arXiv subjects

Fraser Clarke

Publications and source records attributed to Fraser Clarke.

18 recordsLinked to original sources

arXiv2024

HARMONI at ELT: tolerance analysis and expected as-build imaging performance of the infrared spectrograph

HARMONI is the first light visible and near-IR integral field spectrograph for the ELT. It covers a large spectral range from 470nm to 2450nm with resolving powers from 3300 to 18000 and spatial sampling from 60mas to 4mas. It can operate in two Adaptive Optics modes - SCAO (including a High Contrast capability) and LTAO - or with NOAO. The project is preparing for Final Design Reviews. The integral field spectrograph is a key sub-system of HARMONI instrument, which forms the 2D spectral image and projects it onto the scientific detector. It has 40 operational modes with different platescales and gratings covering the band of 811-2450 nm with three resolution grades. In each of this configurations the as-built spectrograph wave-front error is strictly limited. We perform the sensitivity analysis for measurable and unknown errors and build the errors budget on this basis. Then we correct the values for the actual technological limits and perform a three-stage Monte-Carlo analysis combined with simulation of a few specific effect as the holographic grating wavefront error. Eventually, we show that it is possible to reach the target image quality in terms of the wavefront error and spectral resolution for the entire sub-system with practically feasible tolerances on design parameters.

astro-ph.IM↗

arXiv2024

Behind the Mask: can HARMONI@ELT detect biosignatures in the reflected light of Proxima b?

Proxima b is a rocky exoplanet in the habitable zone of the nearest star system and a key test case in the search for extraterrestrial life. Here, we investigate the characterization of a potential Earth-like atmosphere around Proxima b in reflected light via molecule mapping, combining high resolution spectroscopy (HRS) and high contrast imaging, using the first-generation integral field spectrograph HARMONI on the $39$-m Extremely Large Telescope. We simulate comprehensive observations of Proxima b at an assumed $45^{\circ}$ inclination using HARMONI's High Contrast Adaptive Optics mode, with spatial resolution $\sim 8$mas ($3.88$mas/spaxel) and spectral resolving power $R\simeq17,000$ between $1.538$--$1.678 \mu m$, containing the spectral features of water, carbon dioxide and methane. Tellurics, stellar features, and additional noise sources are included, and removed using established molecule mapping techniques. We find that HARMONI's current focal plane mask (FPM) is too large and obscures the orbit of Proxima b and thus explore smaller and offset FPMs to yield a detection. A $\rm{S/N}=5$ detection of Proxima b's reflected light, suitable for atmospheric characterisation, is possible with such modifications, requiring a minimum of $20$ hours, but ideally at least $30$ hours of integration time. We highlight that such detections do not scale with the photon noise, hence suitably detailed simulations of future instruments for the ELTs are needed to fully understand their ability to perform HRS observations of exoplanet atmospheres. Alterations to the HARMONI FPM design are feasible at this stage, but must be considered in context of other science cases.

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arXiv2021

HARMONI: the ELT's First-Light Near-infrared and Visible Integral Field Spectrograph

The High Angular Resolution Monolithic Optical and Near-infrared Integral field spectrograph (HARMONI) is the visible and near-infrared (NIR), adaptive-optics-assisted, integral field spectrograph for ESO's Extremely Large Telescope (ELT). It will have both a single-conjugate adaptive optics (SCAO) mode (using a single bright natural guide star) and a laser tomographic adaptive optics (LTAO) mode (using multiple laser guide stars), providing near diffraction-limited hyper-spectral imaging with high performance and good sky coverage, respectively. A unique high-contrast adaptive optics (HCAO) capability has recently been added for exoplanet characterisation. A large detector complement of eight HAWAII-4RG arrays, four choices of spaxel scale, and 11 grating choices with resolving powers ranging from R~3000 to R~17000 make HARMONI a very versatile instrument that can cater to a wide range of observing programmes.

