > 0.16x + 0.806
CH4-J	CH4-H	0.6 < x < 1.04, y < 1.04 and y < −0.562x + 1.417
CH4-J	H-bump	0.60 < x < 0.74, y > 0.91 and y > 1.00x + 0.24
CH4-H	J-slope	0.94 < x < 1.03, y > 1.03 and y > 1.250x − 0.207
CH4-H	J-curve	0.95 < x < 1.03 and $y\gt 1.245{x}^{2}-1.565x+2.312$
CH4-H	H-bump	0.94 < x < 1.04, y > 0.92 and $y\lt 1.36{x}^{2}-4.26x+3.877$
J-slope	H-dip	1.03 < x < 1.13 and y < 0.20x + 0.27
J-slope	H-bump	1.025 < x < 1.130, y > −2.75x + 3.84 and y > 0.91
K-slope	H2O-Y	0.93 < x < 0.96 and $y\gt 12.036{x}^{2}-20.000x+9.037$
J-curve	H-bump	2.00 < x < 2.45, y > 0.92 and $y\gt 0.269{x}^{2}-1.326x+2.527$

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From the BG14 set, 8 sources were selected as candidates from spectral indices (4 as strong, 4 as weak). Single and binary templates were fit to these index-selected sources, ranked by a χ² statistic. The best fit single and binary templates were compared to each other with an F-test to assess the percentage confidence that the binary fit is statistically better than the single fit. The primary types were constrained to ± 3 subtypes from the combined optical spectral type or, in its absence, near infrared type, and the secondary types were allowed to vary between T1 and T8. After template fitting, 6 sources remained as candidates. From the B10 set, 16 sources were selected as index candidates (11 as strong, 5 as weak) and after fitting, 12 sources remained as candidates. 2MASS J1711+2232 was selected as a candidate on both sets. In all, we classify 17 sources as true spectral binary candidates (Table 1), close to half of the visually selected spectral binaries.

High angular resolution images of our targets were obtained using the Keck II LGS-AO system with NIRC2 on nine nights between 2009 August and 2014 January. Tip-tilt reference stars within 60'' of the targets were selected from the USNO-B catalog (Monet et al. 2003). A 3-point dither pattern was used to avoid the noisy lower left quadrant of the array, and was repeated as needed with different dither offsets to build up long exposures. Total integration times were between 60 and 720 s, depending on the brightness of the source and the atmospheric conditions. All objects were observed with the Mauna Kea Observatories (MKO) H filter (Simons & Tokunaga 2002; Tokunaga et al. 2002) and narrow plate scale (9.970 ± 0.012 mas/pixel for a single-frame field of view of 10'' × 10''; Pravdo et al. 2006). The MKO J and/or K_s filters were also used for targets with apparent companions.

The images were reduced in a standard fashion using interactive data language (IDL) scripts. First, a dark frame was subtracted from each science frame. For each science exposure a sky frame was constructed from the median average of all images acquired for the target, exclusive of the frame being reduced. The sky-subtracted frames were then divided by a normalized dome flat. A bad pixel mask was applied to smooth over bad pixels using the average of the neighboring pixels. All images in a given epoch and common filter were shifted to align the target to a common location, and the stack was median-combined to create the final mosaics.

The reduced image mosaics around each target are shown in Figures 1 and 2. Strehl and signal-to-noise ratios (S/N) are reported in Table 1. The Strehl ratio was calculated by comparing each point source to a theoretical, diffraction-limited, monochromatic, NIRC2 point-spread function (PSF) with the NIRC2Strehl IDL routine.⁷ The S/N was computed assuming Poisson statistics:

$$\begin{eqnarray}&&{\rm{S}}/{\rm{N}}=\displaystyle \frac{{N}_{\mathrm{star}}}{\sqrt{{n}_{\mathrm{sky}}\;{\sigma }_{\mathrm{sky}}^{2}+\displaystyle \frac{{N}_{\mathrm{star}}}{g}}}\end{eqnarray} \tag{ 1 }$$

where N_star is the total counts from the star at a radius of 1.5 times the full width at half maximum, n_sky is the number of pixels used for the standard deviation of the sky counts, σ_sky, which encompasses noise from several sources (read out, dark current, image reduction, etc.) and g is the gain in DN/e⁻ (data number per electron).

