arXiv:1411.1082v1 [astro-ph.SR] 4 Nov 2014 et fteaypoi eidsaig r o available now are spacings period identi- asymptotic the for measure- theoretical of exact used However, ments their tracks. be evolutionary to cannot specific stud- spac- they fying compared these The so offset by however, 2013). counterparts, significantly reported al. are et periods Stello al. ies oscillation et 2011a; addi- between (Bedding are al. cores ings that et those their Mosser and inside 2011; cores helium their burning around tionally shell hydrogen thin only a burning are used in that been the giants stars have between red Unlike oscillations distinguish modes, These to 2009). modes. pressure al. gravity are et show oscillations also Ridder the (De where Sun Sun, the stars like giant red oscillate that revealed has photometry High-precision Introduction 1. i nnmu t to via or ftp anonymous via ⋆ srnm Astrophysics & Astronomy uy2,2018 20, July .Mosser B. al sol vial neetoi oma h CDS the at form electronic in available only is 1 Table Stello Elsworth 10 Methods. 11 atclrtetasto rmtesbin tg oteear the to stage subgiant the the Conclusions. from to definitio transition sequence asteroseismic the main quantified particular the clear from present We evolution tracks. stellar the monitor of to combination us the with drawn Results. then were tracks lutionary riigo utigtescnaycup rsasta coul that stars identified words. or are Key clump, that secondary stars the study quitting prope to or inner us the arriving allow specifying also ste for will for or Modeling used core be helium-burning now the can in information seismic quantitative The Aims. cores. their in conditions Context. 2018 20, July version: online Preprint 9 6 7 1 8 2 3 4 5 http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/ ie oe nrdgat:awno nselrevolution stellar on window a giants: red in modes Mixed ntttfu srpyi,Georg-August-Universit¨at f¨ur G¨ Astrophysik, Institut Denmark Ast C, and Physics Aarhus of Department Centre, Astrophysics Stellar ntttd hsqed ens nvri´ eRne ,CNR 1, Rennes Universit´e de Rennes, de Physique de Institut nvri´ eTuos;USOP NS RP 4 vneEd avenue 14, IRAP; CNRS; UPS-OMP; Toulouse; Universit´e de nttu orSernud,K evn eetjela 2 Celestijnenlaan Leuven, KU Sterrenkunde, voor Instituut EI,CR,UiestePer tMreCre Universit´ Curie, Marie France; cedex, et Universit´e Pierre CNRS, LESIA, ntttdAtohsqee ´ohsqed l’Universit´ G´eophysique de et d’Astrophysique Institut eateto srnm,TeUiest fTko 113-033, Tokyo, of University The Astronomy, of Department colo hsc n srnm,Uiest fBirmingham, of University Astronomy, and Physics of School EI NS nvri´ ei ieo,Osraor ePar de Observatoire Diderot, Universit´e Denis CNRS, GEPI, ynyIsiuefrAtooy colo hsc,Univers Physics, of School Astronomy, for Institute Sydney 5 ihteemxdmds eama eemnn esi marker seismic determining at aim we modes, mixed these With , 9 emaue h smttcpro pcn o oeta 1170 than more for spacing period asymptotic the measured We .Vrard M. , h eeto foclain ihamxdcaatri subg in character mixed a with oscillations of detection The 1 Kepler 3 .Benomar O. , , 9 tr:oclain tr:itros-Sas evolution Stars: - interiors Stars: - oscillations Stars: h esi nomto ss rcs htcerconclusion clear that precise so is information seismic The .Mnabn .Noels A. Montalban, J. , seoesi aawr eetdt a aiu evolutiona various map to selected were data asteroseismic dacusrsgf (130.79.128.5) cdsarc.u-strasbg.fr [email protected] 1 .Barban C. , aucitn.f8 no. manuscript 2 , 5 .Belkacem K. , 1 ..Bedding T.R. , 8 ..Ouazzani R.M. , 1 ..Goupil M.J. , ABSTRACT 5 , tign rerc-udPaz1 77 G¨ottingen, Germ 37077 1, Friedrich-Hund-Platz ottingen, 9 sta hrceietecag nteeouinr stages, evolutionary the in change the characterize that ns eL`g,Ale usxAˆt 7B40 Li`ege, Belgium B-4000 Aoˆut, 17 six Li`ege, All´ee de du e .Deheuvels S. , yrdgatbac,adteedo h oiotlbranch. horizontal the of end the and branch, giant red ly te fsasetrn h e raypoi in branches giant asymptotic or red the entering stars of rties ei h lelo stage. blue-loop the in be d lrmdln,epcal o tdigteeeg transpor energy the studying for especially modeling, llar ainmds eefe eoe ∆ oscil- denoted radial hereafter consecutive modes, between lation 1980). difference (Tassoul have frequency spaced modes The Acoustic equally modes. approximately prop- gravity the frequencies and share acoustic They of that core. the waves stellar erties probe radiative gravity dense that and the waves envelope probe acoustic stellar of convective coupling mostly modes These the oscil- 2011). the from al. observing result et from (Beck obtained pattern be mixed-mode can lation giants red of lope core the to related 2013). directly al. are (Montalb´an et which size 2012b), al. et (Mosser osre l 02;Dhuese l 02 04,adto and 2014), 2012; 2012, al. al. et (Beck et Deheuvels rotation 2012a; its al. monitor cen- et to in Mosser core, stratification ∆Π ∆Π the density Determining denoted probe 1980). the is (Tassoul spacing upon regions tral this dependent spaced modes is equally dipole and are For modes period. gravity in density. modes, stellar mean pressure the Unlike on depends and separation quency ob ntehlu-ufls tg,hg-assaseither stars high-mass stage, helium-subflash the in be to ooy ahsUiest,N ukgd 2,DK-8000 120, Munkegade Ny University, Aarhus ronomy, t fSde,NW20,Australia 2006, NSW Sydney, of ity 0,30 evn Belgium Leuven, 3001 00D, smttcgatbac n rwsimcevolutionary seismic draw and branch giant asymptotic ei ieo,Osraor ePrs 29 Meudon 92195 Paris, de Observatoire Diderot, Denis e rqec n eidspacings. period and frequency 9 1 .Samadi R. , s 29 edncedex, Meudon 92195 is, h obndifraino h oeado h enve- the on and core the on information combined The .Lagarde N. , dbso,Briga 1 T,Uie Kingdom United 2TT, B15 Birmingham Edgbaston, UR65) 54 ens France Rennes, 35042 6251), (UMR S Japan at n e insalw st rb h physical the probe to us allows giants red and iants ur ei,F340Tuos,France Toulouse, F-31400 Belin, ouard a edanidpnetyo vlto models. evolution of independently drawn be can s fselrevolution. stellar of s tr tvroseouinr tgs hsallows This stages. evolutionary various at stars 6 ..Chaplin W.J. , ysae n tla ass esi evo- Seismic masses. stellar and stages ry 1 ..White T.R. , 3 , 9 .Michel E. , 3 10 , 1 9 .Lebreton Y. , .D Ridder De J. , n .Kjeldsen H. and , ν scle h ag fre- large the called is ,

