3.8um Imaging of 400-600K Brown Dwarfs and Orbital Constraints for WISEP J045853.90+643452.6AB
S. K. Leggett, Trent J. Dupuy, Caroline V. Morley, Mark S. Marley, William M. J. Best, Michael C. Liu, D. Apai, S. L. Casewell, T. R. Geballe, John E. Gizis, J. Sebastian Pineda, Marcia Rieke, G. S. Wright
DDraft version August 23, 2019
Typeset using L A TEX preprint style in AASTeX62 µ m Imaging of 400 – 600 K Brown Dwarfs andOrbital Constraints for WISEP J045853.90+643452.6AB S. K. Leggett, Trent J. Dupuy, Caroline V. Morley, Mark S. Marley, William M. J. Best, Michael C. Liu, D. Apai, S. L. Casewell, T. R. Geballe, John E. Gizis, J. Sebastian Pineda, Marcia Rieke, and G. S. Wright Gemini Observatory, Northern Operations Center, 670 N. A’ohoku Place, Hilo, HI 96720, USA University of Texas at Austin, Austin, TX 78712, USA NASA Ames Research Center, Mail Stop 245-3, Moffett Field, CA 94035, USA Institute for Astronomy, University of Hawaii at Manoa, Honolulu, HI 96822, USA Department of Astronomy/Steward Observatory, University of Arizona, 933 N. Cherry Avenue, Tucson, AZ 85721,USA ; Department of Planetary Science/Lunar and Planetary Laboratory, University of Arizona, 1640 E. UniversityBoulevard, Tucson, AZ 85718, USA ; Earths in Other Solar Systems Team, NASA Nexus for Exoplanet SystemScience, USA 0000-0003-3714-5855 Department of Physics and Astronomy, University of Leicester, University Road, Leicester LE1 7RH, UK Department of Physics and Astronomy, University of Delaware, Newark, DE 19716, USA University of Colorado Boulder, Laboratory for Atmospheric and Space Physics, 3665 Discovery Drive, Boulder, CO80303, USA Steward Observatory, University of Arizona, 933 N. Cherry Avenue, Tucson, AZ 85721, USA STFC UK-ATC, Edinburgh, EH9 3HJ, UK
ABSTRACTHalf of the energy emitted by late-T- and Y-type brown dwarfs emerges at 3 . ≤ λ µ m ≤ .
5. We present new L (cid:48) (3 . ≤ λ µ m ≤ .
11) photometry obtained at theGemini North telescope for nine late-T and Y dwarfs, and synthesize L (cid:48) from spectrafor an additional two dwarfs. The targets include two binary systems which wereimaged at a resolution of 0 . (cid:48)(cid:48)
25. One of these, WISEP J045853.90+643452.6AB, showssignificant motion, and we present an astrometric analysis of the binary using
HubbleSpace Telescope , Keck Adaptive Optics, and Gemini images. We compare λ ∼ µ mobservations to models, and find that the model fluxes are too low for brown dwarfscooler than ∼
700 K. The discrepancy increases with decreasing temperature, and isa factor of ∼ T eff = 500 K and ∼ T eff = 400 K. Warming the upper layersof a model atmosphere generates a spectrum closer to what is observed. The thermalstructure of cool brown dwarf atmospheres above the radiative-convective boundarymay not be adequately modelled using pure radiative equilibrium; instead heat maybe introduced by thermochemical instabilities (previously suggested for the L- to T-type transition) or by breaking gravity waves (previously suggested for the solar systemgiant planets). One-dimensional models may not capture these atmospheres, whichlikely have both horizontal and vertical pressure/temperature variations. INTRODUCTIONBrown dwarfs form the extended low-mass tail of the stellar initial mass function, and brown dwarfsas low-mass as four Jupiter-masses ( M Jup ) have been found in young clusters and associations (e.g., a r X i v : . [ a s t r o - ph . S R ] A ug Leggett et al.
Best et al. 2017; Esplin & Luhman 2017). The difference between giant planet and brown dwarfformation is an active research area (e.g., Nielsen et al. 2019; Schlaufman 2018; Wagner et al. 2019).Brown dwarfs have the compositions of stars, but the physics and chemistry of their atmospheres arecomplex and resemble those of giant planets (e.g., Line et al. 2015; Morley et al. 2014b).The thermal radiation of a brown dwarf escapes through an atmosphere that is rich in molecules.Light emerges through windows between the broad molecular absorption bands. One of these windowsspans 3 . ≤ λ µ m ≤ .
5; for late-type T and Y dwarfs with effective temperature ( T eff ) less than600 K (e.g., Beichman et al. 2014; Dupuy & Kraus 2013; Kirkpatrick et al. 2012), 40 – 60% of the totalenergy emerges through this single window. The W2 filter of the Wide-field Infrared Survey Explorer ( WISE , Wright et al. 2010) is centered at λ ∼ . µ m and the coldest known objects outside of thesolar system have been discovered by WISE (Cushing et al. 2011; Luhman 2014). This paper presentsnew ground-based photometry of cool brown dwarfs using the Maunakea Observatories (MKO) L (cid:48) filter, which is centered at λ ∼ . µ m (Tokunaga et al. 2002). In this paper we combine the newphotometry with published data to explore the important λ ∼ µ m spectral region. Figure 1.
Comparison of the observed spectrum of the 500 K brown dwarf UGPS J072227.51 − (cid:46) λ µ m (cid:46) (cid:46) λ µ m (cid:46) WISE
W1 and W2 (cyan),
Spitzer [3.6] and [4.5] (blue), and MKO L (cid:48) and M (cid:48) (green). The primarymolecular absorbers for this region are identified. The model spectrum has been scaled for the measureddistance of the brown dwarf and the evolutionary-implied radius that corresponds to the model temperatureand gravity. Discrepancies between the models and observations are discussed in Section 5. .8 µ m Imaging of 400 – 600 K Brown Dwarfs . ≤ λ µ m ≤ .
