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Michael R. Meyer

Publications and source records attributed to Michael R. Meyer.

At least 19 recordsLinked to original sources

A Candidate Innermost Fifth Planet In the HR 8799 System Revealed By JWST NIRISS Aperture Masking Interferometry

We detect a candidate fifth planet in the HR 8799 system, directly imaged with the JWST/NIRISS Aperture Masking Interferometer (AMI). The detected source lies just above a $3σ$ contrast curve at a contrast of $\sim2\times10^{-4}$ in the F380M filter at a projected separation of $\sim150$ mas, corresponding to a few-to-several Jupiter mass planet at an orbital radius of $\sim 7$au. The separation of the candidate is compatible with absolute proper-motion constraints from Gaia and Hipparcos assuming it is bound, while its orbital position lies near a stable orbital solution of a fifth planet in a 3:1 mean motion resonance with planet e. This detection was made possible by a new JWST/NIRISS AMI data pipeline that reaches the photon noise limited potential of AMI by accounting for the optical and electronic systematics that limited sensitivity in prior analyses. Confirmation of this candidate would make HR 8799 the first directly imaged five-planet system and provide insight into the orbital dynamics and the dynamical evolution of planetary systems with widely-separated gas giants.

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A Century of Radial Velocity and Astrometric Monitoring of 70 Oph AB: New PFS Data and Constraints on Planetary Companions

At a distance of 5.1 pc, the 70 Oph AB binary star system is one of the most favorable targets for future direct imaging and astrometry missions surveying mature, terrestrial planets. We present new radial velocities (RVs) obtained with the Planet Finder Spectrograph (PFS) on the 6.5\,m Magellan II Clay Telescope in Chile. We collected 499 measurements of 70 Oph A and 334 measurements of 70 Oph B during 2023--2025. Combining these data with decades of archival RVs and astrometry, we derive an updated orbital solution for the binary and dynamical masses of $0.88 \pm 0.004\,M_\odot$ and $0.73 \pm 0.003\,M_\odot$ for the primary and secondary components, respectively. We find that the long-term RV variability of both components is consistent with stellar activity modulated by rotation periods, and we detect no coherent planetary signals in either component. We place upper limits on any planets orbiting in the plane of the binary. The 27 yr RV baseline for 70 Oph A excludes Jupiter-mass planets interior to 5 au and reaches a sensitivity of $0.3\,M_{\rm Jup}$ at 1 au or $0.5\,M_{\rm Jup}$ at 2 au. For 70 Oph B, with PFS data we rule out planets more massive than $0.25$--$0.3\,M_{\rm Jup}$ inside 0.5 au. We show that stable S-type orbits around 70 Oph A extend to $\sim2.5$ au, covering the habitable zone. Thus, Saturn-mass planets or smaller on stable orbits in the habitable zone of 70 Oph A are allowed. Overall, our results provide important guidance for future planet searches around this stellar system.

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JWST/NIRCam Imaging of Young Stellar Objects. IV. Detailed Imaging of the Protoplanetary Disk around TW Hya

As the nearest protoplanetary disk to Earth ($d = 60.14$ pc), TW Hya is one of the most studied protoplanetary disks and a critical benchmark for testing planet formation theories. We present high-contrast coronagraphic imaging of the TW Hya disk from JWST/NIRCam across four filters (F187N, F200W, F356W, and F444W). We detect the disk's scattered-light emission in F200W, F356W, and F444W. An elliptical fit to the disk image yields an average inclination of $i = 8.74^{+1.03}_{-0.94}$ degrees and a position angle of $\mathrm{PA} = 75.62^{+7.86}_{-6.56}$ degrees. We find tentative evidence for radial variations in these parameters, a trend consistent with a disk warp. Our companion search yields no new detections, placing the lowest mass limits yet on companions that might be responsible for carving out the dust gap. Assuming no local extinction and a system age of 10 Myr, the F444W data are sensitive to masses down to $\sim 0.4\,M_{\rm Jup}$ at separations of $1$ arcsec ($\sim 60$ AU). Accounting for local disk extinction analogous to the AS 209 system, our limits reach sub-Jupiter masses beyond $2$ arcsec. Furthermore, our analysis provides a detailed view of a previously detected feature in the outer disk at $\sim 120$ AU, confirming its morphology as a distinct bifurcation structure. This feature may indicate the presence of complex substructures arising from dynamical planet-disk interactions. These results demonstrate JWST's ability to characterize the architecture of protoplanetary disks and constrain the properties of forming worlds.