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arXiv2020

Design of the HARMONI Pyramid WFS module

Current designs for all three extremely large telescopes show the overwhelming adoption of the pyramid wavefront sensor (P-WFS) as the WFS of choice for adaptive optics (AO) systems sensing on natural guide stars (NGS) or extended objects. The key advantages of the P-WFS over the Shack-Hartmann are known and are mainly provided by the improved sensitivity (fainter NGS) and reduced sensitivity to spatial aliasing. However, robustness and tolerances of the P-WFS for the ELTs are not currently well understood. In this paper, we present simulation results for the single-conjugate AO mode of HARMONI, a visible and near-infrared integral field spectrograph for the European Extremely Large Telescope. We first explore the wavefront sensing issues related to the telescope itself; namely the island effect (i.e. differential piston) and M1 segments phasing errors. We present mitigation strategies to the island effect and their performance. We then focus on some performance optimisation aspects of the AO design to explore the impact of the RTC latency and the optical gain issues, which will in particular affect the high-contrast mode of HARMONI. Finally, we investigate the influence of the quality of glass pyramid prism itself, and of optical aberrations on the final AO performance. By relaxing the tolerances on the fabrication of the prism, we are able to reduce hardware costs and simplify integration. We show the importance of calibration (i.e. updating the control matrix) to capture any displacement of the telescope pupil and rotation of the support structure for M4. We also show the importance of the number of pixels used for wavefront sensing to relax tolerances of the pyramid prism. Finally, we present a detailed optical design of the pyramid prism, central element of the P-WFS.

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arXiv2018

Sensing and control of segmented mirrors with a pyramid wavefront sensor in the presence of spiders

The segmentation of the telescope pupil (by spiders & the segmented M4) create areas of phase isolated by the width of the spiders on the wavefront sensor (WFS), breaking the spatial continuity of the wavefront. The poor sensitivity of the Pyramid WFS (PWFS) to differential piston leads to badly seen and therefore uncontrollable differential pistons. In close loop operation, differential pistons between segments will settle around integer values of the average sensing wavelength. The differential pistons typically range from one to ten times the sensing wavelength and vary rapidly over time, leading to extremely poor performance. In addition, aberrations created by atmospheric turbulence will contain large amounts of differential piston between the segments. Removing piston contribution over each of the DM segments leads to poor performance. In an attempt to reduce the impact of unwanted differential pistons that are injected by the AO correction, we compare three different approaches. We first limit ourselves to only use the information measured by the PWFS, in particular by reducing the modulation. We show that using this information sensibly is important but will not be sufficient. We discuss possible ways of improvement by using prior information. A second approach is based on phase closure of the DM commands and assumes the continuity of the correction wavefront over the entire unsegmented pupil. The last approach is based on the pair-wise slaving of edge actuators and shows the best results. We compare the performance of these methods using realistic end-to-end simulations. We find that pair-wise slaving leads to a small increase of the total wavefront error, only adding between 20-45 nm RMS in quadrature for seeing conditions between 0.45-0.85 arcsec. Finally, we discuss the possibility of combining the different proposed solutions to increase robustness.

astro-ph.IM↗

arXiv2018

ELT HARMONI: Image Slicer Preliminary Design

Harmoni is the ELT's first light visible and near-infrared integral field spectrograph. It will provide four different spatial scales, ranging from coarse spaxels of 60 x 30 mas best suited for seeing limited observations, to 4 mas spaxels that Nyquist sample the diffraction limited point spread function of the ELT at near-infrared wavelengths. Each spaxel scale may be combined with eleven spectral settings, that provide a range of spectral resolving powers from R 3500 to R 20000 and instantaneous wavelength coverage spanning the 0.47 - 2.45 μm wavelength range of the instrument. The consortium consists of several institutes in Europe under leadership of Oxford University. Harmoni is starting its Final Design Phase after a Preliminary Design Phase in November, 2017. The CRAL has the responsibility of the Integral Field Unit design linking the Preoptics to the 4 Spectrographs. It is composed of a field splitter associated with a relay system and an image slicer that create from a rectangular Field of View a very long (540mm) output slit for each spectrograph. In this paper, the preliminary design and performances of Harmoni Image Slicer will be presented including image quality, pupil distortion and slit geometry. It has been designed by CRAL for Harmoni PDR in November, 2017. Special emphases will be put on straylight analysis and slice diffraction. The optimisation of the manufacturing and slit geometry will also be reported.

astro-ph.IM↗

arXiv2018

Opto-mechanical designs for the HARMONI Adaptive Optics systems

HARMONI is a visible and near-infrared integral field spectrograph equipped with two complementary adaptive optics systems, fully integrated within the instrument. A Single Conjugate AO (SCAO) system offers high performance for a limited sky coverage and a Laser Tomographic AO (LTAO) system provides AO correction with a very high sky-coverage. While the deformable mirror performing real-time correction of the atmospheric disturbances is located within the telescope itself, the instrument contains a suite of state-of-the-art and innovative wavefront sensor systems. Laser guide star sensors (LGSS) are located at the entrance of the instrument and fed by a dichroic beam splitter, while the various natural guide star sensors for LTAO and SCAO are located close to the science focal plane. We present opto-mechanical architecture and design at PDR level for these wavefront sensor systems.