40 spectrum of the 500 K brown dwarfUGPS J072227.51 − Spitzer [3.6] and [4.5],
WISE
W1 and W2, and ground-based MKO L (cid:48) and M (cid:48) filters are alsoshown. The figure shows that these bandpasses sample slightly different regions of the 4 µ m spectrumand shows also that the spectrum is heavily sculpted by strong absorption bands. At λ ≈ . µ mthe atmosphere is opaque; this is the region with the strong P-, Q- and R-branches of the ν bandof methane and the flux emerges from the cold upper layers of the atmosphere. At λ ≈ . µ mthe brown dwarf is bright, the atmosphere is transparent, and flux emerges from very deep, hot,high-pressure regions of the atmosphere. The 3 – 5 µ m colors of brown dwarfs can therefore provideinformation on very physically different layers of the atmosphere. The figure also illustrates thelong-standing problem, for brown dwarfs cooler than 700 K, of significant shortfall in modelled fluxat 3 . (cid:46) λ µ m (cid:46) . WISE and
Spitzer cameras have relatively poor angular resolution with full-width half-maxima(FWHMs) of ∼ . (cid:48)(cid:48) ∼ . (cid:48)(cid:48) James Webb SpaceTelescope ( JWST ) mission. The brown dwarf imaging presented here has a resolution of 0 . (cid:48)(cid:48)
25 to 1 . (cid:48)(cid:48) JWST observation specifications.Section 2 of this paper presents the new L (cid:48) photometry. Section 3 gives the astrometric data forWISEP J045853.90+643452.6AB (hereafter 0458AB) and presents preliminary orbital constraints forthe system. In Section 4 we use astrometric and photometric properties to constrain the masses andages of the 0458AB and WISEPC J121756.91+162640.2AB (hereafter 1217AB) binary systems. InSection 5 we examine the discrepancy between the models and the observations in this waveband.Our conclusions are given in Section 6. The Appendix presents ground-based and space-based 3 –5 µ m colors for T and Y dwarfs, so that these datasets can be more easily utilized in the future. L (cid:48) PHOTOMETRY OF BROWN DWARFS2.1.
Existing Data L (cid:48) photometry of brown dwarfs with spectral type later than T6 has been published by: Burninghamet al. (2009); Geballe et al. (2001); Golimowski et al. (2004); Leggett et al. (2002, 2007). In the nexttwo subsections we present new observations and synthesized L (cid:48) photometry from observed spectra.Figure 2 is a color-magnitude diagram which shows M [4 . as a function of [3.6] − [4.5] (see Figure1 for bandpasses). The Spitzer data are taken from Kirkpatrick et al. (2019); Leggett et al. (2017);Martin et al. (2018) and references therein, the trigonometric parallaxes are taken from Kirkpatricket al. (2019); Leggett et al. (2017); Martin et al. (2018); Smart et al. (2018); Theissen (2018) andreferences therein. T and Y dwarfs with L (cid:48) photometry presented here are identified.2.2. Gemini Observations L (cid:48) photometry was obtained using the Gemini Observatory near-infrared imager (NIRI, Hodappet al. 2003) on the Gemini North telescope. Two binary systems that are targets for JWST
Guar-anteed Time Observations were observed via program GN-2017B-FT-15 in excellent natural seeing
Leggett et al. in order to resolve the binary components: 0458AB and 1217AB. Five (notionally) single browndwarfs were observed via program GN-2018B-FT-112 in poorer seeing: WISE J000517.48+373720.5,WISEPA J031325.96+780744.2, WISEA J041022.75+150247.9, WISEA J140518.32+553421.3 andWISEA J205628.88+145953.6. In the rest of this paper we shorten the object names to the first fourdigits of the Right Ascension values. For GN-2018B-FT-112, brown dwarfs later than T8 with [3.6] <
17 mag that were accessible at the Gemini North telescope were selected. The targets were alsochosen in order to sample the brightness and color space of Figure 2. No evidence of binarity wasseen in the GN-2018B-FT-112 images, for which the seeing was typically 1 . (cid:48)(cid:48) . (cid:48)(cid:48)
02 and a field of view of 20”. Targets and photometric
Figure 2. M [4 . as a function of [3.6] − [4.5] for T and Y dwarfs. Starred symbols have measured L (cid:48) ;double stars represent targets with new data presented here, which are identified by the first four digits oftheir RA. T eff values on the right axis are from Tremblin et al. (2015) non-equilibrium chemistry models. .8 µ m Imaging of 400 – 600 K Brown Dwarfs Table 1.
Observation Log
WISE
Program Date ExposureName Number YYYMMDD minutesJ000517.48+373720.5 GN-2018B-FT-112 20181207 8.9J031325.96+780744.2 GN-2018B-FT-112 20181223 9.2J041022.75+150247.9 GN-2018B-FT-112 20181207 39.0J045853.90+643452.6AB GN-2017B-FT-15 20171224 22.8J121756.91+162640.2AB GN-2017B-FT-15 20180102 26.0J140518.32+553421.3 GN-2018B-FT-112 20181223 31.4J205628.88+145953.6 GN-2018B-FT-112 20181207 15.2 standards were observed in a fixed 5-position grid pattern with 3” telescope offsets. The photometricstandards were selected from the Leggett et al. (2003) catalog and were observed immediately beforeor after the brown dwarf at a similar airmass.To compensate for the variable sky background at L (cid:48) , adjacent frames were subtracted for eachtarget and photometric standard, and then stacked using the known telescope offsets. The singlebrown dwarfs were observed on nights with seeing typically 1 . (cid:48)(cid:48)
0. Aperture photometry with annularsky regions was carried out using apertures of diameter 0 . (cid:48)(cid:48) . (cid:48)(cid:48)
0, corresponding to the seeing on thenight of observation. Aperture corrections were determined from the photometric standards observedclose in time and airmass to the science target.The two binary systems were observed on nights of excellent 0 . (cid:48)(cid:48)
25 seeing. Figure 3 shows the L (cid:48) images of the two binary systems. The components of 0458AB were found to be very close at the epochof observation. Figure 4 shows the L (cid:48) image of 0458AB smoothed by 2 × Figure 3.
Gemini Observatory L (cid:48) images of 0458AB at 20171224 (left) and 1217AB at 20180102 (right).North is up and East is left. Leggett et al.
Table 2.
Separation, and Position Angle, of the 1217AB SystemDate UT Separation mas PA degrees Instrument/Observatory2012 Jan 29 a ± ± ± ± a Weighted mean of six measurements in different filters, Liu et al. (2012). overlaid, and the two photometric on-source apertures of 0 . (cid:48)(cid:48)
12 diameter are shown. The contributionsto the signal from the background and the other binary component were determined from the radialprofile of each source and the outer pixels, for each component. 1217AB is well-separated in the NIRIimages (Figure 3) and aperture photometry with annular skies was carried out, using an aperturediameter of 0 . (cid:48)(cid:48)
24. Aperture corrections were determined from the observations of the photometricstandards. For both binary systems, the magnitude measurement for each component is consistentwith a large-aperture measurement of the system, within the uncertainties.The 0458AB system has shown significant motion compared to previous imaging, and in the nextSection we constrain its orbit. The 1217AB system does not show significant motion and the orbitcannot be constrained. For future reference, Table 2 gives the separation and position angle of this
Figure 4.