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Finding Habitable Exoplanets with Binary Relative Astrometry: Planet Detection and Characterization with the Microarcsecond Astrometric Retrieval Algorithm (MARA)

Binary relative astrometry is a technique to search for rocky planets in the habitable zone of nearby binary stars using 1D relative astrometry at the microarcsecond level. This unprecedented precision would allow a custom-designed space telescope to directly measure the occurrence rate of these planets. The success of such a mission depends on our ability to recover and characterize planets from the unique format of extreme precision binary relative astrometry data. We present MARA, the Microarcsecond Astrometric Retrieval Algorithm, specifically designed for these data. We describe the design and format of the MARA pipeline, and demonstrate its accuracy and performance with a series of validation tests on simulated data, using the SHERA SMEx mission concept as an example. Our injection/recovery tests show that with these data, MARA is able to detect and characterize rocky planets in the habitable zone of alpha Cen A, down to a coplanar mass of about 1 Earth mass in 1 year orbits. Expanding to a range of input planet masses and periods for the same example mission, we find that the results from these injection/recovery tests generally agree with the analytic predictions of binary relative astrometry sensitivity. We use MARA to map out the expected completeness as a function of planet mass and period, which in this case reaches down to about 0.5 M Earth masses at 3 year orbits around alpha Cen A. These depth-of-search calculations will be a vital ingredient in demographics calculations from the final data from a binary relative astrometry mission.

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The JWST Early Release Science Program for Direct Observations of Exoplanetary Systems VIII: patchy forsterite and enstatite clouds in the atmosphere of VHS 1256 b, retrieval lessons learned and outlook to the future

JWST defines a new era for the data-driven approach of retrieval modelling, which has become a cornerstone tool for the statistical inference of exoplanetary and brown dwarf properties. The Early Release Science program #1386 observations of VHS 1256 b represent a huge jump in data quality, data quantity and spectral coverage for such objects. VHS 1256 b is a young, planetary mass and extremely variable companion that populates the enigmatic L/T cohort of substellar atmospheres. In this first retrieval analysis of the full 1 - 18 micron dataset, we apply the Brewster retrieval framework to the NIRSpec and MIRI spectroscopic observations of VHS 1256 b, exploring a variety of cloud species and structures. Using Delta(BIC) we find that the data is best described by a forsterite (Mg$_{2}$SiO$_{4}$) and enstatite (MgSiO$_{3}$) cloud combination. Our analysis shows a strong preference for patchy silicate cloud coverage, which aligns with VHS 1256 b's extensive and well documented spectral variability. Our retrieval is able to place constraints on the abundances of H$_{2}$O, CO, CO$_{2}$, CH$_{4}$ as well as NH$_{3}$. We also show that the retrieved parameters are sensitive to the data used and the relative signal-to-noise ratios between data from different instruments. We conclude with the next steps for the wider retrieval community to better understand young and cloudy exoplanetary atmospheres.

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Searching for Habitable Exoplanets with Relative Astrometry (SHERA). I. The Case for Searching for Planets in Binary Star Systems

Discovering Earth-like planets orbiting Sun-like stars was identified as a priority science goal of the Astronomy 2020 Decadal Survey. It is confounded by many factors, one of which is the high multiplicity of Sun-like stars in the local neighborhood - half of nearby Sun-like stars are in binary or higher-order stellar systems, which are less amenable to the detection of small planets with almost all of the currently productive exoplanet detection techniques. Here we describe the SHERA (Searching for Habitable Exoplanets with Relative Astrometry) NASA Small Explorer mission concept. SHERA utilizes diffractive-pupil technology on a small, simple optical space telescope to achieve microarcsecond precision relative astrometry on 14 Sun-like stars in seven nearby multi-star systems, combining the pupil and stellar binarity to provide a precise reference in the image plane. With this precision, SHERA would enable: (i) a search for rocky planets in the habitable zones of the closest Sun-like stars; (ii) an investigation of the impact of binary star formation on small, widely separated planets; and (iii) the performance of crucial precursor observations on a number of high-priority targets of NASA's future missions to characterize Earth-like planets, such as the Habitable Worlds Observatory. When combined with radial velocity measurements, SHERA relative astrometry will also enable exploration of the three-dimensional orbital structure of planets in binary systems.

