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Rasmus Handberg

Publications and source records attributed to Rasmus Handberg.

At least 19 recordsLinked to original sources

Asteroseismology of the G8 subgiant beta Aquilae with SONG-Tenerife, SONG-Australia and TESS

We present time-series radial velocities of the G8 subgiant star beta Aql obtained in 2022 and 2023 using SONG-Tenerife and, for the first time, SONG-Australia. We also analyse a sector of TESS photometry that overlapped with the 2022 SONG data. The resulting power spectrum clearly shows solar-like oscillations centred at 430 muHz. The TESS light curve shows the oscillations at lower signal-to-noise, reflecting the fact that photometric measurements are much more affected by the granulation background than are radial velocities. The simultaneous observations in velocity and photometry represent the best such measurements for any star apart from the Sun. They allowed us to measure the ratio between the bolometric photometric amplitude and the velocity amplitude to be 26.6 +/- 3.1 ppm/(m/s). We measured this ratio for the Sun from published SOHO data to be 19.5 +/- 0.7 ppm/(m/s) and, after accounting for the difference in effective temperatures of and the Sun, these values align with expectations. In both the Sun and beta Aql, the photometry-to-velocity ratio appears to be a function of frequency. We also measured the phase shift of the oscillations in beta Aql between SONG and TESS to be -113 +/- 7 deg, which agrees with the value for the Sun and also with a 3-D simulation of a star with similar properties to beta Aql. Importantly for exoplanet searches, we argue that simultaneous photometry can be used to predict the contribution of oscillations to radial velocities. We measured frequencies for 22 oscillation modes in beta Aql and carried out asteroseismic modelling, yielding an excellent fit to the frequencies. We derived accurate values for the mass and age, and were able to place quite strong constraints on the mixing-length parameter. Finally, we show that the oscillation properties of beta Aql are very similar to stars in the open cluster M67.

astro-ph.SR

Pushing the boundaries of asteroseismic individual frequency modelling: unveiling two evolved very-low metallicity red giants

Metal-poor stars are key to understanding the first stellar generation in the Galaxy. Asteroseismic characterisation of red giants has traditionally relied on global seismic parameters, not the full spectrum of individual oscillation modes. Here, we present the first characterisation of two evolved very metal-poor stars, including the detailed mixed-mode patterns. We demonstrate that incorporating individual frequencies into grid-based modelling of red-giant stars enhances its precision, enabling detailed studies of these ancient stars and allowing us to infer the stellar properties of two $[\mathrm{Fe}/\mathrm{H}]{\sim}{-}2.5$ dex Kepler stars: KIC 4671239 and KIC 7693833. Recent developments in both observational and theoretical asteroseismology allows for detailed studies of the complex oscillation pattern of evolved giants. We employ Kepler time series and surface properties from high-resolution spectroscopic data to asteroseismically characterise the two stars using the BAyesian STellar Algorithm, BASTA. Both stars show agreement between constraints from seismic and classical observables; an overlap unrecoverable when purely considering the global seismic parameters. KIC 4671239 and KIC 7693833 were determined to have masses of $0.78^{+0.04}_{-0.03}$ and $0.83^{+0.03}_{-0.01} M_{\odot}$ with ages of $12.1^{+1.6}_{-1.5}$ and $10.3^{+0.6}_{-1.4}$ Gyr, respectively. A $\sim10$% discrepancy between observed and modelled $\nu_{\mathrm{max}}$ suggests a metallicity dependence of its scaling relation, leading to overestimated masses and incorrect age inferences for metal-poor stars. Utilising the full spectrum of individual oscillation modes, we circumvent the dependence on the asteroseismic scaling relations, providing direct constraints on the stars themselves, pushing the boundaries of state-of-the-art detailed modelling of evolved stars at metallicities far different from solar.