The NIRI L (cid:48) image of 0458AB, with contours overlaid. The white circles are the 0 . (cid:48)(cid:48)
12 diameterapertures used to measure the signal for each component of the binary. .8 µ m Imaging of 400 – 600 K Brown Dwarfs Table 3.
New L (cid:48) PhotometryName Spectral L (cid:48) Type magWISE J000517.48+373720.5 T8.5 14.43 ± ± ± ± ± − a T9 13.13 ± − a Y1+ 16.31 ± ± ± ± ± aL (cid:48) photometry was synthesized from flux-calibrated spectra. binary measured from the NIRI image presented here, and the values of these parameters in 2012,measured by Liu et al. (2012) using Keck laser guide star adaptive optics (LGS AO, Bouchez et al.2004; Wizinowich et al. 2006). Table 3 lists our L (cid:48) photometry for the nine brown dwarfs.2.3. Synthetic L (cid:48) Photometry L (cid:48) photometry was synthesized from spectra of 0722 and WISE J085510.83071442.5 (hereafter0855). The 2 . ≤ λ µ m ≤ . . ≤ λ µ m ≤ .
13 spectrum of 0855 was published by Morley et al. (2018); each was flux calibratedusing
Spitzer [3.6] photometry. We assumed a zero flux contribution for 3 . ≤ λ µ m ≤ . L (cid:48) photometry. Uncertainties were determined from thenoise in the spectra and the uncertainty in the calibration photometry. THE ORBIT OF 0458AB3.1.
Astrometric Monitoring of 0458AB
Keck LGS AO
We obtained resolved images of 0458AB at four epochs using the facility infrared imager NIRC2with the LGS AO system at the Keck II telescope (Bouchez et al. 2004; Wizinowich et al. 2006). Forthe first two epochs in 2011 and 2012 we used NIRC2’s wide camera (39 . ± .
008 mas pix − ). Thesecond two epochs in 2018 were obtained after the Gemini L (cid:48) imaging with NIRC2’s narrow camera(9 . ± .
004 mas pix − ). For the 2011 and 2018 data sets we used the CH s filter, centered on the H -band flux peak for T dwarfs ( λ = 1 . µ m, ∆ λ = 0 . µ m), and for the 2012 data set we usedthe Y -band filter (see Appendix of Liu et al. 2012).We derived binary parameters from our imaging data in the same fashion as in our past work,using a three-component 2D-Gaussian model for PSF fitting and adopting the rms among individual Leggett et al.
Table 4.
Relative Astrometry and Photometry for 0458AB
Date UT Tel./Inst. Sep. mas PA degree Filter ∆ m mag Ref.2010 Mar 24 Keck/NIRC2 510 ±
20 320 ± J , H . ± .
08, 1 . ± .
09 G112011 Feb 3 Keck/OSIRIS 493 ±
15 321 . ± . H bb · · · B122011 Apr 22 Keck/NIRC2 465 ± ± CH s . ± .
08 *2011 Aug 29 Keck/NIRC2 455 ± . ± . J , H , K s . ± .
01, 1 . ± .
01, 1 . ± .
03 B122012 Jan 14 Keck/NIRC2 432 ± . ± . Y . ± .
04 *2012 Feb 27
HST /ACS-WFC 435 ± . ± . F W , F LP . ± .
11, 0 . ± .
02 *2015 Jan 2
HST /WFC3-IR 273 . ± . . ± . F W . ± .
03 *2017 Dec 27 Gemini-N/NIRI 103 ±
20 29 . ± . L (cid:48) . ± .
18 *2018 Jan 6 Keck/NIRC2 130 . ± . . ± . CH s . ± .
04 *2018 Oct 18 Keck/NIRC2 132 . ± . . ± . CH s . ± .
017 *
Note —* this work, G11: Gelino et al. (2011), B12: Burgasser et al. (2012).
HST data from GO-12504 (PI: Liu), GO-13705 (PI:Patience). images at a given epoch for the uncertainties in those parameters (e.g., Dupuy et al. 2014; Liu et al.2006). To convert the instrumental ( x, y ) measurements into angular separations and position angles(PAs), we used the same methods as in Dupuy et al. (2016) and Dupuy & Liu (2017). We used thecalibration of Fu et al. (2012, priv. comm.) for the first two epochs and the calibration of Serviceet al. (2016) for the second two epochs. We add − . ◦ ± . ◦
020 to our PAs as a correction for theorientation of NIRC2 for data obtained after the AO system realignment in 2015 April (Service et al.2016), and − . ◦ ± . ◦
009 prior to that (Yelda et al. 2010). Figure 5 shows typical images from allfour epochs, and Table 4 reports our derived relative astrometry.3.1.2.
HST Imaging
We analyzed archival
HST images from two epochs. On 2012 Feb 27 UT the program GO-12504 (PI:Liu) observed 0458AB with ACS-WFC as a PSF reference source, and on 2015 Jan 2 UT the programGO-13705 (PI: Patience) obtained pre-imaging with WFC3-IR for their spectroscopic observations.For the ACS-WFC data, we use only the higher signal-to-noise ratio (SNR) F LP imaging. Weanalyzed the ACS-WFC images as described in Section 3.1.2 of Dupuy & Liu (2017), using TinyTim- CH4s Y CH4s
CH4s
Figure 5.
Contour plots of our Keck LGS AO images of 0458AB. Contours are in logarithmic intervalsfrom unity to 10% of the peak flux. North is up and East is left. The separation of the binary changeddramatically, requiring much higher angular resolution imaging at the latest epochs. http://astro.physics.uiowa.edu/ ∼ fu/idl/nirc2wide/ .8 µ m Imaging of 400 – 600 K Brown Dwarfs Table 5.
