Asteroseismology of evolved stars with EGGMiMoSA I. Theoretical mixed-mode patterns from the subgiant to the RGB phase
M. Farnir, C. Pinçon, M-A. Dupret, A. Noels, R. Scuflaire
备注：
21 pages, accepeted on the 30th of June 2021, condensed abstract to meet the 1920 characters requirement (the full abstract will be available in the journal)
This study is the first of a series of papers that provide a technique to analyse the mixed-modes frequency spectra and characterise the structure of stars on the subgiant and red-giant branches. We define seismic indicators, relevant of the stellar structure and study their evolution on a grid of models. The proposed method, EGGMiMoSA, relies on the asymptotic description of mixed modes, defines initial guesses for the parameters, and uses a Levenberg-Marquardt technique to adjust the mixed-modes pattern efficiently. We follow the evolution of the mixed-modes parameters along a grid of models from the subgiant phase to the RGB bump and extend past works. We show the impact of the mass and composition on their evolution. The evolution of the period spacing $Δπ_1$, pressure offset $ε_p$, gravity offset $ε_g$, and coupling factor $q$ as a function of $Δν$ is little affected by the chemical composition and it follows two different regimes depending on the evolutionary stage. On the subgiant branch, the models display a moderate core-envelope density contrast. The evolution of $Δπ_1$, $ε_p$, $ε_g$, and $q$ thus significantly changes with the mass. Also, we demonstrate that, at fixed Z/X and with proper measurements of $Δπ_1$ and $Δν$, we may unambiguously constrain the mass, radius and age of a subgiant star. Conversely, on the red-giant branch, the core-envelope density contrast becomes very large. Consequently, the evolution of $ε_p$, $ε_g$ and $q$ as a function of $Δν$ becomes independent of the mass. This is also true for $Δπ_1$ in stars with masses $\lesssim 1.8M_\odot$ because of core electron degeneracy. This degeneracy is lifted for higher masses, again allowing for a precise measurement of the age. Overall, our computations qualitatively agree with past observed and theoretical studies.
Since few decades, asteroseismology, the study of stellar oscillations, enables us to probe the interiors of stars with great precision. It allows stringent tests of stellar models and can provide accurate radii, masses and ages for individual stars. Of particular interest are the mixed modes that occur in subgiant solar-like stars since they can place very strong constraints on stellar ages. Here we measure the characteristics of the mixed modes, particularly the coupling strength, using a grid of stellar models for stars with masses between 0.9 and 1.5 M_{\odot}. We show that the coupling st…
The presence of mixed modes makes subgiants excellent targets for asteroseismology, providing a probe for the internal structure of stars. Here we study 36 \emph{Kepler} subgiants with solar-like oscillations and report their oscillation mode parameters. We performed a so-called peakbagging exercise, i.e. estimating oscillation mode frequencies, linewidths, and amplitudes with a power spectrum model, fitted in the Bayesian framework and sampled with a Markov Chain Monte Carlo algorithm. The uncertainties of the mode frequencies have a median value of 0.180 $μ$Hz. We obtained seismic parameters…
Detailed modelling of stellar oscillations is able to give precise estimates for stellar ages, but the inferred results typically depend on the adopted model parameters used for the age inference. High-quality asteroseismic data with precise measurements of mixed modes are available for 36 Kepler subgiants. To obtain a handle on the robustness of the ages for these stars, we first study the dependencies of seismic ages on three model input parameters. We find that inferred ages do not change systematically with the helium fraction (Y) or the mixing-length parameter but depend strongly on the m…
The size of convective cores remains uncertain, despite its substantial influence on stellar evolution, and thus on stellar ages. The seismic modeling of young subgiants can be used to obtain indirect constraints on the core structure during main sequence, thanks to the high probing potential of mixed modes. We selected the young subgiant KIC10273246, observed by Kepler, based on its mixed-mode properties. We thoroughly modeled this star, with the aim of placing constraints on the size of its main sequence convective core. We first extracted the parameters of the oscillation modes of the star …