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Exploring Exoplanets with Interferometry

(Extract from the Executive Summary) Humanity stands at the threshold of answering one of its most profound questions: Does life exist beyond Earth? Ongoing and upcoming space missions, together with powerful ground-based instruments, have prepared the way for a transformational next step - the detailed characterization of Earth analogs orbiting Sun-like and other stars and the search for atmospheric biosignatures that may indicate life. Within this context, the European Space Agency's Voyage 2050 process has identified the direct detection of thermal emission from temperate terrestrial exoplanets in the mid-infrared (mid-IR) as a top scientific priority. The Large Interferometer For Exoplanets (LIFE) - a space-based, mid-IR nulling interferometer - is designed to meet this goal. LIFE will be capable of detecting climate-relevant gases such as CO$_2$ and H$_2$O, identifying classical biosignatures like O$_3$ and CH$_4$, and probing additional, non-classical biosignatures. It will also provide key data for determining planetary radius, albedo, and temperature, which are essential for assessing habitability. In parallel, the U.S. National Academy has recommended a complementary mission now called the Habitable Worlds Observatory (HWO) - a ~6-meter space telescope equipped with advanced coronagraphs to suppress starlight by a factor of ~10$^{10}$ across the visible and possibly into the near-infrared and near-ultraviolet. Together, LIFE and HWO offer synergistic capabilities, enabling a comprehensive and robust assessment of the prevalence of life-bearing exoplanets in our galactic neighbourhood - a first in human history. By uniting an international and interdisciplinary community of scientists and engineers, LIFE offers a credible pathway toward the direct detection and characterization of potentially habitable - and even inhabited - worlds.

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The Days Drag On on WASP-121 b: Interpreting its NIRISS Spectroscopic Phase Curve with General Circulation Models

Ultra-hot Jupiters present extreme atmospheric phenomena not found in the Solar System. These planets' daysides experience strong temperature inversions, molecular species (including H2) dissociate, and magnetism disrupts their atmospheric circulation. On their nightsides H2 can recombine and clouds may form. Spectroscopic phase curves let us measure these spatially inhomogeneous conditions, which can then be interpreted with three-dimensional (3-D) models. In this work we compare the JWST/NIRISS spectroscopic phase curve of the ultra-hot Jupiter WASP-121 b to state-of-the-art 3-D models with varying modeling assumptions, including the aforementioned physical phenomena. We demonstrate the importance of accurately accounting for the planet's radius in comparison between data and models, as it changes the implied overall planetary emission. We find that the 3-D models predict planet emission $\sim$12% higher than observed, contributing to a continued tension between measured and predicted hot Jupiter albedos. We identify multiple pieces of evidence that confirm a strong source of drag operating in this planet's atmosphere. In addition, the nightside emission spectrum is devoid of strong absorption features, which may be best explained by nightside clouds. One feature of the dataset that is not matched by the 3-D models is a trend of increasing eastward phase offset with decreasing wavelength, for wavelengths shorter than $\sim$1.4 \textmu m. This result is not consistent with reflection from dayside clouds, nor can it be explained by removing atmospheric opacity sources. Our analysis highlights the complexities in generating 3-D models and interpreting observations of ultra-hot Jupiters in the JWST era.

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High-Contrast Imaging of Forming Protoplanets: VLTs, JWST, and the Promise of ELT

Planet formation remains a fundamentally important yet poorly understood process. Protoplanetary disks, the birthplaces of planetary systems, exhibit a wide range of substructures that are increasingly interpreted as signatures of interactions with forming planets. However, the direct detection rate of protoplanets within these disks remains low, leaving critical gaps in our understanding of the physical mechanisms driving their formation and early evolution. In this chapter, we review recent efforts by the high-contrast imaging community to directly observe forming protoplanets and their immediate environments. These observations aim to provide key constraints on thermal and accretion processes, planetary growth, and the formation of circumplanetary disks and satellite systems. We also propose a path forward for deriving observational estimates of the planet mass-to-radius ratio ($M_p/R_p$), a crucial parameter for distinguishing between competing formation models and understanding the thermal evolution of young planets. Finally, we highlight how upcoming instruments on the Extremely Large Telescope (ELT), with their unprecedented combination of high spatial and spectral resolution, will transform our ability to probe planet formation at the smallest and most critical scales.