Absolute Astrometry of 0458AB in CFHT/WIRCam Integrated Light
Observation Date Right Ascension Declination σ R . A . σ Decl . Airmass SeeingUT MJD deg deg mas mas arcsec2011 Feb 11 55603.2484 074.72535576 +64 . . . . . . . . Note —The quoted uncertainties correspond to relative, not absolute, astrometric errors. based (Krist et al. 2011) PSF-fitting. For the WFC3-IR data, we used the appropriate TinyTimPSFs for that instrument as in our previous work (e.g., Dupuy et al. 2009b,a; Liu et al. 2008). Weused the
D2IMARR and
WCSDVARR
FITS extensions and the CD matrices of the headers to convert ourmeasured ( x, y ) into separations and PAs. Table 4 reports the mean and rms of the mean obtainedfrom individual exposures as our best-fit values and uncertainties.3.1.3. CFHT/WIRCam
We obtained eight epochs of wide-field, unresolved imaging of 0458AB using the facility infraredcamera WIRCam (Puget et al. 2004) at the Canada-France-Hawaii Telescope (CFHT) as part of ourongoing Hawaii Infrared Parallax Program. We used an exposure time of 60 s in the J band andachieved SNR = 40–70. We measured ( x, y ) positions using SExtractor (Bertin & Arnouts 1996)and converted these to relative astrometry using a custom pipeline described in our previous work(Dupuy & Liu 2012; Liu et al. 2016). The absolute calibration of the linear terms of our astrometricsolution was derived by matching low proper motion sources ( <
30 mas yr − ) to the 2MASS pointsource catalog (Cutri et al. 2003). To convert our relative parallax and proper motion to an absoluteframe, we use the mean parallax and proper motion of stars simulated by the Besan¸con model ofthe Galaxy (Robin et al. 2003), selecting stars over the same range of apparent magnitudes as in thedata. The variance in the conversion from relative to absolute is determined by using many differentsubsets of model stars. The resulting astrometry for 0458AB in integrated light is given in Table 5.3.2. The Orbit, Parallax, and Proper Motion of 0458AB
We combined our resolved astrometry with other published measurements and our integrated-lightastrometry in a single analysis, fitting the orbit, parallax, and proper motion. The approach is verysimilar to our past work (Dupuy et al. 2015; Dupuy & Liu 2017). Six of the thirteen parameters areshared between the resolved and integrated-light data, all relating to orbit: period ( P ), eccentricity( e ) and argument of periastron ( ω ) parametrized as √ e sin ω and √ e cos ω , inclination ( i ), PA ofthe ascending node (Ω), and mean longitude at the reference epoch ( λ ref ), defined to be 2010 Jan-uary 1 00:00 UT (2455197.5 JD). There are two parameters for orbit size; the semimajor axis ( a ) inangular units, and the ratio of the semimajor axis of the CFHT photocenter orbit to a ( a phot /a ). Thefive remaining parameters are all related to the CFHT astrometry: parallax ( (cid:36) rel ), proper motion0 Leggett et al. ( µ ) in Right Ascension and Declination, and the Right Ascension and Declination at the referenceepoch t ref . The only parameters without uniform priors were P and a (log-flat), i (sin i , randomviewing angles), and an approximately uniform space density ( (cid:36) − ).We use the parallel-tempering Markov chain Monte Carlo (PT-MCMC) ensemble sampler in emcee v2.1.0 (Foreman-Mackey et al. 2013) that is based on the Earl & Deem (2005) algorithm.“Hot” chains explore essentially all of the allowed parameter space between solutions, while “cold”chains find local minima. Information is exchanged between chains and the solution is the “coldest”of 30 chains. We use 100 walkers to sample our 13-parameter model over 8 × steps. The initialstate is a random, uniform draw over all of parameter space for bounded parameters: e , ω , Ω, i , λ ref ;2 < P/ yr < . (cid:48)(cid:48) < a < . (cid:48)(cid:48) − < a phot /a < ±
100 mas around the reference epoch RightAscension and Declination; ±
30% around the relative proper motion; and ±
20% around the relativeparallax. The resulting distributions of posteriors are shown in Figure 6 and summarized in Table 6.Figure 7 displays the orbit and Table 7 gives estimates of future configurations of the system.
50 100P (yr)0.00.20.40.60.81.0 N / N m a x
50 100P (yr)0.00.20.40.60.81.0 N / N m a x N / N m a x N / N m a x tot (M Jup )0.00.20.40.60.81.0 N / N m a x tot (M Jup )0.00.20.40.60.81.0 N / N m a x −1 0 1e sin ω −1 0 1e sin ω −0.5 0.0 0.5 1.0e cos ω −0.5 0.0 0.5 1.0e cos ω o )70 75 80i ( o )105 110 ϖ (mas)105 110 ϖ (mas)−1 0 1a phot / a−1 0 1a phot / a−500 0 500a phot (mas)−500 0 500a phot (mas) 150 200 250 λ ref ( o )150 200 250 λ ref ( o )150 200 µ RA cos δ (mas yr −1 )150 200 µ RA cos δ (mas yr −1 )−500 0 500RA −RA (mas)−500 0 500RA −RA (mas)0 100 200 300 ω ( o )0 100 200 300 ω ( o ) 120 130 140 Ω ( o )120 130 140 Ω ( o )280 300 320 µ Dec (mas yr −1 )280 300 320 µ Dec (mas yr −1 )−300 0 300Dec −Dec (mas)−300 0 300Dec −Dec (mas)2000 2050T (yr)2000 2050T (yr) Figure 6.
Marginalized posterior distributions for our PT-MCMC analysis of the 0458AB orbit. Dark grayhistograms are directly fitted parameters, and light gray histograms are properties computed from the fits. .8 µ m Imaging of 400 – 600 K Brown Dwarfs Table 6.
PT-MCMC Orbital Posteriors for WISE J0458+6434AB
Property Median ± σ P [yr] 43 +7 −
23, 63 1 /P (log-flat)Semimajor axis, a [mas] 540 +40 − /a (log-flat) √ e sin ω . +0 . − . − √ e cos ω . +0 . − . − i [ ◦ ] 76 . +1 . − . i ), 0 ◦ < i < ◦ ]PA of the ascending node, Ω [ ◦ ] 132 . +2 . − . t ref = 2455197 . λ ref [ ◦ ] 207 +18 − . A . ref − R . A . MLref [mas] − +80 − − . A . MLref = 74 . . ref − decl . MLref [mas] 50 +110 − − . MLref = +64 . µ R . A ., rel [mas yr − ] 194 +15 − µ decl ., rel [mas yr − ] 300 +8 − (cid:36) rel [mas] 107 . +1 . − . /(cid:36) Ratio of photocenter orbit to semimajor axis, a phot /a − . +0 . − . − e . +0 . − . · · · Argument of periastron, ω [ ◦ ] 110 +130 −
0, 350 · · ·
Time of periastron, T = t ref − P λ − ω ◦ [JD] 1994 +12 − · · · Photocenter semimajor axis, a phot [mas] − +160 − − · · · ( a P − ) × [arcsec yr − ] 0 . +0 . − . · · · Correction to absolute R.A. proper motion, ∆ µ R . A . [mas yr − ] 0 . +0 . − . · · · Correction to absolute decl. proper motion, ∆ µ decl . [mas yr − ] − . ± . − − · · · Correction to absolute parallax, ∆ (cid:36) [mas] 0 . +0 . − . · · · Absolute proper motion in R.A., µ R . A . a [mas yr − ] 195 +15 − · · · Absolute proper motion in decl., µ decl . a [mas yr − ] 299 ± · · · Absolute parallax, (cid:36) a [mas] 108 . +1 . − . · · · Distance, d [pc] 9 . +0 . − . · · · Semimajor axis, a [AU] 5 . +0 . − . · · · Total mass, M total [ M Jup ] 70 +15 −
36, 156 · · · a The absolute parallax, proper motion in RA and proper motion in Declination are consistent with the values determined from
Spitzer images by Kirkpatrick et al. (2019), which are 109 . ± .