1 c losu to us allows 4 S 2018 ESO , 7 11 ⋆ Y. , any D. , in t 9 . 1 1 B. Mosser et al.: Stellar evolution investigate how angular momentum is transferred between 25 % in mass, 5-10 % in radius, 15-25 % in luminosity the stellar core and the envelope (Cantiello et al. 2014). (Huber et al. 2012; Silva Aguirre et al. 2012). Here, we use such frequency and period spacings to track evolutionary stages ranging from the end of the main sequence to the asymptotic giant branch (AGB) in a selec- 3. Seismic HR diagram tion of stars observed by Kepler. Seismic observations are precise enough to derive model-independent conclusions. Examining the variation of ∆Π1 as a function of ∆ν in a seismic Hertzsprung-Russell (HR) diagram allows us to map stellar evolution and to distinguish the late evolution- 2. Data and methods ary stages (Fig. 1). This ∆Π1 – ∆ν diagram provides richer information than the classical HR diagram. Without seis- The data set is composed of 38 subgiants observed by mic data, determining precise evolutionary stages for field Kepler during at least one month (Chaplin et al. 2011) stars is uncertain or impossible because of an observable and of about 12700 red giants observed during 44 months quantity that probes the innermost region of the stars and (Stello et al. 2013). Out of these, 2800 were selected to map because of the large uncertainties associated with the fun- the whole range in frequency spacings and masses. This se- damental stellar parameters (luminosity, effective tempera- lection precludes any population analysis, but it provides ture, and chemical composition). Here, the density of stars an exhaustive view on low-mass star evolution. in the ∆Π1 – ∆ν diagram enables constructing seismic evo- We have used an automated method for measuring the lutionary tracks (Fig. 2) directly derived from the mean frequency spacing of radial pressure modes and have devel- location of stars identified in mass ranges 0.2-M⊙ wide. oped a semi-automated method for measuring the period spacing of dipole mixed modes, both based on asymptotic 3.1. Subgiant stage expansions (Mosser et al. 2011b, 2012b). The mean accu- racy of the large separation is about 0.04 µHz; this trans- A star leaves the main sequence and enters the subgiant lates into a relative precision at the red clump of 1 %. The stage (stars S in Fig. 1) when the hydrogen fuel is exhausted measurement of ∆Π1 relies on the number of mixed modes in its core. In a star of mass lower than 1.5 M⊙, the ob- with high signal-to-noise ratio, which depends on the evo- servation of mixed modes indicates a dense radiative core lutionary status (Dupret et al. 2009; Mosser et al. 2012b). and the beginning of the subgiant phase, as is the case for The precise fit of the oscillation spectrum must account the bright F-star Procyon (Bedding et al. 2010). The slow for any rotational splitting (Beck et al. 2012; Mosser et al. contraction of the core on a thermal timescale implies a 2012a; Goupil et al. 2013). quasi-static adjustment, hence the extension of the enve- For red giants, the observed gravity-mode orders are lope. Accordingly, as a subgiant evolves, the mean stellar high enough to ensure the validity of the asymptotic expan- density, and therefore the large separation, decreases. The sion and a high precision of the asymptotic global param- contraction of the radiative core also results in a decreased eters. Hence, the period spacing ∆Π1 is determined with period spacing. We also note a clear mass dependence of the a precision better than 2% and in many cases better than ∆Π1 – ∆ν relation (Fig. 2), as predicted by stellar modeling 0.5 %. For subgiants, the gravity-mode orders of the few (Montalb´an et al. 2013). observed mixed modes are small, down to 2 in many cases, so that the quantitative use of the asymptotic expansion 3.2. From subgiants to the red giant branch may not be accurate. However, comparison with a different approach (Benomar et al. 2013, 2014) indicates agreement As stars evolve from subgiants onto the RGB, the increase in the obtained values of the period spacings to within 10 % of the stellar radius induces the decrease of the large separa- for subgiants and better than 3 % for red giants. tion. We note the convergence of the evolutionary paths in We measured ∆Π1 in 1142 red giants and 36 subgiants. the seismic ∆Π1 – ∆ν diagram. The properties of the stellar Reliable measurements are impossible in oscillation spec- interior become increasingly dominated by the physical con- tra with low signal-to-noise ratio or, most often, in absence ditions of the quasi-isothermal degenerate helium core and of enough gravity-dominated mixed modes. This occurs at its surrounding hydrogen-burning shell (Kippenhahn et al. low ∆ν, when gravity-dominated mixed modes have high 2012). Accordingly, the structural properties of the enve- inertia (Dupret et al. 2009; Grosjean et al. 2014) so that lope are also related to the core mass, which explains the major difficulties occur for stars with ∆ν < 5 µHz on the degeneracy in the ∆Π1 – ∆ν diagram for low-mass red gi- red giant branch (RGB). In that case, measurements are ants (stars R in Fig. 1). Although the transition from the possible only for bright stars seen pole-on, when the rota- subgiant phase to the RGB can be seen in the classical HR tional structure of the dipole mixed modes is simple since diagram, it is impossible to unambiguously infer the evo- only m = 0 modes are visible. The number of ambiguous lutionary status of a given star from its location in that cases, with a large number of mixed modes but a poor fit of diagram. In contrast, the evolution from the subgiant to the mixed-mode oscillation pattern, is less than 0.1 % (the the red giant phase is clear in the ∆Π1 – ∆ν diagram: al- spectra of 2 stars out of 2800 that were treated remain ob- most independent of the initial conditions (mass, metallic- scure despite a decent signal-to-noise ratio; they certainly ity), all low-mass stars on the RGB with the same core corresponds to blended light curves). structure have the same mean density. The influence of The stellar masses and radii were derived from the seis- metallicity should be investigated to understand the higher mic scaling relations calibrated with nine red giants and dispersion seen for stars more massive than 1.5 M⊙; this eleven subgiants (Mosser et al. 2013). Luminosity was de- is beyond the scope of this work. We can summarize the rived from the stellar radius and effective temperature, change of regime with an empirical criterion: a subgiant assuming the Stefan-Boltzmann law. The precision is 15- with a mass below 1.5 M⊙ starts climbing the RGB when

