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Schuyler Wolff

Publications and source records attributed to Schuyler Wolff.

At least 37 records · Page 2Linked to original sources

First Resolved Scattered-Light Images of Four Debris Disks in Scorpius-Centaurus with the Gemini Planet Imager

We present the first spatially resolved scattered-light images of four debris disks around members of the Scorpius-Centaurus (Sco-Cen) OB Association with high-contrast imaging and polarimetry using the Gemini Planet Imager (GPI). All four disks are resolved for the first time in polarized light and one disk is also detected in total intensity. The three disks imaged around HD 111161, HD 143675, and HD 145560 are symmetric in both morphology and brightness distribution. The three systems span a range of inclinations and radial extents. The disk imaged around HD 98363 shows indications of asymmetries in morphology and brightness distribution, with some structural similarities to the HD 106906 planet-disk system. Uniquely, HD 98363 has a wide co-moving stellar companion Wray 15-788 with a recently resolved disk with very different morphological properties. HD 98363 A/B is the first binary debris disk system with two spatially resolved disks. All four targets have been observed with ALMA, and their continuum fluxes range from one non-detection to one of the brightest disks in the region. With the new results, a total of 15 A/F-stars in Sco-Cen have resolved scattered light debris disks, and approximately half of these systems exhibit some form of asymmetry. Combining the GPI disk structure results with information from the literature on millimeter fluxes and imaged planets reveals a diversity of disk properties in this young population. Overall, the four newly resolved disks contribute to the census of disk structures measured around A/F-stars at this important stage in the development of planetary systems.

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An updated visual orbit of the directly-imaged exoplanet 51 Eridani b and prospects for a dynamical mass measurement with Gaia

We present a revision to the visual orbit of the young, directly-imaged exoplanet 51 Eridani b using four years of observations with the Gemini Planet Imager. The relative astrometry is consistent with an eccentric ($e=0.53_{-0.13}^{+0.09}$) orbit at an intermediate inclination ($i=136_{-11}^{+10}$\,deg), although circular orbits cannot be excluded due to the complex shape of the multidimensional posterior distribution. We find a semi-major axis of $11.1_{-1.3}^{+4.2}$\,au and a period of $28.1_{-4.9}^{+17.2}$\,yr, assuming a mass of 1.75\,M$_{\odot}$ for the host star. We find consistent values with a recent analysis of VLT/SPHERE data covering a similar baseline. We investigated the potential of using absolute astrometry of the host star to obtain a dynamical mass constraint for the planet. The astrometric acceleration of 51~Eri derived from a comparison of the {\it Hipparcos} and {\it Gaia} catalogues was found to be inconsistent at the 2--3$σ$ level with the predicted reflex motion induced by the orbiting planet. Potential sources of this inconsistency include a combination of random and systematic errors between the two astrometric catalogs or the signature of an additional companion within the system interior to current detection limits. We also explored the potential of using {\it Gaia} astrometry alone for a dynamical mass measurement of the planet by simulating {\it Gaia} measurements of the motion of the photocenter of the system over the course of the extended eight-year mission. We find that such a measurement is only possible ($>98$\% probability) given the most optimistic predictions for the {\it Gaia} scan astrometric uncertainties for bright stars, and a high mass for the planet ($\gtrsim3.6$\,M$_{\rm Jup}$).

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Detection of a low-mass stellar companion to the accelerating A2IV star HR 1645

The $\sim500$\, Myr A2IV star HR 1645 has one of the most significant low-amplitude accelerations of nearby early-type stars measured from a comparison of the {\it Hipparcos} and {\it Gaia} astrometric catalogues. This signal is consistent with either a stellar companion with a moderate mass ratio ($q\sim0.5$) on a short period ($P<1$\,yr), or a substellar companion at a separation wide enough to be resolved with ground-based high contrast imaging instruments; long-period equal mass ratio stellar companions that are also consistent with the measured acceleration are excluded with previous imaging observations. The small but significant amplitude of the acceleration made HR 1645 a promising candidate for targeted searches for brown dwarf and planetary-mass companions around nearby, young stars. In this paper we explore the origin of the astrometric acceleration by modelling the signal induced by a wide-orbit M8 companion discovered with the Gemini Planet Imager, as well as the effects of an inner short-period spectroscopic companion discovered a century ago but not since followed-up. We present the first constraints on the orbit of the inner companion, and demonstrate that it is a plausible cause of the astrometric acceleration. This result demonstrates the importance of vetting of targets with measured astrometric acceleration for short-period stellar companions prior to conducting targeted direct imaging surveys for wide-orbit substellar companions.

