The PLATO 2.0 mission (original) (raw)

Abstract

PLATO 2.0 has recently been selected for ESA’s M3 launch opportunity (2022/24). Providing accurate key planet parameters (radius, mass, density and age) in statistical numbers, it addresses fundamental questions such as: How do planetary systems form and evolve? Are there other systems with planets like ours, including potentially habitable planets? The PLATO 2.0 instrument consists of 34 small aperture telescopes (32 with 25 s readout cadence and 2 with 2.5 s candence) providing a wide field-of-view (2232 deg 2) and a large photometric magnitude range (4–16 mag). It focusses on bright (4–11 mag) stars in wide fields to detect and characterize planets down to Earth-size by photometric transits, whose masses can then be determined by ground-based radial-velocity follow-up measurements. Asteroseismology will be performed for these bright stars to obtain highly accurate stellar parameters, including masses and ages. The combination of bright targets and asteroseismology results in high accuracy for the bulk planet parameters: 2 %, 4–10 % and 10 % for planet radii, masses and ages, respectively. The planned baseline observing strategy includes two long pointings (2–3 years) to detect and bulk characterize planets reaching into the habitable zone (HZ) of solar-like stars and an additional step-and-stare phase to cover in total about 50 % of the sky. PLATO 2.0 will observe up to 1,000,000 stars and detect and characterize hundreds of small planets, and thousands of planets in the Neptune to gas giant regime out to the HZ. It will therefore provide the first large-scale catalogue of bulk characterized planets with accurate radii, masses, mean densities and ages. This catalogue will include terrestrial planets at intermediate orbital distances, where surface temperatures are moderate. Coverage of this parameter range with statistical numbers of bulk characterized planets is unique to PLATO 2.0. The PLATO 2.0 catalogue allows us to e.g.: - complete our knowledge of planet diversity for low-mass objects, - correlate the planet mean density-orbital distance distribution with predictions from planet formation theories,- constrain the influence of planet migration and scattering on the architecture of multiple systems, and - specify how planet and system parameters change with host star characteristics, such as type, metallicity and age. The catalogue will allow us to study planets and planetary systems at different evolutionary phases. It will further provide a census for small, low-mass planets. This will serve to identify objects which retained their primordial hydrogen atmosphere and in general the typical characteristics of planets in such low-mass, low-density range. Planets detected by PLATO 2.0 will orbit bright stars and many of them will be targets for future atmosphere spectroscopy exploring their atmosphere. Furthermore, the mission has the potential to detect exomoons, planetary rings, binary and Trojan planets. The planetary science possible with PLATO 2.0 is complemented by its impact on stellar and galactic science via asteroseismology as well as light curves of all kinds of variable stars, together with observations of stellar clusters of different ages. This will allow us to improve stellar models and study stellar activity. A large number of well-known ages from red giant stars will probe the structure and evolution of our Galaxy. Asteroseismic ages of bright stars for different phases of stellar evolution allow calibrating stellar age-rotation relationships. Together with the results of ESA’s Gaia mission, the results of PLATO 2.0 will provide a huge legacy to planetary, stellar and galactic science.

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Article Open access 26 March 2021

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Acknowledgments

The authors acknowledge many fruitful discussions with the ESA study team members, in particular the project scientist and the project manager (Ana Heras and Philippe Gondoin), as well as previous ESA members of the PLATO M1/M2 proposal (Osvaldo Piersanti, Anamarija Stankov). The M3 PLATO 2.0 Mission Consortium also thanks the consortium participants, in particular CNES, France, who prepared the M1/M2 PLATO proposal, which forms the basis on which PLATO 2.0’s application as M3 candidate is built on. We also thank Kayser Threde (in particular the study manager Richard Haarmann) for their inputs and fruitful cooperation in the M3 proposal preparation phase. We also thank the referees for their thorough revision and insightful comments, which have led to a significant improvement of this manuscript.