Context: The observations of solar-like oscillations in evolved stars have brought important constraints on their internal rotation rates. To correctly reproduce these data, an efficient transport mechanism is needed in addition to meridional circulation and shear instability. Aims: We study the efficiency of the transport of angular momentum during the subgiant phase. Results: The precise asteroseismic measurements of both core and surface rotation rates available for the six Kepler targets enable a precise determination of the efficiency of the transport of angular momentum needed for each o…
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 wi…
With recent advances in modelling stars using high-precision asteroseismology, the systematic effects associated with our assumptions of stellar helium abundance ($Y$) and the mixing-length theory parameter ($α_\mathrm{MLT}$) are becoming more important. We apply a new method to improve the inference of stellar parameters for a sample of Kepler dwarfs and subgiants across a narrow mass range ($0.8 < M < 1.2\,\mathrm{M_\odot}$). In this method, we include a statistical treatment of $Y$ and the $α_\mathrm{MLT}$. We develop a hierarchical Bayesian model to encode information about the distributio…
Context: Asteroseismic measurements reveal that an unknown efficient angular momentum (AM) transport mechanism is needed for subgiant and red giant stars. A revised prescription for AM transport by the magnetic Tayler instability has been recently proposed as a possible candidate for such a missing mechanism. Results: The revised prescription for the transport by the Tayler instability leads to low core rotation rates after the main sequence that are in better global agreement with asteroseismic measurements than those predicted by models with purely hydrodynamic processes or with the original…
We analyze an asteroseismic binary system: KIC 7107778, a non-eclipsing, unresolved target, with solar-like oscillations in both components. We used \emph{Kepler} short cadence time series spanning nearly two years to obtain the power spectrum. Oscillation mode parameters were determined using Bayesian inference and a nested sampling Monte Carlo algorithm with the \texttt{DIAMONDS} package. The power profiles of the two components fully overlap, indicating their close similarity. We modelled the two stars with \texttt{MESA} and calculated oscillation frequencies with \texttt{GYRE}. Stellar fun…
Determining fundamental properties of stars through stellar modeling has improved substantially due to recent advances in asteroseismology. Thanks to the unprecedented data quality obtained by space missions, particularly CoRoT and Kepler, invaluable information is extracted from the high-precision stellar oscillation frequencies, which provide very strong constraints on possible stellar models for a given set of classical observations. In this work, we have characterized two relatively faint stars, KIC10920273 and KIC11395018, using oscillation data from Kepler photometry and atmospheric cons…
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 r…
Early attempts to apply asteroseismology to study the Galaxy have already shown unexpected discrepancies for the mass distribution of stars between the Galactic models and the data; a result that is still unexplained. Here, we revisit the analysis of the asteroseismic sample of dwarf and subgiant stars observed by Kepler and investigate in detail the possible causes for the reported discrepancy. We investigate two models of the Milky Way based on stellar population synthesis, Galaxia and TRILEGAL. In agreement with previous results, we find that TRILEGAL predicts more massive stars compared to…
Identifying the angular degrees $l$ of oscillation modes is essential for asteroseismology and depends on visual tagging before fitting power spectra in a so-called peakbagging analysis. In oscillating subgiants, radial ($l$= 0) mode frequencies distributed linearly in frequency, while non-radial ($l$ >= 1) modes are p-g mixed modes that having a complex distribution in frequency, which increased the difficulty of identifying $l$. In this study, we trained a 1D convolutional neural network to perform this task using smoothed oscillation spectra. By training simulation data and fine-tuning the …
The asteroseismic modelling of solar-like stars has proved to be valuable in constraining dark matter. In this work we study for the first time the influence of asymmetric dark matter (ADM) in the evolution of a subgiant star (KIC 8228742) by direct comparison with observational data. Both spectroscopic and seismic data are analysed with a new approach to the stellar calibration method, in which DM properties can also be considered as free inputs. In another phase of this study, a calibrated standard stellar model (without DM) is used as the benchmark for DM models. We find that the latter mod…
