Testing Substellar Models with Dynamical Mass Measurements
aa r X i v : . [ a s t r o - ph . S R ] D ec Testing Substellar Models with Dynamical Mass Measurements
Trent J. Dupuy, , a Michael C. Liu, and Michael J. Ireland Institute for Astronomy, University of Hawai‘i, 2680 Woodlawn Drive, Honolulu, HI 96822 School of Physics, University of Sydney, NSW 2006, Australia
Abstract.
We have been using Keck laser guide star adaptive optics to monitor the orbits of ultracool bina-ries, providing dynamical masses at lower luminosities and temperatures than previously available and enablingstrong tests of theoretical models. We have identified three specific problems with theory: (1) We find that modelcolor–magnitude diagrams cannot be reliably used to infer masses as they do not accurately reproduce the colorsof ultracool dwarfs of known mass. (2) E ff ective temperatures inferred from evolutionary model radii are typi-cally inconsistent with temperatures derived from fitting atmospheric models to observed spectra by 100–300 K.(3) For the only known pair of field brown dwarfs with a precise mass (3%) and age determination ( ≈ ∼ × higher than predicted by model cooling rates (i.e., masses inferred from L bol and age are 20–30% larger than measured). To make progress in understanding the observed discrepancies, moremass measurements spanning a wide range of luminosity, temperature, and age are needed, along with moreaccurate age determinations (e.g., via asteroseismology) for primary stars with brown dwarf binary companions.Also, resolved optical and infrared spectroscopy are needed to measure lithium depletion and to characterize theatmospheres of binary components in order to better assess model deficiencies. Detailed theoretical models of stars, developed and obser-vationally tested over the last century, now underlie mostof modern astronomy. However, the lowest mass stars ( M ⋆ . . M ⊙ ) are su ffi ciently cool ( T e ff . ∼ O are the major sources of opacity in the photosphere,and below ∼ ∼ M7) are central tothis e ff ort, but such measurements have previously beenimpeded by observational limitations. Most ultracool bi-naries were discovered ∼ & ∼ . . a e-mail: [email protected] surements via trigonometric parallax are also essential asthey are needed to convert the observed angular scale of theorbit into physical units and equally importantly to providea direct measurement of the luminosity. As a result, previ-ous to our work only three ultracool binaries had measureddynamical masses ([3], [8], [20]), and these were all rela-tively warm ( & We have been using Keck laser guide star (LGS) AO di-rect imaging and aperture masking to monitor the orbitsof ultracool binaries, enabling dynamical mass measure-ments for the lowest mass (30–75 M Jup ), lowest tempera-ture (1000–2800 K), lowest luminosity (10 − to 10 − L ⊙ )objects known. This has allowed models to be tested inthe unexplored area of parameter space shared by browndwarfs and extrasolar giant planets. Keck LGS AO de-livers di ff raction-limited imaging in the infrared for tar-gets over most of the sky ( ∼ ∼ × sharperthan HST), so it is ideally suited for resolving short-periodultracool binaries. By performing a detailed analysis ofthese high-resolution images and accounting for small as-trometric shifts due to di ff erential atmospheric refraction,we routinely achieve sub-milliarcsecond astrometric accu-racy and ∼ µ as for our best data. Such high quality as-trometry has allowed us to precisely measure binary orbits,with the error in the resulting masses (typically 3–10%)dominated by the uncertainty in the distance (Figure 1).We have also undertaken a substantial amount of sup-plementary analysis to enable these mass measurements:PJ Web of Conferences
300 200 100 0 −100 −200 −300 ∆ RA (mas)−300−200−1000100200300 ∆ D e c ( m a s ) KeckHSTGeminiKeckHSTGeminiKeckHSTGeminiKeckHSTGeminiKeckHSTGeminiKeckHSTGemini
HD 130948BC M tot = 0.109 ± Sun
300 200 100 0 −100 −200 −300 ∆ RA (mas)−300−200−1000100200300−300−200−1000100200300 ∆ D E C ( m a s )
2M 1534−2952AB M tot = 0.056 ± Sun
Keck LGSHSTKeck LGSHST
400 200 0 −200 ∆ RA (mas)−2000200 ∆ D e c ( m a s ) VLTGeminiKeckHSTVLTGeminiKeckHSTVLTGeminiKeckHSTVLTGeminiKeckHSTVLTGeminiKeckHSTVLTGeminiKeckHSTVLTGeminiKeckHSTVLTGeminiKeckHST
LHS 2397aAB M tot = 0.146 ± Sun
200 0 −200 ∆ RA (mas)−2000200 ∆ D e c ( m a s ) VLTGeminiKeckHSTVLTGeminiKeckHSTVLTGeminiKeckHSTVLTGeminiKeckHSTVLTGeminiKeckHSTVLTGeminiKeckHSTVLTGeminiKeckHSTVLTGeminiKeckHST M tot = 0.15 +0.05−0.03 M Sun
Fig. 1.