M. Ammler-von Eiff acknowledges support by DLR (Deutsches Zentrum für Luft- und Raumfahrt) under the project 50 OW 0204. M. Bergemann acknowledges the support by the European Research Council/European Community under the FP7 programme through ERC Grant number 320360. I. Boisse acknowledges the support from the Fundacao para a Ciencia e Tecnologia (Portugal) through the grant SFRH/BPD/87857/2012. For J. Christensen-Dalsgard, funding for the Stellar Astrophysics Centre is provided by The Danish National Research Foundation (Grant DNRF106). The research is supported by the ASTERISK project (ASTERoseismic Investigations with SONG and Kepler) funded by the European Research Council (Grant agreement no.: 267864). L. Gizon acknowledges support from Deutsche Forschungsgemeinschaft SFB 963 “Astrophysical Flow Instabilities and Turbulence” (Project A18). M. Godolt and J.L. Grenfell have been partly supported by the Helmholtz Gemeinschaft (HGF) through the HGF research alliance “Planetary Evolution and Life”. S. Hekker acknowledges financial support from the Netherlands Organisation for Scientific Research (NOW) and the Stellar Ages project funded by the European Research Council (Grant agreement number 338251). K. G. Kislyakova, N. V. Erkaev, M. L. Khodachenko, H. Lammer, M. Güdel acknowledge support by the FWF NFN project S116 “Pathways to Habitability: From Disks to Active Stars, Planets and Life”, and subprojects, S116 604-N16 “Radiation & Wind Evolution from T Tauri Phase to ZAMS and Beyond”, S116 606-N16 “Magnetospheric Electrodynamics of Exoplanets”, S116607-N16 “Particle/Radiative Interactions with Upper Atmospheres of Planetary Bodies Under Extreme Stellar Conditions”. F. Kupka is grateful for support through FWF project P25229-N27. M. Mas-Hesse was supported by Spanish MINECO under grant AYA2012-39362-C02-01. L. Noack has been funded by the Interuniversity Attraction Poles Programme initiated by the Belgian Science Policy Office through the Planet Topers alliance. D.R. Reese is supported through a postdoctoral fellowship from the “Subside fèdèral pour la recherche 2012”, University of Liège. I.W. Roxburgh gratefully acknowledges support from the Leverhulme Foundation under grant EM-2012-035/4. A. Santerne and N.C. Santos acknowledge the support by the European Research Council/European Community under the FP7 through Starting Grant agreement number 239953. S. G. Sousa acknowledges the support by the European Research Council/European Community under the FP7 through Starting Grant agreement number 239953. Gy.M. Szabó acknowledges the Hungarian OTKA Grants K104607, the HUMAN MB08C 81013 grant, by the City of Szombathely under agreement No. S-11-1027 and the János Bolyai Research Scholarship of the Hungarian Academy of Sciences. R. Szabó was supported by the János Bolyai Research Scholarship, Hungarian OTKA grant K83790, KTIA URKUT_10-1-2011-0019 grant Lendület-2009 Young Researchers’ Program and the European Community’s Seventh Framework Programme (FP7/2007-2013) under grant agreements no. 269194 (IRSES/ASK) and no. 312844 (SPACEINN).