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Three of our sources are resolved: 2MASS 1341–3052, SDSS 1511+0607 and SDSS 2052–1609; these are shown in Figure 1 and discussed further in Section 3.3. One source, 2MASS J1733–1654, has a feature that we cannot distinguish between bona fide source and PSF structure, so we consider this to be a "source of interest." The remaining sources are unresolved at the limits of our sensitivity and image quality. Because the PSF of the images vary considerably, we determined detection limits through a source implantation simulation of representative images. We organized the targets by Strehl and S/N and selected two representative sources of high Strehl (WISE J0047+6308) and low Strehl (2MASS J0032+0219), as shown in Figure 3. For these sources, we simulated binary companions by scaling down the brightness of each image, and then shifting and superimposing it onto the original image. The implanted image was scaled down by a maximum of 6 mag, which was the largest magnitude difference inferred from the template fitting of spectral binary candidates, and shifted by up to 50 pixels or ∼05 in any angle. Magnitude difference, separation and position angle were all drawn from a uniform random distribution.

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We visually examined each image at multiple contrast ratios to search for the implanted companion. This experiment was performed N ≳ 12,000 times per source, varying the target, scale factor and offset. A "detection" required clicking within 15 pixels of the implanted secondary, with the option to decide if an implanted companion was visually undetectable. We determined the maximum relative magnitude as a function of separation for which the detection fraction exceeded 50%. The detection fraction was calculated in steps of 0.5 mag and 005, sliding by half a step along both axes for a total of ∼400 overlapping bins. Figure 4 shows that the PSF dominates the sensitivity close to the star centroid. For the case of low Strehl ratio, detections reach a minimum at ΔH ≈ 5 mag, 03 away from the center of the PSF, beyond which our sensitivity is limited by sky noise. For the high Strehl ratio case the floor lies around 5.5 mag difference at radii greater than 04.

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We applied the sensitivity curves of our representative sources to systems with similar Strehl ratios. For the 30 unresolved spectral binary candidates, we compared these sensitivity limits to the magnitude differences predicted from template fitting to determine separation limits (Table 3). Figure 5 shows an example of the sensitivity curve and separation constraint for the spectral binary candidate 2MASS J1711+2232. Five of our unresolved spectral binaries have been previously confirmed as true binaries (See Section 3.2), but our separation limits are up to 40% greater, i.e., these binaries can not be resolved with our observations. For the case of 2MASS J1209–1004, our estimated separation limit is smaller than the measured separation, suggesting that the secondary has moved to a closer configuration. Similarly, for our three resolved systems the calculated separation limit is always smaller than the measured separation, which means that our separation limits correctly constrain the PSF of the primary. The remaining 9 unresolved spectral binaries have angular separation limits between 004 and 028.

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3.2.1. 2MASS J05185995–2828372

3.2.2. WISEP J072003.20–084651.2

3.2.3. SDSS J080531.84+481233.0

3.2.4. 2MASS J11061197+2754225

3.2.5. 2MASS J12095613–1004008

3.3.1. 2MASS J13411160–30525049

The L3 2MASS 1341–3052 was first discovered by Reid et al. (2008) in the Two Micron All Sky Survey (2MASS; Cutri et al. 2003) and later identified as a spectral binary candidate with L1.0 ± 0.5 and T6.0 ± 1.0 components (BG14). Our NIRC2 observations resolve the source with an angular separation of 279 ± 17 mas at a position angle of 3179 ± 06. The original template matching analysis assumed relative spectral fluxes on the Looper et al. (2008a) absolute magnitude to spectral type relation. We repeated this analysis using the relative photometry in all three JHK_s bands to scale and select binary templates in a similar fashion as described in Burgasser et al. (2011a). Our revised template fit analysis resulted in component spectral types of L2.5 ± 1.0 and T6.0 ± 1.0; i.e., we infer a primary classification more consistent with the combined-light optical classification.

2MASS J1341–3052 is the only one of the three resolved systems that does not have a parallax measurement. We estimated its distance using the calculated component apparent magnitudes with the Dupuy & Liu (2012) spectral type to absolute magnitude relation and component spectral types from template fitting. Uncertainties were propagated from spectral type, apparent magnitudes and spectral type relation, accordingly. We calculated one distance per filter and then obtained the weighted average distance from the MKO JHK_s filters. The distances for both components (29 ± 3 pc for the primary and 31 ± 6 pc for the secondary) were consistent across filters. The uncertainty-weighted average yields a distance estimate of 29 ± 3 pc. From this we infer a projected separation of 8.1 ± 0.5 AU.