Although playing a key role in the understanding of the supernova phenomenon, the evolution of massive stars still suffers from uncertainties in their structure, even during their "quiet" main sequence phase and later on during their subgiant and helium burning phases. What is the extent of the mixed central region? In the local mixing length theory (LMLT) frame, are there structural differences using Schwarzschild or Ledoux convection criterion? Where are located the convective zone boundaries? Are there intermediate convection zones during MS and post-MS phase, and what is their extent and l…
In oscillating stars, mixed modes have p-mode character in the envelope and g-mode character in the core. They are observed in subgiants and red giants, in which the large density gradient outside the core effectively divides the star into two coupled cavities. This leads to the phenomenon of mode bumping, in which mode frequencies are shifted from their regular spacing as they undergo avoided crossings. This short contribution introduces a new diagram that involves extending the traditional echelle diagram by replication. This new diagram should prove a useful way of displaying mixed modes an…
With the observations of an unprecedented number of oscillating subgiant stars expected from NASA's TESS mission, the asteroseismic characterization of subgiant stars will be a vital task for stellar population studies and for testing our theories of stellar evolution. To determine the fundamental properties of a large sample of subgiant stars efficiently, we developed a deep learning method that estimates distributions of fundamental parameters like age and mass over a wide range of input physics by learning from a grid of stellar models varied in eight physical parameters. We applied our met…
We present an in-depth analysis of the bright subgiant HR 7322 (KIC 10005473) using Kepler short-cadence photometry, optical interferometry from CHARA, high-resolution spectra from SONG, and stellar modelling using GARSTEC grids and the Bayesian grid-fitting algorithm BASTA. HR 7322 is only the second subgiant with high-quality Kepler asteroseismology for which we also have interferometric data. We find a limb-darkened angular diameter of $0.443 \pm 0.007$ mas, which, combined with a distance derived using the parallax from Gaia DR2 and a bolometric flux, yields a linear radius of $2.00 \pm 0.…
If appropriately excited, a star will oscillate like a giant spherical instrument. In most stars, including the Sun, surface convection provides the excitation mechanism (Goldreich and Keeley, 1977). With turbulent velocities reaching speeds comparable to the local sound speed near the surface of the star, the vigorous convective motions can excite standing acoustic waves. These are known as pressure or p modes because the restoring force arises from the pressure gradient. The broad frequency spectrum of this excitation mechanism gives rise to many oscillation modes, both radial and non-radial…
With the success of the Kepler and CoRoT missions, the number of stars with detected solar-like oscillations has increased by several orders of magnitude, for the first time we are able to perform large-scale ensemble asteroseismology of these stars. In preparation for this golden age of asteroseismology we have computed expected values of various asteroseismic observables from models of varying mass and metallicity. The relationships between these asteroseismic observables, such as the separations between mode frequencies, are able to significantly constrain estimates of the ages and masses o…
Asteroseismology provides a powerful way to constrain stellar parameters. Solar-like oscillations have been observed on subgiant stars with the \emph{Kepler\/} mission. The continuous and high-precision time series enables us to carry out a detailed asteroseismic study for these stars. We carry out data processing of two subgiants of spectral type G: KIC 6442183 and KIC 11137075 observed with the \emph{Kepler} mission, and perform seismic analysis for the two evolved stars. We estimate the values of global asteroseismic parameters: $Δν=64.9\pm 0.2 $ $μ$Hz and $ν_{\rm max}=1225 \pm 17$ $μ$Hz fo…
We present the first detections by the NASA K2 Mission of oscillations in solar-type stars, using short-cadence data collected during K2 Campaign\,1 (C1). We understand the asteroseismic detection thresholds for C1-like levels of photometric performance, and we can detect oscillations in subgiants having dominant oscillation frequencies around $1000\,\rm μHz$. Changes to the operation of the fine-guidance sensors are expected to give significant improvements in the high-frequency performance from C3 onwards. A reduction in the excess high-frequency noise by a factor of two-and-a-half in amplit…