astro-ph.SR

The metamorphosis of the Type Ib SN 2019yvr: late-time interaction

We present observational evidence of late-time interaction between the ejecta of the hydrogen-poor Type Ib supernova (SN) 2019yvr and hydrogen-rich circumstellar material (CSM), similar to the Type Ib SN 2014C. A narrow H{\alpha} emission line appears simultaneously with a break in the light-curve decline rate at around 80-100 d after explosion. From the interaction delay and the ejecta velocity, under the assumption that the CSM is detached from the progenitor, we estimate the CSM inner radius to be located at ~6.5-9.1 {\times} 10^{15} cm. The H{\alpha} emission line persists throughout the nebular phase at least up to +420 d post-explosion, with a full width at half maximum of ~2000 km/s. Assuming a steady mass-loss, the estimated mass-loss rate from the luminosity of the H{\alpha} line is ~3-7 {\times} 10^{-5} M_\odot yr^{-1}. From hydrodynamical modelling and analysis of the nebular spectra, we find a progenitor He-core mass of 3-4 M{_\odot}, which would imply an initial mass of 13-15 M{_\odot}. Our result supports the case of a relatively low-mass progenitor possibly in a binary system as opposed to a higher mass single star undergoing a luminous blue variable phase.

astro-ph.HE

The carbon-rich type Ic supernova 2016adj in the iconic dust lane of Centaurus A: signatures of interaction with circumstellar hydrogen?

We present a comprehensive data set of supernova (SN) 2016adj located within the central dust lane of Centaurus A. SN 2016adj is significantly reddened and after correcting the peak apparent $B$-band magnitude ($m_B = 17.48\pm0.05$) for Milky Way reddening and our inferred host-galaxy reddening parameters (i.e., $R_{V}^{host} = 5.7\pm0.7$ and $A_{V}^{host} = 6.3\pm0.2$), we estimate it reached a peak absolute magnitude of $M_B \sim -18$. Detailed inspection of the optical/NIR spectroscopic time-series reveals a carbon-rich SN Ic and not a SN Ib/IIb as previously suggested in the literature. The NIR spectra shows prevalent carbon-monoxide formation occurring already by +41 days past $B$-band maximum, which is $\approx 11$ days earlier than previously reported in the literature for this object. Interestingly around two months past maximum, the NIR spectrum of SN~2016adj begins to exhibit H features, with a +97~d medium resolution spectrum revealing both Paschen and Bracket lines with absorption minima of $\sim 2000$ km/s, full-width-half-maximum emission velocities of $\sim 1000$ km/s, and emission line ratios consistent with a dense emission region. We speculate these attributes are due to circumstellar interaction (CSI) between the rapidly expanding SN ejecta and a H-rich shell of material formed during the pre-SN phase. A bolometric light curve is constructed and a semi-analytical model fit suggests the supernova synthesized 0.5 solar masses of $^{56}$Ni and ejected 4.2 solar masses of material, though these values should be approached with caution given the large uncertainties associated with the adopted reddening parameters, possible CSI contamination, and known light echo emission. Finally, inspection of Hubble Space Telescope archival data yielded no progenitor detection.

astro-ph.HE

The Astropy Project: Sustaining and Growing a Community-oriented Open-source Project and the Latest Major Release (v5.0) of the Core Package

The Astropy Project supports and fosters the development of open-source and openly-developed Python packages that provide commonly needed functionality to the astronomical community. A key element of the Astropy Project is the core package $\texttt{astropy}$, which serves as the foundation for more specialized projects and packages. In this article, we summarize key features in the core package as of the recent major release, version 5.0, and provide major updates for the Project. We then discuss supporting a broader ecosystem of interoperable packages, including connections with several astronomical observatories and missions. We also revisit the future outlook of the Astropy Project and the current status of Learn Astropy. We conclude by raising and discussing the current and future challenges facing the Project.

astro-ph.IM

TESS Data for Asteroseismology: Light Curve Systematics Correction

Data from the Transiting Exoplanet Survey Satellite (TESS) has produced of order one million light curves at cadences of 120 s and especially 1800 s for every ~27-day observing sector during its two-year nominal mission. These data constitute a treasure trove for the study of stellar variability and exoplanets. However, to fully utilize the data in such studies a proper removal of systematic noise sources must be performed before any analysis. The TESS Data for Asteroseismology (T'DA) group is tasked with providing analysis-ready data for the TESS Asteroseismic Science Consortium, which covers the full spectrum of stellar variability types, including stellar oscillations and pulsations, spanning a wide range of variability timescales and amplitudes. We present here the two current implementations for co-trending of raw photometric light curves from TESS, which cover different regimes of variability to serve the entire seismic community. We find performance in terms of commonly used noise statistics to meet expectations and to be applicable to a wide range of different intrinsic variability types. Further, we find that the correction of light curves from a full sector of data can be completed well within a few days, meaning that when running in steady-state our routines are able to process one sector before data from the next arrives. Our pipeline is open-source and all processed data will be made available on TASOC and MAST.