6, 207 . ± . . ± .
2, respectively.
Note —The full 13-parameter fit has χ = 28 . χ = 17 . δ log M total = 0 .
26 dex, δe = 0 .
27, and ∆ t obs /P = 0 .
20, indicating a poorly constrained orbit determination. ML is Maximum Likelihood. It should be noted that the total dynamical mass is not well measured from the current data spanning8.6 years. The derived mass is dependent on the choice of priors for parameters such as period,semimajor axis, and eccentricity.
Under our current assumptions, the minimum system mass is36 M Jup (2 σ ), suggesting that neither of the components is planetary mass ( < M Jup ). One reliableprediction from our orbit analysis is that the separation will continue increasing for the next few years,at least until 2021, the nominal launch year of
JWST (Figure 7, Table 7). Our analysis also provides2
Leggett et al.
Table 7.
Predicted Separation, and Position Angle, of the 0458AB SystemDate UT Separation mas PA degrees Date UT Separation mas PA degrees2019 Sep 1 160 . ± . . ± . ±
18 112 . ± . . ± . . ± . ±
21 113 . ± . . ± . . ± . ±
34 117 ± ± . ± . ±
40 119 ± ± . ± . ±
50 120 ± ± . ± . ±
60 123 ± ±
13 109 . ± . ±
70 126 ± ±
70 127 ± T o t a l M a ss ( M J up )
200 0 −200 −400 ∆α cos δ (mas)−2000200400 ∆ δ ( m a s ) KeckHSTGemini
WISE J0458+6434AB S epa r a t i on ( m a s ) PA ( o ) −150152008 2012 2016 2020 2024Epoch (yr)−0.50.00.52010 2012 2014 2016Epoch (yr)−50510 PM+parallax subtracted −1000100
PM+orbit subtracted ∆ α c o s δ ( m a s ) PM+parallax subtracted −1000100
PM+orbit subtracted ∆ δ ( m a s ) Figure 7.
Orbital analysis for 0458AB. The highest-likelihood orbit is a thick black line, and 100 randomlydrawn PT-MCMC solutions are thin lines color-coded by total mass.
Top left:
Relative astrometry fromKeck LGS AO (red diamonds),
HST (purple squares), and Gemini (gold triangle). Open circles mark thetimes corresponding to CFHT/WIRCam observations. The dashed line is the line of nodes, and the arrowindicating motion direction is plotted at periastron.
Top right:
Relative astrometry as a function of timewith the lower subpanels showing residuals from the highest-likelihood orbit.
Bottom:
Integrated-lightastrometry from CFHT/WIRCam as a function of time. Upper subpanels show the parallax curve aftersubtracting proper motion and orbital motion (error bars are too small to be visible). Lower subpanels showthe orbital motion after subtracting proper motion and parallax. This is for display purposes only, as ouranalysis fits proper motion, parallax, and orbital motion simultaneously. .8 µ m Imaging of 400 – 600 K Brown Dwarfs CONSTRAINTS ON THE PROPERTIES OF 0458AB AND 1217AB FROM PHOTOMETRYFigure 8 is a color-magnitude and color-color plot using the 1 – 4 µ m photometry of T and Ydwarfs. Brown dwarfs with T eff <
750 K ( H − L (cid:48) > .
5) show a brightening at 4 µ m relative to thenear-infrared. The components of the 0458AB and 1217AB binaries have colors typical of late-T andY dwarfs, suggesting that their composition and age are typical of a field population. Figure 8 shows Figure 8.
J HL (cid:48) colors of T and Y dwarfs. Open circles indicate the components of the 0458AB system,and open squares indicate the components of the 1217AB system. In the upper plot, well-studied T dwarfsare identified and their T eff values are given (Section 4). The T eff ranges for the Y dwarfs are also shown(derived from near-infrared spectra and mid-infrared photometry, Leggett et al. 2017). The reddest (coolest)objects are identified in the lower plot. The dashed line in the upper plot is a model sequence from Tremblinet al. (2015, see Section 5). Leggett et al.
Table 8.
Physical Properties of the 0458AB and 1217AB Systems a M Jup , log g Name Age=0.6 1.0 3.0 4.0 6.0 8.0 10.0 Gyr0458A 9, 4.4 15, 4.5 25, 4.8 28, 4.9 34, 5.0 37, 5.1 41, 5.20458B 12, 4.3 11, 4.4 19, 4.7 22, 4.8 26, 4.9 29, 5.0 32, 5.01217A 12, 4.3 11, 4.4 19, 4.7 22, 4.8 26, 4.9 29, 5.0 32, 5.01217B 7, 4.1 9, 4.3 15, 4.6 17, 4.6 20, 4.7 23, 4.8 25, 4.9 a If 0458A has T eff ≈
600 K, 0458B and 1217A have T eff ≈
500 K, and 1217Bhas T eff ≈
425 K; using Saumon & Marley (2008) evolutionary models. that, as would be expected, the T8.5 0458A lies in a similar region of the color-magnitude diagramsas the T8.5 Wolf 940B, and the T9 0458B lies in a similar region as the T9 0722. The T9 1217A alsolies in a similar region as the T9 0722, and the Y0 1217B is similar to the Y0 2056.Wolf 940B is a benchmark object, with age and composition constrained by its distant M dwarfcompanion. A large amount of data is available for Wolf 940B, including a mid-infrared spectrumfrom
Spitzer . The studies by Burningham et al. (2009) and Leggett et al. (2010a) show this T8.5 tohave T eff = 605 ±
20 K, log g = 5 . ± . − ) and a metallicity within 0.2 dex of solar. 0722 isbright and has also been well studied, although it does not have a stellar companion or a spectrumbeyond 4 µ m. Leggett et al. (2012) and Lucas et al. (2010) find for 0722 that T eff = 505 ±
10 K, log g = 4 . ± . T eff = 425 ±
15 K, log g = 4 . ± .
25 and metallicity is solar or slightly super-solar.Using Wolf 940B, 0722 and 2056 as reference objects, the photometric comparison indicates that0458A has T eff ≈
600 K, 0458B and 1217A have T eff ≈
500 K, and 1217B has T eff ≈
425 K; the valuesfor the 1217AB system are consistent with previous analyses (e.g., Leggett et al. 2014). Assumingthat the binary components have the same age, evolutionary models can be used to constrain gravitiesand masses for the two systems. Table 8 lists these values as a function of age.Our preliminary orbit for 0458AB gives a total mass for the system of 70 +15 − M Jup (1 σ , Table 6).Combining the astrometry with the observed photometric difference of ∆( J ) = 0 . ± .
