arXiv subjects

Eugene Serabyn

Publications and source records attributed to Eugene Serabyn.

At least 19 recordsLinked to original sources

arXiv2026

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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arXiv2026

Dimpled scalar vortex coronagraph laboratory demonstration

Achieving the Habitable Worlds Observatory (HWO) goal of 10^-10 contrast at a separation of 3 $\lambda$/D across a 20% bandwidth requires coronagraph focal plane masks with both broadband high contrast performance and high planet throughput. Scalar vortex coronagraphs (SVCs) offer a promising alternative to polarization-sensitive vector vortex designs but face chromatic limitations. This work presents the latest laboratory demonstrations of second-generation scalar vortex prototypes that incorporate radial phase dimples to improve broadband starlight suppression. We compare these new "dimpled" sawtooth masks to previous-generation scalar designs through high-contrast imaging experiments on the In-Air Coronagraph Testbed. Using electric field conjugation, we achieve near testbed-limited contrasts across both narrow (2%) and broadband (10%) spectral ranges. We report the best in-air contrasts achieved to date for scalar vortex masks across narrow and broadband spectral ranges and we also show that the dimpled vortex predicted bench-limited contrast performances for 2%, 10% and 18% bandwidths agree with the measured lab contrasts within a factor of two. These results highlight the potential of topographically achromatized scalar vortex masks as candidates for future space-based high-contrast imaging missions and mark a significant step toward polarization-independent coronagraphs capable of meeting HWO performance requirements.

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arXiv2025

Worlds Next Door: A Candidate Giant Planet Imaged in the Habitable Zone of $\alpha$ Cen A. I. Observations, Orbital and Physical Properties, and Exozodi Upper Limits

We report on coronagraphic observations of the nearest solar-type star, $\alpha$ Cen A, using the MIRI instrument on the James Webb Space Telescope. With three epochs of observation (August 2024, February 2025, and April 2025), we achieve a sensitivity sufficient to detect $T_{\rm eff}\approx$ 225-250 K (1-1.2 $R_{\rm Jup}$) planets between 1"-2" and exozodiacal dust emission at the level of $>$5-8$\times$ the brightness of our own zodiacal cloud. The lack of exozodiacal dust emission sets an unprecedented limit of a few times the brightness of our own zodiacal cloud$-$a factor of $\gtrsim$10 more sensitive than measured toward any other stellar system to date. In August 2024, we detected a F$_\nu$(15.5 $\mu$m) = 3.5 mJy point source, called $S1$, at a separation of 1.5" from $\alpha$ Cen A. Because the August 2024 epoch had only one successful observation at a single roll angle, it is not possible to unambiguously confirm $S1$ as a bona fide planet. Our analysis confirms that $S1$ is neither a background nor a foreground object. $S1$ is not recovered in the February and April 2025 epochs. However, if $S1$ is the counterpart of the object, $C1$, seen by the VLT/NEAR program in 2019, we find that there is a 52% chance that the $S1+C1$ candidate was missed in both follow-up JWST/MIRI observations due to orbital motion. Incorporating constraints from the non-detections, we obtain families of dynamically stable orbits for $S1+C1$ with periods between 2-3 years. These suggest that the planet candidate is on an eccentric ($e \approx 0.4$) orbit significantly inclined with respect to $\alpha$ Cen AB orbital plane ($i_{\rm mutual} \approx 50^\circ$, or $\approx 130^\circ$). Based on the photometry and orbital properties, the planet candidate could have a temperature of 225 K, a radius of $\approx$1-1.1 $R_{\rm Jup}$ and a mass between 90-150 $M_{\rm Earth}$, consistent with RV limits.

