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Michael C. Liu

Publications and source records attributed to Michael C. Liu.

At least 73 records · Page 4Linked to original sources

A Volume-Limited Sample of Ultracool Dwarfs. I. Construction, Space Density, and a Gap in the L/T Transition

We present a new volume-limited sample of L0-T8 dwarfs out to 25 pc defined entirely by parallaxes, using our recent measurements from UKIRT/WFCAM along with Gaia DR2 and literature parallaxes. With 369 members, our sample is the largest parallax-defined volume-limited sample of L and T dwarfs to date, yielding the most precise space densities for such objects. We find the local L0-T8 dwarf population includes $5.5\%\pm1.3\%$ young objects ($\lesssim$200 Myr) and $2.6\%\pm1.6\%$ subdwarfs, as expected from recent studies favoring representative ages $\lesssim$4 Gyr for the ultracool field population. This is also the first volume-limited sample to comprehensively map the transition from L to T dwarfs (spectral types $\approx$L8-T4). After removing binaries, we identify a previously unrecognized, statistically significant (>4.4$σ$) gap $\approx$0.5 mag wide in $(J-K)_{\rm MKO}$ colors in the L/T transition, i.e., a lack of such objects in our volume-limited sample, implying a rapid phase of atmospheric evolution. In contrast, the most successful models of the L/T transition to date $-$ the "hybrid" models of Saumon & Marley (2008) $-$ predict a pile-up of objects at the same colors where we find a deficit, demonstrating the challenge of modeling the atmospheres of cooling brown dwarfs. Our sample illustrates the insights to come from even larger parallax-selected samples from the upcoming Legacy Survey of Space and Time (LSST) by the Vera Rubin Obsevatory.

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A wide planetary-mass companion to a young low-mass brown dwarf in Ophiuchus

We present the discovery of a planetary-mass companion to CFHTWIR-Oph 98, a low-mass brown dwarf member of the young Ophiuchus star-forming region, with a wide 200-au separation (1.46 arcsec). The companion was identified using Hubble Space Telescope images, and confirmed to share common proper motion with the primary using archival and new ground-based observations. Based on the very low probability of the components being unrelated Ophiuchus members, we conclude that Oph 98 AB forms a binary system. From our multi-band photometry, we constrain the primary to be an M9-L1 dwarf, and the faint companion to have an L2-L6 spectral type. For a median age of 3 Myr for Ophiuchus, fits of evolutionary models to measured luminosities yield masses of $15.4\pm0.8$ M$_\mathrm{Jup}$ for Oph 98 A and $7.8\pm0.8$ M$_\mathrm{Jup}$ for Oph 98 B, with respective effective temperatures of $2320\pm40$ K and $1800\pm40$ K. For possible system ages of 1-7 Myr, masses could range from 9.6-18.4 M$_\mathrm{Jup}$ for the primary, and from 4.1-11.6 M$_\mathrm{Jup}$ for the secondary. The low component masses and very large separation make this binary the lowest binding energy system imaged to date, indicating that the outcome of low-mass star formation can result in such extreme, weakly-bound systems. With such a young age, Oph 98 AB extends the growing population of young free-floating planetary-mass objects, offering a new benchmark to refine formation theories at the lowest masses.

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Individual Dynamical Masses of DENIS J063001.4$-$184014AB Reveal A Likely Young Brown Dwarf Triple

The binary nature of the M8.5 dwarf DENIS J063001.4$-$184014AB (DE0630$-$18) was discovered with astrometric monitoring from the ground, which determined the unresolved photocentric orbit and the trigonometric parallax of the system. Here we present radial-velocity monitoring and resolved observations in the near-infrared with Keck aperture masking that allow us to measure the system's relative separation and brightness. By combining all available information, we determine the individual dynamical masses of the binary components to be $M_1 = 0.052^{+0.009}_{-0.008} M_\mathrm{Sun}$ and $M_2 = 0.052^{+0.005}_{-0.004} M_\mathrm{Sun}$, both firmly in the substellar regime. These masses are surprising given the object's M8.5 optical spectral type and equivalent absolute magnitude, and the significant difference in brightness between the components ($Δ{K}$ = 1.74$\pm$0.06 mag). Our results suggest that DE0630$-$18 is a relatively young system ($\sim$200 Myr) with a secondary component that is itself a potentially unresolved binary.