Anti-Solar Differential Rotation May Have Revived Magnetic Braking in the Subgiant 31 Aquilae
Center for Solar-Stellar Connections, WDRC（太阳-恒星联系中心，WDRC）；Institute for Astronomy, University of Hawai‘i（夏威夷大学天体物理研究所）；Department of Astronomy & Astrophysics, University of Chicago（芝加哥大学天文与天体物理系）；Lockheed Martin Solar and Astrophysics Laboratory（洛克希德·马丁太阳与天体物理实验室）；Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM（巴黎萨克雷大学、巴黎西岱大学、CEA、CNRS、AIM）；Department of Physics and Astronomy, Uppsala University（乌普萨拉大学物理与天文系）；Harvard-Smithsonian Center for Astrophysics（哈佛-史密森尼天体物理中心）；Vanderbilt University, Department of Physics & Astronomy（范德堡大学物理与天文系）；Department of Astronomy, Yale University（耶鲁大学天文系）；Sydney Institute for Astronomy (SIfA), School of Physics, University of Sydney（悉尼大学物理学院悉尼天体物理研究所(SIfA)）
We present a comparison of parallaxes and radii from asteroseismology and Gaia DR1 (TGAS) for 2200 Kepler stars spanning from the main sequence to the red giant branch. We show that previously identified offsets between TGAS parallaxes and distances derived from asteroseismology and eclipsing binaries have likely been overestimated for parallaxes <~ 5-10 mas (~ 90-98% of the TGAS sample). The observed differences in our sample can furthermore be partially compensated by adopting a hotter Teff scale (such as the infrared flux method) instead of spectroscopic temperatures for dwarfs and subgiant…
We analysed solar-like oscillations in 1523 $\textit{Kepler}$ red giants which have previously been misclassified as subgiants, with predicted $ν_{\rm max}$ values (based on the Kepler Input Catalogue) between 280$μ$Hz to 700$μ$Hz. We report the discovery of 626 new oscillating red giants in our sample, in addition to 897 oscillators that were previously characterized by Hekker et al. (2011) from one quarter of $\textit{Kepler}$ data. Our sample increases the known number of oscillating low-luminosity red giants by $26\%$ (up to $\sim$ 1900 stars). About three quarters of our sample are classi…
Convective boundary mixing (CBM) is ubiquitous in stellar evolution. It is a necessary ingredient in the models in order to match observational constraints from clusters, binaries and single stars alike. We compute `effective overshoot' measures that reflect the extent of mixing and which can differ significantly from the input overshoot values set in the stellar evolution codes. We use constraints from pressure modes to infer the CBM properties of Kepler and CoRoT main-sequence and subgiant oscillators, as well as in two radial velocity targets (Procyon A and $α$ Cen A). Collectively these ta…
Solar-like oscillations have been observed by Kepler and CoRoT in several solar-type stars, thereby providing a way to probe the stars using asteroseismology. We provide the mode frequencies of the oscillations of various stars required to perform a comparison with those obtained from stellar modelling. We used a time series of nine months of data for each star. The 61 stars observed were categorised in three groups: simple, F-like and mixed-mode. The simple group includes stars for which the identification of the mode degree is obvious. The F-like group includes stars for which the identifica…
Yellow straggler stars (YSSs) fall above the subgiant branch in optical color-magnitude diagrams, between the blue stragglers and the red giants. YSSs may represent a population of evolved blue stragglers, but none have the direct and precise mass and radius measurements needed to determine their evolutionary states and formation histories. Here we report the first asteroseismic mass and radius measurements of such a star, the yellow straggler S1237 in the open cluster M67. We apply asteroseismic scaling relations to a frequency analysis of the Kepler K2 light curve and find a mass of 2.9 $\pm…
Doppler-based planet surveys point to an increasing occurrence rate of giant planets with stellar mass. Such surveys rely on evolved stars for a sample of intermediate-mass stars (so-called retired A stars), which are more amenable to Doppler observations than their main-sequence progenitors. However, it has been hypothesised that the masses of subgiant and low-luminosity red-giant stars targeted by these surveys --- typically derived from a combination of spectroscopy and isochrone fitting --- may be systematically overestimated. Here, we test this hypothesis for the particular case of the ex…
