arXiv subjects

Daniel Huber

Publications and source records attributed to Daniel Huber.

At least 73 records · Page 4Linked to original sources

arXiv2024

Orbital Architectures of Planet-Hosting Binaries III. Testing Mutual Inclinations of Stellar and Planetary Orbits in Triple-Star Systems

Transiting planets in multiple-star systems, especially high-order multiples, make up a small fraction of the known planet population but provide unique opportunities to study the environments in which planets would have formed. Planet-hosting binaries have been shown to have an abundance of systems in which the stellar orbit aligns with the orbit of the transiting planet, which could give insights into the planet formation process in such systems. We investigate here if this trend of alignment extends to planet-hosting triple-star systems. We present long-term astrometric monitoring of a novel sample of triple-star systems that host Kepler transiting planets. We measured orbit arcs in 21 systems, including 12 newly identified triples, from a homogeneous analysis of our Keck adaptive optics data and, for some systems, Gaia astrometry. We examine the orbital alignment within the nine most compact systems ($\lesssim500$ au), testing if either (or both) of the stellar orbits align with the edge-on orbits of their transiting planets. Our statistical sample of triple systems shows a tendency toward alignment, especially when assessing the alignment probability using stellar orbital inclinations computed from full orbital fits, but is formally consistent with isotropic orbits. Two-population tests where half of the stellar orbits are described by a planet-hosting-binary-like moderately aligned distribution give the best match when the other half (non-planet-hosting) has a Kozai-like misaligned distribution. Overall, our results suggest that our sample of triple-star planet-hosting systems are not fully coplanar systems and have at most one plane of alignment.

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arXiv2024

Asteroseismology of the Nearby K-Dwarf $σ$ Draconis using the Keck Planet Finder and TESS

Asteroseismology of dwarf stars cooler than the Sun is very challenging due to the low amplitudes and rapid timescales of oscillations. Here, we present the asteroseismic detection of solar-like oscillations at 4-minute timescales ($ν_{\mathrm{max}}\sim4300μ$Hz) in the nearby K-dwarf $σ$ Draconis using extreme precision Doppler velocity observations from the Keck Planet Finder and 20-second cadence photometry from NASA's Transiting Exoplanet Survey Satellite. The star is the coolest dwarf star to date with both velocity and luminosity observations of solar-like oscillations, having amplitudes of $5.9\pm0.8\,$cm$\,\text{s}^{-1}$ and $0.8\pm0.2$ ppm, respectively. These measured values are in excellent agreement with established luminosity-velocity amplitude relations for oscillations and provide further evidence that mode amplitudes for stars with $T_{\mathrm{eff}}<\,5500\,$K diminish in scale following a $(L/M)^{1.5}$ relation. By modeling the star's oscillation frequencies from photometric data, we measure an asteroseismic age of $4.5\pm0.9\,\rm{(ran)} \pm 1.2\,\rm{(sys)}$ Gyr. The observations demonstrate the capability of next-generation spectrographs and precise space-based photometry to extend observational asteroseismology to nearby cool dwarfs, which are benchmarks for stellar astrophysics and prime targets for directly imaging planets using future space-based telescopes.

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arXiv2024

The TESS-Keck Survey. XXII. A sub-Neptune Orbiting TOI-1437

Exoplanet discoveries have revealed a dramatic diversity of planet sizes across a vast array of orbital architectures. Sub-Neptunes are of particular interest; due to their absence in our own solar system, we rely on demographics of exoplanets to better understand their bulk composition and formation scenarios. Here, we present the discovery and characterization of TOI-1437 b, a sub-Neptune with a 18.84 day orbit around a near-Solar analog (Mstar = 1.10 +/- 0.10 Msun, Rstar = 1.17 +/- 0.12 Rsun). The planet was detected using photometric data from the Transiting Exoplanet Survey Satellite (TESS) mission and radial velocity follow-up observations were carried out as a part of the TESS-Keck Survey (TKS) using both the HIRES instrument at Keck Observatory and the Levy Spectrograph on the Automated Planet Finder (APF) telescope. A combined analysis of these data reveal a planet radius of Rp = 2.24 +/- 0.23 Rearth and a mass measurement of Mp = 9.6 +/- 3.9 Mearth). TOI-1437 b is one of few (~50) known transiting sub-Neptunes orbiting a solar-mass star that has a radial velocity mass measurement. As the formation pathway of these worlds remains an unanswered question, the precise mass characterization of TOI-1437 b may provide further insight into this class of planet.