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Direct radio discovery of a cold brown dwarf

Magnetospheric processes seen in gas-giants such as aurorae and circularly-polarized cyclotron maser radio emission have been detected from some brown dwarfs. However, previous radio observations targeted known brown dwarfs discovered via their infrared emission. Here we report the discovery of BDR J1750+3809, a circularly polarized radio source detected around 144 MHz with the LOFAR telescope. Follow-up near-infrared photometry and spectroscopy show that BDR J1750+3809 is a cold methane dwarf of spectral type T$6.5\pm 1$ at a distance of $65^{+9}_{-8}\,{\rm pc}$. The quasi-quiescent radio spectral luminosity of BDR J1750+3809 is $\approx 5\times 10^{15}\,{\rm erg}\,{\rm s}^{-1}\,{\rm Hz}^{-1}$ which is over two orders of magnitude larger than that of the known population of comparable spectral type. This could be due to a preferential geometric alignment or an electrodynamic interaction with a close companion. In addition, as the emission is expected to occur close to the electron gyro-frequency, the magnetic field strength at the emitter site in BDR J1750+3809 is $B\gtrsim 25\,{\rm G}$, which is comparable to planetary-scale magnetic fields. Our discovery suggests that low-frequency radio surveys can be employed to discover sub-stellar objects that are too cold to be detected in infrared surveys.

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Early High-contrast Imaging Results with Keck/NIRC2-PWFS: The SR 21 Disk

High-contrast imaging of exoplanets and protoplanetary disks depends on wavefront sensing and correction made by adaptive optics instruments. Classically, wavefront sensing has been conducted at optical wavelengths, which made high-contrast imaging of red targets such as M-type stars or extincted T Tauri stars challenging. Keck/NIRC2 has combined near-infrared (NIR) detector technology with the pyramid wavefront sensor (PWFS). With this new module we observed SR~21, a young star that is brighter at NIR wavelengths than at optical wavelengths. Compared with the archival data of SR~21 taken with the optical wavefront sensing we achieved $\sim$20\% better Strehl ratio in similar natural seeing conditions. Further post-processing utilizing angular differential imaging and reference-star differential imaging confirmed the spiral feature reported by the VLT/SPHERE polarimetric observation, which is the first detection of the SR~21 spiral in total intensity at $L^\prime$ band. We also compared the contrast limit of our result ($10^{-4}$ at $0\farcs4$ and $2\times10^{-5}$ at $1\farcs0$) with the archival data that were taken with optical wavefront sensing and confirmed the improvement, particularly at $\leq0\farcs5$. Our observation demonstrates that the NIR PWFS improves AO performance and will provide more opportunities for red targets in the future.

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The Hawaii Infrared Parallax Program. IV. A Comprehensive Parallax Survey of L0-T8 dwarfs with UKIRT

We present parallaxes, proper motions, and $J$-band photometry for 348 L and T dwarfs measured using the wide-field near-infrared camera WFCAM on the United Kingdom Infrared Telescope. This is the largest single batch of infrared parallaxes for brown dwarfs to date. Our parallaxes have a median uncertainty of 3.5 mas, similar to most previous ground-based infrared parallax surveys. Our target list was designed to complete a volume-limited parallax sample of L0-T8 dwarfs out to 25 pc spanning declinations $-30^\circ$ to $+60^\circ$ (68% of the sky). We report the first parallaxes for 165 objects, and we improve on previous measurements for another 53 objects. Our targets include 104 objects (mostly early-L dwarfs) having $Gaia$ DR2 parallax measurements, with which our parallaxes are consistent. We include an extensive comparison of previous literature parallaxes for L and T dwarfs with both our results and $Gaia$ DR2 measurements, identifying systematic offsets for some previous surveys. Our parallaxes confirm that 14 objects previously identified as wide common proper motion companions to main-sequence stars have distances consistent with companionship. We also report new $J_\mathrm{MKO}$ photometry for our targets, including the first measurements for 193 of our targets and improvements over previously published $J_\mathrm{MKO}$ photometry for another 60 targets. Altogether, our parallaxes will enable the first population studies using a volume-limited sample spanning spectral types L0-T8 defined entirely by parallaxes.