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An Exo-Kuiper Belt and An Extended Halo around HD 191089 in Scattered Light

We have obtained Hubble Space Telescope STIS and NICMOS, and Gemini/GPI scattered light images of the HD 191089 debris disk. We identify two spatial components: a ring resembling Kuiper Belt in radial extent (FWHM: ${\sim}$25 au, centered at ${\sim}$46 au), and a halo extending to ${\sim}$640 au. We find that the halo is significantly bluer than the ring, consistent with the scenario that the ring serves as the "birth ring" for the smaller dust in the halo. We measure the scattering phase functions in the 30°-150° scattering angle range and find the halo dust is both more forward- and backward-scattering than the ring dust. We measure a surface density power law index of -0.68${\pm}$0.04 for the halo, which indicates the slow-down of the radial outward motion of the dust. Using radiative transfer modeling, we attempt to simultaneously reproduce the (visible) total and (near-infrared) polarized intensity images of the birth ring. Our modeling leads to mutually inconsistent results, indicating that more complex models, such as the inclusion of more realistic aggregate particles, are needed.

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Performance of the Gemini Planet Imager Non-Redundant Mask and spectroscopy of two close-separation binaries HR 2690 and HD 142527

The Gemini Planet Imager (GPI) contains a 10-hole non-redundant mask (NRM), enabling interferometric resolution in complement to its coronagraphic capabilities. The NRM operates both in spectroscopic (integral field spectrograph, henceforth IFS) and polarimetric configurations. NRM observations were taken between 2013 and 2016 to characterize its performance. Most observations were taken in spectroscopic mode with the goal of obtaining precise astrometry and spectroscopy of faint companions to bright stars. We find a clear correlation between residual wavefront error measured by the AO system and the contrast sensitivity by comparing phase errors in observations of the same source, taken on different dates. We find a typical 5-$σ$ contrast sensitivity of $2-3~\times~10^{-3}$ at $\simλ/D$. We explore the accuracy of spectral extraction of secondary components of binary systems by recovering the signal from a simulated source injected into several datasets. We outline data reduction procedures unique to GPI's IFS and describe a newly public data pipeline used for the presented analyses. We demonstrate recovery of astrometry and spectroscopy of two known companions to HR 2690 and HD 142527. NRM+polarimetry observations achieve differential visibility precision of $σ\sim0.4\%$ in the best case. We discuss its limitations on Gemini-S/GPI for resolving inner regions of protoplanetary disks and prospects for future upgrades. We summarize lessons learned in observing with NRM in spectroscopic and polarimetric modes.

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The Gemini Planet Imager Exoplanet Survey: Giant Planet and Brown Dwarf Demographics From 10-100 AU

We present a statistical analysis of the first 300 stars observed by the Gemini Planet Imager Exoplanet Survey (GPIES). This subsample includes six detected planets and three brown dwarfs; from these detections and our contrast curves we infer the underlying distributions of substellar companions with respect to their mass, semi-major axis, and host stellar mass. We uncover a strong correlation between planet occurrence rate and host star mass, with stars M $>$ 1.5 $M_\odot$ more likely to host planets with masses between 2-13 M$_{\rm Jup}$ and semi-major axes of 3-100 au at 99.92% confidence. We fit a double power-law model in planet mass (m) and semi-major axis (a) for planet populations around high-mass stars (M $>$ 1.5M$_\odot$) of the form $\frac{d^2 N}{dm da} \propto m^αa^β$, finding $α$ = -2.4 $\pm$ 0.8 and $β$ = -2.0 $\pm$ 0.5, and an integrated occurrence rate of $9^{+5}_{-4}$% between 5-13 M$_{\rm Jup}$ and 10-100 au. A significantly lower occurrence rate is obtained for brown dwarfs around all stars, with 0.8$^{+0.8}_{-0.5}$% of stars hosting a brown dwarf companion between 13-80 M$_{\rm Jup}$ and 10-100 au. Brown dwarfs also appear to be distributed differently in mass and semi-major axis compared to giant planets; whereas giant planets follow a bottom-heavy mass distribution and favor smaller semi-major axes, brown dwarfs exhibit just the opposite behaviors. Comparing to studies of short-period giant planets from the RV method, our results are consistent with a peak in occurrence of giant planets between ~1-10 au. We discuss how these trends, including the preference of giant planets for high-mass host stars, point to formation of giant planets by core/pebble accretion, and formation of brown dwarfs by gravitational instability.

