arXiv subjects

T. Arentoft

Publications and source records attributed to T. Arentoft.

At least 19 recordsLinked to original sources

arXiv2026

The Stellar Observations Network Group (SONG) -- A Legacy Archive of Stellar Time-Domain Spectroscopy

The Stellar Observations Network Group (SONG) network has operated for more than a decade, providing long-baseline, high-cadence spectroscopic observations of bright stars and the Sun. The observations, from 2014 through 2025, constitute a substantial archive of high-resolution spectra and precise radial velocities for a broad range of time-domain stellar astrophysics. We present an overview of the status, instrumentation, and scientific capabilities of the SONG network, and describe the scope and accessibility of the SONG Data Archive (SODA). We further illustrate the breadth of science enabled by SONG observations, including asteroseismology, stellar variability studies, binary-star characterisation, and exoplanet research. We summarise the operational status and observing strategies of the SONG facilities, describe the available data products and archive infrastructure, and outline procedures for accessing archival observations and proposing new observations within the SONG community framework. The SODA archive currently contains more than 580,000 spectra of 3091 stars obtained with SONG using either iodine-cell or Thorium-Argon wavelength calibration. The archive spans over a decade and includes extensive time-series data for bright targets across a wide range of stellar types and variability classes. Access to the archive is available to members of the SONG community, which remains open to new participants who agree to follow the community policies. The SONG archive has developed into a major long-baseline resource for stellar spectroscopy and radial-velocity time-series analysis. Continued expansion of the archive, together with coordinated observations obtained contemporaneously with TESS and future PLATO observations, is expected to enable new studies of stellar oscillations, variability, and exoplanet host stars through combined radial-velocity and photometric analyses.

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arXiv2025

Attempting an accurate age estimate of the open cluster NGC 6633 using CoRoT and Gaia

Asteroseismology of solar-like oscillations in giant stars allow the derivation of their masses and radii. For members of open clusters, this provides an age of the cluster that should be identical to the one derived from the colour-magnitude diagram, but independent of the uncertainties that are present for that type of analysis. We aim to identify and measure the properties of giant members of the open cluster NGC6633, and combine these with asteroseismic measurements to derive a precise and self-consistent cluster age. Importantly, we wish to constrain the effects of rotational mixing on stellar evolution, since assumptions about internal mixing can have a significant impact on stellar age estimates. We identify five giant members of NGC6633 using photometry and Gaia data, supplemented by spectroscopic literature measurements. These are combined with asteroseismic measurements from CoRoT data and compared to stellar-model isochrones. This constrains the interior mixing to a low level and enables the most precise, accurate and self-consistent age estimate so far for this cluster. Asteroseismology of the giants and the cluster colour-magnitude diagram provide self-consistent masses of the giant members and their radii constrain the stellar interior mixing to a low level. The [C/N] ratios and Li abundances also suggest that rotation has had very little influence on the evolution of the stars in NGC 6633. This results in an age estimate of 0.55+0.05-0.10 Gyr for NGC6633. Four giant members appear to be in the helium-core burning evolutionary phase as also expected from evolutionary timescales. For the largest giant, the evidence remains inconclusive. A comparison to other age and mass estimates for the same stars in the literature uncovers biases for automated age estimates of helium-core burning stars.

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arXiv2025

Advancing accuracy in age determinations of old-disk stars using an oscillating red giant in an eclipsing binary

The study of resonant oscillation modes in low-mass red giant branch stars enables their ages to be inferred with exceptional ($\sim$10%) precision, unlocking the possibility to reconstruct the temporal evolution of the Milky Way at early cosmic times. Ensuring the accuracy of such a precise age scale is a fundamental yet difficult challenge. Since the age of red giant branch stars primarily hinges on their mass, an independent mass determination for an oscillating red giant star provides the means for such assessment. We analyze the old eclipsing binary KIC10001167, which hosts an oscillating red giant branch star and is a member of the thick disk of the Milky Way. Of the known red giants in eclipsing binaries, this is the only member of the thick disk that has asteroseismic signal of high enough quality to test the seismic mass inference at the 2% level. We measure the binary orbit and obtain fundamental stellar parameters through combined analysis of light curve eclipses and radial velocities, and perform a detailed asteroseismic, photospheric, and Galactic kinematic characterization of the red giant and binary system. We show that the dynamically determined mass $0.9337\pm0.0077 \rm\ M_{\odot}$ (0.8%) of this 10 Gyr-old star agrees within 1.4% with the mass inferred from detailed modelling of individual pulsation mode frequencies (1.6%). This is now the only thick disk stellar system, hosting a red giant, where the mass has been determined both asteroseismically with better than 2% precision, and through a model-independent method at 1% precision, and we hereby affirm the potential of asteroseismology to define an accurate age scale for ancient stars to trace the Milky Way assembly history.