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Authors and Affiliations

1. Institute of Planetary Research, German Aerospace Center, Rutherfordstrasse 2, 12489, Berlin, Germany
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2. Department of Astronomy and Astrophysics, Berlin University of Technology, Hardenbergstrasse 36, 10623, Berlin, Germany
   H. Rauer & C. Dreyer
3. LESIA, Observatoire de Paris, PSL Research University, CNRS, UPMC, University Paris-Diderot, 5 Pl Jules Janssen, 92195, Meudon Cedex, France
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4. Instituut voor Sterrenkunde, KU Leuven, Celestijnenlaan 200D, 3001, Leuven, Belgium
   C. Aerts, P. Marcos-Arenal, E. Moravveji, P. Pápics, A. Tkachenko & K. Zwintz
5. Institut d’Astrophysique Spatiale, Université Paris 11, Batiment 12191405, Orsay, Cedex, France
   T. Appourchaux & F. Baudin
6. Center for Space and Habitability, University of Bern, Physikalisches Institut, Sidlerstrasse 5, 3012, Bern, Switzerland
   W. Benz, Y. Alibert & K. Heng
7. Department of Astronomy, AlbaNova University Center, Stockholm University, 106 91, Stockholm, Sweden
   A. Brandeker
8. Stellar Astrophysics Centre, Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, 8000, Aarhus C, Denmark
   J. Christensen-Dalsgaard
9. Laboratoire d’Astrophysique de Marseille, 38 rue Frédéric Joliot-Curie, 13388, Marseille Cedex 13, France
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10. Max-Planck-Institut für Sonnensystemforschung, Justus-von-Liebig-Weg 337077, Göttingen, Germany
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11. Institute for Astronomy, University of Vienna, Türkenschanzstrasse 17, 1180, Vienna, Austria
    M. Güdel
12. Instituto de Astronomia, Geofísica e Ciências Atmosféricas - IAG/USP, São Paulo, Brazil
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13. Centro de Astrobiología (CSIC–INTA), Madrid, Spain
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14. INAF- Osservatorio Astrofisico di Catania, Via S. Sofia 78, 95123, Catania, Italy
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15. Dipartimento di Fisica e Astronomia “Galileo Galilei”, Università di Padova, Vicolo dell’Osservatorio 3, 35122, Padova, Italy
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16. Department of Physics, Warwick University, Gibbet Hill Rd, Coventry CV4 7AL, UK
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17. Centro de Astrofísica, Universidade do Porto, Rua das Estrelas, 4150-762, Porto, Portugal
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21. Observatoire de Genève, 51 chemin des Maillettes, 1290, Sauverny, Switzerland
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23. Thüringer Landessternwarte Tautenburg, Sternwarte 5, 07778, Tautenburg, Germany
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24. INAF-Osservatorio Astronomico di Brera, Via E. Bianchi 46, 23807, Merate, LC, Italy
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25. Institute for Astrophysics, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, 37077, Göttingen, Germany
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26. Leibniz Institute for Astrophysics, An der Sternwarte 16, 14482, Potsdam, Germany
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27. Institute of Astronomy, University of Cambridge, CB3 OHA, Cambridge, UK
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28. INAF - Osservatorio Aastrofisico di Torino, Via Osservatorio 20, 10025, Pino Torinese, Italy
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30. CEA, DSM/IRFU/Service d’Astrophysique, Bat 709, CEA-Saclay, 91191, Gif-sur-Yvette, France
    S. Brun, R. A. García & S. Mathis
31. Department of Physics and Astronomy, University of Leicester, Leicester LE1 7RH, UK
    M. Burleigh
32. Royal Observatory of Belgium, Ringlaan 3, 1180, Brussels, Belgium
    L. Noack
33. INAF - Osservatorio Astronomico di Teramo, Via Mentore Maggini s.n.c., 64100, Teramo, Italy
    S. Cassisi & G. Raimondo
34. School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham, B152TT, UK
    W. Chaplin & A. Miglio
35. Université de Toulouse, UPS-OMP, IRAP, 14 Av. E. Belin, 31400, Toulouse, France