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The compositions of the HR 8799 planets reflect accretion of both solids and metal-enriched gas

With four giant planets ($m\sim5-10~M_{\rm Jup}$, $T_\rm{eff}\sim900-1200$ K) orbiting between 15-70 au, HR 8799 provides an unparalleled testbed for studying giant planet formation and probing compositional trends across the protoplanetary disk. We present new JWST/NIRSpec IFU observations ($2.85-5.3~μ$m, $R\approx2700$) that now include the spectrum of HR 8799 b, and higher S/N spectra for HR 8799 c, d, and e compared to that in Ruffio & Xuan et al. We detect CO, CH$_4$, H$_2$O, H$_2$S, CO$_2$, and for planet b, NH$_3$. We combine the NIRSpec spectra with $1-5 μ$m photometry to perform atmospheric retrievals that account for disequilibrium chemistry and clouds, and allow C/H, O/H, N/H, and S/H to scale independently. While the four planets are similarly enriched in carbon and oxygen, with C/H and O/H between $3-5\times$ stellar, we observe a tentative trend of increasing S/H - a tracer of refractory solids - from $2-5 \times$ stellar with increasing orbital distance. From HR 8799 b's NH$_3$ abundance, we estimate $\rm N/H=21.2^{+16.2}_{-8.8}\times$ stellar, suggesting the outer planet accreted significant amounts of N-rich gas. Overall, the elemental abundance patterns we observe are consistent with a picture where planet b formed between the CO snowline and the more-distant N$_2$ snowline, while the inner planets accreted $3 \times$ stellar CO-enriched disk gas within the CO snowline. The excess volatile mass from pebble drift and evaporation implies an integrated pebble flux of $750 \pm 200~M_{\oplus}$. The increase in the planets' S/H with orbital distance implies more solid accretion further out, which is quantitatively compatible with expectations from both pebble and planetesimal accretion ($2 \times$ Minimum Mass Solar Nebula) paradigms.

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Precise Constraints on the Energy Budget of WASP-121 b from its JWST NIRISS/SOSS Phase Curve

Ultra-hot Jupiters exhibit day-to-night temperature contrasts upwards of 1000 K due to competing effects of strong winds, short radiative timescales, magnetic drag, and H2 dissociation/recombination. Spectroscopic phase curves provide critical insights into these processes by mapping temperature distributions and constraining the planet's energy budget across different pressure levels. Here, we present the first NIRISS/SOSS phase curve of an ultra-hot Jupiter, WASP-121 b. The instrument's bandpass [0.6 - 2.85 micron] captures an estimated 50-83% of the planet's bolometric flux, depending on orbital phase, allowing for unprecedented constraints on the planet's global energy budget; previous measurements with HST/WFC3 and JWST/NIRSpec/G395H captured roughly 20% of the planetary flux. Accounting for the unobserved regions of the spectrum, we estimate effective day and nightside temperatures of T_day = 2717 +/- 17 K and T_night = 1562 +/- 19 K corresponding to a Bond albedo of A_B = 0.277 +/- 0.016 and a heat recirculation efficiency of epsilon = 0.246 +/- 0.014. Matching the phase-dependent effective temperature with energy balance models yields a similar Bond albedo of 0.3 and a mixed layer pressure of 1 bar consistent with photospheric pressures, but unexpectedly slow winds of 0.2 km/s, indicative of inefficient heat redistribution. The shorter optical wavelengths of the NIRISS/SOSS Order 2 yield a geometric albedo of A_g = 0.093 +/- 0.029 (3 sigma upper limit of 0.175), reinforcing the unexplained trend of hot Jupiters exhibiting larger Bond albedos than geometric albedos. We also detect near-zero phase curve offsets for wavelengths above 1.5 micron, consistent with inefficient heat transport, while shorter wavelengths potentially sensitive to reflected light show eastward offsets.

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The Hubble Ultracool Multiplicity (HUM) Survey. I. Characterizing Sensitivity to Companions at Sub-Diffraction Limit Separations with HST WFC3/IR

We characterize the sensitivity of a double point-spread function (PSF) fitting algorithm -- employing empirical, position-dependent PSF models -- for detecting companions using the infrared channel of the Wide Field Camera 3 (WFC3/IR) on the Hubble Space Telescope (HST). The observed separation distribution of known brown dwarf (BD) binaries is potentially biased towards separations larger than the angular resolution limits of current techniques. Previous imaging analyses suffer from incompleteness at separations $<2λ/D$; our aim is to probe within this limit to identify previously missed companions. We evaluate the performance of our technique on artificial data across 8 WFC3/IR filters and a broad range of signal-to-noise ratios (S/N), determining our ability to accurately recover injected companions and identifying the region of parameter space where false positive fits are likely. Here, we demonstrate the capability of this technique to recover companions at sub-pixel separations on the WFC3/IR detector -- below the diffraction limit in multiple filters. For F160W at a typical S/N of 75, we resolve companions separated by 0.8 pixels (104 mas, $0.759λ/D$) at 1.5 magnitudes contrast with $>90\%$ confidence. We achieve the closest angular resolution for any detection method with WFC3/IR imaging to date. Compared to previous BD multiplicity surveys with WFC3/IR, we achieve a 2.5$\times$ improvement in separation sensitivity at contrasts of 0-3 magnitudes in F127M. We have demonstrated that applying our improved technique to archival HST images of field BDs will thus probe down to separations of 1 au, in one of the largest high angular resolution surveys of such objects to date.