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arXiv2025

MIRI-JWST mid-infrared direct imaging of the debris disk of HD106906

We report MIRI-JWST coronagraphic observations at 11.3 and 15.5 mic of the debris disk around the young star HD 106906. The observations were made to characterize the structure, temperature and mass of the disk through the thermal emission of the dust heated by the central star. Another goal was also to constrain the size distribution of the grains. The data were reduced and calibrated using the JWST pipeline. The analysis was based on a forward-modeling of the images using a multiparameter radiative transfer model coupled to an optical code for coronagraphy processing. The disk is clearly detected at both wavelengths. The slight asymmetry is geometrically consistent with the asymmetry observed in the near-IR, but it is inconsistent the brightness distribution. The observed structure is well reproduced with a model of a disk (or belt) with a critical radius 70 au, a mildly inward-increasing density (index 2) and a steeper decrease outward (index -6). This indication of a filled disk inside the critical radius is inconsistent with sculpting from an inner massive planet. The size distribution of the grains that cause the mid-IR emission is well constrained by the flux ratio at the two wavelengths : 0.45 10 mic and 0.65 10 mic for silicate and graphite grains, respectively. The minimum size is consistent with predictions of blowout through radiative pressure. We derive a mass of the dust that causes the mid-IR emission of 3.3 5.0 E3 Mearth. When the larger grains (up to 1 cm) that cause the millimeter emission are included, we extrapolate this mass to 0.10 0.16 Mearth. We point out to that this is fully consistent with ALMA observations of the disk in terms of dust mass and of its millimeter flux. We estimate the average dust temperature in the planetesimal belt to be 74 K, and a temperature range within the whole disk from 40 to 130 K.

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arXiv2025

First unambiguous detection of ammonia in the atmosphere of a planetary mass companion with JWST/MIRI coronagraphs

The newly accessible mid-infrared (MIR) window offered by the James Webb Space Telescope (JWST) for exoplanet imaging is expected to provide valuable information to characterize their atmospheres. In particular, coronagraphs on board the JWST Mid-InfraRed instrument (MIRI) are capable of imaging the coldest directly imaged giant planets at the wavelengths where they emit most of their flux. The MIRI coronagraphs have been specially designed to detect the NH3 absorption around 10.5 microns, which has been predicted by atmospheric models. We aim to assess the presence of NH3 while refining the atmospheric parameters of one of the coldest companions detected by directly imaging GJ 504 b. Its mass is still a matter of debate and depending on the host star age estimate, the companion could either be placed in the brown dwarf regime or in the young Jovian planet regime. We present an analysis of MIRI coronagraphic observations of the GJ 504 system. We took advantage of previous observations of reference stars to build a library of images and to perform a more efficient subtraction of the stellar diffraction pattern. We detected the presence of NH3 at 12.5 sigma in the atmosphere, in line with atmospheric model expectations for a planetary-mass object and observed in brown dwarfs within a similar temperature range. The best-fit model with Exo-REM provides updated values of its atmospheric parameters, yielding a temperature of Teff = 512 K and radius of R = 1.08 RJup. These observations demonstrate the capability of MIRI coronagraphs to detect NH3 and to provide the first MIR observations of one of the coldest directly imaged companions. Overall, NH3 is a key molecule for characterizing the atmospheres of cold planets, offering valuable insights into their surface gravity. These observations provide valuable information for spectroscopic observations planned with JWST.

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arXiv2025

Technical description and performance of the phase II version of the Keck Planet Imager and Characterizer

The Keck Planet Imager and Characterizer (KPIC) is a series of upgrades for the Keck II Adaptive Optics (AO) system and the NIRSPEC spectrograph to enable diffraction limited, high resolution (R>30000) spectroscopy of exoplanets and low mass companions in the K and L bands. Phase I consisted of single mode fiber injection/extraction units (FIU/FEU) used in conjunction with a H band pyramid wavefront sensor. The use of single mode fibers provides a gain in stellar rejection, a substantial reduction in sky background, and an extremely stable line spread function in the spectrograph. Phase II, deployed and commissioned in 2022, brought a 1000 actuator deformable mirror, beam shaping optics, a vortex mask, and other upgrades to the FIU/FEU. An additional service mission in 2024 extended operations down to y band, delivered an atmospheric dispersion corrector, and provided access to two laser frequency combs. KPIC phase II brings higher planet throughput, lower stellar leakage and many new observing modes which extend its ability to characterize exoplanets at high spectral resolution, building on the success of phase I. In this paper we present a description of the final phase II version of KPIC, along with results of system level laboratory testing and characterization showing the instrument's phase II throughput, stability, repeatability, and other key performance metrics prior to delivery and during installation at Keck. We outlined the capabilities of the various observing modes enabled by the new modules as well as efforts to compensate for static aberrations and non common path errors at Keck, which were issues that plagued phase I. Finally, we show results from commissioning.