    S. Charpinet & S. D. Vauclair
36. Lund Observatory, Box 43, 221 00, Lund, Sweden
    R. P. Church, M. B. Davies, S. Feltzing & A. Johansen
37. Instituto de Astrofísica de Canarias, Tenerife, Spain
    H. J. Deeg
38. Laboratory of Automation and Control, Polytechnic School of the University of São Paulo, São Paulo, Brazil
    F. de Oliveira Fialho
39. Department of Physical Sciences, The Open University, Walton Hall, Milton Keynes, MK7 6AA, UK
    R. Farmer, C. A. Haswell, U. Kolb & A. J. Norton
40. Observatoire de Grenoble, Institut de Planetologie et d’Astrophysique de Grenoble, 38041, Grenoble Cedex 9, France
    X. Bonfils & T. Forveille
41. ASI Science Data Center, Via del Politecnico snc, 00133, Rome, Italy
    P. Giommi, G. Giuffrida & P. M. Marrese
42. Research School of Astronomy and Astrophysics, Australian National University, Cotter Road, Weston ACT, 2611, Australia
    M. Asplund
43. Institut d’Astrophysique et Géophysique de l’Université de Liège, Allée du 6 Août 17, 4000, Liège, Belgium
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44. Institut d’Astrophysique de Paris, UMR7095 CNRS, Université Pierre & Marie Curie, 98bis Bd Arago, 75014, Paris, France
    G. Hébrard
45. Sterrenkundig Instituut Anton Pannekoek, Universiteit van Amsterdam, Postbus 94249, 1090 GE, Amsterdam, The Netherlands
    S. Hekker
46. Department of Geophysics, Atmospheric and Planetary Sciences, Tel-Aviv University, Tel-Aviv, Israel
    R. Helled
47. SETI Institute, NASA Ames Research Center, Mountain View, CA, USA
    J. M. Jenkins
48. Austrian Academy of Sciences, Schmiedlstrasse 6, 8042, Graz, Austria
    M. L. Khodachenko, K. G. Kislyakova & H. Lammer
49. Institut für Astronomie and Astrophysik, Universität Tübingen, Morgenstelle 10, 72076, Tübingen, Germany
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50. Fakultät für Mathematik, Universität Wien, Oskar-Morgenstern-Platz 1, 1090, Wien, Austria
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51. INAF - Astronomical Observatory of Padova, Padua,, Italy
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52. Space Science Institute, 4750 Walnut Street, Suite#205, Boulder, CO, 80301, USA
    S. Mathur
53. Monash Centre for Astrophysics, School of Mathematical Sciences, Monash University, Victoria, 3800, Australia
    H. Moradi
54. Planet and Star Formation Department, Max Planck Institute for Astronomy, Königstuhl 17, 69117, Heidelberg, Germany
    C. Mordasini
55. Instituto Mauá de Tecnologia, São Paulo, Brazil
    V. C. Parro
56. Observatoire Midi-Pyrenées, 14 Av E Belin, 31400, Toulouse Cedex, France
    P. Petit
57. Laboratoire Univers et Particules de Montpellier, Université Montpellier 2, CNRS, 34095, Montpellier cedex 5, France
    B. Plez
58. ZAH, Landessternwarte, Universität Heidelberg, Königstuhl 12, 69117, Heidelberg, Germany
    A. Quirrenbach & S. Reffert
59. Institute of Physics, University of Rostock, 18051, Rostock, Germany
    R. Redmer
60. Astronomy Unit, School of Physics and Astronomy, Queen Mary University of London, Mile End Rd, London, E1 4NS, UK
    R. P. Nelson & I. W. Roxburgh
61. CRAAM - Mackenzie University, Sao Paulo, Brazil
    A. Silva-Valio
62. Isaac Newton Group of Telescopes, Astronomy Group, Apartado 321, 38700, Santa Cruz de La Palma, Spain
    I. Skillen
63. Leiden Observatory, Leiden University, Postbus 9513, 2300 RA, Leiden, The Netherlands
    I. Snellen
64. Astronomical Institute, Faculty of Mathematics and Physics, Charles University in Prague, V Holešovičkách 2, 18000, Prague 8, Czech Republic
    M. Švanda
65. ELTE Gothard Astrophysical Observatory, Szent Imre herceg út 112, 9704, Szombathely, Hungary
    Gy. M. Szabó
66. Atmosphere and Planetary Sciences Department, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA, 02139, USA
    D. Valencia
67. Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge, CB3 0HA, UK
    N. A. Walton
68. Comparative Planetology, Centre for Earth Evolution and Dynamics, University of Oslo, PO 1048 Blindern, 0316, Oslo, Norway
    S. C. Werner
69. Sydney Institute for Astronomy (SIfA), School of Physics, University of Sydney, Sydney, NSW, 2006, Australia
    D. Stello