We present results of a long-baseline interferometry campaign using the PAVO beam combiner at the CHARA Array to measure the angular sizes of five main-sequence stars, one subgiant and four red giant stars for which solar-like oscillations have been detected by either Kepler or CoRoT. By combining interferometric angular diameters, Hipparcos parallaxes, asteroseismic densities, bolometric fluxes and high-resolution spectroscopy we derive a full set of near model-independent fundamental properties for the sample. We first use these properties to test asteroseismic scaling relations for the freq…
New insights on stellar evolution and stellar interiors physics are being made possible by asteroseismology. Throughout the course of the Kepler mission, asteroseismology has also played an important role in the characterization of exoplanet-host stars and their planetary systems. The upcoming NASA Transiting Exoplanet Survey Satellite (TESS) will be performing a near all-sky survey for planets that transit bright nearby stars. In addition, its excellent photometric precision, combined with its fine time sampling and long intervals of uninterrupted observations, will enable asteroseismology of…
Using the Navy Precision Optical Interferometer, we measured the angular diameters of 10 stars that have previously measured solar-like oscillations. Our sample covered a range of evolutionary stages but focused on evolved subgiant and giant stars. We combined our angular diameters with Hipparcos parallaxes to determine the stars' physical radii, and used photometry from the literature to calculate their bolometric fluxes, luminosities, and effective temperatures. We then used our results to test the scaling relations used by asteroseismology groups to calculate radii and found good agreement …
Doppler-based planet surveys have shown that, besides metallicity, the planet occurrence is also correlated with stellar mass, increasing from M to F-A spectral types. However, it has recently been argued that the subgiants (which represent A stars after they evolve off the main sequence) may not be as massive as suggested initially, which would significantly change the correlation found. To start investigating this claim, we have studied the subgiant star HD 185351, which has precisely measured physical properties based on asteroseismology and interferometry. An independent spectroscopic diff…
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 o…
We have used asteroseismology to determine fundamental properties for 66 Kepler planet-candidate host stars, with typical uncertainties of 3% and 7% in radius and mass, respectively. The results include new asteroseismic solutions for four host stars with confirmed planets (Kepler-4, Kepler-14, Kepler-23 and Kepler-25) and increase the total number of Kepler host stars with asteroseismic solutions to 77. A comparison with stellar properties in the planet-candidate catalog by Batalha et al. shows that radii for subgiants and giants obtained from spectroscopic follow-up are systematically too lo…
Asteroseismology of evolved solar-like stars is experiencing a growing interest due to the wealth of observational data from space-borne instruments such as the \emph{CoRoT} and \emph{Kepler} spacecraft. In particular, the recent detection of mixed modes, which probe both the innermost and uppermost layers of stars, paves the way for inferring the internal structure of stars along their evolution through the subgiant and red giant phases. Mixed modes can also place stringent constraints on the physics of such stars and on their global properties (mass, age, etc...). Here, using two \emph{Keple…
Asteroseismology of bright stars has become increasingly important as a method to determine fundamental properties (in particular ages) of stars. The Kepler Space Telescope initiated a revolution by detecting oscillations in more than 500 main-sequence and subgiant stars. However, most Kepler stars are faint, and therefore have limited constraints from independent methods such as long-baseline interferometry. Here, we present the discovery of solar-like oscillations in $α$ Men A, a naked-eye (V=5.1) G7 dwarf in TESS's Southern Continuous Viewing Zone. Using a combination of astrometry, spectro…
The power of asteroseismology relies on the capability of global oscillations to infer the stellar structure. For evolved stars, we benefit from unique information directly carried out by mixed modes that probe their radiative cores. This third article of the series devoted to mixed modes in red giants focuses on their coupling factors that remained largely unexploited up to now. With the measurement of the coupling factors, we intend to give physical constraints on the regions surrounding the radiative core and the hydrogen-burning shell of subgiants and red giants. A new method for measuring…