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arXiv2023

An asteroseismic age estimate of the open cluster NGC 6866 using Kepler and Gaia

Asteroseismology of solar-like oscillations in giant stars allow the derivation of their masses and radii. For members of open clusters this allows an age estimate of the cluster which should be identical to the age estimate from the colour-magnitude diagram, but independent of the uncertainties that are present for that type of analysis. Thus, a more precise and accurate age estimate can be obtained. We aim to measure asteroseismic properties of oscillating giant members of the open cluster NGC 6866 and utilise these for a cluster age estimate. Model comparisons allow constraints on the stellar physics, and here we investigate the efficiency of convective-core overshoot and effects of rotation during the main-sequence, which has a significant influence on the age for these relatively massive giants. We identify six giant members of NGC 6866 and derive asteroseismic measurements for five of them. This constrains the convective-core overshoot and enables a more precise and accurate age estimate than previously possible. Asteroseismology establishes the helium-core burning evolutionary phase for the giants, which have a mean mass of 2.8 $M_{\odot}$. Their radii are significantly smaller than predicted by current 1D stellar models unless the amount of convective-core overshoot on the main sequence is reduced to $α_{ov} \leq 0.1 H_p$ in the step-overshoot description. Our measurements also suggest that rotation has affected the evolution of the stars in NGC 6866 in a way that is consistent with 3D simulations but not with current 1D stellar models. The cluster age is estimated to be 0.43 $\pm$ 0.05 Gyr, significantly younger and more precise than most previous estimates. We derive a precise cluster age while constraining convective-core overshooting and effects of rotation in the models. We uncover potential biases for automated age estimates of helium-core burning stars.

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arXiv2022

Establishing the accuracy of asteroseismic mass and radius estimates of giant stars III. KIC4054905, an eclipsing binary with two 10 Gyr thick disk RGB stars

Eclipsing binary stars with an oscillating giant component allow accurate stellar parameters to be derived and asteroseismic methods to be tested and calibrated. To this aim, suitable systems need to be firstly identified and secondly measured precisely and accurately. KIC 4054905 is one such system, which has been identified, but with measurements of a relatively low precision and with some confusion regarding its parameters and evolutionary state. Our aim is to provide a detailed and precise characterisation of the system and to test asteroseismic scaling relations. Dynamical and asteroseismic parameters of KIC4054905 were determined from Kepler photometry and multi-epoch high-resolution spectra from FIES at the Nordic Optical Telescope. KIC 4054905 was found to belong to the thick disk and consist of two lower red giant branch (RGB) components with nearly identical masses of 0.95$M_{\odot}$ and an age of $9.9\pm0.6$ Gyr. The most evolved star displays solar-like oscillations, which suggest that the star belongs to the RGB, supported also by the radius, which is significantly smaller than the red clump phase for this mass and metallicity. Masses and radii from corrected asteroseismic scaling relations can be brought into full agreement with the dynamical values if the RGB phase is assumed, but a best scaling method could not be identified. We measured dynamical masses and radii with a precision better than 1.0%. We firmly establish the evolutionary nature of the system to be that of two early RGB stars with an age close to 10 Gyr, unlike previous findings. The metallicity and Galactic velocity suggest that the system belongs to the thick disk of the Milky Way. We investigate the agreement between dynamical and asteroseismic parameters for KIC 4054905. Consistent solutions exist, but the need to analyse more systems continues in order to establish the accuracy of asteroseismic methods.