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Corresponding author

Correspondence toH. Rauer.

Appendix A

Appendix A

Methods: characterizing planets and their host stars

Since the PLATO 2.0 mission addresses science goals in very different scientific communities, we briefly describe the key aspects of the methods used.

1.1 A1 Planetary transits, a method to detect planets and determine their parameters

The transit method photometrically measures the flux of target stars over time, searching for a dimming of stellar flux by an orbiting planet passing through the line-of-sight to Earth. When the planet is in front of the star, it shades an area on the stellar surface proportional to its size. The dimming of stellar flux is therefore proportional to the square of the radius of the planet, Rplanet, relative to the radius of the star, RStar:ΔF α(Rplanet/RStar)2. Figure 17 shows as an example the transit light curve of Kepler-10b, the smallest known exoplanet with radius and mass measurement so far (Rplanet=1.416+/−0.03 REarth, Mplanet=4.6+/−1.2 MEarth, [24]). The round shape during transit is caused by the limb darkening of the host star. The transit method allows us to directly measure a planet’s size once the size of the star is known.

Fig. 17

Transit light curve of Kepler-10b [23]. The planet has an orbital period of about 0.8 days and was observed by Kepler for a period over 8 months for this data set. The V magnitude of the host star is 10.96 mag

Full size image

The mass of a detected transiting planet then has to be determined by other means, for example by spectroscopic radial-velocity follow-up. Once radius and true mass of the detected object are known, its bulk parameters are well determined and the object can be clearly separated from possible false-alarm events also causing periodic dimming of stellar intensity, such as spots or eclipsing binaries. The combination of radius and true mass provides the mean density of the planet. In combination with models of planetary interiors, the inner structures of planets can be constrained.

The periodicity of transit events allows us to derive the orbital period and therefore orbital distance according to Kepler’s 3rd law. If the secondary eclipse can be detected, i.e. the planet disappears behind its host star, the orbital eccentricity can also be derived. Furthermore, the combination of transits with spectroscopic radial-velocity follow-up allows us to determine the alignment of the planetary orbital plane with the projected stellar rotation axis and the sense of orbital revolution of the planet around its star by the Rossiter-McLaughlin effect [244, 306].

High-precision light curves, such as those provided by the PLATO 2.0 mission, will allow us to detect exomoons and possibly even rings of Saturn-like exoplanets.

What makes the transit method a ‘gold-mine’ for planetary research is the ability to not only detect planets, but also characterize them physically. The prime planet parameters radius, true mass and therefore mean planet density have already been mentioned. Furthermore, photometric measurements of the stellar light reflected on the surface of the orbiting planet allow us to determine the planetary albedo. During secondary eclipse the emitted infrared flux can be derived and the planet’s effective temperature determined. Spectroscopic observations during primary transit and during secondary eclipse permit detection of atmospheric absorption by atoms and molecules in the planetary atmosphere. The analysis of the transit ingress and egress can be used to map the planetary atmosphere, at least for close-in hot giants.

In summary, transiting planets allow us to derive the following parameters of a planet:

∙ Orbit: – Period, semi-major axis, spin-orbit alignment

∙ Planet parameters: –radius, mass, density, constrain inner structure and composition

– effective temperature, albedo, atmospheric composition, surface heat distribution and reflectivity variations from phase curves for gas giants in IR and optical

– exomoons, planetary rings, Trojan objects

The main detection and characterization goal of PLATO 2.0 is focused on small, terrestrial planets, down to Earth-sized and smaller. An Earth-sized planet around a solar-like star causes a transit depth of about 0.008 %. It is obvious that high signal-to-noise-ratio (SNR) light curves are needed to detect such small signals and disentangle them from stellar activity. As an example, one can look at CoRoT-7b and Kepler-10b [23, 218] two planets slightly larger than Earth (1.6+/−0.1 REarth, Hatzes et al. [163] and 1.416+/−0.03 REarth, Batalha et al. [23], respectively) on short-period orbits (<1 day period), orbiting stars around 11 mag. Transits of both planets were clearly detected by the satellite telescopes and allowed determination of their radii. However, several transit events were co-added to achieve this precision. It is clear that brighter target stars must be screened when targeting small planets on long orbital periods. Furthermore, the investment of observing time to determine the planetary mass from radial-velocity measurements for such low-mass planets around faint stars is large and restricted to relatively bright host stars. This will be even worse for Earth-mass planets. This is the particular strength of the PLATO 2.0 mission which is designed to detect planets around bright stars in large numbers, allowing for such follow-up investigations and thereby providing statistical information on planet properties.