astro-ph.IM

TESS Data for Asteroseismology (T'DA) Stellar Variability Classification Pipeline: Set-Up and Application to the Kepler Q9 Data

The NASA Transiting Exoplanet Survey Satellite (TESS) is observing tens of millions of stars with time spans ranging from $\sim$ 27 days to about 1 year of continuous observations. This vast amount of data contains a wealth of information for variability, exoplanet, and stellar astrophysics studies but requires a number of processing steps before it can be fully utilized. In order to efficiently process all the TESS data and make it available to the wider scientific community, the TESS Data for Asteroseismology working group, as part of the TESS Asteroseismic Science Consortium, has created an automated open-source processing pipeline to produce light curves corrected for systematics from the short- and long-cadence raw photometry data and to classify these according to stellar variability type. We will process all stars down to a TESS magnitude of 15. This paper is the next in a series detailing how the pipeline works. Here, we present our methodology for the automatic variability classification of TESS photometry using an ensemble of supervised learners that are combined into a metaclassifier. We successfully validate our method using a carefully constructed labelled sample of Kepler Q9 light curves with a 27.4 days time span mimicking single-sector TESS observations, on which we obtain an overall accuracy of 94.9%. We demonstrate that our methodology can successfully classify stars outside of our labeled sample by applying it to all $\sim$ 167,000 stars observed in Q9 of the Kepler space mission.

astro-ph.SR

TESS Data for Asteroseismology: Photometry

Over the last two decades, asteroseismology has increasingly proven to be the observational tool of choice for the study of stellar physics, aided by the high quality of data available from space-based missions such as CoRoT, Kepler, K2 and TESS. TESS in particular will produce more than an order of magnitude more such data than has ever been available before. While the standard TESS mission products include light curves from 120-sec observations suitable for both exoplanet and asteroseismic studies, they do not include light curves for the vastly larger number of targets observed by the mission at a longer 1800-sec cadence in Full Frame Images (FFIs). To address this lack, the TESS Data for Asteroseismology (T'DA) group under the TESS Asteroseismic Science Consortium (TASC), has constructed an open-source pipeline focused on producing light curves for all stars observed by TESS at all cadences, currently including stars down to a TESS magnitude of 15. The pipeline includes target identification, background estimation and removal, correction of FFI timestamps, and a range of potential photometric extraction methodologies, though aperture photometry is currently the default approach. For the brightest targets, we transparently apply a halo photometry algorithm to construct a calibrated light curve from unsaturated pixels in the image. In this paper, we describe in detail the algorithms, functionality, and products of this pipeline, and summarize the noise metrics for the light curves. Companion papers will address the removal of systematic noise sources from our light curves, and a stellar variability classification from these.

astro-ph.IM

The Evolution of Rotation and Magnetic Activity in 94 Aqr Aa from Asteroseismology with TESS

Most previous efforts to calibrate how rotation and magnetic activity depend on stellar age and mass have relied on observations of clusters, where isochrones from stellar evolution models are used to determine the properties of the ensemble. Asteroseismology employs similar models to measure the properties of an individual star by matching its normal modes of oscillation, yielding the stellar age and mass with high precision. We use 27 days of photometry from the Transiting Exoplanet Survey Satellite to characterize solar-like oscillations in the G8 subgiant of the 94 Aqr triple system. The resulting stellar properties, when combined with a reanalysis of 35 yr of activity measurements from the Mount Wilson HK project, allow us to probe the evolution of rotation and magnetic activity in the system. The asteroseismic age of the subgiant agrees with a stellar isochrone fit, but the rotation period is much shorter than expected from standard models of angular momentum evolution. We conclude that weakened magnetic braking may be needed to reproduce the stellar properties, and that evolved subgiants in the hydrogen shell-burning phase can reinvigorate large-scale dynamo action and briefly sustain magnetic activity cycles before ascending the red giant branch.

