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The CoRoT Legacy Book c The authors, 2016 DOI: 10.1051/978-2-7598-1876-1.c041 IV.1 Insights on the internal structure of stars as provided by seismology Classical pulsators and Solar-like oscillations A. Grotsch-Noels1 and S. Deheuvels2; 3 1 Institut d’Astrophysique et de Geophysique,´ Liege` University, Allee´ du 6 Aout,ˆ 17, 4000 Liege,` Belgium 2 Universite´ de Toulouse, UPS-OMP, IRAP, Toulouse, France 3 CNRS, IRAP, 14, avenue Edouard Belin, 31400 Toulouse, France oscillating stars yields very precise oscillation frequencies 1. Introduction intricately related to the internal structure of stars. The One of the key objectives of the CoRoT mission relied on absolute values of oscillation frequencies bear a lot of infor- stellar seismology, as a tool to infer the physical mecha- mation content on physical processes taking place in stars nisms taking place in stellar interiors. Stellar pulsations can but previously out of reach (Sect. 3.2). For instance, spe- be split into two sub-classes; classical pulsations and solar- cific frequency combinations enable us to isolate and probe like pulsations. The first, thoroughly discussed in Sect.2, localized regions of the star such as the interfaces between are encountered in a wide variety of stars and mainly origi- radiative and convective regions, allowing us to measure the nate from thermal instabilities. Such oscillations have been extra-mixing related to penetration of convective elements observed for a long time from the ground and enabled us to (Sect. 3.3) or rotation (Sect. 3.5). Consequently, significant unveil several fundamental physical questions such as stellar advances are now possible given this propitious context pro- opacities (see for instance the reviews by Gautschy & Saio vided one brings together theoretical efforts and highly ac- 1995, 1996; Samadi et al. 2015). However, by allowing us curate observational constrains. CoRoT also opened new to measure micro-variability, CoRoT helped us to make a opportunities such as the precise and accurate characteri- leap forward by providing access to the internal inner-most zation of planet-host stars (Sect. 3.5) and as such was the layers of a number of stars such as γ Doradus or β Cephei pathfinder for future missions such as PLATO (Rauer et al. stars (Sects. 2.1 and 2.6). Moreover, it raised new questions 2014). about the nature of several type of pulsations as exemplified by the δ Scuti or Be stars (Sects. 2.2 and 2.7). As the nature of these oscillations is not always fully understood and is 2. Classical pulsators sometimes complexified by intricate combinations with ro- tation or magnetic fields, CoRoT's observations provided a (by A. Grotsch-Noels) large number of observational constraints that will certainly Classical pulsators cover nearly all the populated area of the be breeding ground for future theoretical progress. Hertzsprung-Russell (HR) diagram. Figure IV.1.1 shows The second type of pulsations, called solar-like oscilla- their location along the main sequence (MS) and in the tions, concerns all stars that develop an outer convective classical instability strip (IS), defined by long-dashed cyan envelope (so mainly low-mass stars) as the latter drives lines. and damps these oscillations. This is addressed in Sect.3. Although some pulsation properties were already known Indeed, prior to the CoRoT's launch, only a handful of tar- in the nineties, the amazing successes gathered by SOHO gets were known to exhibit solar-like oscillations and their for the Sun (surface helium abundance, importance of dif- interpretation was quite thorny as ground-based observa- fusion, rotation profile. ) were stimulating incentives to tions do not allow for the necessary precision, duration, attempt at reaching similar goals in stars, despite enormous and duty-cycle. Only a few years after, the situation dra- technical challenges. The aim was to detect extremely small matically changed and several hundreds oscillating main- light variations (down to one ppm) and to extract the fre- sequence stars and thousands of red-giant stars have been quencies responsible for these brightness fluctuations. To detected (Sect. 3.1). Thus, both the number and quality reach such performances, long observing times devoid of of the observations have been considerably improved and day/night alternations were required and space was thus it is not much of a stretch to think that CoRoT enabled the ideal asteroseismic laboratory. By revealing their mi- us to make a great leap forward. Analyzing light-curves of crovariability, measuring their oscillations at the ppm level, 181 The CoRoT Legacy Book instability strip are very sensitive to the mixing-length pa- rameter used