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arXiv2014

Wavefront sensing from the image domain with the Oxford-SWIFT integral field spectrograph

The limits for adaptive-optics (AO) imaging at high contrast and high resolution are determined by residual phase errors from non-common-path aberrations not sensed by the wavefront sensor, especially for integral field spectrographs, where phase diversity techniques are complicated by the image slicer. We present the first application of kernel phase-based wavefront sensing to ground-based AO, where an asymmetric pupil mask and a single image are sufficient to map aberrations up to high order. We push toward internally diffraction-limited performance with the Oxford-SWIFT integral field spectrograph coupled with the PALM-3000 extreme AO system on the Palomar 200-inch telescope. This represents the first observation in which the PALM-3000 + SWIFT internal point-spread-function has closely approached the Airy pattern. While this can only be used on SWIFT with an internal stimulus source, as at short wavelengths the uncorrected atmospheric wavefront errors are still > 1 radian, this nevertheless demonstrates the feasibility of detecting non-common-path errors with this method as an active optics paradigm for near-infrared, AO-corrected instruments at Palomar. We note that this is a particularly promising approach for correcting integral field spectrographs, as the diversity of many narrowband images provides strong constraints on the wavefront error estimate, and the average of reconstructions from many narrow bands can be used to improve overall reconstruction quality.

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arXiv2013

The mass-metallicity relation at z~1.4 revealed with Subaru/FMOS

We present a stellar mass-metallicity relation at z~1.4 with an unprecedentedly large sample of ~340 star-forming galaxies obtained with FMOS on the Subaru Telescope. We observed K-band selected galaxies at 1.2 < z_{ph} < 1.6 in the SXDS/UDS fields with M_{*} > 10^{9.5} M_{\sun}, and expected F(Hα) > 5 \times 10^{-17} erg s^{-1} cm^{-2}. Among the observed ~1200 targets, 343 objects show significant Hαemission lines. The gas-phase metallicity is obtained from [NII]λ6584/Hαline ratio, after excluding possible active galactic nuclei (AGNs). Due to the faintness of the [NII]λ6584 lines, we apply the stacking analysis and derive the mass-metallicity relation at z~1.4. Our results are compared to past results at different redshifts in the literature. The mass-metallicity relation at z~1.4 is located between those at z~0.8 and z~2.2; it is found that the metallicity increases with decreasing redshift from z~3 to z~0 at fixed stellar mass. Thanks to the large size of the sample, we can study the dependence of the mass-metallicity relation on various galaxy physical properties. The average metallicity from the stacked spectra is close to the local FMR in the higher metallicity part but >0.1 dex higher in metallicity than the FMR in the lower metallicity part. We find that galaxies with larger E(B-V), B-R, and R-H colours tend to show higher metallicity by ~0.05 dex at fixed stellar mass. We also find relatively clearer size dependence that objects with smaller half light radius tend to show higher metallicity by ~0.1 dex at fixed stellar mass, especially in the low mass part.

astro-ph.CO↗

arXiv2013

The Gemini NICI Planet-Finding Campaign: The Frequency of Planets around Young Moving Group Stars