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Enriched volatiles and refractories but deficient titanium on the dayside atmosphere of WASP-121b revealed by JWST/NIRISS

With dayside temperatures elevated enough for all atmospheric constituents to be present in gas form, ultra-hot Jupiters offer a unique opportunity to probe the composition of giant planets. We aim to infer the composition and thermal structure of the dayside atmosphere of the ultra-hot Jupiter WASP-121b from two NIRISS$/$SOSS secondary eclipses observed as part of a full phase curve. We extract the eclipse spectrum of WASP-121b with two independent data reduction pipelines and analyse it using different atmospheric retrieval prescriptions to explore the effects of thermal dissociation, reflected light, and titanium condensation on the inferred atmospheric properties. We find that the observed dayside spectrum of WASP-121b is best fit by atmosphere models possessing a stratospheric inversion with temperatures reaching over 3000K, with spectral contributions from H2O, CO, VO, H-, and either TiO or reflected light. We measure the atmosphere of WASP-121b to be metal enriched (~10x stellar) but comparatively titanium poor (~1x stellar), potentially due to partial cold-trapping. The inferred C/O depends on model assumptions such as whether reflected light is included, ranging from being consistent with stellar if a geometric albedo of zero is assumed to being super-stellar for a freely fitted Ag = 0.16 +/- 0.02. The volatile-to-refractory ratio is measured to be consistent with the stellar value. We infer that WASP-121b has an atmosphere enriched in both volatile and refractory metals, but not in ultra-refractory titanium, suggesting the presence of a nightside cold-trap. Considering H2O dissociation is critical in free retrieval analyses, leading to order-of-magnitude differences in retrieved abundances for WASP-121b if neglected. Simple chemical equilibrium retrievals assuming that all species are governed by a single metallicity parameter drastically overpredict the TiO abundance.

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Why Estimating $η_\oplus$ is Difficult: A Kepler-Centric Perspective

$η_{\oplus}$, the occurrence rate of rocky habitable zone exoplanets orbiting Sun-like stars, is of great interest to both the astronomical community and the general public. The Kepler space telescope has made it possible to estimate $η_{\oplus}$, but estimates by different groups vary by more than an order of magnitude. We identify several causes for this range of estimates. We first review why, despite being designed to estimate $η_{\oplus}$, Kepler's observations are not sufficient for a high-confidence estimate, due to Kepler's detection limit coinciding with the $η_{\oplus}$ regime. This results in a need to infer $η_{\oplus}$, for example extrapolating from a regime of non-habitable zone, non-rocky exoplanets. We examine two broad classes of causes that can account for the large discrepancy in $η_\oplus$ found in the literature: a) differences in definitions and input data between studies, and b) fundamental limits in Kepler data that lead to large uncertainties and poor accuracy. We highlight the risk of large biases when using extrapolation to describe small exoplanet populations in the habitable zone. We discuss how $η_{\oplus}$ estimates based on Kepler data can be improved, such as reprocessing Kepler data for more complete, higher-reliability detections and better exoplanet catalog characterization. We briefly survey upcoming space telescopes capable of measuring $η_{\oplus}$, and how they can be used to supplement Kepler data.

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Are We There Yet? Challenges in Quantifying the Frequency of Earth Analogs in the Habitable Zone

Searching for life elsewhere in the universe is one of the most highly prioritized pursuits in astronomy today. However, the ability to observe evidence of Earth-like life through biosignatures is limited by the number of planets in the solar neighborhood with conditions similar to Earth. The occurrence rate of Earth-like planets in the habitable zones of Sun-like stars, $η_{\oplus}$, is therefore crucial for addressing the apparent lack of consensus on its value in the literature. Here we present a review of the current understanding of $η_{\oplus}$. We first provide definitions for parameters that contribute to $η_{\oplus}$. Then, we discuss the previous and current estimated parameter values and the context of the limitations on the analyses that produced these estimates. We compile an extensive list of the factors that go into any calculation of $η_{\oplus}$, and how detection techniques and surveys differ in their sensitivity and ability to accurately constrain $η_{\oplus}$. Understanding and refining the value of $η_{\oplus}$ is crucial for upcoming missions and telescopes, such as the planned Habitable Worlds Observatory and the Large Interferometer for Exoplanets, which aim to search for biosignatures on exoplanets in the solar neighborhood.