01 mag(Burgasser et al. 2012) constrains the individual masses to 57 +25 − M Jup and 14 +21 − M Jup (1 σ ). Notethat when the photocenter orbit a phot is poorly constrained, as it is here (Table 6), the uncertaintiesin the individual masses are large. Assuming coevality and T eff ≈
600 K for the primary and ≈
500 Kfor the secondary, the evolutionary models give a broad age range for this system of 3 – 13 Gyr(Table 8). For the 1217AB system, fits to the near-infrared spectrum and mid-infrared photometryof 1217B constrain the likely age to be 0.7 – 6 Gyr (Leggett et al. 2017). The tangential velocitiesof the 0458AB and 1217AB systems are 16 ± − (Table 6) and 62 ± − (Leggett et al.2017) respectively, suggesting thin disk membership and an age <
10 Gyr (Dupuy & Liu 2012; Robinet al. 2003). Adopting a likely age of a few Gyr for both systems, the masses of the primary andsecondary are around 35 and 25 M Jup for 0458AB, and around 20 and 15 M Jup for 1217AB. THE λ ≈ .8 µ m Imaging of 400 – 600 K Brown Dwarfs µ m region that are too low for the late-T and Y dwarfs. These include the cloud-free non-equilibrium chemistry models of Marley et al.(2002), the cloud-free chemical equilibrium models with updated opacities of Saumon et al. (2012),the cloudy chemical equilibrium models of Morley et al. (2012, 2014b), and the cloud-free non-equilibrium chemistry models with updated opacities of Tremblin et al. (2015), as demonstrated byLeggett et al. (2010b, 2012, 2013, 2015, 2017) and Luhman & Esplin (2016). The discrepancy isillustrated in Figure 1 for the T eff = 500 K object 0722 (Leggett et al. 2012).In Figure 1 we show the observed spectrum, and synthetic spectra generated by the models ofMorley et al. (2012) and Tremblin et al. (2015), for this 500 K brown dwarf. These two sets of modelgrids are the best available at this temperature, at the time of writing; the former includes clouds butnot the non-equilibrium chemistry brought about by mixing, and the latter includes non-equilibriumchemistry but does not include clouds (work on a grid of model atmospheres that includes bothclouds and non-equilibrium chemistry is ongoing by members of our team (Marley et al. 2017)).Morley et al. (2012, 2014b) show that clouds of chloride and sulfide condensates are important for400 (cid:46) T eff K (cid:46) T eff (cid:46)
300 K. The effect of the clouds isprimarily a reduction in the λ ∼ µ m flux with that energy redistributed to longer wavelengths(Morley et al. 2012, 2014b). Vertical mixing in brown dwarf atmospheres leads to an increase in theabundances of the more stable CO and N , and a decrease in the abundances of the less stable CH and NH (e.g., Saumon et al. 2006). The resulting non-equilibrium chemistry has been shown to beimportant for both T and Y dwarfs (Leggett et al. 2007, 2015; Saumon et al. 2006, 2007; Stephenset al. 2009). The decrease in NH absorption leads to an increase in near-infrared flux, especially inthe H -band, and an increase in flux at λ ∼ . µ m, while the increase in CO absorption leads toless flux at λ ∼ . µ m (e.g. Figure 1; Saumon et al. 2006; Morley et al. 2014b).Figure 1 suggests that cloudy models are required to reproduce the Y -band flux, which is thewavelength most impacted by clouds at this temperature (Morley et al. 2014b). Non-equilibriumchemistry is required to reproduce the H -band shape and the 4.5 µ m flux. Neither model reproducesthe shape of the K -band flux peak and both models are deficient at λ ∼ µ m. In this work weuse as a primary reference the non-equilibrium models of Tremblin et al. (2015); this is because thedominant opacities at λ ∼ µ m consist of carbon- and nitrogen-bearing molecules (Figure 1), andclouds (as currently modelled) do not significantly impact this wavelength region.The upper panel of Figure 8 explores the H − L (cid:48) colors of T and Y dwarfs, and shows the colorsequence generated by the Tremblin et al. (2015) models. This comparison suggests that the λ ∼ µ mflux discrepancy starts at T eff ≈
700 K and increases to lower temperatures. Figure 8 suggests thatat L (cid:48) the models are too faint by ∼ . ∼ . L -band spectra to synthetic spectra generatedby Tremblin et al. (2015) models. Observed spectra are shown for 2MASS J04151954 − T eff ∼
750 K. However for cooler atmospheres there is a significantdiscrepancy. Although the principal opacity appears to be CH in both the observed and syntheticspectra, the observed slope is flatter than the calculated slope. The strong absorption features at6 Leggett et al. . ≤ λ µ m ≤ . T eff , but the fluxes between theabsorption features are much higher than calculated.In their analysis of the cold brown dwarf 0855, Morley et al. (2018) find that the 3.5 – 4.1 µ mand 4.5 – 5.1 µ m spectra can be fit by metal-poor models with a C/O ratio half solar (althoughthe models are then too bright in the near-infrared). As pointed out by Morley et al. (2018), it isunlikely that all the late-T and Y dwarfs have such an unusual atmospheric composition and so itis more likely that there is something occurring in these cool atmospheres that is not captured by Figure 9.