We report results of a direct imaging survey for giant planets around 80 members of the Beta Pic, TW Hya, Tucana-Horologium, AB Dor, and Hercules-Lyra moving groups, observed as part of the Gemini NICI Planet-Finding Campaign. For this sample, we obtained median contrasts of ΔH=13.9 mag at 1" in combined CH4 narrowband ADI+SDI mode and median contrasts of ΔH=15.1 mag at 2" in H-band ADI mode. We found numerous (>70) candidate companions in our survey images. Some of these candidates were rejected as common-proper motion companions using archival data; we reobserved with NICI all other candidates that lay within 400 AU of the star and were not in dense stellar fields. The vast majority of candidate companions were confirmed as background objects from archival observations and/or dedicated NICI campaign followup. Four co-moving companions of brown dwarf or stellar mass were discovered in this moving group sample: PZ Tel B (36+-6 MJup, 16.4+-1.0 AU, Biller et al. 2010), CD -35 2722B (31+-8 MJup, 67+-4 AU, Wahhaj et al. 2011), HD 12894B (0.46+-0.08 MSun, 15.7+-1.0 AU), and BD+07 1919C (0.20+-0.03 MSun, 12.5+-1.4 AU). From a Bayesian analysis of the achieved H band ADI and ASDI contrasts, using power-law models of planet distributions and hot-start evolutionary models, we restrict the frequency of 1--20 MJup companions at semi-major axes from 10--150 AU to <18% at a 95.4% confidence level using DUSTY models and to <6% at a 95.4% using COND models.

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arXiv2013

The Gemini NICI Planet-Finding Campaign: The Frequency of Giant Planets around Young B and A Stars

We have carried out high contrast imaging of 70 young, nearby B and A stars to search for brown dwarf and planetary companions as part of the Gemini NICI Planet-Finding Campaign. Our survey represents the largest, deepest survey for planets around high-mass stars (~1.5-2.5 M_sun) conducted to date and includes the planet hosts beta Pic and Fomalhaut. We obtained follow-up astrometry of all candidate companions within 400 AU projected separation for stars in uncrowded fields and identified new low-mass companions to HD 1160 and HIP 79797. We have found that the previously known young brown dwarf companion to HIP 79797 is itself a tight (3 AU) binary, composed of brown dwarfs with masses 58 (+21, -20) M_Jup and 55 (+20, -19) M_Jup, making this system one of the rare substellar binaries in orbit around a star. Considering the contrast limits of our NICI data and the fact that we did not detect any planets, we use high-fidelity Monte Carlo simulations to show that fewer than 20% of 2 M_sun stars can have giant planets greater than 4 M_Jup between 59 and 460 AU at 95% confidence, and fewer than 10% of these stars can have a planet more massive than 10 M_Jup between 38 and 650 AU. Overall, we find that large-separation giant planets are not common around B and A stars: fewer than 10% of B and A stars can have an analog to the HR 8799 b (7 M_Jup, 68 AU) planet at 95% confidence. We also describe a new Bayesian technique for determining the ages of field B and A stars from photometry and theoretical isochrones. Our method produces more plausible ages for high-mass stars than previous age-dating techniques, which tend to underestimate stellar ages and their uncertainties.

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arXiv2012

The Gemini NICI Planet-Finding Campaign: Discovery of a Multiple System Orbiting the Young A Star HD 1160

We report the discovery by the Gemini NICI Planet-Finding Campaign of two low-mass companions to the young A0V star HD 1160 at projected separations of 81 +/- 5 AU (HD 1160 B) and 533 +/- 25 AU (HD 1160 C). VLT images of the system taken over a decade for the purpose of using HD 1160 A as a photometric calibrator confirm that both companions are physically associated. By comparing the system to members of young moving groups and open clusters with well-established ages, we estimate an age of 50 (+50,-40) Myr for HD 1160 ABC. While the UVW motion of the system does not match any known moving group, the small magnitude of the space velocity is consistent with youth. Near-IR spectroscopy shows HD 1160 C to be an M3.5 +/- 0.5 star with an estimated mass of 0.22 (+0.03,-0.04) M_Sun, while NIR photometry of HD 1160 B suggests a brown dwarf with a mass of 33 (+12,-9) M_Jup. The very small mass ratio (0.014) between the A and B components of the system is rare for A star binaries, and would represent a planetary-mass companion were HD 1160 A to be slightly less massive than the Sun.

astro-ph.SR↗

arXiv2011

NIR Spectroscopy of Star-Forming Galaxies at z~1.4 with Subaru/FMOS: The Mass-Metallicity Relation