astro-ph.SR

TESS Data for Asteroseismology: Timing verification

The Transiting Exoplanet Survey Satellite (TESS) is NASA's latest space telescope dedicated to the discovery of transiting exoplanets around nearby stars. Besides the main goal of the mission, asteroseismology is an important secondary goal and very relevant for the high-quality time series that TESS will make during its two year all-sky survey. Using TESS for asteroseismology introduces strong timing requirements, especially for coherent oscillators. Although the internal clock on board TESS is precise in its own time, it might have a constant drift and will thus need calibration, or offsets might inadvertently be introduced. Here we present simultaneously ground- and space-based observations of primary eclipses of several binary systems in the Southern ecliptic hemisphere, used to verify the reliability of the TESS timestamps. From twelve contemporaneous TESS/ground observations we determined a time offset equal to 5.8 +/- 2.5 sec, in the sense that the Barycentric time measured by TESS is ahead of real time. The offset is consistent with zero at 2.3-sigma level. In addition, we used 405 individually measured mid-eclipse times of 26 eclipsing binary stars observed solely by TESS to test the existence of a potential drift with a monotonic growth (or decay) affecting the observations of all stars. We find a drift corresponding to sigma_drift = 0.009 +/- 0.015 sec/day. We find that the measured offset is of a size that will not become an issue for comparing ground-based and space data for coherent oscillations for most of the targets observed with TESS.

astro-ph.EP

TOI-257b (HD 19916b): A Warm sub-Saturn Orbiting an Evolved F-type Star

We report the discovery of a warm sub-Saturn, TOI-257b (HD 19916b), based on data from NASA's Transiting Exoplanet Survey Satellite (TESS). The transit signal was detected by TESS and confirmed to be of planetary origin based on radial velocity observations. An analysis of the TESS photometry, the Minerva-Australis, FEROS, and HARPS radial velocities, and the asteroseismic data of the stellar oscillations reveals that TOI-257b has a mass of $M_P=0.138\pm0.023$\,$\rm{M_J}$ ($43.9\pm7.3$\,$M_{\rm \oplus}$), a radius of $R_P=0.639\pm0.013$\,$\rm{R_J}$ ($7.16\pm0.15$\,$R_{\rm \oplus}$), bulk density of $0.65^{+0.12}_{-0.11}$ (cgs), and period $18.38818^{+0.00085}_{-0.00084}$\,$\rm{days}$. TOI-257b orbits a bright ($\mathrm{V}=7.612$\,mag) somewhat evolved late F-type star with $M_*=1.390\pm0.046$\,$\rm{M_{\odot}}$, $R_*=1.888\pm0.033$\,$\rm{R_{\odot}}$, $T_{\rm eff}=6075\pm90$\,$\rm{K}$, and $v\sin{i}=11.3\pm0.5$\,km\,s$^{-1}$. Additionally, we find hints for a second non-transiting sub-Saturn mass planet on a $\sim71$\,day orbit using the radial velocity data. This system joins the ranks of a small number of exoplanet host stars ($\sim100$) that have been characterized with asteroseismology. Warm sub-Saturns are rare in the known sample of exoplanets, and thus the discovery of TOI-257b is important in the context of future work studying the formation and migration history of similar planetary systems.

astro-ph.EP

Age dating of an early Milky Way merger via asteroseismology of the naked-eye star $\nu$ Indi

Over the course of its history, the Milky Way has ingested multiple smaller satellite galaxies. While these accreted stellar populations can be forensically identified as kinematically distinct structures within the Galaxy, it is difficult in general to precisely date the age at which any one merger occurred. Recent results have revealed a population of stars that were accreted via the collision of a dwarf galaxy, called \textit{Gaia}-Enceladus, leading to a substantial pollution of the chemical and dynamical properties of the Milky Way. Here, we identify the very bright, naked-eye star $\nu$\,Indi as a probe of the age of the early in situ population of the Galaxy. We combine asteroseismic, spectroscopic, astrometric, and kinematic observations to show that this metal-poor, alpha-element-rich star was an indigenous member of the halo, and we measure its age to be $11.0 \pm 0.7$ (stat) $\pm 0.8$ (sys)$\,\rm Gyr$. The star bears hallmarks consistent with it having been kinematically heated by the \textit{Gaia}-Enceladus collision. Its age implies that the earliest the merger could have begun was 11.6 and 13.2 Gyr ago at 68 and 95% confidence, respectively. Input from computations based on hierarchical cosmological models tightens (i.e. reduces) slightly the above limits.