A spectral type versus absolute magnitude plot is shown in Figure 6, using the Dupuy & Liu (2012) parallax sample of 259 objects as a reference. The primary absolute magnitude is anchored to the Dupuy & Liu (2012) relation due to the lack of a trigonometric distance, while the secondary absolute magnitude was derived from the primary's using the measured relative magnitude. In the J band, the secondary adds 0.09 mags to the primary, barely enough to make the combined absolute magnitude look like an outlier. In the K band, the secondary adds 0.02 mags to the primary, so it appears as if the secondary absolute magnitude also falls on the relation and the combined magnitude is within the +1σ curve. This source could not have been detected as an overluminous binary candidate because of the late type of the secondary. The properties of all three resolved binary systems are summarized in Table 4.

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3.3.2. SDSS J151114.66+060742.9

3.3.3. SDSS J205235.31–160929.8

Our observations of SDSS J2052–1609AB confirm prior results by Stumpf et al. (2011) and adds to coverage of its orbital motion first detected in that study. We identified additional archival NIRC2 + LGSAO images of the system taken on 2005 October 11, 2007 April 23 (PI M. Liu) and 2010 May 1 (PI B. Biller), and analyzed these data in the same manner as described above. The resulting six epochs of relative astrometry spanning just over 4.5 years are listed in Table 5 and displayed in Figure 7. These measurements confirm the direction of motion previously identified and cover a significant fraction of the system's orbit.

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To more tightly constrain the orbit of this system, we used an Markov Chain Monte Carlo (MCMC) routine with Metropolis-Hasting algorithm (Metropolis et al. 1953; Hastings 1970) to iteratively fit a seven-parameter orbit model to the twelve astrometric measurements (six each in relative R.A. and decl.) and parallax distance measurement (d = 29.5± 0.7 pc; Dupuy & Liu 2012). The methodology used is described in detail in Burgasser et al. (2015b). The parameter vector is

$$\begin{eqnarray}&&{\boldsymbol{\theta }}=\left(P,a,e,i,\omega ,{\rm{\Omega }},{M}_{0},d\right)\end{eqnarray} \tag{ 2 }$$

where P is the period of the orbit in years, a the semimajor axis in AU, e the eccentricity, i the inclination, ω the argument of periastron, Ω the longitude of nodes, M₀ the mean anomaly at epoch τ₀ = 2453654.31 (Julian Date), and d is the distance in pc. We computed an MCMC chain of 10⁷ parameter sets, at each step varying parameters using a normal distribution with scale factors that were allowed to vary dynamically to improve convergence.⁹ We applied additional constraints of 1 year < P < 100 years and 0 < e < 0.6 to eliminate improbable regions of parameter space, and constained the distance to lie within 28 pc < d < 31 pc; our parameter chain was largely insensitive to these limits. Convergence of the chain was monitored through autocorrelation of parameters and evolution of divergence in sequential subchains, and acceptance rates were typically 0.5%–1%. The first 10% of the MCMC chain was removed from subsequent analysis.

Figure 7 shows the best-fit relative visual orbit compared to the measurements, which is an acceptable fit (χ² = 12.05 for 6 degrees of freedom). Table 6 lists the best-fit orbital parameters, as well as median values and 16% and 84% quartiles, while Figure 8 displays the distributions and correlations of P, a, e, i and M_tot = a³/P², the total system mass in Solar units. All of the parameters are reasonably well-determined despite the limited phase coverage, although there are strong correlations between P, a, i and e and a hint of a secondary solution (double-peaked distributions). From the primary solution, we estimate an orbit period of 33${}_{-2}^{+4}$ years and total system mass of 0.0823${}_{-0.0017}^{+0.0037}$ M_⊙, which is consistent with the lower limit of 0.074 M_⊙ proposed by Stumpf et al. (2011) assuming a circular orbit. Indeed, the orbit of SDSS J2052–1609AB appears to be fairly circular (0.014${}_{-0.010}^{+0.023}$) and significantly inclined to the line of sight (45${^\circ }_{-{2}^{^\circ }}^{+{4}^{^\circ }}$). The best fit template fitting results suggest component spectral types of L5.8 ± 1.8 and T2.1 ± 0.5. Assuming effective temperatures corresponding to these spectral types (1544 ± 181 K for the primary and 1248 ± 101 K for the secondary; Stephens et al. 2009), and using the evolutionary models of Saumon & Marley (2008) to estimate age-dependent component masses, we estimate an age of 0.4–1.4 Gyr for this system, where the range accounts for the total mass uncertainty, effective temperature uncertainties, and cloud effects on brown dwarf evolution. Observations over the next decade should greatly improve the mass and orbit constraints on this system, and resolved spectroscopy should make it possible to critically test evolutionary models (e.g., Konopacky et al. 2010; Dupuy et al. 2014).