We furthermore note that planetary masses and radii cannot be determined independently from the properties of their host stars. For both of these parameters, the result is expressed in terms of the corresponding stellar parameter. The accuracy of the planetary parameters derived, therefore, is ultimately limited by our knowledge of the star. PLATO 2.0 addresses this key issue by performing asteroseismology analysis of all planet hosting stars in its main magnitude range (4–11 mag), thereby providing radii and masses with unprecedented accuracy. In addition, the asteroseismology analysis allows determining the age of stars, hence planetary systems, as accurate as 10 %.

A disadvantage of the transit method is the required transit geometry. The so-called geometrical probability is the probability to see a system edge-on. Table 3 provides some examples. The geometrical probability mainly scales with the orbital distance, a, of the planet as 1/a. It is around 10 % for a close-in hot Jupiter and decreases to about 0.5 % for a planet on a 1 year orbit like Earth. The transit event itself is always short compared to the orbital period of planets. Searching for transits therefore requires continuous coverage of planetary orbits not to miss the short transit events. PLATO 2.0 addresses these challenges of the transit method by providing a very large field-of-view (FoV) and many pointings on the sky covering a very large number of stars, combined with a flexible observing strategy.

Table 3 Examples for transit parameters in our Solar System, for the hot Jupiter planet CoRoT-1b [17, 145] and the super-Earths CoRoT-7b [218]

Full size table

1.2 A2 Asteroseismology: a technique for determining highly accurate stellar and planetary parameters

1.2.1 Properties of stellar oscillations

Modes of stellar oscillations can be described by spherical harmonics Yℓ,m(𝜃,ϕ) as functions of position (𝜃, ϕ) on the stellar surface. The eigenfrequencies ν n,ℓ,m are described by the three “quantum numbers” (n,ℓ,m), where n is the radial order, ℓ the latitudinal degree, and m azimuthal order of the spherical harmonic. For a spherical star there is no dependence on the azimuthal order m; but this degeneracy is broken by rotation and/or magnetic fields. For slow rotation, the frequencies ν n,ℓ,m=ν n,ℓ+m<Ω>, where m belongs to {−ℓ,ℓ}, and <Ω> is a weighted average of the interior rotation depending on the internal structure of the star and the particular eigenmode. This can be used to probe the internal angular velocity of the star. Measurements of modes with ℓ values only up to 3 are expected for PLATO 2.0 targets; since the stellar disk cannot be resolved the signal from modes of higher degree is strongly suppressed by averaging over regions with different oscillation phases.

The oscillation frequencies, including the rotational splitting, are found by fitting peaks in the power spectrum of the light curve. Determining frequencies of modes with _ℓ_=0,1,2,3 with the solar data is quite straightforward giving estimated errors <0.1 μHz, while for the 137 day run on HD 49385, we can extract frequencies with errors ∼0.3 μHz. The goal with the much longer monitoring to be performed with PLATO 2.0 is to achieve accuracies ∼0.1 μHz.

The power spectra show characteristic spacings between the peaks. These are usually described in terms of separations such as the large separations Δ ℓ =ν n,ℓ −ν n_−1,ℓ between modes of the same degree ℓ and adjacent n values and the small separations, e.g., δ 02=ν n,0−_ν _n_−1,2 between the narrowly separated peaks corresponding to modes _ℓ_=0,2. Additionally we have the small separations δ 01=ν n,0−(ν _n_−1,1+ν n,1)/2. These are particularly valuable when only modes of degree _ℓ_=0,1 can be reliably determined. The separations provide diagnostic information on the stellar internal structure near the core and hence information on the age of the star. The large separations provide a measurement of the star’s acoustic radius, i.e., the travel time of a sound wave from the stellar centre to the surface, which is related to the stellar mean density ∼ M/R 3, while the small separations such as δ 01, δ 02 give diagnostics of the interior structure. Periodic modulations in the frequencies or separations give diagnostics of the location of the boundaries of convective cores and envelopes, as well as properties of the helium ionization zone (e.g., [14, 87, 174, 226, 249, 311]. The outer layers of the star are poorly understood and their contribution to the frequencies must be modeled or corrected for in the asteroseismic analysis [194, 308].