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Dynamical Constraints on the HR 8799 Planets with GPI

The HR 8799 system uniquely harbors four young super-Jupiters whose orbits can provide insights into the system's dynamical history and constrain the masses of the planets themselves. Using the Gemini Planet Imager (GPI), we obtained down to one milliarcsecond precision on the astrometry of these planets. We assessed four-planet orbit models with different levels of constraints and found that assuming the planets are near 1:2:4:8 period commensurabilities, or are coplanar, does not worsen the fit. We added the prior that the planets must have been stable for the age of the system (40 Myr) by running orbit configurations from our posteriors through $N$-body simulations and varying the masses of the planets. We found that only assuming the planets are both coplanar and near 1:2:4:8 period commensurabilities produces dynamically stable orbits in large quantities. Our posterior of stable coplanar orbits tightly constrains the planets' orbits, and we discuss implications for the outermost planet b shaping the debris disk. A four-planet resonance lock is not necessary for stability up to now. However, planet pairs d and e, and c and d, are each likely locked in two-body resonances for stability if their component masses are above $6~M_{\rm{Jup}}$ and $7~M_{\rm{Jup}}$, respectively. Combining the dynamical and luminosity constraints on the masses using hot-start evolutionary models and a system age of $42 \pm 5$~Myr, we found the mass of planet b to be $5.8 \pm 0.5~M_{\rm{Jup}}$, and the masses of planets c, d, and e to be $7.2_{-0.7}^{+0.6}~M_{\rm{Jup}}$ each.

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Direct Imaging of the HD 35841 Debris Disk: A Polarized Dust Ring from Gemini Planet Imager and an Outer Halo from HST/STIS

We present new high resolution imaging of a light-scattering dust ring and halo around the young star HD 35841. Using spectroscopic and polarimetric data from the Gemini Planet Imager in H-band (1.6 microns), we detect the highly inclined (i=85 deg) ring of debris down to a projected separation of ~12 au (~0.12") for the first time. Optical imaging from HST/STIS shows a smooth dust halo extending outward from the ring to >140 au (>1.4"). We measure the ring's scattering phase function and polarization fraction over scattering angles of 22-125 deg, showing a preference for forward scattering and a polarization fraction that peaks at ~30% near the ansae. Modeling of the scattered-light disk indicates that the ring spans radii of ~60-220 au, has a vertical thickness similar to that of other resolved dust rings, and contains grains as small as 1.5 microns in diameter. These models also suggest the grains have a low porosity, are more likely to consist of carbon than astrosilicates, and contain significant water ice. The halo has a surface brightness profile consistent with that expected from grains pushed by radiation pressure from the main ring onto highly eccentric but still bound orbits. We also briefly investigate arrangements of a possible inner disk component implied by our spectral energy distribution models, and speculate about the limitations of Mie theory for doing detailed analyses of debris disk dust populations.

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GPI spectra of HR 8799 c, d, and e from 1.5 to 2.4$μ$m with KLIP Forward Modeling

We explore KLIP forward modeling spectral extraction on Gemini Planet Imager coronagraphic data of HR 8799, using PyKLIP and show algorithm stability with varying KLIP parameters. We report new and re-reduced spectrophotometry of HR 8799 c, d, and e in H & K bands. We discuss a strategy for choosing optimal KLIP PSF subtraction parameters by injecting simulated sources and recovering them over a range of parameters. The K1/K2 spectra for HR 8799 c and d are similar to previously published results from the same dataset. We also present a K band spectrum of HR 8799 e for the first time and show that our H-band spectra agree well with previously published spectra from the VLT/SPHERE instrument. We show that HR 8799 c and d show significant differences in their H & K spectra, but do not find any conclusive differences between d and e or c and e, likely due to large error bars in the recovered spectrum of e. Compared to M, L, and T-type field brown dwarfs, all three planets are most consistent with mid and late L spectral types. All objects are consistent with low gravity but a lack of standard spectra for low gravity limit the ability to fit the best spectral type. We discuss how dedicated modeling efforts can better fit HR 8799 planets' near-IR flux and discuss how differences between the properties of these planets can be further explored.