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arXiv2024

TESS asteroseismology of $β$ Hydri: a subgiant with a born-again dynamo

The solar-type subgiant $β$ Hyi has long been studied as an old analog of the Sun. Although the rotation period has never been measured directly, it was estimated to be near 27 days. As a southern hemisphere target it was not monitored by long-term stellar activity surveys, but archival International Ultraviolet Explorer data revealed a 12 year activity cycle. Previous ground-based asteroseismology suggested that the star is slightly more massive and substantially larger and older than the Sun, so the similarity of both the rotation rate and the activity cycle period to solar values is perplexing. We use two months of precise time-series photometry from the Transiting Exoplanet Survey Satellite (TESS) to detect solar-like oscillations in $β$ Hyi and determine the fundamental stellar properties from asteroseismic modeling. We also obtain a direct measurement of the rotation period, which was previously estimated from an ultraviolet activity-rotation relation. We then use rotational evolution modeling to predict the rotation period expected from either standard spin-down or weakened magnetic braking (WMB). We conclude that the rotation period of $β$ Hyi is consistent with WMB, and that changes in stellar structure on the subgiant branch can reinvigorate the large-scale dynamo and briefly sustain magnetic activity cycles. Our results support the existence of a "born-again" dynamo in evolved subgiants -- previously suggested to explain the cycle in 94 Aqr Aa -- which can best be understood within the WMB scenario.

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arXiv2024

TESS Giants Transiting Giants. VI. Newly Discovered Hot Jupiters Provide Evidence for Efficient Obliquity Damping after the Main Sequence

The degree of alignment between a star's spin axis and the orbital plane of its planets (the stellar obliquity) is related to interesting and poorly understood processes that occur during planet formation and evolution. Hot Jupiters orbiting hot stars ($\gtrsim$6250 K) display a wide range of obliquities, while similar planets orbiting cool stars are preferentially aligned. Tidal dissipation is expected to be more rapid in stars with thick convective envelopes, potentially explaining this trend. Evolved stars provide an opportunity to test the damping hypothesis, particularly stars that were hot on the main sequence and have since cooled and developed deep convective envelopes. We present the first systematic study of the obliquities of hot Jupiters orbiting subgiants that recently developed convective envelopes using Rossiter-McLaughlin observations. Our sample includes two newly discovered systems in the Giants Transiting Giants Survey (TOI-6029 b, TOI-4379 b). We find that the orbits of hot Jupiters orbiting subgiants that have cooled below $\sim$6250 K are aligned or nearly aligned with the spin-axis of their host stars, indicating rapid tidal realignment after the emergence of a stellar convective envelope. We place an upper limit for the timescale of realignment for hot Jupiters orbiting subgiants at $\sim$500 Myr. Comparison with a simplified tidal evolution model shows that obliquity damping needs to be $\sim$4 orders of magnitude more efficient than orbital period decay to damp the obliquity without destroying the planet, which is consistent with recent predictions for tidal dissipation from inertial waves excited by hot Jupiters on misaligned orbits.

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arXiv2024

An Earth-sized Planet on the Verge of Tidal Disruption

TOI-6255~b (GJ 4256) is an Earth-sized planet (1.079$\pm0.065$ $R_\oplus$) with an orbital period of only 5.7 hours. With the newly commissioned Keck Planet Finder (KPF) and CARMENES spectrographs, we determined the planet's mass to be 1.44$\pm$0.14 $M_{\oplus}$. The planet is just outside the Roche limit, with $P_{\rm orb}/P_{\rm Roche}$ = 1.13 $\pm0.10$. The strong tidal force likely deforms the planet into a triaxial ellipsoid with a long axis that is $\sim$10\% longer than the short axis. Assuming a reduced stellar tidal quality factor $Q_\star^\prime \approx10^7$, we predict that tidal orbital decay will cause TOI-6255 to reach the Roche limit in roughly 400 Myr. Such tidal disruptions may produce the possible signatures of planet engulfment that have been on stars with anomalously high refractory elemental abundances compared to its conatal binary companion. TOI-6255 b is also a favorable target for searching for star-planet magnetic interactions, which might cause interior melting and hasten orbital decay. TOI-6255 b is a top target (Emission Spectroscopy Metric of about 24) for phase curve observations with the James Webb Space Telescope.