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A Novel Survey for Young Substellar Objects with the W-band Filter. I. Filter Design and New Discoveries in Ophiuchus and Perseus

We present the design and implementation of a medium-band near-IR filter tailored for detecting low-mass stars and brown dwarfs from the summit of Maunakea. The W-band filter is centered at 1.45 micron with a bandpass width of 6%, designed to measure the depth of the H2O water absorption prominent in objects with spectral types of M6 and later. When combined with standard J- and H-band photometry, the W-band filter is designed to determine spectral types to $\approx$1.4 subtypes for late-M and L dwarfs, largely independent of surface gravity and reddening. This filter's primary application is completing the census of young substellar objects in star-forming regions, using W-band selection to greatly reduce contamination by reddened background stars that impede broad-band imaging surveys. We deployed the filter on the UH 88-inch telescope to survey $\approx$3 sq. deg. of the NGC 1333, IC 348, and rho Ophiuchus star-forming regions. Our spectroscopic followup of W-band selected candidates resulted in the confirmation of 48 ultracool dwarfs with a success rate of 89%, demonstrating the efficacy of this new filter and selection method.

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ACRONYM IV: Three New, Young, Low-mass Spectroscopic Binaries

As part of our search for new low-mass members of nearby young moving groups (YMG), we discovered three low-mass, spectroscopic binaries, two of which are not kinematically associated with any known YMG. Using high-resolution optical spectroscopy, we measure the component and systemic radial velocities of the systems, as well as their lithium absorption and H$α$ emission, both spectroscopic indicators of youth. One system (2MASS J02543316-5108313, M2.0+M3.0) we confirm as a member of the 40 Myr old Tuc-Hor moving group, but whose binarity was previously undetected. The second young binary (2MASS J08355977-3042306, K5.5+M1.5) is not a kinematic match to any known YMG, but each component exhibits lithium absorption and strong and wide H$α$ emission indicative of active accretion, setting an upper age limit of 15 Myr. The third system (2MASS J10260210-4105537, M1.0+M3.0) has been hypothesized in the literature to be a member of the 10 Myr old TW Hya Association (TWA), but with our measured systemic velocity, shows the binary is in fact not part of any known YMG. This last system also has lithium absorption in each component, and has strong and variable H$α$ emission, setting an upper age limit of 15 Myr based on the lithium detection.

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Spitzer Variability Properties of Low-Gravity L Dwarfs

We present \textit{Spitzer Space Telescope} variability monitoring observations of three low-gravity L dwarfs with previous detections of variability in the near-IR, 2MASS J0045+16, 2MASS J0501-00 and 2MASS J1425-36. We detect significant, periodic variability in two of our targets, 2MASS J0045+16 and 2MASS J0501-00. We do not detect variability in 2MASS J1425-36. Combining our new rotation periods with rotational velocities, we calculate inclination angles of $22\pm1^{\circ}$, ${60^{+13 }_{-8}} ^{\circ}$ and $52^{+19}_{-13}~^{\circ}$ for 2MASS J0045+16, 2MASS J0501-00 and 2MASS J1425-36 respectively. Our three new objects are consistent with the tentative relations between inclination, amplitude and color anomaly previously reported. Objects with the highest variability amplitudes are inclined equator-on, while the maximum observed amplitude decreases as the inclination angle decreases. We also find a correlation between the inclination angle and $(J-K)_{\mathrm{2MASS}}$ color anomaly for the sample of objects with measured inclinations. Compiling the entire sample of brown dwarfs with \textit{Spitzer} variability detections, we find no enhancement in amplitude for young, early-L dwarfs compared to the field dwarf population. We find a possible enhancement in amplitude of low-gravity late-L dwarfs at $4.5~μ$m. We do not find a correlation between amplitude ratio and spectral type for field dwarfs or for the young population. Finally, we compile the rotation periods of a large sample of brown dwarfs with ages 1 Myr to 1 Gyr and compare the rotation rates predicted by evolutionary models assuming angular momentum conservation. We find that the rotation rates of the current sample of brown dwarfs fall within the expected range set by evolutionary models and breakup limits.