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GPI Spectroscopy of the Mass, Age, and Metallicity Benchmark Brown Dwarf HD 4747 B

The physical properties of brown dwarf companions found to orbit nearby, solar-type stars can be benchmarked against independent measures of their mass, age, chemical composition, and other parameters, offering insights into the evolution of substellar objects. The TRENDS high-contrast imaging survey has recently discovered a (mass/age/metallicity) benchmark brown dwarf orbiting the nearby (d=18.69+/-0.19 pc), G8V/K0V star HD 4747. We have acquired follow-up spectroscopic measurements of HD 4747 B using the Gemini Planet Imager to study its spectral type, effective temperature, surface gravity, and cloud properties. Observations obtained in the H-band and K1-band recover the companion and reveal that it is near the L/T transition (T1+/-2). Fitting atmospheric models to the companion spectrum, we find strong evidence for the presence of clouds. However, spectral models cannot satisfactorily fit the complete data set: while the shape of the spectrum can be well-matched in individual filters, a joint fit across the full passband results in discrepancies that are a consequence of the inherent color of the brown dwarf. We also find a $2σ$ tension in the companion mass, age, and surface gravity when comparing to evolutionary models. These results highlight the importance of using benchmark objects to study "secondary effects" such as metallicity, non-equilibrium chemistry, cloud parameters, electron conduction, non-adiabatic cooling, and other subtleties affecting emergent spectra. As a new L/T transition benchmark, HD 4747 B warrants further investigation into the modeling of cloud physics using higher resolution spectroscopy across a broader range of wavelengths, polarimetric observations, and continued Doppler radial velocity and astrometric monitoring.

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Automated data processing architecture for the Gemini Planet Imager Exoplanet Survey

The Gemini Planet Imager Exoplanet Survey (GPIES) is a multi-year direct imaging survey of 600 stars to discover and characterize young Jovian exoplanets and their environments. We have developed an automated data architecture to process and index all data related to the survey uniformly. An automated and flexible data processing framework, which we term the Data Cruncher, combines multiple data reduction pipelines together to process all spectroscopic, polarimetric, and calibration data taken with GPIES. With no human intervention, fully reduced and calibrated data products are available less than an hour after the data are taken to expedite follow-up on potential objects of interest. The Data Cruncher can run on a supercomputer to reprocess all GPIES data in a single day as improvements are made to our data reduction pipelines. A backend MySQL database indexes all files, which are synced to the cloud, and a front-end web server allows for easy browsing of all files associated with GPIES. To help observers, quicklook displays show reduced data as they are processed in real-time, and chatbots on Slack post observing information as well as reduced data products. Together, the GPIES automated data processing architecture reduces our workload, provides real-time data reduction, optimizes our observing strategy, and maintains a homogeneously reduced dataset to study planet occurrence and instrument performance.

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Evidence that the Directly-Imaged Planet HD 131399 Ab is a Background Star

We present evidence that the recently discovered, directly-imaged planet HD 131399 Ab is a background star with non-zero proper motion. From new JHK1L' photometry and spectroscopy obtained with the Gemini Planet Imager, VLT/SPHERE, and Keck/NIRC2, and a reanalysis of the discovery data obtained with VLT/SPHERE, we derive colors, spectra, and astrometry for HD 131399 Ab. The broader wavelength coverage and higher data quality allow us to re-investigate its status. Its near-infrared spectral energy distribution excludes spectral types later than L0 and is consistent with a K or M dwarf, which are the most likely candidates for a background object in this direction at the apparent magnitude observed. If it were a physically associated object, the projected velocity of HD 131399 Ab would exceed escape velocity given the mass and distance to HD 131399 A. We show that HD 131399 Ab is also not following the expected track for a stationary background star at infinite distance. Solving for the proper motion and parallax required to explain the relative motion of HD 131399 Ab, we find a proper motion of 12.3 mas/yr. When compared to predicted background objects drawn from a galactic model, we find this proper motion to be high, but consistent with the top 4% fastest-moving background stars. From our analysis we conclude that HD 131399 Ab is a background K or M dwarf.