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arXiv2024

Obliquity Constraints for the Extremely Eccentric Sub-Saturn Kepler-1656 b

The orbits of close-in exoplanets provide clues to their formation and evolutionary history. Many close-in exoplanets likely formed far out in their protoplanetary disks and migrated to their current orbits, perhaps via high-eccentricity migration (HEM), a process that can also excite obliquities. A handful of known exoplanets are perhaps caught in the act of HEM, as they are observed on highly eccentric orbits with tidal circularization timescales shorter than their ages. One such exoplanet is Kepler-1656 b, which is also the only known non-giant exoplanet (<100 $M_\oplus$) with an extreme eccentricity (e=0.84). We measured the sky-projected obliquity of Kepler-1656 b by observing the Rossiter-McLaughlin effect during a transit with the Keck Planet Finder. Our data are consistent with an aligned orbit, but are also consistent with moderate misalignment with $λ< 50$ deg at 95% confidence, with the most likely solution of $35^{+14.9}_{-21.6}$ deg. A low obliquity would be an unlikely outcome of most eccentricity-exciting scenarios, but we show that the properties of the outer companion in the system are consistent with the coplanar HEM mechanism. Alternatively, if the system is not relatively coplanar (<20 deg mutual inclination), Kepler-1656 b may be presently at a rare snapshot of long-lived eccentricity oscillations that do not induce migration. Kepler-1656 b is only the fourth exoplanet with e>0.8 to have its obliquity constrained; expanding this population will help establish the degree to which orbital misalignment accompanies migration. Future work that constrains the mutual inclinations of outer perturbers will be key for distinguishing plausible mechanisms.

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arXiv2024

Stellar Models are Reliable at Low Metallicity: An Asteroseismic Age for the Ancient Very Metal-Poor Star KIC 8144907

Very metal-poor stars ([Fe/H]<-2) are important laboratories for testing stellar models and reconstructing the formation history of our galaxy. Asteroseismology is a powerful tool to probe stellar interiors and measure ages, but few asteroseismic detections are known in very metal-poor stars and none have allowed detailed modeling of oscillation frequencies. We report the discovery of a low-luminosity Kepler red giant (KIC 8144907) with high S/N oscillations, [Fe/H]=-2.66+/-0.08 and [alpha/Fe]=0.38+/-0.06, making it by far the most metal-poor star to date for which detailed asteroseismic modeling is possible. By combining the oscillation spectrum from Kepler with high-resolution spectroscopy we measure an asteroseismic mass and age of 0.79+/-0.02(ran)+/-0.01(sys) Msun and 12.0+/-0.6(ran)+/-0.4(sys) Gyr, with remarkable agreement across different codes and input physics, demonstrating that stellar models and asteroseismology are reliable for very metal-poor stars when individual frequencies are used. The results also provide a direct age anchor for the early formation of the Milky Way, implying that substantial star formation did not commence until redshift z~3 (if the star formed in-situ) or that the Milky Way has undergone merger events for at least ~12 Gyr (if the star was accreted by a dwarf satellite merger such as Gaia Enceladus).

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arXiv2024

Realistic Uncertainties for Fundamental Properties of Asteroseismic Red Giants and the Interplay Between Mixing Length, Metallicity and $ν_{\rm max}$

Asteroseismic modelling is a powerful way to derive stellar properties. However, the derived quantities are limited by built-in assumptions used in stellar models. This work presents a detailed characterisation of stellar model uncertainties in asteroseismic red giants, focusing on the mixing-length parameter $α_{\rm MLT}$, the initial helium fraction $Y_{\rm init}$, the solar abundance scale, and the overshoot parameters. First, we estimate error floors due to model uncertainties to be $\approx$0.4\% in mass, $\approx$0.2\% in radius, and $\approx$17\% in age, primarily due to the uncertain state of $α_{\rm MLT}$ and $Y_{\rm init}$. The systematic uncertainties in age exceed typical statistical uncertainties, suggesting the importance of their evaluation in asteroseismic applications. Second, we demonstrate that the uncertainties from $α_{\rm MLT}$ can be entirely mitigated by direct radius measurements or partially through $ν_{\rm max}$. Utilizing radii from Kepler eclipsing binaries, we determined the $α_{\rm MLT}$ values and calibrated the $α_{\rm MLT}$--[M/H] relation. The correlation observed between the two variables is positive, consistent with previous studies using 1-D stellar models, but in contrast with outcomes from 3-D simulations. Third, we explore the implications of using asteroseismic modelling to test the $ν_{\rm max}$ scaling relation. We found that a perceived dependency of $ν_{\rm max}$ on [M/H] from individual frequency modelling can be largely removed by incorporating the calibrated $α_{\rm MLT}$--[M/H] relation. Variations in $Y_{\rm init}$ can also affect $ν_{\rm max}$ predictions. These findings suggest that $ν_{\rm max}$ conveys information not fully captured by individual frequencies, and that it should be carefully considered as an important observable for asteroseismic modelling.