We present near-infrared spectroscopic observations of star-forming galaxies at z~1.4 with FMOS on the Subaru Telescope. We observed K-band selected galaxies in the SXDS/UDS fields with K<23.9 mag, 1.2 10^{9.5} Msun, and expected F(Halpha)>10^{-16} erg s^{-1} cm^{-2}. 71 objects in the sample have significant detections of Halpha. For these objects, excluding possible AGNs identified from the BPT diagram, gas-phase metallicities are obtained from [NII]/Halpha line ratio. The sample is split into three stellar mass bins, and the spectra are stacked in each stellar mass bin. The mass-metallicity relation obtained at z~1.4 is located between those at z~0.8 and z~2.2. We constrain an intrinsic scatter to be ~0.1 dex or larger in the mass-metallicity relation at z~1.4; the scatter may be larger at higher redshifts. We found trends that the deviation from the mass-metallicity relation depends on the SFR and the half light radius: Galaxies with higher SFR and larger half light radii show lower metallicities at a given stellar mass. One possible scenario for the trends is the infall of pristine gas accreted from IGM or through merger events. Our data points show larger scatter than the fundamental metallicity relation (FMR) at z~0.1 and the average metallicities slightly deviate from the FMR. The compilation of the mass-metallicity relations at z~3 to z~0.1 shows that they evolve smoothly from z~3 to z~0 without changing the shape so much except for the massive part at z~0.

astro-ph.CO↗

arXiv2011

SWIFT Observations of the Arp 147 Ring galaxy system

We present observations of Arp 147, a galaxy system comprising a collisionally-created ring galaxy and an early-type galaxy, using the Oxford SWIFT integral field spectrograph (IFS) at the 200-inch Hale telescope. We derive spatially resolved kinematics from the IFS data and use these to study the interaction between the two galaxies. We find the edge-to-edge expansion velocity of the ring is 225 +/- 8 km/s, implying an upper limit on the timescale for the collision of 50 Myrs. We also calculate that the angle of impact for the collision is between 33 degrees-54 degrees, where 0 degrees would imply a perpendicular collision. The ring galaxy is strongly star-forming with the star formation likely to have been triggered by the collision between the two galaxies. We measure some key physical parameters in an integrated and spatially resolved manner for the ring galaxy. Using observed B-I colours and the H-alpha equivalent widths, we conclude that two stellar components (a young and an old population) are required to simultaneously match both observed quantities. We constrain the age range, light and mass fractions of the young star formation in the ring, finding a modest age range, a light fraction of less than a third, and a negligible (<1%) mass fraction. We postulate that the redder colours observed in the SE corner of the ring galaxy could correspond to the nuclear bulge of the original disk galaxy from which the ring was created, consistent with the stellar mass in the SE quadrant being 30-50% of the total. The ring appears to have been a typical disk galaxy prior to the encounter. The ring shows electron densities consistent with typical values for star-forming HII regions. The eastern half of the ring exhibits a metallicity a factor of ~2 higher than the western half. The ionisation parameter, measured across the ring, roughly follows the previously observed trend with metallicity.

astro-ph.GA↗

arXiv2011

The Gemini NICI Planet-Finding Campaign : Discovery of a Substellar L Dwarf Companion to the Nearby Young M Dwarf CD-35 2722

We present the discovery of a wide (67 AU) substellar companion to the nearby (21 pc) young solar-metallicity M1 dwarf CD-35 2722, a member of the ~100 Myr AB Doradus association. Two epochs of astrometry from the NICI Planet-Finding Campaign confirm that CD-35 2722 B is physically associated with the primary star. Near-IR spectra indicate a spectral type of L4\pm1 with a moderately low surface gravity, making it one of the coolest young companions found to date. The absorption lines and near-IR continuum shape of CD-35 2722 B agree especially well the dusty field L4.5 dwarf 2MASS J22244381-0158521, while the near-IR colors and absolute magnitudes match those of the 5 Myr old L4 planetary-mass companion, 1RXS J160929.1-210524 b. Overall, CD-35 2722 B appears to be an intermediate-age benchmark for L-dwarfs, with a less peaked H-band continuum than the youngest objects and near-IR absorption lines comparable to field objects. We fit Ames-Dusty model atmospheres to the near-IR spectra and find T=1700-1900 K and log(g) =4.5\pm0.5. The spectra also show that the radial velocities of components A and B agree to within \pm10 km/s, further confirming their physical association. Using the age and bolometric luminosity of CD-35 2722 B, we derive a mass of 31\pm8 Mjup from the Lyon/Dusty evolutionary models. Altogether, young late-M to mid-L type companions appear to be over-luminous for their near-IR spectral type compared to field objects, in contrast to the under-luminosity of young late-L and early-T dwarfs.