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arXiv2024

Unveiling the HD 95086 system at mid-infrared wavelengths with JWST/MIRI

Mid-infrared imaging of exoplanets and disks is now possible with the coronagraphs of the MIRI on the JWST. This wavelength range unveils new features of young directly imaged systems and allows us to obtain new constraints for characterizing the atmosphere of young giant exoplanets and associated disks. These observations aim to characterize the atmosphere of the planet HD 95086 b by adding mid-infrared information so that the various hypotheses about its atmospheric parameters values can be unraveled. Improved images of circumstellar disks are provided. We present the MIRI coronagraphic imaging of the system HD 95086 obtained with the F1065C, F1140, and F2300C filters at central wavelengths of 10.575, 11.3, and 23 microns, respectively. We explored the method for subtracting the stellar diffraction pattern in the particular case when bright dust emitting at short separation is present. Furthermore, we compared different methods for extracting the photometry of the planet. Using the atmospheric models Exo-REM and ATMO, we measured the atmospheric parameters of HD 95086 b. The planet HD 95086 b and the contribution from the inner disk are detected at the two shortest MIRI wavelengths F1065C and F1140C. The outer colder belt is imaged at 23 microns. The mid-infrared photometry provides better constraints on the atmospheric parameters. We evaluate a temperature of 800-1050 K, consistent with one previous hypothesis that only used NIR data. The radius measurement of 1.0-1.14 RJup is better aligned with evolutionary models, but still smaller than predicted. These observations allow us to refute the hypothesis of a warm circumplanetary disk. HD 95086 is one of the first exoplanetary systems to be revealed at mid-infrared wavelengths. This highlights the interests and challenges of observations at these wavelengths.

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arXiv2024

Stellar Coronagraphy

Detecting exoplanets and other faint sources of emitted and reflected light near a bright star requires deeply suppressing the starlight while efficiently transmitting the dim light from its surroundings. This suppression can be carried out by coronagraphs, nulling interferometers, and starshades. This chapter provides a brief overview of these technologies, emphasizing coronagraphs.

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arXiv2024

A new atmospheric characterization of the sub-stellar companion HR\,2562\,B with JWST/MIRI observations

Context: HR2562B is a planetary-mass companion located 0.56arcsec (19au) from its host star. It is one of a few L/T transitional objects orbiting a young star. This companion provides insight into the evolution of young objects in the L/T transition. However, its key physical properties, such as Teff and mass, remain poorly constrained, with large uncertainties (34% for Teff, 22% for log(g)) based on near-infrared observations alone. Aims: We aim to refine these uncertainties, especially for Teff (1200-1700K) and log(g) (4-5), using new MIR data from the JWST/MIRI filters (10.65, 11.40, and 15.50 microns), and better understand the companion's chemical composition and its role in the L/T transition. Methods: MIRI data were processed using reference star differential imaging, revealing HR2562B at high S/N (16) in all 3 filters. We used 2 atmospheric models, ATMO and ExoREM, to fit the SED, combining MIR and NIR datasets. Additionally, we used CMD with brown dwarfs to explore the chemical composition of HR2562B's atmosphere and compare it to another L/T transition object, VHS1256b. Results: Our analysis improved the temperature precision (Teff=1255+-15K) by 6x compared to previous estimates. We also narrowed its luminosity to -4.69+-0.01 dex. Surface gravity remains uncertain (4.4-4.8), and its mass is estimated between 8 and 18.5Mj, depending on modeling and astrometry. Sensitivity analysis revealed the ability to detect objects between 2-5Mj at 100au. Conclusions: HR2562B likely has a near cloud-free atmosphere, with the ATMO model fitting better than ExoREM. Silicate absorption features are weak, requiring further spectroscopic observations. While HR2562B and VHS1256b share similarities, they are in different evolutionary stages, making HR2562B key to understanding young objects in the L/T transition. It is likely a planetary-mass companion, suggesting a reclassification as HR2562b.