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arXiv2024

Revising Properties of Planet-Host Binary Systems. IV. The Radius Distribution of Small Planets in Binary Star Systems is Dependent on Stellar Separation

Small planets ($R_{p} \leq 4 R_{\oplus}$) are divided into rocky super-Earths and gaseous sub-Neptunes separated by a radius gap, but the mechanisms that produce these distinct planet populations remain unclear. Binary stars are the only main-sequence systems with an observable record of the protoplanetary disk lifetime and mass reservoir, and the demographics of planets in binaries may provide insights into planet formation and evolution. To investigate the radius distribution of planets in binary star systems, we observed 207 binary systems hosting 283 confirmed and candidate transiting planets detected by the Kepler mission, then recharacterized the planets while accounting for the observational biases introduced by the secondary star. We found that the population of planets in close binaries ($ρ\leq 100$ au) is significantly different from the planet population in wider binaries ($ρ> 300$ au) or single stars. In contrast to planets around single stars, planets in close binaries appear to have a unimodal radius distribution with a peak near the expected super-Earth peak of $R_{p} \sim 1.3 R_{\oplus}$ and a suppressed population of sub-Neptunes. We conclude that we are observing the direct impact of a reduced disk lifetime, smaller mass reservoir, and possible altered distribution of solids reducing the sub-Neptune formation efficiency. Our results demonstrate the power of binary stars as a laboratory for exploring planet formation and as a controlled experiment of the impact of varied initial conditions on mature planet populations.

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arXiv2024

A New Catalog of 100,000 Variable \emph{TESS} A-F Stars Reveals a Correlation Between $δ$ Scuti Pulsator Fraction and Stellar Rotation

δ Scuti variables are found at the intersection of the classical instability strip and the main sequence on the Hertzsprung-Russell diagram. With space-based photometry providing millions of light-curves of A-F type stars, we can now probe the occurrence rate of δ Scuti pulsations in detail. Using 30-min cadence light-curves from NASA's Transiting Exoplanet Survey Satellite's (TESS) first 26 sectors, we identify variability in 103,810 stars within 5-24 cycles per day down to a magnitude of $T=11.25$. We fit the period-luminosity relation of the fundamental radial mode for δ Scuti stars in the Gaia $G$-band, allowing us to distinguish classical pulsators from contaminants for a subset of 39,367 stars. Out of this subset, over 15,918 are found on or above the expected period-luminosity relation. We derive an empirical red edge to the classical instability strip using Gaia photometry. The center where pulsator fraction peaks at 50-70%, combined with the red edge, agree well with previous work in the Kepler field. While many variable sources are found below the period-luminosity relation, over 85% of sources inside of the classical instability strip derived in this work are consistent with being δ Scuti stars. The remaining 15% of variables within the instability strip are likely hybrid or γ Doradus pulsators. Finally, we discover strong evidence for a correlation between pulsator fraction and spectral line broadening from the Radial Velocity Spectrometer (RVS) aboard the Gaia spacecraft, confirming that rotation has a role in driving pulsations in δ Scuti stars.