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Keck/NIRC2 $L$'-Band Imaging of Jovian-Mass Accreting Protoplanets around PDS 70

We present $L$'-band imaging of the PDS 70 planetary system with Keck/NIRC2 using the new infrared pyramid wavefront sensor. We detected both PDS 70 b and c in our images, as well as the front rim of the circumstellar disk. After subtracting off a model of the disk, we measured the astrometry and photometry of both planets. Placing priors based on the dynamics of the system, we estimated PDS 70 b to have a semi-major axis of $20^{+3}_{-4}$~au and PDS 70 c to have a semi-major axis of $34^{+12}_{-6}$~au (95\% credible interval). We fit the spectral energy distribution (SED) of both planets. For PDS 70 b, we were able to place better constraints on the red half of its SED than previous studies and inferred the radius of the photosphere to be 2-3~$R_{Jup}$. The SED of PDS 70 c is less well constrained, with a range of total luminosities spanning an order of magnitude. With our inferred radii and luminosities, we used evolutionary models of accreting protoplanets to derive a mass of PDS 70 b between 2 and 4 $M_{\textrm{Jup}}$ and a mean mass accretion rate between $3 \times 10^{-7}$ and $8 \times 10^{-7}~M_{\textrm{Jup}}/\textrm{yr}$. For PDS 70 c, we computed a mass between 1 and 3 $M_{\textrm{Jup}}$ and mean mass accretion rate between $1 \times 10^{-7}$ and $5 \times~10^{-7} M_{\textrm{Jup}}/\textrm{yr}$. The mass accretion rates imply dust accretion timescales short enough to hide strong molecular absorption features in both planets' SEDs.

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The Parallax of VHS J1256-1257 from CFHT and Pan-STARRS 1

We present new parallax measurements from the CFHT Infrared Parallax Program and the Pan-STARRS 3$π$ Steradian Survey for the young ($\approx150-300$ Myr) triple system VHS J125601.92$-$125723.9. This system is composed of a nearly equal-flux binary ("AB") and a wide, possibly planetary-mass companion ("b"). The system's published parallactic distance ($12.7\pm1.0$ pc) implies absolute magnitudes unusually faint compared to known young objects and is in tension with the spectrophotometric distance for the central binary ($17.2\pm2.6$ pc). Our CFHT and Pan-STARRS parallaxes are consistent, and the more precise CFHT result places VHS J1256-1257 at $22.2^{+1.1}_{-1.2}$ pc. Our new distance results in higher values for the companion's mass ($19\pm5$ M$_{\rm Jup}$) and temperature ($1240\pm50$ K), and also brings the absolute magnitudes of all three components into better agreement with known young objects.

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A Novel Survey for Young Substellar Objects with the W-band filter II. The Coolest and Lowest Mass Members of the Serpens-South Star-forming Region

Given its relative proximity (~430 pc), compact size (< 20'), young age (~ 0.5 Myr) and rich number of young stellar objects, the Serpens-South star forming region is a promising site for studying young sub-stellar objects, yet the low-mass members of this region remain largely undiscovered. In this paper we report on a deep photometric survey using a custom 1.45 um filter (W-band), as well as standard J and H near-IR filters, in order to identify candidate low-mass young brown-dwarfs in the Serpens-South region. We constructed a reddening-insensitive index (Q) by combining J, H and W-band photometry for survey objects, in order to identify candidate low-mass members of Serpens based on the strength of the water absorption feature at 1.45 um in the atmospheres of mid-M and later objects. We then conducted spectroscopic follow up to confirm youth and spectral type for our candidates. This is the first survey to identify the very low-mass and coolest members of Serpens-South. We identify 4 low-mass candidate Serpens members, which all display IR excess emission, indicating the likely presence of circumstellar disks around them. One of the four candidate low-mass members in our list, SERP182918-020245, exhibits Pa_beta and Br_gamma emission features, confirming its youth and ongoing magnetospheric accretion. Our new candidate members have spectral types >M4 and are the coolest and lowest mass candidate members yet identified in Serpens-South.