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arXiv2024

A Survey of Protoplanetary Disks Using the Keck/NIRC2 Vortex Coronagraph

Recent Atacama Large Millimeter/submillimeter Array (ALMA) observations of protoplanetary disks in the millimeter continuum have shown a variety of radial gaps, cavities, and spiral features. These substructures may be signposts for ongoing planet formation, and therefore these systems are promising targets for direct imaging planet searches in the near-infrared. To this end, we present results from a deep imaging survey in the $L'$-band (3.8 $μ$m) with the Keck/NIRC2 vortex coronagraph to search for young planets in 43 disks with resolved features in the millimeter continuum or evidence for gaps/central cavities from their spectral energy distributions. Although we do not detect any new point sources, using the vortex coronagraph allows for high sensitivity to faint sources at small angular separations (down to ${\sim}$0$^{\prime\prime}$.1), allowing us to place strong upper limits on the masses of potential gas giant planets. We compare our mass sensitivities to the masses of planets derived using ALMA observations, and while we are sensitive to $\sim$1 M$_{Jup}$ planets in the gaps in some of our systems, we are generally not sensitive to planets of the masses expected from the ALMA observations. In addition to placing upper limits on the masses of gas giant planets that could be interacting with the dust in the disks to form the observed millimeter substructures, we are also able to map the micron-sized dust as seen in scattered light for 8 of these systems. Our large sample of systems also allows us to investigate limits on planetary accretion rates and disk viscosities.

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arXiv2024

Benefits of adding radial phase dimples on scalar coronagraph phase masks

Current scalar coronagraph focal plane mask designs are performance-limited by chromaticity. We investigate the effects of adding central Roddier and dual zone phase dimples to scalar vortex masks to improve broadband performance by suppressing the chromatic stellar leakage. We present hybrid designs with radial phase dimples integrated with the sawtooth vortex, wrapped vortex, and cosine phase mask. We show that using these dimples, it is possible to substantially improve the broadband contrast performance of scalar phase masks. We also show that although adding a phase dimple does not increase the sensitivity to low-order aberrations, suppressing the central leakage of scalar vortex coronagraphs does not restore the aberrations sensitivities to their notional state.

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arXiv2024

Current laboratory performance of starlight suppression systems, and potential pathways to desired Habitable Worlds Observatory exoplanet science capabilities

We summarize the current best polychromatic (10 to 20 % bandwidth) contrast performance demonstrated in the laboratory by different starlight suppression approaches and systems designed to directly characterize exoplanets around nearby stars. We present results obtained by internal coronagraph and external starshade experimental testbeds using entrance apertures equivalent to off-axis or on-axis telescopes, either monolithic or segmented. For a given angular separation and spectral bandwidth, the performance of each starlight suppression system is characterized by the values of raw contrast (before image processing), off-axis (exoplanet) core throughput, and post-calibration contrast (the final 1 sigma detection limit of off-axis point sources, after image processing). To place the current laboratory results in the perspective of the future Habitable Worlds Observatory (HWO) mission, we simulate visible observations of a fiducial Earth/Sun twin system at 12 pc, assuming a 6m (inscribed diameter) collecting aperture and a realistic end-to-end optical throughput. The exposure times required for broadband exoearth detection (20% bandwidth around a wavelength of 0.55 microns) and visible spectroscopic observations (R=70) are then computed assuming various levels of starlight suppression performance, including the values currently demonstrated in the laboratory. Using spectroscopic exposure time as a simple metric, our results point to key starlight suppression system design performance improvements and trades to be conducted in support of HWO exoplanet science capabilities. These trades may be explored via numerical studies, lab experiments, as well as high contrast space-based observations and demonstrations.