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arXiv2021

Asteroseismology of overmassive, undermassive, and potential past members of the open cluster NGC6791

We perform an asteroseismic investigation of giant stars in the field of NGC 6791 with previous indications of atypical evolution. The analysis makes use of observations from Kepler and Gaia in combination with ground-based photometry, a literature radial-velocity study, and measurements of eclipsing binaries in the cluster. We derive mass, radius, effective temperature, evolutionary stage and apparent distance modulus of each target. Among the investigated cluster giants we find clear evidence of overmassive and undermassive members, and non-members with strong hints of potential past membership. Our results indicate that about 10% of the red giants in the cluster have experienced mass-transfer or a merger. High resolution, high-S/N spectroscopic follow-up could confirm potential past membership of the non-members, and reveal whether certain element abundances might expose the non-standard evolution of overmassive and undermassive stars. If so, field stars of similar type could be identified as what they are, i.e. over- or undermassive stars, and not mistakenly classified as younger or older than they are.

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arXiv2021

Age and helium content of the open cluster NGC 6791 from multiple eclipsing binary members. III. Constraints from a subgiant

Models of stellar structure and evolution can be constrained using accurate measurements of the parameters of eclipsing binary members of open clusters. Multiple binary stars provide the means to tighten the constraints and, in turn, to improve the precision and accuracy of the age estimate of the host cluster. In the previous two papers of this series, we have demonstrated the use of measurements of multiple eclipsing binaries in the old open cluster NGC6791 to set tighter constraints on the properties of stellar models than was previously possible, thereby improving both the accuracy and precision of the cluster age. We identify and measure the properties of a non-eclipsing cluster member, V56, in NGC\,6791 and demonstrate how this provides additional model constraints that support and strengthen our previous findings. We analyse multi-epoch spectra of V56 from FLAMES in conjunction with the existing photometry and measurements of eclipsing binaries in NGC6971. The parameters of the V56 components are found to be $M_{\rm p}=1.103\pm 0.008 M_{\odot}$ and $M_{\rm s}=0.974\pm 0.007 M_{\odot}$, $R_{\rm p}=1.764\pm0.099 R_{\odot}$ and $R_{\rm s}=1.045\pm0.057 R_{\odot}$, $T_{\rm eff,p}=5447\pm125$ K and $T_{\rm eff,s}=5552\pm125$ K, and surface [Fe/H]=$+0.29\pm0.06$ assuming that they have the same abundance. The derived properties strengthen our previous best estimate of the cluster age of $8.3\pm0.3$ Gyr and the mass of stars on the lower red giant branch (RGB), which is $M_{\rm RGB} = 1.15\pm0.02M_{\odot}$ for NGC6791. These numbers therefore continue to serve as verification points for other methods of age and mass measures, such as asteroseismology.

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arXiv2020

Properties of the Hyades, the eclipsing binary HD27130, and the oscillating red giant $ε$ Tau

Eclipsing binary stars allow derivation of accurate and precise masses and radii. When they reside in star clusters, properties of even higher precision, along with additional information, can be extracted. Asteroseismology of solar-like oscillations offers similar possibilities for single stars. We improve the previously established properties of the Hyades eclipsing binary HD27130 and re-assess the asteroseismic properties of the giant star $ε$ Tau. The physical properties of these members of the Hyades are then used to constrain the helium content and age of the cluster. New multi-colour light curves were combined with multi-epoch radial velocities to yield masses and radii of HD27130. $T_{\rm eff}$ was derived from spectroscopy and photometry, and verified using the Gaia parallax. We estimate the cluster age from re-evaluated asteroseismic properties of $ε$ Tau while using HD27130 to constrain the helium content. The masses and radii, and $T_{\rm eff}$ of HD 27130 were found to be $M=1.0245\pm0.0024 M_{\odot}$, $R=0.9226\pm0.015 R_{\odot}$, $T_{\rm eff}=5650\pm50$ K for the primary, and $M=0.7426\pm0.0016 M_{\odot}$, $R=0.7388\pm0.026 R_{\odot}$, $T_{\rm eff}=4300\pm100$ K for the secondary component. Our re-evaluation of $ε$ Tau suggests that the previous literature estimates are trustworthy, and that the Hipparcos parallax is more reliable than the Gaia DR2 parallax. The helium content of HD27130 and thus of the Hyades is found to be $Y=0.27$ but with significant model dependence. Correlations with the adopted metallicity results in a robust helium enrichment law with $\frac{ΔY}{ΔZ}$ close to 1.2. We estimate the age of the Hyades to be 0.9 $\pm$ 0.1 (stat) $\pm$ 0.1 (sys) Gyr in slight tension with recent age estimates based on the cluster white dwarfs. (abridged)