Observed spectra (black lines) and calculated spectra (colored lines) at λ ∼ . µ m for browndwarfs with T eff ∼ F λ ≈ . λ ≈ . µ m.Dotted vertical lines indicate CH absorption features (Tennyson & Yurchenko 2012; Yurchenko & Tennyson2014). Although the CH features map well between the observations and the models, the flux between theabsorption bands is much lower in the models — for example at λ ≈ µ m the500 K model flux is too low by a factor of ∼ . .8 µ m Imaging of 400 – 600 K Brown Dwarfs K -band ( λ = 2 . µ m, see Figure1) but the discrepancy at [3.6] remained.The fact that the observed flux is higher than calculated suggests that the 3.6 – 4.1 µ m flux isemerging from warmer atmospheric layers than the models generate. Figure 10 shows a T eff = 500 Ksynthetic spectrum generated by us, based on the models of Morley et al. (2014b), which demonstratesthe changes in the spectrum that could be brought about if the atmosphere is heated at 1 bar or 0.1bar. The pressure-temperature profile for this atmosphere is also shown, illustrating the size of thetemperature differential in the upper atmosphere. The heated-atmosphere spectrum is very similarto the standard spectrum in the near-infrared and at λ ≈ µ m, but is much brighter at λ ≈ . µ mand at λ ≈ µ m. This preliminary result suggests that upper atmosphere heating in late-T andY dwarfs could be the cause of the brighter than expected W1, [3.6] and L (cid:48) magnitudes, and mayalso give rise to the (less well-defined) discrepancy seen in the W3 magnitudes (7 . (cid:46) λ µ m (cid:46) . T eff increases from 500 K to550 K; this implies that temperatures determined for late-T and Y dwarfs by fitting models to red,near-infrared and 4.5 µ m data could be significantly too low. However, this heated-atmosphere modelis exploratory only, and needs further study.A cool brown dwarf atmosphere is assumed to be undergoing adiabatic cooling in the deep at-mosphere and radiative cooling in the upper atmosphere (e.g., Marley & Robinson 2015, Figure 1).The retrieval analysis of late-T and Y dwarf atmospheres by Zalesky et al. (2019) found temper-ature structures largely consistent with radiative-convective equilibrium, and chemical abundancesfor water, methane and ammonia to be as expected. Their analysis explored fits to spectra covering0 . (cid:46) λ µ m (cid:46) . wavelength ( µ m) f l u x ( W / m / µ m ) standard1 bar0.1 bar 250 500 750 1000 temperature (K) -4 -3 -2 -1 p r e ss u r e ( b a r ) standard1 bar0.1 bar Figure 10.
A synthetic 500 K spectrum (left) and Pressure-Temperature profile (right) demonstrating theeffect of adding heat at 1 or 0.1 bar by adding energy at those altitudes over a scale height. Leggett et al.
Energy (or heat) could be introduced into a brown dwarf atmosphere by thermochemical instabilities(Tremblin et al. 2015, 2019) or cloud clearing (Morley et al. 2012). Interestingly, measurements of theatmospheres of the solar system giant planets show the upper layers to be warmer than expected; heatsources such as breaking gravity waves have been invoked (Matcheva & Strobel 1999; O’Donoghueet al. 2016). The same effect may be present in cold brown dwarfs, which have similar radii androtation periods (Cushing et al. 2016; Leggett et al. 2016; Manjavacas et al. 2019), and highlydynamic atmospheres (Apai et al. 2017; Showman & Kaspi 2013).It is also important to note that these models are one-dimensional, and it is likely that the atmo-spheres have both horizontal and vertical pressure/temperature variations. Variability at 1 (cid:46) λ µ m (cid:46) CONCLUSIONWe have imaged two brown dwarf binary systems at high angular resolution using NIRI and its L (cid:48) filter on the Gemini North telescope: the T8.5 + T9 0458AB, and the T9 + Y0 1217AB. We havealso imaged five single brown dwarfs in L (cid:48) at lower angular resolution: 0005 (T8.5), 0313 (T9), 0410(Y0), 1405 (Y0.5), and 2056 (Y0). In addition, we have synthesized L (cid:48) photometry from publishedspectra for 0722 (T9) and 0855 (Y1+).The 0458AB system has shown significant orbital motion. The separation of the components was0 . (cid:48)(cid:48)
46 in 2011 and 0 . (cid:48)(cid:48)
13 in 2018, a decrease in projected separation from 4.3 AU to 1.2 AU. We havecombined the Gemini images with higher resolution Keck LGS AO and
HST images to monitor theorbit of the 0458AB system, and with wide-field CFHT images to determine the proper motion andparallax of the system. Our preliminary orbital analysis gives a period of 43 +7 − years and a totalmass for the system of 70 +15 − M Jup (1 σ ). Our analysis will aid the acquisition of the target for JWST observations. The orbital analysis, together with photometry and evolutionary models, suggests thatthe age of the system is a few Gyr with component masses of around 35 and 25 M Jup .We verify that model fluxes at 3 . (cid:46) λ µ m (cid:46) . T eff ≈
700 K and gets worse to lower temperatures — at T eff = 500 K modelfluxes are about a factor of two too low and at T eff = 400 K the fluxes are about a factor of four toolow. The spectra suggest that the dominant opacity source in this region is CH as expected, and thedepths of the features are approximately correct; however, the flux emerging between the features,the pseudo-continuum, is brighter than calculated by the models. We have generated model spectrawhere heat is introduced into the upper layers of the atmosphere. Such models can significantlyincrease the flux at λ ∼ µ m and λ ∼ µ m without impacting the near-infrared or λ ∼ µ mflux, offering the potential of a much better match to observations. Departures from pure radiative-convective equilibrium temperature-pressure profiles, such as in the test model, can arise from severalphysical mechanisms. Tremblin et al. (2019) use hydrodynamic simulations to show that a diabaticprofile is appropriate in the event of instabilities brought about by the conversion between CO andCH for warmer brown dwarfs with T eff ≈ T eff ≈
500 K similar instabilities could beintroduced by the conversion between N and NH (e.g., Lodders 1999, Figure 2). Another possible .8 µ m Imaging of 400 – 600 K Brown Dwarfs λ ∼ . µ m,for brown dwarfs with T eff <
700 K. For example, the heated-atmosphere model predicts that the6 (cid:46) λ µ m (cid:46) T eff are systematically and significantly low. We eagerly await JWST spectracovering these wavelengths, and anticipate that the λ > µ m spectra delivered by JWST and
SPHEREx will reveal unexpected climate physics for cool brown dwarfs. This physics is likely to beimportant not only for the brown dwarfs, but also for exoplanets and the solar system giant planets.This publication makes use of data from the Wide-field Infrared Survey Explorer, a joint projectof the University of California, Los Angeles, and the Jet Propulsion Laboratory/California Instituteof Technology, funded by the National Aeronautics and Space Administration. This work is basedin part on archival data obtained with the Spitzer Space Telescope, operated by the Jet PropulsionLaboratory, California Institute of Technology under a contract with NASA. This work is also basedin part on observations made with the NASA/ESA Hubble Space Telescope, obtained from the dataarchive at the Space Telescope Science Institute. STScI is operated by the Association of Universitiesfor Research in Astronomy, Inc. under NASA contract NAS 5-26555.Some of the data presented herein were obtained at the W. M. Keck Observatory, which is operatedas a scientific partnership among the California Institute of Technology, the University of Californiaand the National Aeronautics and Space Administration. The Observatory was made possible bythe generous financial support of the W. M. Keck Foundation. Some of the data presented hereinwere obtained with WIRCam, a joint project of CFHT, the Academia Sinica Institute of Astronomyand Astrophysics (ASIAA) in Taiwan, the Korea Astronomy and Space Science Institute (KASI) inKorea, Canada, France, and the Canada-France-Hawaii Telescope (CFHT) which is operated by theNational Research Council (NRC) of Canada, the Institut National des Sciences de l’Univers of theCentre National de la Recherche Scientifique of France, and the University of Hawaii.This work is based on observations obtained at the Gemini Observatory, which is operated by theAssociation of Universities for Research in Astronomy, Inc., under a cooperative agreement with theNSF on behalf of the Gemini partnership: the National Science Foundation (United States), NationalResearch Council (Canada), CONICYT (Chile), Ministerio de Ciencia, Tecnolog´ıa e Innovaci´on Pro-ductiva (Argentina), Minist´erio da Ciˆencia, Tecnologia e Inova¸c˜ao (Brazil), and Korea Astronomyand Space Science Institute (Republic of Korea).MCL and WMJB acknowledge support from NSF grant AST-1518339.0
Leggett et al.