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arXiv2024

Vortex Fiber Nulling for Exoplanet Observations: First Direct Detection of M Dwarf Companions around HIP 21543, HIP 94666, and HIP 50319

Vortex fiber nulling (VFN) is a technique for detecting and characterizing faint companions at small separations from their host star. A near-infrared ($\sim2.3 μ$m) VFN demonstrator mode was deployed on the Keck Planet Imager and Characterizer (KPIC) instrument at the Keck Observatory and presented earlier. In this paper, we present the first VFN companion detections. Three targets, HIP 21543 Ab, HIP 94666 Ab, and HIP 50319 B, were detected with host-companion flux ratios between 70 and 430 at and within one diffraction beamwidth ($λ/D$). We complement the spectra from KPIC VFN with flux ratio and position measurements from the CHARA Array to validate the VFN results and provide a more complete characterization of the targets. This paper reports the first direct detection of these three M dwarf companions, yielding their first spectra and flux ratios. Our observations provide measurements of bulk properties such as effective temperatures, radial velocities, and v$\sin{i}$, and verify the accuracy of the published orbits. These detections corroborate earlier predictions of the KPIC VFN performance, demonstrating that the instrument mode is ready for science observations.

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arXiv2024

Direct detection and characterization of exoplanets using imaging Fourier transform spectroscopy

Space-based direct imaging provides prospects for detection and spectral characterization of exoplanets at optical and near-infrared wavelengths. Integral field spectrographs (IFS) have been historically baselined for these mission concepts. However, multiple studies have revealed that detector noise is a serious obstacle for such instruments when observing extremely faint targets such as Earth-like planets. Imaging Fourier transform spectrographs (iFTS) are generally less sensitive to detector noise, and have several other compelling features such as simultaneous imaging and spectroscopy, smaller-format detector requirements, and variable spectral resolution. To date, they have not been studied as options for such missions. In this work, we compare the capabilities of integral field spectrographs and imaging Fourier transform spectrographs to directly obtain spectra from an Earth-like planet using analytic and numerical models. Specifically, we compare the required exposure time to achieve the same signal-to-noise ratio of the two architectures over a range of detector and optical system parameters. We find that for a 6-meter telescope, an IFS outperforms an iFTS at optical wavelengths. In the near-IR, the relative efficiency of an IFS and iFTS depends on the instrument design and detector noise. An iFTS will be more efficient than an IFS if the readout noise of near-IR detector is above 2-3 e-/pix/frame (t_frame=1000s), which correspond to half to one-third of detector noise of the state-of-art. However, if the readout noise is further reduced to below this threshold, the performance of an IFS will experience a substantial improvement and become more efficient. These results motivate consideration of an iFTS as an alternative option for future direct imaging space missions in the near-IR.

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arXiv2024

Laboratory demonstration of the wrapped staircase scalar vortex coronagraph

Of the over 5000 exoplanets that have been detected, only about a dozen have ever been directly imaged. Earth-like exoplanets are on the order of 10 billion times fainter than their host star in visible and near-infrared, requiring a coronagraph instrument to block primary starlight and allow for the imaging of nearby orbiting planets. In the pursuit of direct imaging of exoplanets, scalar vortex coronagraphs (SVCs) are an attractive alternative to vector vortex coronagraphs (VVCs). VVCs have demonstrated 2e-9 raw contrast in broadband light but have several limitations due to their polarization properties. SVCs imprint the same phase ramp as VVCs on the incoming light and do not require polarization splitting, but they are inherently chromatic. Discretized phase ramp patterns such as a wrapped staircase help reduce SVC chromaticity and simulations show it outperforms a chromatic classical vortex in broadband light. We designed, fabricated, and tested a wrapped staircase SVC, and here we present the broadband characterization on the high contrast spectroscopy testbed. We also performed wavefront correction on the in-air coronagraph testbed at NASA's Jet Propulsion Laboratory and achieved an average raw contrasts of 3.2e-8 in monochromatic light and 2.2e-7 across a 10% bandwidth.