astro-ph.GA

Detection and characterisation of oscillating red giants: first results from the TESS satellite

Since the onset of the `space revolution' of high-precision high-cadence photometry, asteroseismology has been demonstrated as a powerful tool for informing Galactic archaeology investigations. The launch of the NASA TESS mission has enabled seismic-based inferences to go full sky -- providing a clear advantage for large ensemble studies of the different Milky Way components. Here we demonstrate its potential for investigating the Galaxy by carrying out the first asteroseismic ensemble study of red giant stars observed by TESS. We use a sample of 25 stars for which we measure their global asteroseimic observables and estimate their fundamental stellar properties, such as radius, mass, and age. Significant improvements are seen in the uncertainties of our estimates when combining seismic observables from TESS with astrometric measurements from the Gaia mission compared to when the seismology and astrometry are applied separately. Specifically, when combined we show that stellar radii can be determined to a precision of a few percent, masses to 5-10% and ages to the 20% level. This is comparable to the precision typically obtained using end-of-mission Kepler data

astro-ph.SR

TESS Asteroseismology of the known red-giant host stars HD 212771 and HD 203949

The Transiting Exoplanet Survey Satellite (TESS) is performing a near all-sky survey for planets that transit bright stars. In addition, its excellent photometric precision enables asteroseismology of solar-type and red-giant stars, which exhibit convection-driven, solar-like oscillations. Simulations predict that TESS will detect solar-like oscillations in nearly 100 stars already known to host planets. In this paper, we present an asteroseismic analysis of the known red-giant host stars HD 212771 and HD 203949, both systems having a long-period planet detected through radial velocities. These are the first detections of oscillations in previously known exoplanet-host stars by TESS, further showcasing the mission's potential to conduct asteroseismology of red-giant stars. We estimate the fundamental properties of both stars through a grid-based modeling approach that uses global asteroseismic parameters as input. We discuss the evolutionary state of HD 203949 in depth and note the large discrepancy between its asteroseismic mass ($M_\ast = 1.23 \pm 0.15\,{\rm M}_\odot$ if on the red-giant branch or $M_\ast = 1.00 \pm 0.16\,{\rm M}_\odot$ if in the clump) and the mass quoted in the discovery paper ($M_\ast = 2.1 \pm 0.1\,{\rm M}_\odot$), implying a change $>30\,\%$ in the planet's mass. Assuming HD 203949 to be in the clump, we investigate the planet's past orbital evolution and discuss how it could have avoided engulfment at the tip of the red-giant branch. Finally, HD 212771 was observed by K2 during its Campaign 3, thus allowing for a preliminary comparison of the asteroseismic performances of TESS and K2. We estimate the ratio of the observed oscillation amplitudes for this star to be $A_{\rm max}^{\rm TESS}/A_{\rm max}^{\rm K2} = 0.75 \pm 0.14$, consistent with the expected ratio of $\sim0.85$ due to the redder bandpass of TESS.

astro-ph.SR

A giant impact as the likely origin of different twins in the Kepler-107 exoplanet system

Measures of exoplanet bulk densities indicate that small exoplanets with radius less than 3 Earth radii ($R_\oplus$) range from low-density sub-Neptunes containing volatile elements to higher density rocky planets with Earth-like or iron-rich (Mercury-like) compositions. Such astonishing diversity in observed small exoplanet compositions may be the product of different initial conditions of the planet-formation process and/or different evolutionary paths that altered the planetary properties after formation. Planet evolution may be especially affected by either photoevaporative mass loss induced by high stellar X-ray and extreme ultraviolet (XUV) flux or giant impacts. Although there is some evidence for the former, there are no unambiguous findings so far about the occurrence of giant impacts in an exoplanet system. Here, we characterize the two innermost planets of the compact and near-resonant system Kepler-107. We show that they have nearly identical radii (about $1.5-1.6~R_\oplus$), but the outer planet Kepler-107c is more than twice as dense (about $12.6~\rm g\,cm^{-3}$) as the innermost Kepler-107b (about $5.3~\rm g\,cm^{-3}$). In consequence, Kepler-107c must have a larger iron core fraction than Kepler-107b. This imbalance cannot be explained by the stellar XUV irradiation, which would conversely make the more-irradiated and less-massive planet Kepler-107b denser than Kepler-107c. Instead, the dissimilar densities are consistent with a giant impact event on Kepler-107c that would have stripped off part of its silicate mantle. This hypothesis is supported by theoretical predictions from collisional mantle stripping, which match the mass and radius of Kepler-107c.