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Type Ia Supernova Distances at z > 1.5 from the Hubble Space Telescope Multi-Cycle Treasury Programs: The Early Expansion Rate

We present an analysis of 15 Type Ia supernovae (SNe Ia) at redshift z > 1 (9 at 1.5 < z < 2.3) recently discovered in the CANDELS and CLASH Multi-Cycle Treasury programs using WFC3 on the Hubble Space Telescope. We combine these SNe Ia with a new compilation of 1050 SNe Ia, jointly calibrated and corrected for simulated survey biases to produce accurate distance measurements. We present unbiased constraints on the expansion rate at six redshifts in the range 0.07 < z < 1.5 based only on this combined SN Ia sample. The added leverage of our new sample at z > 1.5 leads to a factor of ~3 improvement in the determination of the expansion rate at z = 1.5, reducing its uncertainty to ~20%, a measurement of H(z=1.5)/H0=2.67 (+0.83,-0.52). We then demonstrate that these six measurements alone provide a nearly identical characterization of dark energy as the full SN sample, making them an efficient compression of the SN Ia data. The new sample of SNe Ia at z > 1 usefully distinguishes between alternative cosmological models and unmodeled evolution of the SN Ia distance indicators, placing empirical limits on the latter. Finally, employing a realistic simulation of a potential WFIRST SN survey observing strategy, we forecast optimistic future constraints on the expansion rate from SNe Ia.

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Improving and Assessing Planet Sensitivity of the GPI Exoplanet Survey with a Forward Model Matched Filter

We present a new matched filter algorithm for direct detection of point sources in the immediate vicinity of bright stars. The stellar Point Spread Function (PSF) is first subtracted using a Karhunen-Loéve Image Processing (KLIP) algorithm with Angular and Spectral Differential Imaging (ADI and SDI). The KLIP-induced distortion of the astrophysical signal is included in the matched filter template by computing a forward model of the PSF at every position in the image. To optimize the performance of the algorithm, we conduct extensive planet injection and recovery tests and tune the exoplanet spectra template and KLIP reduction aggressiveness to maximize the Signal-to-Noise Ratio (SNR) of the recovered planets. We show that only two spectral templates are necessary to recover any young Jovian exoplanets with minimal SNR loss. We also developed a complete pipeline for the automated detection of point source candidates, the calculation of Receiver Operating Characteristics (ROC), false positives based contrast curves, and completeness contours. We process in a uniform manner more than 330 datasets from the Gemini Planet Imager Exoplanet Survey (GPIES) and assess GPI typical sensitivity as a function of the star and the hypothetical companion spectral type. This work allows for the first time a comparison of different detection algorithms at a survey scale accounting for both planet completeness and false positive rate. We show that the new forward model matched filter allows the detection of $50\%$ fainter objects than a conventional cross-correlation technique with a Gaussian PSF template for the same false positive rate.

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Characterizing 51 Eri b from 1-5 $μ$m: a partly-cloudy exoplanet

We present spectro-photometry spanning 1-5 $μ$m of 51 Eridani b, a 2-10 M$_\text{Jup}$ planet discovered by the Gemini Planet Imager Exoplanet Survey. In this study, we present new $K1$ (1.90-2.19 $μ$m) and $K2$ (2.10-2.40 $μ$m) spectra taken with the Gemini Planet Imager as well as an updated $L_P$ (3.76 $μ$m) and new $M_S$ (4.67 $μ$m) photometry from the NIRC2 Narrow camera. The new data were combined with $J$ (1.13-1.35 $μ$m) and $H$ (1.50-1.80 $μ$m) spectra from the discovery epoch with the goal of better characterizing the planet properties. 51 Eri b photometry is redder than field brown dwarfs as well as known young T-dwarfs with similar spectral type (between T4-T8) and we propose that 51 Eri b might be in the process of undergoing the transition from L-type to T-type. We used two complementary atmosphere model grids including either deep iron/silicate clouds or sulfide/salt clouds in the photosphere, spanning a range of cloud properties, including fully cloudy, cloud free and patchy/intermediate opacity clouds. Model fits suggest that 51 Eri b has an effective temperature ranging between 605-737 K, a solar metallicity, a surface gravity of $\log$(g) = 3.5-4.0 dex, and the atmosphere requires a patchy cloud atmosphere to model the SED. From the model atmospheres, we infer a luminosity for the planet of -5.83 to -5.93 ($\log L/L_{\odot}$), leaving 51 Eri b in the unique position as being one of the only directly imaged planet consistent with having formed via cold-start scenario. Comparisons of the planet SED against warm-start models indicates that the planet luminosity is best reproduced by a planet formed via core accretion with a core mass between 15 and 127 M$_{\oplus}$.