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W1 and W2 and
Spitzer [3.6] and [4.5] photometry, so that datasets can bebetter utilized. See Figure 1 for the location of the filters with respect to a 500 K brown dwarfspectrum. The
Spitzer data are taken from Kirkpatrick et al. (2019); Leggett et al. (2017); Martinet al. (2018) and references therein, the trigonometric parallaxes are taken from Kirkpatrick et al.(2019); Leggett et al. (2017); Martin et al. (2018); Smart et al. (2018); Theissen (2018) and referencestherein. In addition, for this work, we determined W1 magnitudes from images downloaded fromthe unWISE database (Schlafly et al. 2019) for four Y dwarfs, WISE J033605.05-014350.4 with W . ± .
10, WISEA J035000.31-565830.5 with W . ± .
2, WISE J064723.23-623235.5with W . ± .
2, and WISEA J235402.79+024014.1 with W . ± . µ m and 5 µ m filters. We find that theuncertainty in the W1 colors of the T and Y dwarfs may be underestimated, as the large scatter in Figure 11.
Color-magnitude diagrams for the 4 µ m filters. Circled points in the left panel indicate late-Tand Y dwarfs with L (cid:48) photometry that appear in the right panel. http://unwise.me/imgsearch/// Leggett et al. the W1 − [3.6] color is not seen in the [3.6] − L (cid:48) color. A spot check of the outliers suggests that theW1 photometry is contaminated by nearby background sources — the brown dwarfs are faint in W1and the WISE pixels are large (see also Kirkpatrick et al. 2019).The [3.6] − L (cid:48) color becomes redder for later spectral types, however W2 − [4.5] and M (cid:48) − [4.5] stayclose to zero. This is not surprising given the large degree of overlap in the W2, [4.5] and M (cid:48) filters(Figure 1).Figure 13 shows [3.6] − L (cid:48) , L (cid:48) − [4.5], M (cid:48) − [4.5], and [3.6] − M (cid:48) as a function of [3.6] − [4.5]. Knownbinaries have been excluded from the sample. Excluding the extremely red 0855, and the low gravitySDSS J111009.99+011613.0 (Gagn´e et al. 2015) which appears discrepant, we find that weightedlinear fits can be used to estimate the differences between the ground-based L (cid:48) and M (cid:48) magnitudesand the Spitzer [3.6] and [4.5] magnitudes as a function of the [3.6] − [4.5] color:[3.6] − L (cid:48) = 0 .
338 + 0 . × ([3.6] − [4.5])and L (cid:48) − [4.5] = − .
344 + 0 . × ([3.6] − [4.5]) Figure 12.
Color-magnitude diagrams for the 5 µ m filters. Note that the x -axis range is much smaller thanthat of Figure 11 — these filters give similar magnitudes for the late-T and Y dwarfs. .8 µ m Imaging of 400 – 600 K Brown Dwarfs . ≤ ([3.6] − [4.5]) ≤ . M (cid:48) − [4.5] = 0 . − . × ([3.6] − [4.5])and [3.6] − M (cid:48) = − .
435 + 1 . × ([3.6] − [4.5])for 0 . ≤ ([3.6] − [4.5]) ≤ .
2. The rms uncertainty in the linear fit is 0.09 mag for all colors.Figure 14 shows [3.6] − L (cid:48) , L (cid:48) − [4.5], M (cid:48) − [4.5], and [3.6] − M (cid:48) as a function of H − L (cid:48) and H − M (cid:48) .Weighted quadratic fits were made, excluding known binaries, the extremely red 0855, and the lowgravity SDSS J111009.99+011613.0, as above. These relationships can be used to estimate [3.6] and[4.5] if only L (cid:48) or M (cid:48) are available, for example in the case of close binaries unresolved by Spitzer .We use the H bandpass to provide the near-infrared color — more H measurements are availablethan K (which can be faint for late-type dwarfs), and shorter wavelengths are impacted by clouds(e.g. Section 5). We find:[3.6] − L (cid:48) = − .
255 + 0 . × ( H − L (cid:48) ) − . × ( H − L (cid:48) ) for 1 . ≤ ( H − L (cid:48) ) ≤
6, with rms uncertainty 0.08 mag, and
Figure 13.
Color-color diagrams for the 4 and 5 µ m filters. The weighted linear fits shown in cyan excludeSDSS J111009.99+011613.0 for the L (cid:48) colors and 0855 for all colors. Leggett et al. L (cid:48) − [4.5] = − .
080 + 0 . × ( H − L (cid:48) ) − . × ( H − L (cid:48) ) for 1 . ≤ ( H − L (cid:48) ) ≤ M (cid:48) − [4.5] = 0 . − . × ( H − M (cid:48) ) + 0 . × ( H − M (cid:48) ) for 1 . ≤ ( H − M (cid:48) ) ≤
6, with rms uncertainty 0.08 mag, and[3.6] − M (cid:48) = − .
290 + 1 . × ( H − M (cid:48) ) − . × ( H − M (cid:48) ) for 1 . ≤ ( H − M (cid:48) ) ≤
6, with rms uncertainty 0.13 mag.
Figure 14.
Color-color diagrams for the H , 4 µ m and 5 µ m filters. The weighted quadratic fits shown incyan exclude SDSS J111009.99+011613.0 and 0855. Also, the fit to H − L (cid:48) : L (cid:48) − [4.5] excludes objects earlierthen T6 spectral type due to the rapid increase in L (cid:48) − [4.5] color at H − L (cid:48) ≈≈