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arXiv2024

The K2 Asteroseismic KEYSTONE sample of Dwarf and Subgiant Solar-Like Oscillators. I: Data and Asteroseismic parameters

The KEYSTONE project aims to enhance our understanding of solar-like oscillators by delivering a catalogue of global asteroseismic parameters (${Δν}$ and ${ν_{\rm max}}$) for 173 stars, comprising mainly dwarfs and subgiants, observed by the K2 mission in its short-cadence mode during campaigns 6-19. We derive atmospheric parameters and luminosities using spectroscopic data from TRES, astrometric data from $\textit{Gaia}$, and the infrared flux method (IRFM) for a comprehensive stellar characterisation. Asteroseismic parameters are robustly extracted using three independent methods, complemented by an iterative refinement of the spectroscopic analyses using seismic ${\log g}$ values to enhance parameter accuracy. Our analysis identifies new detections of solar-like oscillations in 159 stars, providing an important complement to already published results from previous campaigns. The catalogue provides homogeneously derived atmospheric parameters and luminosities for the majority of the sample. Comparison between spectroscopic ${T_{\rm eff}}$ and those obtained from the IRFM demonstrates excellent agreement. The iterative approach to spectroscopic analysis significantly enhances the accuracy of the stellar properties derived.

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arXiv2024

The TESS-Keck Survey XX: 15 New TESS Planets and a Uniform RV Analysis of all Survey Targets

The Transiting Exoplanet Survey Satellite (TESS) has discovered hundreds of new worlds, with TESS planet candidates now outnumbering the total number of confirmed planets from $\textit{Kepler}$. Owing to differences in survey design, TESS continues to provide planets that are better suited for subsequent follow-up studies, including mass measurement through radial velocity (RV) observations, compared to Kepler targets. In this work, we present the TESS-Keck Survey's (TKS) Mass Catalog: a uniform analysis of all TKS RV survey data which has resulted in mass constraints for 126 planets and candidate signals. This includes 58 mass measurements that have reached $\geq5σ$ precision. We confirm or validate 32 new planets from the TESS mission either by significant mass measurement (15) or statistical validation (17), and we find no evidence of likely false positives among our entire sample. This work also serves as a data release for all previously unpublished TKS survey data, including 9,204 RV measurements and associated activity indicators over our three year survey. We took the opportunity to assess the performance of our survey, and found that we achieved many of our goals including measuring the mass of 38 small ($<4R_{\oplus}$) planets, nearly achieving the TESS mission's basic science requirement. In addition, we evaluated the performance of the Automated Planet Finder (APF) as survey support and observed meaningful constraints on system parameters due to its more uniform phase coverage. Finally, we compared our measured masses to those predicted by commonly used mass-radius relations and investigated evidence of systematic bias.

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arXiv2024

A New Asteroseismic $\textit{Kepler}$ Benchmark Constrains the Onset of Weakened Magnetic Braking in Mature Sun-Like Stars

Stellar spin down is a critical yet poorly understood component of stellar evolution. In particular, results from the Kepler Mission imply that mature age, solar-type stars have inefficient magnetic braking, resulting in a stalled spin down rate. However, a large number of precise asteroseismic ages are needed for mature ($\geq$ 3Gyr) stars in order to probe the regime where traditional and stalled spin-down models differ. In this paper, we present a new asteroseismic benchmark star for gyrochronology discovered using reprocessed Kepler short cadence data. KIC 11029516 (Papayu) is a bright ($K_{p}$ = 9.6 mag) solar-type star with well-measured rotation period (21.1$\pm$0.8 days) from spot modulation using 4 years of Kepler long cadence data. We combine asteroseismology and spectroscopy to obtain $T_{eff}=5888\pm100$ K, $\rm{[Fe/H]} = 0.30 \pm 0.06\,$ dex, $M = 1.24 \pm 0.05 M_{\odot}$, $R = 1.34 \pm 0.02 R_{\odot}$ and age of 4.0 $\pm$ 0.4 Gyr, making Papayu one of the most similar stars to the Sun in terms of temperature and radius with an asteroseismic age and a rotation period measured from spot modulation. We find that Papayu sits at the transition of where traditional and weakened spin-down models diverge. A comparison with stars of similar zero-age main-sequence temperatures supports previous findings that weakened spin-down models are required to explain the ages and rotation periods of old solar-type stars.