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arXiv2020

Extremely precise age and metallicity of the open cluster NGC 2506 using detached eclipsing binaries

Accurate stellar parameters of stars in open clusters can help constrain models of stellar structure and evolution. Here we wish to determine the age and metallicity content of the open cluster NGC 2506. To this end we investigated three detached eclipsing binaries (DEBs; V2032, V4, and V5) for which we determined their masses and radii, as well as four red giant branch stars for which we determined their effective temperatures, surface gravities, and metallicities. Three of the stars in the DEBs have masses close to the cluster turn-off mass, allowing for extremely precise age determination. Comparing the values for the masses and radii of the binaries to BaSTI isochrones we estimated a cluster age of $2.01 \pm 0.10$ Gyr. This does depend on the models used in the comparison, where we have found that the inclusion of convective core-overshooting is necessary to properly model the cluster. From red giant branch stars we determined values for the effective temperatures, the surface gravities, and the metallicities. From these we find a cluster metallicity of $-0.36 \pm 0.10$ dex. Using this value and the values for the effective temperatures we determine the reddening to be E$(b - y) = 0.057 \pm 0.004$ mag. Furthermore, we derived the distance to the cluster from Gaia parallaxes and found $3.101 \pm 0.017$ kpc, and we have performed a radial velocity membership determination for stars in the field of the cluster. Finally, we report on the detection of oscillation signals in $γ$ Dor and $δ$ Scuti members in data from the TESS mission, including the possible detection of solar-like oscillations in two of the red giants.

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arXiv2019

Oscillations in the Sun with SONG: Setting the scale for asteroseismic investigations

Context. We present the first high-cadence multi-wavelength radial-velocity observations of the Sun-as-a-star, carried out during 57 consecutive days using the stellar échelle spectrograph at the Hertzsprung SONG Telescope operating at the Teide Observatory. Aims. The aim was to produce a high-quality data set and reference values for the global helioseismic parameters {ν_{max}}, and {Δν} of the solar p-modes using the SONG instrument. The obtained data set or the inferred values should then be used when the scaling relations are applied to other stars showing solar-like oscillations which are observed with SONG or similar instruments. Methods. We used different approaches to analyse the power spectrum of the time series to determine {ν_{max}}; simple Gaussian fitting and heavy smoothing of the power spectrum. {Δν} was determined using the method of autocorrelation of the power spectrum. The amplitude per radial mode was determined using the method described in Kjeldsen et al. (2008). Results. We found the following values for the solar oscillations using the SONG spectrograph: {ν_{max}} = 3141 {\pm} 12 μHz, {Δν} = 134.98 {\pm} 0.04 μHz and an average amplitude of the strongest radial modes of 16.6 {\pm} 0.4 cm/s. These values are consistent with previous measurements with other techniques.

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arXiv2018

The blue straggler V106 in NGC6791: A prototype progenitor of old single giants masquerading as young

We determine the properties of the binary star V106 in the old open cluster NGC6791. We identify the system to be a blue straggler cluster member by using a combination of ground-based and Kepler photometry and multi-epoch spectroscopy. The properties of the primary component are found to be $M_{\rm p}\sim1.67 \rm M_{\odot}$, more massive than the cluster turn-off, with $R_{\rm p}\sim1.91 \rm R_{\odot}$ and $T_{\rm eff}=7110\pm100$ K. The secondary component is highly oversized and overluminous for its low mass with $M_{\rm s}\sim0.182 \rm M_{\odot}$, $R_{\rm s}\sim0.864 \rm R_{\odot}$ and $T_{\rm eff}=6875\pm200$ K. We identify this secondary star as a bloated (proto) extremely low-mass helium white dwarf. These properties of V106 suggest that it represents a typical Algol-paradox system and that it evolved through a mass-transfer phase which provides insight into its past evolution. We present a detailed binary stellar evolution model for the formation of V106 using the MESA code and find that the mass-transfer phase only ceased about 40 Myr ago. Due to the short orbital period (P=1.4463 d) another mass-transfer phase is unavoidable once the current primary star evolves towards the red giant phase. We argue that V106 will evolve through a common-envelope phase within the next 100 Myr and merge to become a single over-massive giant. The high mass will make it appear young for its true age, which is revealed by the cluster properties. Therefore, V106 is potentially a prototype progenitor of old field giants masquerading as young.