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COol Companions ON Ultrawide orbiTS (COCONUTS). I. A High-Gravity T4 Benchmark around an Old White Dwarf and A Re-Examination of the Surface-Gravity Dependence of the L/T Transition

We present the first discovery from the COol Companions ON Ultrawide orbiTS (COCONUTS) program, a large-scale survey for wide-orbit planetary and substellar companions. We have discovered a co-moving system COCONUTS-1, composed of a hydrogen-dominated white dwarf (PSO J058.9855+45.4184; $d=31.5$ pc) and a T4 companion (PSO J058.9869+45.4296) at a $40.6''$ (1280 au) projected separation. We derive physical properties for COCONUTS-1B from (1) its near-infrared spectrum using cloudless Sonora atmospheric models, and (2) its luminosity and the white dwarf's age ($7.3_{-1.6}^{+2.8}$ Gyr) using Sonora evolutionary models. The two methods give consistent temperatures and radii, but atmospheric models infer a lower surface gravity and therefore an unphysically young age. Assuming evolutionary model parameters ($T_{\rm eff}=1255^{+6}_{-8}$ K, $\log{g}=5.44^{+0.02}_{-0.03}$ dex, $R=0.789^{+0.011}_{-0.005}$ R$_{\rm Jup}$), we find cloudless model atmospheres have brighter Y- and J-band fluxes than the data, suggesting condensate clouds have not fully dispersed around 1300 K. The W2 flux (4.6 $μ$m) of COCONUTS-1B is fainter than models, suggesting non-equilibrium mixing of CO. To investigate the gravity dependence of the L/T transition, we compile all 60 known L6-T6 benchmarks and derive a homogeneous set of temperatures, surface gravities, and masses. As is well-known, young, low-gravity late-L dwarfs have significantly fainter, redder near-infrared photometry and $\approx200-300$ K cooler temperatures than old, high-gravity objects. Our sample now reveals such gravity dependence becomes weaker for T dwarfs, with young objects having comparable near-infrared photometry and $\approx100$ K cooler temperatures compared to old objects. Finally, we find that young objects have a larger amplitude J-band brightening than old objects, and also brighten at H band as they cross the L/T transition.

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3.8um Imaging of 400-600K Brown Dwarfs and Orbital Constraints for WISEP J045853.90+643452.6AB

Half of the energy emitted by late-T- and Y-type brown dwarfs emerges at 3.5 < lambda um < 5.5. We present new L' (3.43 < lambda um < 4.11) photometry obtained at the Gemini North telescope for nine late-T and Y dwarfs, and synthesize L' from spectra for an additional two dwarfs. The targets include two binary systems which were imaged at a resolution of 0.25". One of these, WISEP J045853.90+643452.6AB, shows significant motion, and we present an astrometric analysis of the binary using Hubble Space Telescope, Keck Adaptive Optics, and Gemini images. We compare lambda ~4um observations to models, and find that the model fluxes are too low for brown dwarfs cooler than ~700K. The discrepancy increases with decreasing temperature, and is a factor of ~2 at T_eff=500K and ~4 at T_eff=400K. Warming the upper layers of a model atmosphere generates a spectrum closer to what is observed. The thermal structure of cool brown dwarf atmospheres above the radiative-convective boundary may not be adequately modelled using pure radiative equilibrium; instead heat may be introduced by thermochemical instabilities (previously suggested for the L- to T-type transition) or by breaking gravity waves (previously suggested for the solar system giant planets). One-dimensional models may not capture these atmospheres, which likely have both horizontal and vertical pressure/temperature variations.

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WISE J072003.20-084651.2B Is A Massive T Dwarf

We present individual dynamical masses for the nearby M9.5+T5.5 binary WISE J072003.20$-$084651.2AB, a.k.a. Scholz's star. Combining high-precision CFHT/WIRCam photocenter astrometry and Keck adaptive optics resolved imaging, we measure the first high-quality parallactic distance ($6.80_{-0.06}^{+0.05}$ pc) and orbit ($8.06_{-0.25}^{+0.24}$ yr period) for this system composed of a low-mass star and brown dwarf. We find a moderately eccentric orbit ($e = 0.240_{-0.010}^{+0.009}$), incompatible with previous work based on less data, and dynamical masses of $99\pm6$ $M_{\rm Jup}$ and $66\pm4$ $M_{\rm Jup}$ for the two components. The primary mass is marginally inconsistent (2.1$σ$) with the empirical mass$-$magnitude$-$metallicity relation and models of main-sequence stars. The relatively high mass of the cold ($T_{\rm eff} = 1250\pm40$ K) brown dwarf companion indicates an age older than a few Gyr, in accord with age estimates for the primary star, and is consistent with our recent estimate of $\approx$70 $M_{\rm Jup}$ for the stellar/substellar boundary among the field population. Our improved parallax and proper motion, as well as an orbit-corrected system velocity, improve the accuracy of the system's close encounter with the solar system by an order of magnitude. WISE J0720$-$0846AB passed within $68.7\pm2.0$ kAU of the Sun $80.5\pm0.7$ kyr ago, passing through the outer Oort cloud where comets can have stable orbits.