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arXiv2024

HIP 65426 is a High-Frequency Delta Scuti Pulsator in Plausible Spin-Orbit Alignment with its Directly Imaged Exoplanet

HIP 65426 hosts a young giant planet that has become the first exoplanet directly imaged with JWST. Using time-series photometry from the Transiting Exoplanet Survey Satellite (TESS), we classify HIP 65426 as a high-frequency $δ$ Scuti pulsator with a possible large frequency separation of $Δν=$7.23$\pm$0.02 cycles day$^{-1}$. We check the TESS data for pulsation timing variations and use the nondetection to estimate a 95% dynamical mass upper limit of 12.8 Mjup for HIP 65426 b. We also identify a low-frequency region of signal that we interpret as stellar latitudinal differential rotation with two rapid periods of 7.85$\pm$0.08 hr and 6.67$\pm$0.04 hr. We use our TESS rotation periods together with published values of radius and $v \sin{i}$ to jointly measure the inclination of HIP 65426 to $i_{\star}=107_{-11}^{+12}$$^\circ$. Our stellar inclination is consistent with the orbital inclination of HIP 65426 b ($108_{-3}^{+6}$$^{\circ}$) at the $68\%$ percent level based on our orbit fit using published relative astrometry. The lack of significant evidence for spin-orbit misalignment in the HIP 65426 system supports an emerging trend consistent with preferential alignment between imaged long-period giant planets and their host stars.

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arXiv2024

A Multiwavelength Survey of Nearby M dwarfs: Optical and Near-Ultraviolet Flares and Activity with Contemporaneous TESS, Kepler/K2, \textit{Swift}, and HST Observations

We present a comprehensive multiwavelength investigation into flares and activity in nearby M~dwarf stars. We leverage the most extensive contemporaneous dataset obtained through the Transiting Exoplanet Sky Survey (TESS), Kepler/K2, the Neil Gehrels Swift Observatory (\textit{Swift}), and the Hubble Space Telescope (HST), spanning the optical and near-ultraviolet (NUV) regimes. In total, we observed 213 NUV flares on 24 nearby M dwarfs, with $\sim$27\% of them having detected optical counterparts, and found that all optical flares had NUV counterparts. We explore NUV/optical energy fractionation in M dwarf flares. Our findings reveal a slight decrease in the ratio of optical to NUV energies with increasing NUV energies, a trend in agreement with prior investigations on G-K stars' flares at higher energies. Our analysis yields an average NUV fraction of flaring time for M0-M3 dwarfs of 2.1\%, while for M4-M6 dwarfs, it is 5\%. We present an empirical relationship between NUV and optical flare energies and compare to predictions from radiative-hydrodynamic and blackbody models. We conducted a comparison of the flare frequency distribution (FFDs) of NUV and optical flares, revealing the FFDs of both NUV and optical flares exhibit comparable slopes across all spectral subtypes. NUV flares on stars affect the atmospheric chemistry, the radiation environment, and the overall potential to sustain life on any exoplanets they host. We find that early and mid-M dwarfs (M0-M5) have the potential to generate NUV flares capable of initiating abiogenesis.

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arXiv2024

A simple method to measure numax for asteroseismology: application to 16,000 oscillating Kepler red giants

The importance of numax (the frequency of maximum oscillation power) for asteroseismology has been demonstrated widely in the previous decade, especially for red giants. With the large amount of photometric data from CoRoT, Kepler and TESS, several automated algorithms to retrieve numax values have been introduced. Most of these algorithms correct the granulation background in the power spectrum by fitting a model and subtracting it before measuring numax. We have developed a method that does not require fitting to the granulation background. Instead, we simply divide the power spectrum by a function of the form nu^-2, to remove the slope due to granulation background, and then smooth to measure numax. This method is fast, simple and avoids degeneracies associated with fitting. The method is able to measure oscillations in 99.9% of previously-studied Kepler red giants, with a systematic offset of 1.5 % in numax values that that we are able to calibrate. On comparing the seismic radii from this work with Gaia, we see similar trends to those observed in previous studies. Additionally, our values of width of the power envelope can clearly identify the dipole mode suppressed stars as a distinct population, hence as a way to detect them. We also applied our method to stars with low (0.19--18.35 muHz) and found it works well to correctly identify the oscillations.

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arXiv2024

The Hybrid Debris Disk Host Star HD 21997 is a High-Frequency Delta Scuti Pulsator

HD 21997 is host to a prototypical "hybrid" debris disk characterized by debris disk-like dust properties and a CO gas mass comparable to a protoplanetary disk. We use Transiting Exoplanet Survey Satellite time series photometry to demonstrate that HD 21997 is a high-frequency delta Scuti pulsator. If the mode identification can be unambiguously determined in future works, an asteroseismic age of HD 21997 may become feasible.

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