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Complex Spiral Structure in the HD 100546 Transitional Disk as Revealed by GPI and MagAO

We present optical and near-infrared high contrast images of the transitional disk HD 100546 taken with the Magellan Adaptive Optics system (MagAO) and the Gemini Planet Imager (GPI). GPI data include both polarized intensity and total intensity imagery, and MagAO data are taken in Simultaneous Differential Imaging mode at Hα. The new GPI H -band total intensity data represent a significant enhancement in sensitivity and field rotation compared to previous data sets and enable a detailed exploration of substructure in the disk. The data are processed with a variety of differential imaging techniques (polarized, angular, reference, and simultaneous differential imaging) in an attempt to identify the disk structures that are most consistent across wavelengths, processing techniques, and algorithmic parameters. The inner disk cavity at 15 au is clearly resolved in multiple datasets, as are a variety of spiral features. While the cavity and spiral structures are identified at levels significantly distinct from the neighboring regions of the disk under several algorithms and with a range of algorithmic parameters, emission at the location of HD 100546 c varies from point-like under aggressive algorithmic parameters to a smooth continuous structure with conservative parameters, and is consistent with disk emission. Features identified in the HD100546 disk bear qualitative similarity to computational models of a moderately inclined two-armed spiral disk, where projection effects and wrapping of the spiral arms around the star result in a number of truncated spiral features in forward-modeled images.

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1 to 2.4 micron Near-IR spectrum of the Giant Planet $β$ Pictoris b obtained with the Gemini Planet Imager

Using the Gemini Planet Imager (GPI) located at Gemini South, we measured the near-infrared (1.0-2.4 micron) spectrum of the planetary companion to the nearby, young star $β$ Pictoris. We compare the spectrum obtained with currently published model grids and with known substellar objects and present the best matching models as well as the best matching observed objects. Comparing the empirical measurement of the bolometric luminosity to evolutionary models, we find a mass of $12.9\pm0.2$ $\mathcal{M}_\mathrm{Jup}$, an effective temperature of $1724\pm15$ K, a radius of $1.46\pm0.01$ $\mathcal{R}_\mathrm{Jup}$, and a surface gravity of $\log g = 4.18\pm0.01$ [dex] (cgs). The stated uncertainties are statistical errors only, and do not incorporate any uncertainty on the evolutionary models. Using atmospheric models, we find an effective temperature of $1700-1800$ K and a surface gravity of $\log g = 3.5$-$4.0$ [dex] depending upon model. These values agree well with other publications and with "hot-start" predictions from planetary evolution models. Further, we find that the spectrum of $β$ Pic b best matches a low-surface gravity L2$\pm$1 brown dwarf. Finally comparing the spectrum to field brown dwarfs we find the the spectrum best matches 2MASS J04062677-381210 and 2MASS J03552337+1133437.

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Bringing "The Moth" to Light: A Planet-Sculpting Scenario for the HD 61005 Debris Disk

The HD 61005 debris disk ("The Moth") stands out from the growing collection of spatially resolved circumstellar disks by virtue of its unusual swept-back morphology, brightness asymmetries, and dust ring offset. Despite several suggestions for the physical mechanisms creating these features, no definitive answer has been found. In this work, we demonstrate the plausibility of a scenario in which the disk material is shaped dynamically by an eccentric, inclined planet. We present new Keck NIRC2 scattered-light angular differential imaging of the disk at 1.2-2.3 microns that further constrains its outer morphology (projected separations of 27-135 AU). We also present complementary Gemini Planet Imager 1.6 micron total intensity and polarized light detections that probe down to projected separations less than 10 AU. To test our planet-sculpting hypothesis, we employed secular perturbation theory to construct parent body and dust distributions that informed scattered-light models. We found that this method produced models with morphological and photometric features similar to those seen in the data, supporting the premise of a planet-perturbed disk. Briefly, our results indicate a disk parent body population with a semimajor axis of 40-52 AU and an interior planet with an eccentricity of at least 0.2. Many permutations of planet mass and semimajor axis are allowed, ranging from an Earth mass at 35 AU to a Jupiter mass at 5 AU.

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