Our Keck LGS AO data combined with discovery andarchival data from 5 to 10 years ago enables precise orbit deter-minations for ultracool binaries.
Top left:
HD 130948B and C arecompanions to a young solar analog (G2V, 0 . ± . + L4) with a well-determinedage and masses ( M tot = . ± . M ⊙ ; [10]). Top right: − + T5.5, M tot = . ± . M ⊙ ), revealing incon-sistencies between the atmospheric model-derived temperatures,evolutionary model H–R diagram, and measured mass [14]. Bot-tom left:
LHS 2397aAB (M8 + L7, M tot = . ± . M ⊙ ) is thefirst dynamical mass benchmark at the L / T transition, showingconsistency between temperatures estimated from atmosphericand evolutionary models and supporting the idea that the temper-ature of the L / T transition is surface gravity dependent [11].
Bot-tom right: − + M8) is a pair of starsat the bottom of the main sequence that have J -band colors 0.2–0.3 mag redder than predicted by evolutionary model tracks forobjects of their measured masses [9]. This implies that massesand / or ages inferred from model color–magnitude diagrams willbe in error for such objects. (1) We have re-analyzed archival HST images from 5 to10 years ago, improving astrometric errors by a factor of2 to 8 compared to published values, and this has provedcritical for accurate orbit determination (e.g., [11], [14]).(2) We have developed a novel Monte Carlo technique todetermine the orbital period probability distribution frommotion observed between discovery and our first Keck dataobtained &
400 200 0 −200 −400 ∆ RA (mas)−400−2000200400 ∆ D e c ( m a s ) random subset of 10 simulated orbits HST/WFPC22000Keck LGS2006 B component A component B component A component N o r m a li z ed P r obab ili t y D i s t r i bu t i on est = 10−43 years 2 epochs: P est > 26 years0 10 20 30 40 50Orbital period (years)0.00.20.40.60.81.01.2 N o r m a li z ed P r obab ili t y D i s t r i bu t i on Fig. 2.
We have developed a novel Monte Carlo technique to de-termine the orbital period probability distribution from orbitalmotion observed between only two epochs.
Left:
For the ultra-cool binary 2MASS J1728 + ∼ Right:
The orbital period distribu-tion of the randomly drawn orbits (red) compared to the estimatedperiod distribution using only the discovery epoch (black), fol-lowing the method of Torres [19], with ± σ confidence limitsshaded gray. Although the two-epoch distribution appears at facevalue to be broader and thus less precise, it is actually stronglypreferred as it is free of the somewhat arbitrary assumptions re-quired by the single-epoch estimate (i.e., a uniform eccentricitydistribution between 0 < e < M ⊙ ).In the case of 2MASS J1728 + P >
26 years, 68.3% c.l.) of theoriginal estimate (10–43 years, 68.3% c.l.), reducing its priorityin our orbital monitoring program. and even with these assumptions the ± σ confidence lim-its span a factor of ∼ M tot ∝ d . Only about 1 in 4 ofthe shortest period ultracool binaries have previously pub-lished parallaxes, so our program targeting ∼
30 binariesenables a greatly expanded sample of masses.ew Technologies for Probing the Diversity of Brown Dwarfs and Exoplanets −4000400 ∆ R A ( m a s ) ∆ D e c ( m a s ) π = 85.8 ± proper motionparallaxtotal offset Fig. 3.