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A complex structure of escaping helium spanning more than half the orbit of the ultra-hot Jupiter WASP-121\,b

Atmospheric escape of planets on short orbital periods, driven by the host star's irradiation, influences their evolution, composition, and atmospheric dynamics. Our main avenue to probe atmospheric escape is through the near-infrared metastable helium triplet, which has enabled mass loss rate measurements for tens of exoplanets. Among them, only a few studies show evidence for out-of-transit absorption, supporting the presence of a hydrodynamic outflow. However, none of these observations precisely identified the physical extent of the outflow, either due to non-continuous or short-duration observations. This limits our measurements of accurate mass loss rates. Here we present the first continuous, full-orbit helium phase curve monitoring of an exoplanet, the ultra-hot Jupiter WASP-121b, obtained with JWST/NIRISS. It reveals helium absorption for nearly 60% of the orbit at >3sigma significance. Our results show that WASP-121b sustains a strong outflow, separating into two tails trailing and leading the planet. The persistent absorption from these tails, together with their measured radial velocity shifts, suggests that they remain in a collisional fluid regime at large distances from the planet and display very different dynamics. The leading trail has a higher density and moves toward the star, whereas the trailing trail is being pushed away from the star, with the latter being blue-shifted due to stellar irradiation pressure. While qualitatively agreeing with theoretical expectations, the observed structure of helium is not self-consistently reproducible by current models, limiting constraints on the mass loss rate. Furthermore, we show that while ground-based observations of the helium triplet are essential to measure the outflow dynamics precisely, they ideally should be combined with continuous JWST phase curves to constrain the absolute level of helium absorption.

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Ross 458c: Gas Giant or Brown Dwarf?

Ross 458c is a widely separated planetary mass companion at a distance of 1100 AU from its host binary, Ross 458AB. It is a member of a class of very low-mass companions at distances of hundreds to thousands of AU from their host stars. We aim to constrain Ross 458c's formation history by fitting its near-IR spectrum to models to constrain its composition. If its composition is similar to its host star, we infer that it likely formed through turbulent fragmentation of the same molecular cloud that formed the host. If its composition is enhanced in heavy elements relative to the host, this lends evidence to formation in the disk and subsequent migration to its current separation. Here, we present high-resolution (R$\sim$2700) emission spectra of Ross 458c with JWST NIRSpec Fixed Slit in the F070LP, F100LP, and F170LP filters from 0.8 to 3.1 $μ$m. We fit these spectra using both grids of forward models (Sonora Bobcat, Sonora Elf Owl, and ExoREM) and atmospheric retrievals (POSEIDON). We also constrain the composition of Ross 458AB by fitting an archival SpeX spectrum with PHOENIX forward models. The forward model grids prefer an enhanced atmospheric metallicity for Ross 458c relative to the host, but our retrievals return a metallicity consistent with the host within 1$σ$. Our results offer new insights into the formation history of Ross 458c, as well as the efficacy of fitting forward model grids versus retrievals to derive atmospheric properties of directly imaged companions.

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Theoretical Mass Function for Secondaries Forming via Gravitational Instability in Circumstellar Disks

This paper constructs a theoretical framework for calculating the distribution of masses for secondary bodies forming via gravitational instability in the outer regions of circumstellar disks. We show that several alternate ways to specify the mass scale of forming objects converge to the same result under the constraint that the parental disks are marginally stable with stability parameter $Q=1$. Next we show that the well-known constraint that the formation of secondary bodies requires rapid cooling is equivalent to that of opacity limited fragmentation. These results are then used to derive a mass function for secondary objects forming through disk instablity. The resulting distribution is relatively narrow, with log-normal-like shape, a characteristic mass scale of order $M_{\scriptstyle \rm P}\sim10M_{\scriptstyle \rm Jup}$ and an approximate range of $4-80M_{\scriptstyle \rm Jup}$. Current estimates for the occurrence rate suggest that these objects are outnumbered by both stars and planets formed via core accretion.

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