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arXiv2018

The mass and age of the first SONG target: the red giant 46 LMi

The Stellar Observation Network Group (SONG) is an initiative to build a worldwide network of 1m telescopes with highprecision radial-velocity spectrographs. Here we analyse the first radial-velocity time series of a red-giant star measured by the SONG telescope at Tenerife. The asteroseismic results demonstrate a major increase in the achievable precision of the parameters for redgiant stars obtainable from ground-based observations. Reliable tests of the validity of these results are needed, however, before the accuracy of the parameters can be trusted. We analyse the first SONG time series for the star 46 LMi, which has a precise parallax and an angular diameter measured from interferometry, and therefore a good determination of the stellar radius. We use asteroseismic scaling relations to obtain an accurate mass, and modelling to determine the age. A 55-day time series of high-resolution, high S/N spectra were obtained with the first SONG telescope. We derive the asteroseismic parameters by analysing the power spectrum. To give a best guess on the large separation of modes in the power spectrum, we have applied a new method which uses the scaling of Kepler red-giant stars to 46 LMi. Several methods have been applied: classical estimates, seismic methods using the observed time series, and model calculations to derive the fundamental parameters of 46 LMi. Parameters determined using the different methods are consistent within the uncertainties. We find the following values for the mass M (scaling), radius R (classical), age (modelling), and surface gravity (combining mass and radius): M = 1.09 +- 0.04Msun, R = 7.95 +- 0.11 Rsun, age t = 8.2 +- 1.9Gy, and log g = 2.674 +- 0.013.

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arXiv2018

Establishing the accuracy of asteroseismic mass and radius estimates of giant stars. I. Three eclipsing systems at [Fe/H]~ -0.3 and the need for a large high-precision sample

We aim to establish and improve the accuracy level of asteroseismic estimates of mass, radius, and age of giant stars. This can be achieved by measuring independent, accurate, and precise masses, radii, effective temperatures and metallicities of long period eclipsing binary stars with a red giant component that displays solar-like oscillations. We measured precise properties of the three eclipsing binary systems KIC 7037405, KIC 9540226, and KIC 9970396 and estimated their ages be $5.3\pm0.5$, $3.1\pm0.6$, and $4.8\pm0.5$ Gyr. The measurements of the giant stars were compared to corresponding measurements of mass, radius, and age using asteroseismic scaling relations and grid modeling. We found that asteroseismic scaling relations without corrections to $Δν$ systematically overestimate the masses of the three red giants by 11.7%, 13.7%, and 18.9%, respectively. However, by applying theoretical correction factors $f_{Δν}$ according to Rodrigues et al. (2017), we reached general agreement between dynamical and asteroseismic mass estimates, and no indications of systematic differences at the precision level of the asteroseismic measurements. The larger sample investigated by Gaulme et al. (2016) showed a much more complicated situation, where some stars show agreement between the dynamical and corrected asteroseismic measures while others suggest significant overestimates of the asteroseismic measures. We found no simple explanation for this, but indications of several potential problems, some theoretical, others observational. Therefore, an extension of the present precision study to a larger sample of eclipsing systems is crucial for establishing and improving the accuracy of asteroseismology of giant stars.

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arXiv2017

Convective-core overshoot and suppression of oscillations: Constraints from red giants in NGC6811

Using data from the NASA spacecraft Kepler, we study solar-like oscillations in red-giant stars in the open cluster NGC6811. We determine oscillation frequencies, frequency separations, period spacings of mixed modes and mode visibilities for eight cluster giants. The oscillation parameters show that these stars are helium-core-burning red giants. The eight stars form two groups with very different oscillation power spectra; the four stars with lowest Delta_nu-values display rich sets of mixed l=1 modes, while this is not the case for the four stars with higher Delta_nu. For the four stars with lowest Delta_nu, we determine the asymptotic period spacing of the mixed modes, DeltaP, which together with the masses we derive for all eight stars suggest that they belong to the so-called secondary clump. Based on the global oscillation parameters, we present initial theoretical stellar modeling which indicate that we can constrain convective-core overshoot on the main sequence and in the helium-burning phase for these ~2M_sun stars. Finally, our results indicate less mode suppression than predicted by recent theories for magnetic suppression of certain oscillation modes in red giants.