2 B. Mosser et al.: Stellar evolution

S

S f f S S S f S S S S f f f S f ?f A S S f A CCCC S ACCCCCCCCCCACCACCACAAC2AACA S f CCCCCCCCCCCCCCCACCACCACCACC2CC2AA2A2 2 S f f CACCCACCCCCCACCCCACCCACCCCCp2CACCp2AC2222AAA2 22A22 S S CCACCACCCCACCCCCp2CCC CCCCp2p2Cp2CCp2CCCp2CAA 2A A2A2A 2222222 S f CCCCCCCCCCCCCCCCp2CCCCCCCCp2p2p2A2 AAp2A22 22 S CCACC CCCCCp2CCp2CC p2p22 2 p2AAp2p2A22 222 S S CCCCCCCCCCCCCCCCCp2CCp2C p2 2 A222 22222 AC CCCCCCCCCCCCCp2C 2p2p2p2222 S S A ACCC p2p2CCCCC Cp2p2 2p2 2 222222 S AA AA CC C 2 2222222 S A A p2 Cp2CCC p2p2 2 22222 AAAAAAA ? C p2 2 2 S AAAA 222 2 S S AAAAA 2 S A f 22 S S 2 f 2 S 222 S SS R S RR S R RRR RR RRRRR R R R R R R RRRR R R R RR R RR RR R RRRRRRRRRR R R RR RRRRRRR R R R RRRRRRRRRRRRR R R RRRRRRRRRRRRRRR RRR RRRRRRRRRRRRRRRRRRRRR R RRRR RRRRRRRRRRRRRRRRRRRR R R R RRRRRRRRRRRRRRRRRRRRR R RR R R RR RRRRRRRRRRRRRRRRRRRRR RR R RRR R RRRRRRRRRRRRRRRRRRRRRRR RRRR R R R RR RRRRRR R RRRR R R R R R RR RRR R

f f f f f ?f A f CCC A C C C A 2 A C CCCCCCCCCCCCCC ACA A CCCCCCCCCCCCACC CCCCAA A AC A CCC CCCCCCCCCCACACACC ACC CC A A CC CCCCCCCCCCCCCCCCCCCCCCCCAAC C 2 AA f CC CC CCC CCCCCCCCCCCCCC 2 C2 2 2 CC ACCCCC CACCCCACCCCCCC C AC 2 22 2 CCCCC CCCCCCCCCCCCCCACCCCCCC C C A 2 2 A f f CA CCCCCCCCCCCCCCCp2CCCCCCCCp2CACC Cp2 AA 2 22 CC CCC CCACCCCCCCCCCCCCCCC CCp2CAAA 2 AA A2 A 22222 C ACCCC CCCCCCCCCCCCp2Cp2p2 A 2 2 2 C ACCCCCC CCC p2p2CCC p2 A A 2 2 f CCC C CCCCp2CCCCC C C p2 p2A 2 2 CCCCC CCCCCCCCCCCCC C p2 2 Ap2 2 2 22 ACC CCCCC C C p2C C p2p2 2 A p2 A 2 C C C CCC CCp2C p2 2 22 C CC C CC CCCC Cp2C 2 2 p2 A 222 2 CCCCCCCCCCCCCCCCC p2 A2 2 2 C C CCC CCCC C p2 22 2222 CCCCC CC CCC CC p2 p22 A CCCC C p2 Cp2 2 p2 A A C C C p2 p2 2 2 2 2 222 CC p2p2C C C 2 2 2 A CC C 2 2 2 AA A 2 2 22 2 A A p2 C p2CCC 2 2 22 A AAAA C p2 p2 222 AAAAAA 2 AA A A A ? p2 2 2 A 2 2 2 AAAAA 2 A f 2 2 2 f 2 2 2 2

Fig. 1. Period spacing ∆Π1 as a function of the frequency spacing ∆ν. Top: The seismic proxy for the stellar mass is indicated by the color code. The evolutionary states are indicated by S (subgiants), R (RGB), f (helium subflash stage), C (red clump), p2 (pre secondary clump), 2 (secondary clump), and A (stars leaving the red clump moving toward the AGB). The error boxes on the right side indicate the mean uncertainties, as a function of ∆Π1, for stars on the RGB; for clump stars, uncertainties are indicated on the left side. Dotted lines indicate the boundaries between evolutionary stages. Bottom: Zoom in the red-clump region. Data used in this figure are available at the CDS.