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Table 6.  Orbital Analysis of SDSS J2052–1609AB Relative Astrometry

Parameter	Best	Median
Best χ2 (dof)	12.05 (6)	...
Pa (year)	32	33${}_{-2}^{+4}$
a (AU)	4.4	4.5${}_{-0.2}^{+0.5}$
ea	0.005	0.014${}_{-0.010}^{+0.023}$
i (°)	45	45${}_{-3}^{+5}$
ω (°)	98	100${}_{-13}^{+15}$
Ω (°)	327	327${}_{-4}^{+3}$
M0 (°)	318	313${}_{-8}^{+15}$
da (pc)	30.5	30.7${}_{-0.4}^{+0.2}$
Mtot (M⊙)	0.081	0.0823${}_{-0.0017}^{+0.0037}$

Note.

^aParameter was constrained to a limited value range in MCMC analysis.

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For 2MASS J1341–3052 and SDSS J1511+0607 only a single epoch of astrometry is available. Hence, we performed a simple Monte Carlo simulation to find the distributions of likely semimajor axes and periods for these systems. Following the procedure described in Burgasser et al. (2015a), we created random uniformly distributed vectors for eccentricity 0 < < 0.6 (Dupuy & Liu 2011), inclination $0\lt \mathrm{sin}\;i\lt 1$, longitude of ascending node 0 < Ω < 2π, argument of periapse 0 < ω < 2π, and mean anomaly angle 0 < M < 2π for 10⁵ hypothetical orbits with a fixed semimajor axis of a = 1 AU. We numerically solved the Kepler equation to find the eccentric anomaly, calculated the Thiele-Innes constants (Innes 1907; van den Bos 1927), and found the x and y projected positions on the sky leading to the total projected separation, r_tot. The distributions of semimajor axes for the resolved systems were inferred by transforming variables:

$$\begin{eqnarray}&&a=(1\mathrm{AU})\times \displaystyle \frac{\rho d}{{r}_{\mathrm{tot}}}\end{eqnarray} \tag{ 3 }$$

where a is the semimajor axis in AU, ρ is the angular separation in arc seconds, d is the distance to the system in parsecs and r_tot is in AU. The observed projected separation, r_obs = ρd, constrains the array of allowed orbits, r_tot, and as a result we arrive at a distribution of probable semimajor axes, a.

The cumulative probability distributions for the semimajor axes of 2MASS J1341–3052 and SDSS J1511+0607 are shown in Figure 9. The most likely semimajor axes are demarcated by a dashed red line and the central 68% (±1σ equivalent) of the data are shaded in lavender. We estimated the periods for these orbits in years assuming P² = a³/M_tot, with M_tot = M₁ + M₂ in Solar masses estimated from the models of Baraffe et al. (2003) for ages of 0.5, 1, 5 and 10 Gyr (Table 7). For 2MASS J1341–3052, we obtain most likely semimajor axis and period of ${8.6}_{-1.8}^{+5.2}$ AU and 63–85 years for decreasing ages, while for SDSS J1511+0607 the most likely semimajor axis and periods are ${3.4}_{-0.8}^{+1.8}$ AU and 15–21 years.