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ACRONYM III: Radial Velocities for 336 Candidate Young Low-Mass Stars in the Solar Neighborhood, Including 78 Newly Confirmed Young Moving Group Members

Young, low-mass stars in the solar neighborhood are vital for completing the mass function for nearby, young coeval groups, establishing a more complete census for evolutionary studies, and providing targets for direct-imaging exoplanet and/or disk studies. We present properties derived from high-resolution optical spectra for 336 candidate young nearby, low-mass stars. These include measurements of radial velocities and age diagnostics such as H$α$ and Li $λ$6707 equivalent widths. Combining our radial velocities with astrometry from Gaia DR2, we provide full 3D kinematics for the entire sample. We combine the measured spectroscopic youth information with additional age diagnostics (e.g., X-ray and UV fluxes, CMD positions) and kinematics to evaluate potential membership in nearby, young moving groups and associations. We identify 78 objects in our sample as bonafide members of 10 different moving groups, 15 of which are completely new members or have had their group membership reassigned. We also reject 44 previously proposed candidate moving group members. Furthermore, we have newly identified or confirmed the youth of numerous additional stars that do not belong to any currently known group, and find 69 co-moving systems using Gaia DR2 astrometry. We also find evidence that the Carina association is younger than previously thought, with an age similar to the $β$ Pictoris moving group ($\sim$22 Myr).

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The Elusive Majority of Young Moving Groups. I. Young Binaries and Lithium-Rich Stars in the Solar Neighborhood

Young stars in the solar neighborhood serve as nearby probes of stellar evolution and represent promising targets to directly image self-luminous giant planets. We have carried out an all-sky search for late-type ($\approx$K7$-$M5) stars within 100 pc selected primarily on the basis of activity indicators from $GALEX$ and $ROSAT$. Approximately two thousand active and potentially young stars are identified, over 600 of which we have followed up with low-resolution optical spectroscopy and over 1000 with diffraction-limited imaging using Robo-AO at the Palomar 1.5-m telescope. Strong lithium is present in 58 stars, implying ages spanning $\approx$10$-$200 Myr. Most of these lithium-rich stars are new or previously known members of young moving groups including TWA, $β$ Pic, Tuc-Hor, Carina, Columba, Argus, AB Dor, Upper Centaurus Lupus, and Lower Centaurus Crux; the rest appear to be young low-mass stars without connections to established kinematic groups. Over 200 close binaries are identified down to 0.2$''$ $-$ the vast majority of which are new $-$ and will be valuable for dynamical mass measurements of young stars with continued orbit monitoring in the future.

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A Search for Variability in Exoplanet Analogues and Low-Gravity Brown Dwarfs

We report the results of a $J$-band survey for photometric variability in a sample of young, low-gravity objects using the New Technology Telescope (NTT) and the United Kingdom InfraRed Telescope (UKIRT). Surface gravity is a key parameter in the atmospheric properties of brown dwarfs and this is the first large survey that aims to test the gravity dependence of variability properties. We do a full analysis of the spectral signatures of youth and assess the group membership probability of each target using membership tools from the literature. This results in a 30 object sample of young low-gravity brown dwarfs. Since we are lacking in objects with spectral types later than L9, we focus our statistical analysis on the L0-L8.5 objects. We find that the variability occurrence rate of L0-L8.5 low-gravity brown dwarfs in this survey is $30^{+16}_{-8}\%$. We reanalyse the results of Radigan 2014 and find that the field dwarfs with spectral types L0-L8.5 have a variability occurrence rate of $11^{+13}_{-4}\%$. We determine a probability of $98\%$ that the samples are drawn from different distributions. This is the first quantitative indication that the low-gravity objects are more likely to be variable than the field dwarf population. Furthermore, we present follow-up $J_S$ and $K_S$ observations of the young, planetary-mass variable object PSO 318.5-22 over three consecutive nights. We find no evidence of phase shifts between the $J_S$ and $K_S$ bands and find higher $J_S$ amplitudes. We use the $J_S$ lightcurves to measure a rotational period of $8.45\pm0.05~$hr for PSO 318.5-22.

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