3 B. Mosser et al.: Stellar evolution

hydrogen shell that produces the largest part of the stel- lar luminosity. During the first stage of helium burning, the core grows in mass and expands, so that the envelope contracts: both ∆Π1 and ∆ν increase. In a second stage, both decrease, due to a less efficient energy production. This evolution is predicted by models (Lagarde et al. 2012; Montalb´an et al. 2013; Stello et al. 2013). Now, we can pre- cisely quantify it (Fig. 2).

3.4. Structure of the secondary clump

In stars with masses above about 1.9 M⊙, the ignition of he- lium occurs gradually rather than in a flash because the core is not fully degenerate (Girardi 1999; Huber et al. 2012; Miglio et al. 2012). Therefore, these secondary-clump stars (stars 2 in Fig. 1) show a wider spread in the diagram Fig. 2. Evolutionary tracks reconstructed from the seis- (Bildsten et al. 2012): ∆Π1 decreases with increasing stel- mic observations for stellar masses in the [0.9 − 2.9 M⊙] lar mass up to 2.7 M⊙, as does the mass of the helium core range. The 1.9 M⊙ track is not shown because more in- at ignition. Then, for masses above 2.8 M⊙, ∆Π1 increases formation is needed to define the limit between the clump significantly with increasing stellar mass. This behavior is and secondary-clump stars. On the RGB, the dispersion expected from stellar modeling, which however often fails due to the first luminosity bump is too high to allow an un- at reproducing the mass corresponding to minimum ∆Π1 ambiguous definition of the evolutionary tracks for stellar values (e.g., Stello et al. 2013). This again emphasizes the masses above 1.9 M⊙. Dotted lines indicates the boundaries crucial role of the seismic HR diagram and the necessity of between evolutionary stages. accurately calibrating seismic scaling relations. We defined the p2 status for each mass range; this sta- tus corresponds to possible progenitors of secondary-clump (∆ν/36.5 µHz) (∆Π1/126 s) < 1. This threshold is deter- mined to better than 8 %, based on the identification of the stars. The mass-dependent threshold value between the two ‘elbow’ in the evolutionary tracks. The boundary and its stages p2 and 2 was arbitrarily defined at ∆ν lower than uncertainties are indicated with dotted lines in Figs. 1 and 25 % of the median value in the secondary clump and ∆Π1 2. Translated into a stellar age, this uncertainty represents below the mean value observed in the secondary clump for a very short event, much shorter than 0.5 % of the evolution the considered mass range. Progenitors of secondary-clump time on the main sequence. stars have a lower ∆ν (a higher luminosity) than the median stage in each mass interval, and also a low ∆Π1 correspond- ing to an extended inner radiative region. Comparison with 3.3. Structure of the red clump modeling is necessary to confirm the nature of these pro- genitors. When the helium core of a low-mass star on the RGB reaches about 0.47 M⊙, runaway ignition in degenerate con- ditions produces the helium flash, which very rapidly trans- 3.5. From the red and secondary clumps to the asymptotic ports the star from the tip of the RGB to the red clump giant branch (Salaris et al. 2002). The highest mass a star can have to undergo the helium flash is 1.9 M⊙, with an uncertainty of A few stars appear in the vicinity of the clump, but with about 10 %. We did not take into account the scaling revi- significantly smaller period spacings. They most probably sion proposed by Miglio et al. (2012) for red-clump stars. correspond to stars in which the core is contracting because Red-clump stars (stars C in Fig. 1) occupy a small re- helium becomes exhausted, leaving the main region of the gion of the ∆Π1 – ∆ν diagram, around 300s and 4.1 µHz red clump and preparing to ascend the AGB (Lagarde et al. (Mosser et al. 2012b). They have similar core masses, hence 2012; Corsaro et al. 2012; Montalb´an & Noels 2013). Since similar luminosities, and are therefore used as standard can- a wide range of masses, including high masses, are present dles (Paczy´nski & Stanek 1998). Seismic information pro- on the same trajectory, we exclude the scenario that these vides useful constraints for improving the structure of the stars are entering the red clump. We empirically consid- red clump, hence for improving distance measurements. ered that a star leaves the red clump and enters this stage, Models still have difficulties in reproducing the pe- labeled with A in the ∆Π1 – ∆ν diagram, when its large riod spacing in the red clump (Bildsten et al. 2012; separation is 15 % below the mean value observed in the clump for stars with similar masses. For low-mass stars, Montalb´an et al. 2013; Stello et al. 2013). In part this is 1.5 due to an incorrect treatment of a chemical discontinu- this occurs when (∆ν/3.3 µHz) (∆Π1/245 s) < 1. This ity at the convective-core boundary in core-helium-burning threshold is determined to better than 6 %, based on the models (Gabriel et al. 2014), resulting in insufficient mixing narrowing of the evolutionary tracks. In the classical HR di- in the core (Noels & Montalb´an 2013). More importantly, agram, such low-mass stars remain hidden in the red clump the accuracy of the measurements of ∆ν and ∆Π1 is high since they have similar luminosity. This better character- enough to track the evolution of the stars in the helium- ization of the clump stars is important for using them as burning phase. Low-mass stars have lower ∆ν than more accurate standard candles. massive stars, hence lower mean density. This is in agree- High-mass stars exiting the secondary clump can also be ment with the fact that the inner pressure is fixed by the identified. When core-helium burning becomes inefficient,