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Table 7.  Estimated Masses and Orbit Results from Monte Carlo Simulation

System	Age (Gyr)	Primary Mass (M⊙)	Secondary Mass (M⊙)	Semimajor Axis (AU)	Period (years)
2MASS J1341–3052AB	0.5	0.052 ± 0.005	0.022 ± 0.005	${8.6}_{-1.8}^{+5.2}$	${85}_{-20}^{+104}$
SpT = L2.5 ± 1.0 and T6.0 ± 1.0	1.0	0.065 ± 0.004	0.030 ± 0.007	${8.6}_{-1.8}^{+5.3}$	${71}_{-18}^{+91}$
Primary Teff = 1904 ± 165 K	5.0	0.075 ± 0.002	0.054 ± 0.007	${8.6}_{-1.8}^{+5.3}$	${64}_{-15}^{+79}$
Secondary Teff = 1027 ± 144 K	10	0.075 ± 0.001	0.061 ± 0.006	${8.6}_{-1.8}^{+5.2}$	${63}_{-14}^{+76}$
SDSS J1511+0607AB	0.5	0.041 ± 0.004	0.026 ± 0.003	${3.4}_{-0.8}^{+1.8}$	${21}_{-5}^{+25}$
SpT = L5.0 ± 1.0 and T5.0 ± 0.5	1.0	0.052 ± 0.005	0.035 ± 0.004	${3.4}_{-0.9}^{+1.8}$	${18}_{-5}^{+22}$
Primary Teff = 1617 ± 139 K	5.0	0.070 ± 0.002	0.059 ± 0.004	${3.4}_{-0.9}^{+1.7}$	${15}_{-3}^{+18}$
Secondary Teff = 1115 ± 107 K	10	0.072 ± 0.001	0.065 ± 0.003	${3.4}_{-0.9}^{+1.8}$	${15}_{-4}^{+17}$

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Starting from a sample of LGS-AO observations of 43 brown dwarfs, we resolved 3 of 17 spectral binary candidates and none of the other targets. 2MASS J1733–1654 has a particularly asymmetrical PSF shape which could indicate the presence of a marginally resolved companion NE of the primary, but this is inconclusive from our images. The fraction of resolved systems from the spectral binary sample is $3/17={18}_{-6}^{+13}\%$ (binomial uncertainties), which is consistent with the observed binary fractions reported in the literature from imaging programs (10%–20%; Bouy et al. 2003; Close et al. 2003; Basri & Reiners 2006; Allen 2007; Burgasser 2007a; Kraus & Hillenbrand 2012). Among the spectral binaries, 2MASS J0518–2828, WISEP J0720–0846, SDSS J0805+4812, 2MASS J1106+2754 and 2MASS J1209–1004 are known binaries unresolved in our images. This indicates a minimum binary fraction for spectral binaries in this sample of $(3+5)/17={47}_{-11}^{+12}\%$. This is considerably higher than typical VLM binary search samples and indicates that the spectral binary sample is positively biased toward binaries. The fact that over half of the known binaries in this sample are not resolved suggests that imaging programs are similarly missing binaries, and that the true binary fraction may be significantly higher than what is currently reported. Note that the fraction reported here remains a lower limit; an unknown number of the 9 unresolved and unconfirmed spectral binaries may be true binaries with separations ≲1.5–9.2 AU.

Of the 12 confirmed spectral binaries to date (Table 8), about half have been unresolved in reported LGS-AO imaging, which is roughly consistent with the 3 resolved and 5 unresolved binaries in our sample. While follow-up of unresolved systems is more time-consuming and resource-intensive (RV and astrometric monitoring), we speculate that the number of unresolved but confirmed spectral binaries will increase as follow-up is completed. A high incidence of unresolved but confirmed spectral binaries implies a high incidence of currently unresolved binaries in general. For example, if all of the unresolved spectral binaries in our sample actually are binaries, this would indicate a ratio of unresolved-to-resolved systems of 4.7:1. Given that the resolved binary fraction is roughly 15%, this rate of unresolved pairs would imply an overall binary fraction of over 60%. It is more likely that the current pool of spectral binary candidates contains some number of contaminants, such as blue L dwarfs (BG14) and variable brown dwarfs (Radigan et al. 2012; Khandrika et al. 2013) which will need to be identified through more detailed spectral and photometric variability analysis. Nevertheless, it is important to note that all 17 spectral binary systems studied here have resolved or upper limit separations near or below the peak of the resolved binary separation of VLM dwarfs (Allen 2007). This is strong evidence that a large number of VLM binaries are being missed in current imaging surveys.