in the MLT treatment of convection and the observed location of its red edge is indeed a strong con- straint on the mixing-length parameter. These stars are of particular interest since their mass Red Giants range covers the transition between a structure with a ra- diative core and a structure with a convective core, which can grow in mass during part of their main-sequence phase of evolution. The transition is due to the growing contribu- tion of CNO cycle reactions to the total nuclear energy pro- duction. This constitutes a sharp transition in the chemical composition profile, which induces a very subtle signature in the gravity modes frequency spectrum. According to the asymptotic theory, periods of high-order (k) g-modes are regularly spaced with a spacing (∆P = Pk+1 − Pk) decreas- ing as the degree of the modes increases. As the star evolves during MS, a higher and higher peak, starting at the limit of the fully mixed region, develops in the Brunt-V¨ais¨al¨a frequency distribution, as a result of the formation of the Fig. IV.1.1. Location of classical, solar-like and red giant pul- µ-gradient region. This sharp feature in the Brunt-V¨ais¨al¨a sators in the HR diagram. Long dashed cyan lines show the frequency shows up as a periodic component in the g-mode Cepheids and RR Lyrae stars classical instability strip. Cour- period spacing. The period spacing is no longer constant tesy of A. Miglio. but it oscillates around a constant mean value. The non- rotating theory was extensively discussed in Miglio et al. CoRoT has provided a new vision of stars, never reached (2008) for γ Doradus stars and SPB stars. before by any ground-based observation. However, γ Doradus stars frequencies can be of the or- Discoveries were indeed numerous. For classical pul- der or even higher than their rotation frequencies. There- sators let us cite just a few examples: the first detec- fore, rotation has a non-negligible effect on their oscilla- tion of pre main sequence (PMS) γ Doradus variables tion properties. Using the Traditional Approximation of (Zwintz et al. 2013, see Sect. 2.1), the discovery of hun- Rotation (TAR), Bouabid et al.(2013) carried out a non- dreds of frequencies in δ Scuti stars (Poretti et al. 2009, adiabatic analysis on a grid of models covering the γ Dor see Sect. 2.2), the first detection of a deviation from a mass range. With this TAR approximation, the effect of the constant period spacing in gravity modes in a Slowly Pul- Coriolis force on the frequencies and the stability of high- sating B (SPB) star (Degroote et al. 2010a, see Sect. 2.5) order g-modes could be estimated. The effect of the Corio- and the spectacular time evolution of the frequency spec- lis force depends on the type (prograde sectoral or not) of trum of a Be (emission lines B) star during an outburst mode and increases with their periods. This analysis showed (Huat et al. 2009, see Sect. 2.7), but also innovative prob- that the g-mode period spacing is no longer periodically os- ing in RR Lyrae stars (Poretti et al. 2010b, see Sect. 2.3), cillating around a constant value. The mean value between Cepheids (Poretti et al. 2014, see Sect. 2.4), OB stars two consecutive period-spacing minima decreases with in- (Degroote et al. 2010b, see Sects. 2.6 and 2.8), and sdB creasing period for non prograde sectoral modes and in- stars (Van Grootel et al. 2010, see Sect. 2.9). Interpreting creases with the period for prograde sectoral modes. More- those results opened new horizons in our vision of stars and over, the periodicity of the oscillation depends on the mode galaxies. In the following sections we shall travel among the periods. For non prograde sectoral modes, the period in- regions of the HR diagram populated by classical pulsators terval between two consecutive period-spacing minima de- and we shall discuss these breakthrough contributions to creases with increasing period, while it is the contrary for stellar astrophysics, based on CoRoT's data. prograde sectoral modes. However, the number of modes between two minima remains constant. It was thus highly challenging to search for the pres- 2.1. A nursery for young γ Doradus stars ence of periodic components in the period spacing. The fre- quency resolution from a CoRoT long run was however too γ Doradus stars are pulsating in a high-order g-mode small to clearly reveal such components in period spacing regime. They have periods similar to SPB stars (see for γ Dor stars. But CoRoT had opened up the way and Sect. 2.5), from 0.3 to 3 days. Their masses are how- in a recent paper (Van Reeth et al. 2015), 67 γ Dor stars ever much smaller, about 1.4 to 2.1 M . These stars are observed by Kepler during 4 years were analyzed with un- cool enough to have a convective envelope.