4 B. Mosser et al.: Stellar evolution

∆ν decreases and ∆Π1 first increases. This behavior and Science Mission Directorate. JDR acknowledges support of the FWO the mass criterion ensure a significant difference between Flanders under project O6260-G.0728.11 This work partially used data analyzed under the NASA grant NNX12AE17GPGB and un- the p2 and A stages. In a second step, ∆ν and ∆Π1 vary der the European Communityfs Seventh Framework Program grant as for lower mass stars, but with a wider spread. This leads (FP7/2007–2013)/ERC grant agreement n. PROSPERITY. to a reliable definition of the A stage when M ≥ 1.9 M⊙, even with a limited set of stars. References 3.6. Helium flash Beck, P. G., Bedding, T. R., Mosser, B., et al. 2011, Science, 332, 205 Beck, P. G., Montalban, J., Kallinger, T., et al. 2012, Nature, 481, 55 Finally, we identified a small number of stars that clearly Bedding, T. R., Kjeldsen, H., Campante, T. L., et al. 2010, ApJ, 713, lie outside the evolutionary paths mentioned above. It is 935 Bedding, T. R., Mosser, B., Huber, D., et al. 2011, Nature, 471, 608 likely that these stars have very recently undergone the he- Benomar, O., Bedding, T. R., Mosser, B., et al. 2013, ApJ, 767, 158 lium flash (stars f in Fig. 1). At low ∆ν, we identified stars Benomar, O., Belkacem, K., Bedding, T. R., et al. 2014, ApJ, 781, with an unusually high period spacing, corresponding to a L29 small inner radiative region. For low-mass stars, this situ- Bildsten, L., Paxton, B., Moore, K., & Macias, P. J. 2012, ApJ, 744, ation matches a helium subflash (Bildsten et al. 2012). For L6 Cantiello, M., Mankovich, C., Bildsten, L., Christensen-Dalsgaard, J., higher mass, the evolutionary stage cannot be determined & Paxton, B. 2014, ApJ, 788, 93 among helium ignition or blue-loop stage; two stars that Chaplin, W. J., Kjeldsen, H., Christensen-Dalsgaard, J., et al. 2011, may be in this stage are marked with the symbol ‘?’. Stages Science, 332, 213 between subflashes are hard to detect because they have si- Corsaro, E., Stello, D., Huber, D., et al. 2012, ApJ, 757, 190 De Ridder, J., Barban, C., Baudin, F., et al. 2009, Nature, 459, 398 multaneously small ∆Π1 and ∆ν (Lagarde et al. 2012). We Deheuvels, S., Do˘gan, G., Goupil, M. J., et al. 2014, A&A, 564, A27 also identified stars with ∆Π1 just below the main clump, Deheuvels, S., Garc´ıa, R. A., Chaplin, W. J., et al. 2012, ApJ, 756, which certainly evolve toward the clump with an almost 19 fully ignited helium core. Dupret, M., Belkacem, K., Samadi, R., et al. 2009, A&A, 506, 57 Gabriel, M., Noels, A., Montalb´an, J., & Miglio, A. 2014, A&A, 569, A63 Girardi, L. 1999, MNRAS, 308, 818 4. Conclusion Goupil, M. J., Mosser, B., Marques, J. P., et al. 2013, A&A, 549, A75 Grosjean, M., Dupret, M.