1.2.2 Asteroseismic inferences

From the frequencies determined from the power spectrum of the light curve we need to extract physical information. There are several techniques for this, the choice depending on the quality of the data and the type of information desired, ranging from overall properties such as mass and radius of the star to detailed information about its internal structure.

We first consider the case where the S/N ratio in the seismic data is insufficient to allow robust extraction of individual p mode frequencies; here it may still be possible to extract average estimates of the large and perhaps small separations < Δ0 >< Δ1 >, < _d_ 01 >, < _d_ 02 < and their ratios over one or more frequency ranges, owing to their regularity. For very low signal-to-noise data the mean large separation > Δ <, some indication of its variation with frequency, and possibly an average value of the small separation d 02, can be determined from frequency-windowed autocorrelation of the time series [263, 310, 312]. These average values provide a set of seismic data well-suited to constraining the exoplanet host star parameters (cf. [77]). Coupled with classical observations of L, T e f f , [Fe/H], log g delivered by Gaia (or even more precisely by other means) this has considerably better diagnostic power than the classical observables alone.

For most stars measurement of the average large separation should allow the stellar density to be constrained to a precision of several percent from model fitting (e.g., [388]). With an accurate knowledge of the effective temperature and/or luminosity, a seismic radius can be determined with a similar precision. The use of the average large separation together with the radius from Gaia can also provide a seismic mass with a precision higher than provided by the classical observables alone. For example, scaling relations relate the averaged large separation, > Δ_ν_ <, and the frequency at maximum power, _ν_ max, to the mass, radius and effective temperature of the star [193], leading to: \begin{array}{@{}rcl@{}} \frac{R}{R_{sun} }&=&\left({\frac{135~\mu \text{Hz}}{\left\langle {\Delta \nu} \right\rangle }} \right)^{2}\left({\frac{\nu_{\max } }{3050~\mu \text{Hz}}} \right)\left({\frac{T_{\mathit{eff}} }{5777K}} \right)^{1/2};\frac{M}{M_{sun} }=\left({\frac{135~\mu \text{Hz}}{\left\langle {\Delta \nu} \right\rangle }} \right)^{4}\\ &&\times\left({\frac{\nu_{\max } }{3050~\mu \text{Hz}}} \right)^{3}\left({\frac{T_{\mathit{eff}} }{5777K}} \right)^{3/2} \end{array}

where the radius and mass are normalized to the solar values.

Mass and radius determinations that are based on average seismic quantities will also be used to yield a first, very rapid determination of mass and radius for a large sample of stars. These seismic radii and masses will also serve as initial input for the more precise forward and inversion techniques described below.

Averaged oscillation quantities or individual frequencies can be used in forward model fitting which has been extensively used. Here one compares an observed data set with the predictions from a grid of evolutionary stellar models in order to find the model that best fits the observables (e.g., [2, 52, 245, 248]). The grid is composed of stellar models that are computed under a range of assumptions about the physical processes that govern stellar evolution. The search in the grid is restricted to satisfy the fundamental properties of the star (magnitude, effective temperature, gravity, metallicity, projected rotational velocity (mV, Teff, log g, [Fe/H], v sin i,..) and the oscillation observables. In practice one seeks to minimize the differences between observed and computed, seismic and non-seismic, parameters. Several methods can be used to carry out such minimization (see for instance [295, 350]). The unknown effect of the surface layers on the absolute values of the frequencies can be overcome by different techniques (e.g., [194, 308]). The best fit model then gives values for the mass, radius, age and internal structure of the stars. If individual frequencies are used the fit is typically overdetermined, and significant differences between the observed and model values may indicate inadequacies in the stellar modelling being used.

The minimum seismic information necessary in the fitting process can be estimated following Metcalfe et al. [245]. The authors found that with half a dozen surface-corrected frequencies available at each of _ℓ_=0 and _ℓ_=1, it becomes possible to constrain the model-dependent masses to within 3 %, and the corresponding ages that the star has spent on the main sequence to within 5 %, if the heavy-element abundances are known to within a factor of two. Note that this result assumes that the model physics is correct. With the addition of more frequency estimates (i.e., of _ℓ_=2 modes, and of more overtones) further improvement of the parameter uncertainties will be possible. For a main-sequence target observed at m V =11, we would expect to be able to measure more than ten overtones of its _ℓ_=0,1 and 2 frequencies.