astro-ph.SR↗

arXiv2010

The Gemini NICI Planet-Finding Campaign

Our team is carrying out a multi-year observing program to directly image and characterize young extrasolar planets using the Near-Infrared Coronagraphic Imager (NICI) on the Gemini-South 8.1-meter telescope. NICI is the first instrument on a large telescope designed from the outset for high-contrast imaging, comprising a high-performance curvature adaptive optics system with a simultaneous dual-channel coronagraphic imager. Combined with state-of-the-art observing methods and data processing, NICI typically achieves ~2 magnitudes better contrast compared to previous ground-based or space-based programs, at separations inside of ~2 arcsec. In preparation for the Campaign, we carried out efforts to identify previously unrecognized young stars, to rigorously construct our observing strategy, and to optimize the combination of angular and spectral differential imaging. The Planet-Finding Campaign is in its second year, with first-epoch imaging of 174 stars already obtained out of a total sample of 300 stars. We describe the Campaign's goals, design, implementation, performance, and preliminary results. The NICI Campaign represents the largest and most sensitive imaging survey to date for massive (~1 Mjup) planets around other stars. Upon completion, the Campaign will establish the best measurements to date on the properties of young gas-giant planets at ~5-10 AU separations. Finally, Campaign discoveries will be well-suited to long-term orbital monitoring and detailed spectrophotometric followup with next-generation planet-finding instruments.

astro-ph.SR↗

arXiv2010

The Gemini NICI Planet-Finding Campaign: Discovery of a Close Substellar Companion to the Young Debris Disk Star PZ Tel

We report the discovery of a tight substellar companion to the young solar analog PZ Tel, a member of the Beta Pictoris moving group observed with high contrast adaptive optics imaging as part of the Gemini NICI Planet-Finding Campaign. The companion was detected at a projected separation of 16.4 +/- 1.0 AU (0.33 +/- 0.01") in April 2009. Second-epoch observations in May 2010 demonstrate that the companion is physically associated and shows significant orbital motion. Monte Carlo modeling constrains the orbit of PZ Tel B to eccentricities > 0.6. The near-IR colors of PZ Tel B indicate a spectral type of M7+/-2 and thus this object will be a new benchmark companion for studies of ultracool, low-gravity photospheres. Adopting an age of 12 +8 -4 Myr for the system, we estimate a mass of 36 +/- 6 Mjup based on the Lyon/DUSTY evolutionary models. PZ Tel B is one of few young substellar companions directly imaged at orbital separations similar to those of giant planets in our own solar system. Additionally, the primary star PZ Tel A shows a 70 um emission excess, evidence for a significant quantity of circumstellar dust that has not been disrupted by the orbital motion of the companion.

astro-ph.SR↗

arXiv2007

New Photometry and Spectra of AB Doradus C: An Accurate Mass Determination of a Young Low-Mass Object with Theoretical Evolutionary Tracks

We present new photometric and spectroscopic measurements for the unique, young, low-mass evolutionary track calibrator AB Dor C. While the new Ks photometry is similar to that previously published in Close et al. (2005) the spectral type is found to be earlier. Based on new H & K IFS spectra of AB Dor C (Thatte et al. 2007; paper 1) we adopt a spectral type of M5.5+/-1.0 for AB Dor C. This is considerably earlier than the M8+/-1 estimated in Close et al. (2005) and Nielsen et al. (2005) yet is consistent with the M6+/-1 independently derived by Luhman & Potter (2005). However, the spectrum presented in paper 1 and analyzed here is a significant improvement over any previous spectrum of AB Dor C. We also present new astrometry for the system which further supports a 0.090+/-0.005 Msun mass for the system. Once armed with an accurate spectrum and Ks flux we find L=0.0021+/-0.0005 Lsun and Teff=2925{+170}{-145}K for AB Dor C. These values are consistent with a ~75 Myr 0.090+/-0.005 Msun object like AB Dor C according to the DUSTY evolutionary tracks (Chabrier et al. 2000). Hence masses can be estimated from the HR diagram with the DUSTY tracks for young low-mass objects like AB Dor C. However, we cautiously note that underestimates of the mass from the tracks can occur if one lacks a proper (continuum preserved) spectra or is relying on NIR fluxes alone.

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