A Homogeneous Catalog of Oscillating Solar-Type Stars Observed by the Kepler Mission and a New Amplitude Scaling Relation Including Chromospheric Activity
Columbia University（哥伦比亚大学）；University of Hawai‘i（夏威夷大学）；University of Sydney（悉尼大学）；Princeton University（普林斯顿大学）
The Transiting Exoplanet Survey Satellite (TESS) is observing bright known planet-host stars across almost the entire sky. These stars have been subject to extensive ground-based observations, providing a large number of radial velocity (RV) measurements. In this work we use the new TESS photometric observations to characterize the star $λ^2$ Fornacis, and following this to update the parameters of the orbiting planet $λ^2$ For b. We measure the p-mode oscillation frequencies in $λ^2$ For, and in combination with non-seismic parameters estimate the stellar fundamental properties using stellar …
The last decade has seen a rapid development in asteroseismology thanks to the CoRoT and Kepler missions. With more detailed asteroseismic observations available, it is becoming possible to infer exactly how oscillations are driven and dissipated in solar-type stars. We have carried out three-dimensional (3D) stellar atmosphere simulations together with one-dimensional (1D) stellar structural models of key benchmark turn-off and subgiant stars to study this problem from a theoretical perspective. Mode excitation and damping rates are extracted from 3D and 1D stellar models based on analytical …
The period 2035-50 considered in the ESA Voyage long-term plan will coincide with a series of foreseeable advances in the characterization of the stellar content of the Milky Way. The Gaia mission, combined with large-scale spectroscopic surveys, is helping to build an unprecedented census in terms of the astrometric, kinematic and chemical properties of Galactic stellar populations. Within a decade, precise measurements of such properties will be available for hundreds of millions of stars. Meanwhile, time-domain surveys initiated with CoRoT and Kepler/K2 and carried on by space missions such…
The nearby star Procyon is a visual binary containing the F5 IV-V subgiant Procyon A, orbited in a 40.84 yr period by the faint DQZ white dwarf Procyon B. Using images obtained over two decades with the Hubble Space Telescope, and historical measurements back to the 19th century, we have determined precise orbital elements. Combined with measurements of the parallax and the motion of the A component, these elements yield dynamical masses of 1.478 +/- 0.012 Msun and 0.592 +/- 0.006 Msun for A and B, respectively. The mass of Procyon A agrees well with theoretical predictions based on asteroseis…
Characterizing the physical properties of exoplanets, and understanding their formation and orbital evolution requires precise and accurate knowledge of their host stars. Accurately measuring stellar masses is particularly important because they likely influence planet occurrence and the architectures of planetary systems. Single main-sequence stars typically have masses estimated from evolutionary tracks, which generally provide accurate results due to their extensive empirical calibration. However, the validity of this method for subgiants and giants has been called into question by recent s…
Exoplanet searches through space-based photometric time series have shown to be very efficient in recent years. However, follow-up efforts on the detected planet candidates have been demonstrated to be critical to uncover the true nature of the transiting objects. In this paper we show a detailed analysis of one of those false positives hidden as planetary signals. In this case, the candidate KOI-3886.01 showed clear evidence of a planetary nature from various techniques. Indeed, the properties of the fake planet set it among the most interesting and promising for the study of planetary evolut…
Plato benchmark stars I. The initial benchmark sample
Royal Observatory of Belgium（比利时皇家天文台）；Keele University（基尔大学）；Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange（蔚蓝海岸大学，蔚蓝海岸天文台，法国国家科学研究中心，拉格朗日实验室）；Uppsala University（乌普萨拉大学）；Institut d’Astrophysique Spatiale (IAS), CNRS, Université Paris-Saclay（天体物理研究所，法国国家科学研究中心，巴黎萨克雷大学）；Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences（尼古拉·哥白尼天文中心，波兰科学院）；Instituto de Astrofísica, Pontificia Universidad Católica de Chile（智利天主教Pontificia大学天体物理研究所）；Heidelberg Institute for Theoretical Studies（海德堡理论研究所）；INAF – Astronomical Observatory of Abruzzo（意大利国家天体物理研究所 - 阿布鲁佐天文台）；INFN, Sezione di Pisa（意大利国家核物理研究所，比萨分部）；INAF – Osservatorio Astrofisico di Arcetri（意大利国家天体物理研究所 - 阿尔切特里天文台）；Instituto de Estudios Astrofísicos, Universidad Diego Portales（迭戈·波特莱斯大学天体研究所以）；LESIA, Observatoire de Paris, Université PSL, CNRS, Sorbonne Université（空间与天体力学实验室，巴黎天文台，巴黎文理研究大学，法国国家科学研究中心，索邦大学）