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arXiv2017

First Results From The Hertzsprung Song Telescope: Asteroseismology Of The G5 Subgiant Star {\Mu}Her

We report the first asteroseismic results obtained with the Hertzsprung SONG Telescope from an extensive high-precision radial-velocity observing campaign of the subgiant muHerculis. The data set was collected during 215 nights in 2014 and 2015. We detected a total of 49 oscillation modes with l values from 0 to 3, including some l = 1 mixed modes. Based on the rotational splitting observed in l = 1 modes, we determine a rotational period of 52 days and a stellar inclination angle of 63 degrees. The parameters obtained through modeling of the observed oscillation frequencies agree very well with independent observations and imply a stellar mass between 1.11 and 1.15M_sun and an age of 7.8+/-0.4 Gyr. Furthermore, the high-quality data allowed us to determine the acoustic depths of the He II ionization layer and the base of the convection zone.

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arXiv2016

Detection of solar-like oscillations in relics of the Milky Way: asteroseismology of K giants in M4 using data from the NASA K2 mission

Asteroseismic constraints on K giants make it possible to infer radii, masses and ages of tens of thousands of field stars. Tests against independent estimates of these properties are however scarce, especially in the metal-poor regime. Here, we report the detection of solar-like oscillations in 8 stars belonging to the red-giant branch and red-horizontal branch of the globular cluster M4. The detections were made in photometric observations from the K2 Mission during its Campaign 2. Making use of independent constraints on the distance, we estimate masses of the 8 stars by utilising different combinations of seismic and non-seismic inputs. When introducing a correction to the Delta nu scaling relation as suggested by stellar models, for RGB stars we find excellent agreement with the expected masses from isochrone fitting, and with a distance modulus derived using independent methods. The offset with respect to independent masses is lower, or comparable with, the uncertainties on the average RGB mass (4-10%, depending on the combination of constraints used). Our results lend confidence to asteroseismic masses in the metal poor regime. We note that a larger sample will be needed to allow more stringent tests to be made of systematic uncertainties in all the observables (both seismic and non-seismic), and to explore the properties of RHB stars, and of different populations in the cluster.

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arXiv2016

Hot super-Earths stripped by their host stars

Simulations predict that hot super-Earth sized exoplanets can have their envelopes stripped by photo-evaporation, which would present itself as a lack of these exoplanets. However, this absence in the exoplanet population has escaped a firm detection. Here we demonstrate, using asteroseismology on a sample of exoplanets and exoplanet candidates observed during the Kepler mission that, while there is an abundance of super-Earth sized exoplanets with low incident fluxes, none are found with high incident fluxes. We do not find any exoplanets with radii between 2.2 and 3.8 Earth radii with incident flux above 650 times the incident flux on Earth. This gap in the population of exoplanets is explained by evaporation of volatile elements and thus supports the predictions. The confirmation of a hot-super-Earth desert caused by evaporation will add an important constraint on simulations of planetary systems, since they must be able to reproduce the dearth of close-in super-Earths.

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arXiv2016

Testing the asymptotic relation for period spacings from mixed modes of red giants observed with the Kepler mission

Dipole mixed pulsation modes of consecutive radial order have been detected for thousands of low-mass red-giant stars with the NASA space telescope Kepler. Such modes have the potential to reveal information on the physics of the deep stellar interior. Different methods have been proposed to derive an observed value for the gravity-mode period spacing, the most prominent one relying on a relation derived from asymptotic pulsation theory applied to the gravity-mode character of the mixed modes. Our aim is to compare results based on this asymptotic relation with those derived from an empirical approach for three pulsating red-giant stars. We developed a data-driven method to perform frequency extraction and mode identification. Next, we used the identified dipole mixed modes to determine the gravity-mode period spacing by means of an empirical method and by means of the asymptotic relation. In our methodology, we consider the phase offset, $ε_{\mathrm{g}}$, of the asymptotic relation as a free parameter. Using the frequencies of the identified dipole mixed modes for each star in the sample, we derived a value for the gravity-mode period spacing using the two different methods. These differ by less than 5%. The average precision we achieved for the period spacing derived from the asymptotic relation is better than 1%, while that of our data-driven approach is 3%. Good agreement is found between values for the period spacing derived from the asymptotic relation and from the empirical method. Full abstract in PDF file.

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