Individual frequencies can de determined as in Appourchaux et al. [10]. When this is done, more precise and detailed information about the stars can also be obtained through inversion techniques.

The probably most suitable technique is model-independent and seeks to infer the internal density profile inside a star which best fits a set of observed frequencies (see e.g., [309] for more details on the technique. Alternative inversion techniques are described in e.g., [300]). Once we know the density profile, the total mass of the star can be simply computed as the integral of the density over the radius of the star. It is assumed that this will be determined from Gaia results. Note that the regions where the density is least well constrained make only a small contribution to the total mass: in the centre the radius r is small and in the outer layers the density is small. The resulting density profiles can then be compared with those predicted by stellar evolution models to estimate the evolutionary age of the star. The analysis is iterative, with the mass and radius for the initial model derived for instance from observed average seismic properties, as discussed above. It should also be stressed that the derivation of a model-independent mass requires that the radius R of the star is determined by non-seismic means. As mentioned earlier, radii of the PLATO 2.0 exoplanet host stars will be known to an accuracy better than 2 % thanks to Gaia, which translates into a well constrained model-independent exoplanet host star mass with a relative precision better than 2 %.

As a star evolves towards the end of, and beyond, the main sequence it becomes more centrally condensed. As a result, an increasing number of frequencies of oscillation modes behave like g modes in the core and p modes in the envelope (“mixed modes”). Their frequencies deviate from the regular spacing of asymptotic pure p modes and can therefore be identified. This behavior changes very quickly with stellar age, and the modes therefore yield a strong (though model-dependent) constraint on the age of the star. Both CoRoT and Kepler have observed stars presenting such modes (e.g., [95, 246]). For the non-seismic parameters, the largest source of observational uncertainty comes from the estimated heavy-element abundances. From the luminosity precision expected from Gaia, it would in principle be possible to constrain the abundances seismically to a precision of about 10 % [245], thus further improving the accuracy of the star’s mass and age.

1.2.3 Effects of rotation

As mentioned above, stellar rotation induces a splitting of the frequencies according to the azimuthal order m of the mode, by an amount which is essentially a weighted average of the internal rotation rate. The weight function (the so-called rotational kernel) can be determined given the inferred structure of the star. For predominantly acoustic modes most weight is given to the stellar envelope, with little dependence on the mode, and the rotational splitting thus predominantly gives an average of the rotation rate in the outer parts of the star. If in addition the surface rotation rate can be determined from spot modulation, as has been done in several cases from CoRoT and Kepler data (e.g., Nielsen et al. [273]), some indication can be obtained of the variation of rotation with depth. In evolved stars, on the other hand, the observation of mixed modes provides information about the rotation in the deep interior (e.g., [28, 96, 265]).

Equally important are the inferences that can be made from the amplitudes of the rotationally split components. Given the stochastic nature of the mode excitation, all components are expected to be excited to the same intrinsic amplitude, on average. However, the observed amplitudes depend on the inclination of the rotation axis relative to the line of sight [148]. If the rotation axis points towards the observer only the m_=0 modes are visible, while if it is in the plane of the sky only modes where ℓ_−_m is even are seen. For intermediate inclination all 2_ℓ+1 components are visible, and from their relative amplitudes the inclination can be inferred. This is particularly interesting in the case of stars where planetary systems have been detected using the transit technique, as will be the case for PLATO 2.0; here such observations can test the alignment or otherwise of the orbital planes of the planets with the stellar equator [69, 149].

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Rauer, H., Catala, C., Aerts, C. et al. The PLATO 2.0 mission.Exp Astron 38, 249–330 (2014). https://doi.org/10.1007/s10686-014-9383-4

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• Published: 04 September 2014
• Issue Date: November 2014
• DOI: https://doi.org/10.1007/s10686-014-9383-4

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