Analysis of data from our infrared parallax program atCFHT demonstrates the capability to measure precise distancesto visual binaries in our Keck LGS AO sample, which is criti-cal as the derived dynamical mass depends strongly on the dis-tance ( M tot ∝ d ). Our parallaxes of “control” objects that havepublished parallaxes, such as the object shown here, agree wellwith published results. Our astrometric measurements are shownas open circles (error bars are smaller than the plotting symbols)along with the best-fit astrometric solution (solid black) whichincludes parallax (red dashed) and proper motion (blue dotted)components. Our Keck program has been yielding dynamical masseswith the needed precision (3–10%) to perform fundamen-tal tests of theory (Figure 1). To date, we have identifiedthree specific problems with substellar models:(1) We find inconsistencies between predicted near-infraredcolors and those observed for field objects of known massover a wide range of spectral types ([9], [10], [11], [14]).For example, the M8 + M8 components of 2MASS J2206 − + L4 components of HD 130948BC appearto be ≈ + T5.5 components of 2MASS J1534 − ≈ / or ages inferred from theoretical color–magnitude di-agrams should be treated with caution.(2) If theoretically predicted radii are correct, we have foundthat temperatures derived from atmospheric models are sys-tematically in error ([9], [10], [14]). This points either toinaccurate theoretical radii or to incomplete modeling ofsuch low-temperature atmospheres. The one object for whichthis is not the case is LHS 2397aB, currently the only massbenchmark at the L / T transition [11]. This is surprising asexisting atmospheric models should not be appropriate forsuch transitional objects as their predictions are only validin the limiting cases of maximal dust (Dusty, [6]) and thetotal absence of dust (COND, [2]). Thus, in the case ofLHS 2397aB it is likely that large systematic errors cancelout to produce apparent agreement.
Fig. 4.
We have tested substellar cooling rates by measuring themasses and luminosities of HD 130948B and C, brown dwarfswith a well-determined age of 0.8 ± ∼ × more luminousthan evolutionary models predict. Two independent sets of the-oretical luminosity tracks are shown as colored isomass lines,where the thickness corresponds to the uncertainty in the mea-sured mass. Such a systematic error would imply that model-inferred masses are over estimated by ∼ (3) For the only system with both a known mass and age,we have found the measured luminosities of the individ-ual components to be ∼ × higher than predicted (Fig-ure 4; [10]). This would imply that model-derived massesare significantly over estimated by ∼ ∼
30% too high [12]. However, we emphasize that this ap-parent over-luminosity is based on a single system whoseage is estimated from the primary star HD 130948A. Whilethis young solar analog is fortuitously amenable to multi-ple age-dating techniques using stellar rotation, chromo-spheric and x-ray activity, and isochrone fitting, preciseage estimation is notoriously di ffi cult for an arbitrary fieldstar. Thus, refining the age estimate for HD 130948A (e.g.,via asteroseismology) is essential. Also, more dynamicalmasses for the substellar binaries in triple systems withstars of known age (e.g., ǫ Ind Bab, Gl 417BC, GJ 1001BC)are critically needed to address this potential problem withmodel cooling rates.
To make progress in understanding the problems we havefound with substellar models, we are in the process of de-veloping a larger sample of masses spanning a wide rangein temperature, mass, and age. For example, more massmeasurements should determine whether the observed over-luminosity of brown dwarfs (Figure 4) persists for di ff erentsurface temperatures. If so, this would point to a problemPJ Web of Conferenceswith the interior structure model (e.g., convection) ratherthan a surface e ff ect (e.g., magnetic fields).Resolved spectroscopy is also needed to enable detailedcharacterization of the individual components’ tempera-tures, surface gravities, and abundances. Binaries with knownmasses can provide stronger tests of atmospheric modelsthan field brown dwarfs of unknown age or mass. Suchmeasurements will be able to assess poorly understood at-mospheric e ff ects such as dust formation and sedimenta-tion (e.g., [1]) and vertical mixing that can drive nonequi-librium chemistry (e.g., [16]).In addition, optical spectra from HST / STIS will enablemeasurements of lithium absorption at 6708 Å for bina-ries that we have shown are very close to the theoreti-cally predicted lithium burning limit at ≈ M Jup , provid-ing a novel test of substellar interior models ([10], [11]).As shown in Figure 5, independent groups make di ff erentpredictions for the mass limit of lithium depletion. Bina-ries close to this limit o ff er the chance to empirically de-termine the lithium boundary for the first time, with a pre-cision comparable to our dynamical mass measurements( ∼ ff erent eccentricity distributions forultracool binaries: Stamatellos & Whitworth predict higheccentricities ( e & .
5) for ultracool binaries formed viagravitational fragmentation in a massive circumstellar disk[17], while Bate predicts modest eccentricities ( e . . References
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