-A., Belkacem, K., et al. 2014, ArXiv e- Precise markers of stellar evolution of low-mass stars were prints: 1409.6121G derived in the ∆Π1 – ∆ν diagram. For each stellar mass Huber, D., Ireland, M. J., Bedding, T. R., et al. 2012, ApJ, 760, 32 interval, evolutionary tracks were derived. All transitions Kippenhahn, R., Weigert, A., & Weiss, A. 2012, Stellar Structure and between the various stages of evolution, such as hydrogen- Evolution shell burning, helium-core burning, and the end of helium Lagarde, N., Decressin, T., Charbonnel, C., et al. 2012, A&A, 543, A108 burning in the core, are marked by changes in the rela- Miglio, A., Brogaard, K., Stello, D., et al. 2012, MNRAS, 419, 2077 tionship between the frequency and period spacings. For Montalb´an, J., Miglio, A., Noels, A., et al. 2013, ApJ, 766, 118 low-mass stars arriving on the RGB, the period spacing Montalb´an, J. & Noels, A. 2013, in European Physical Journal varies with the frequency spacing because the core and en- Web of Conferences, Vol. 43, European Physical Journal Web of Conferences, 3002 velope structures are closely linked at that stage. Similar Mosser, B., Barban, C., Montalb´an, J., et al. 2011a, A&A, 532, A86 variation is seen for core-helium-burning stars, but with a Mosser, B., Belkacem, K., Goupil, M., et al. 2011b, A&A, 525, L9 mass-dependent relationship since nuclear burning in the Mosser, B., Goupil, M. J., Belkacem, K., et al. 2012a, A&A, 548, A10 core removes the degeneracy of helium. When helium is Mosser, B., Goupil, M. J., Belkacem, K., et al. 2012b, A&A, 540, A143 exhausted, the core is degenerate again, so that the rela- Mosser, B., Michel, E., Belkacem, K., et al. 2013, A&A, 550, A126 Noels, A. & Montalb´an, J. 2013, in Astronomical Society of the Pacific tion between ∆Π1 and ∆ν is independent of mass, as on Conference Series, Vol. 479, Astronomical Society of the Pacific the RGB. A few outliers are identified as stars starting the Conference Series, ed. H. Shibahashi & A. E. Lynas-Gray, 435 helium-burning stage in the unstable contraction phase fol- Paczy´nski, B. & Stanek, K. Z. 1998, ApJ, 494, L219 lowing the helium flash (Bildsten et al. 2012). Salaris, M., Cassisi, S., & Weiss, A. 2002, PASP, 114, 375 Silva Aguirre, V., Casagrande, L., Basu, S., et al. 2012, ApJ, 757, 99 Comparison with modeling will help to link the phe- Stello, D., Huber, D., Bedding, T. R., et al. 2013, ApJ, 765, L41 nomenological threshold values with evolution parameters Tassoul, M. 1980, ApJS, 43, 469 such as the helium fraction in the core, especially for secondary-clump stars, to assess the p2 stage. This com- parison is currently impossible, since modeling has first to accurately reproduce the observed tracks. Independent of this forthcoming analysis, we note that there are fewer than 1% of stars with ambiguous identifications in the clump, which are identified as stars close to the boundaries. Among these, we identified two high-mass stars that might be in a blue-loop stage.

Acknowledgements. We thank the referee for his/her constructive comments. We acknowledge the entire Kepler team, whose efforts made these results possible. BM, KB, MJG, EM, MV, CB, and RS acknowledge financial support from the Programme National de Physique Stellaire (CNRS/INSU) and from the ANR program IDEE Interaction Des Etoiles´ et des Exoplan`etes. OB is supported by the Japan society for promotion of science fellowship for research (n◦ 25- 13316). Funding for this Discovery mission was provided by NASA’s

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