astro-ph.EP

Asteroseismology of the Hyades red giant and planet host epsilon Tauri

Asteroseismic analysis of solar-like stars allows us to determine physical parameters such as stellar mass, with a higher precision compared to most other methods. Even in a well-studied cluster such as the Hyades, the masses of the red giant stars are not well known, and previous mass estimates are based on model calculations (isochrones). The four known red giants in the Hyades are assumed to be clump (core-helium-burning) stars based on their positions in colour-magnitude diagrams, however asteroseismology offers an opportunity to test this assumption. Using asteroseismic techniques combined with other methods, we aim to derive physical parameters and the evolutionary stage for the planet hosting star epsilon Tau, which is one of the four red giants located in the Hyades. We analysed time-series data from both ground and space to perform the asteroseismic analysis. By combining high signal-to-noise (S/N) radial-velocity data from the ground-based SONG network with continuous space-based data from the revised Kepler mission K2, we derive and characterize 27 individual oscillation modes for epsilon Tau, along with global oscillation parameters such as the large frequency separation and the ratio between the amplitude of the oscillations measured in radial velocity and intensity as a function of frequency. The latter has been measured previously for only two stars, the Sun and Procyon. Combining the seismic analysis with interferometric and spectroscopic measurements, we derive physical parameters for epsilon Tau, and discuss its evolutionary status.

astro-ph.SR

A Hot Saturn Orbiting An Oscillating Late Subgiant Discovered by TESS

We present the discovery of TOI-197.01, the first transiting planet identified by the Transiting Exoplanet Survey Satellite (TESS) for which asteroseismology of the host star is possible. TOI-197 (HIP116158) is a bright (V=8.2 mag), spectroscopically classified subgiant which oscillates with an average frequency of about 430 muHz and displays a clear signature of mixed modes. The oscillation amplitude confirms that the redder TESS bandpass compared to Kepler has a small effect on the oscillations, supporting the expected yield of thousands of solar-like oscillators with TESS 2-minute cadence observations. Asteroseismic modeling yields a robust determination of the host star radius (2.943+/-0.064 Rsun), mass (1.212 +/- 0.074 Msun) and age (4.9+/-1.1 Gyr), and demonstrates that it has just started ascending the red-giant branch. Combining asteroseismology with transit modeling and radial-velocity observations, we show that the planet is a "hot Saturn" (9.17+/-0.33 Rearth) with an orbital period of ~14.3 days, irradiance of 343+/-24 Fearth, moderate mass (60.5 +/- 5.7 Mearth) and density (0.431+/-0.062 gcc). The properties of TOI-197.01 show that the host-star metallicity - planet mass correlation found in sub-Saturns (4-8 Rearth) does not extend to larger radii, indicating that planets in the transition between sub-Saturns and Jupiters follow a relatively narrow range of densities. With a density measured to ~15%, TOI-197.01 is one of the best characterized Saturn-sized planets to date, augmenting the small number of known transiting planets around evolved stars and demonstrating the power of TESS to characterize exoplanets and their host stars using asteroseismology.

astro-ph.EP

Modelling linewidths of Kepler red giants in NGC 6819

We present a comparison between theoretical, frequency-dependent, damping rates and linewidths of radial-mode oscillations in red-giant stars located in the open cluster NGC 6819. The calculations adopt a time-dependent non-local convection model, with the turbulent pressure profile being calibrated to results of 3D hydrodynamical simulations of stellar atmospheres. The linewidths are obtained from extensive peakbagging of Kepler lightcurves. These observational results are of unprecedented quality owing to the long continuous observations by Kepler. The uniqueness of the Kepler mission also means that, for asteroseismic properties, this is the best data that will be available for a long time to come. We therefore take great care in modelling nine RGB stars in NGC 6819 using information from 3D simulations to obtain realistic temperature stratifications and calibrated turbulent pressure profiles. Our modelled damping rates reproduce well the Kepler observations, including the characteristic depression in the linewidths around the frequency of maximum oscillation power. Furthermore, we thoroughly test the sensitivity of the calculated damping rates to changes in the parameters of the nonlocal convection model.

astro-ph.SR