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arXiv2023

Vortex Fiber Nulling for Exoplanet Observations: Implementation and First Light

Vortex fiber nulling (VFN) is a single-aperture interferometric technique for detecting and characterizing exoplanets separated from their host star by less than a diffracted beam width. VFN uses a vortex mask and single mode fiber to selectively reject starlight while coupling off-axis planet light with a simple optical design that can be readily implemented on existing direct imaging instruments that can feed light to an optical fiber. With its axially symmetric coupling region peaking within the inner working angle of conventional coronagraphs, VFN is more efficient at detecting new companions at small separations than conventional direct imaging, thereby increasing the yield of on-going exoplanet search campaigns. We deployed a VFN mode operating in K band ($2.0{-}2.5~μ$m) on the Keck Planet Imager and Characterizer (KPIC) instrument at the Keck II Telescope. In this paper we present the instrument design of this first on-sky demonstration of VFN and the results from on-sky commissioning, including planet and star throughput measurements and predicted flux-ratio detection limits for close-in companions. The instrument performance is shown to be sufficient for detecting a companion $10^3$ times fainter than a $5^{\mathrm{th}}$ magnitude host star in 1 hour at a separation of 50 mas (1.1$λ/D$). This makes the instrument capable of efficiently detecting substellar companions around young stars. We also discuss several routes for improvement that will reduce the required integration time for a detection by a factor ${>}$3.

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arXiv2023

Debris Disk Color with the Hubble Space Telescope

Multi-wavelength scattered light imaging of debris disks may inform dust properties including typical size and mineral composition. Existing studies have investigated a small set of individual systems across a variety of imaging instruments and filters, calling for uniform comparison studies to systematically investigate dust properties. We obtain the surface brightness of dust particles in debris disks by post-processing coronagraphic imaging observations, and compare the multi-wavelength reflectance of dust. For a sample of resolved debris disks, we perform a systematic analysis on the reflectance properties of their birth rings. We reduced the visible and near-infrared images of 23 debris disk systems hosted by A through M stars using two coronagraphs onboard the Hubble Space Telescope: the STIS instrument observations centering at 0.58 $μ$m, and the NICMOS instrument at 1.12 $μ$m or 1.60 $μ$m. For proper recovery of debris disks, we used classical reference differential imaging for STIS, and adopted non-negative matrix factorization with forward modeling for NICMOS. By dividing disk signals by stellar signals to take into account of intrinsic stellar color effects, we systematically obtained and compared the reflectance of debris birth rings at ~90 deg scattering angle. Debris birth rings typically exhibit a blue color at ~90 deg scattering angle. As the stellar luminosity increases, the color tends to be more neutral. A likely L-shaped color-albedo distribution indicates a clustering of scatterer properties. The observed color trend correlates with the expected blow-out size of dust particles. The color-albedo clustering likely suggests different populations of dust in these systems. More detailed radiative transfer models with realistic dust morphology will contribute to explaining the observed color and color-albedo distribution of debris systems.

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arXiv2023

An Earth-sized Planet around an M5 Dwarf Star at 22 pc

We report on the discovery of an Earth-sized transiting planet ($R_p=1.015\pm0.051\,R_\oplus$) in a $P=4.02$ day orbit around K2-415 (EPIC 211414619), an M5V star at 22 pc. The planet candidate was first identified by analyzing the light curve data by the K2 mission, and is here shown to exist in the most recent data from TESS. Combining the light curves with the data secured by our follow-up observations including high-resolution imaging and near infrared spectroscopy with IRD, we rule out false positive scenarios, finding a low false positive probability of $2\times 10^{-4}$. Based on IRD's radial velocities of K2-415, which were sparsely taken over three years, we obtain the planet mass of $3.0\pm 2.7\,M_\oplus$ ($M_p<7.5\,M_\oplus$ at $95\,\%$ confidence) for K2-415b. Being one of the lowest mass stars ($\approx 0.16\,M_\odot$) known to host an Earth-sized transiting planet, K2-415 will be an interesting target for further follow-up observations, including additional radial velocity monitoring and transit spectroscopy.

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