Asteroseismology of red giants as a tool for studying stellar populations: first steps
aa r X i v : . [ a s t r o - ph . S R ] A ug Asteroseismology of red giants as a tool forstudying stellar populations: first steps
Andrea Miglio
Abstract
The detection of solar-like oscillations in G and K giants with the CoRoTand
Kepler space-based satellites allows robust constraints to be set on the massand radius of such stars. The availability of these constraints for thousands of giantssampling different regions of the Galaxy promises to enrich our understanding onthe Milky Way’s constituents. In this contribution we briefly recall which are therelevant constraints that red-giants seismology can currently provide to the study ofstellar populations. We then present, for a few nearby stars, the comparison betweenradius and mass determined using seismic scaling relations and those obtained byother methods.
Since the data from the first CoRoT observational runs were analysed, and solar-likeoscillations were detected in thousands of red giant stars (De Ridder et al., 2009;Hekker et al., 2009; Mosser et al., 2010; Kallinger et al., 2010), it has become clearthat the newly available observational constraints will allow novel approaches in thestudy of so far poorly constrained galactic stellar populations (Miglio et al., 2009).While CoRoT continues to monitor giants in different regions of the Milky Way,
Kepler is contributing significantly to the characterisation not only of red-giant pop-ulations (see De Ridder, this volume for a review) but it has also opened the way for“ensemble seismology” of solar-like stars. The detection of solar-like oscillations inabout 500 F and G dwarfs allowed Chaplin et al. (2011) to perform a first quanti-tative comparison between the distributions of observed masses and radii of thesestars with predictions from models of synthetic populations in the Galaxy.
A. MiglioSchool of Physics and Astronomy, University of Birmingham, United KingdomInstitut d’Astrophysique et de G´eophysique de l’Universit´e de Li`ege, Belgiume-mail: [email protected]
We outline in Sec. 2 the innovative aspects of seismic constraints, highlightingthe importance of being able to determine the mass of giant stars, while we willdiscuss in detail the implications of the radius (hence distance) estimates in a futurepaper. In Sec. 3 we first review how mass and radius of giants are estimated usingthe average seismic parameters Dn (average large frequency separation) and n max (frequency corresponding to the maximum observed oscillation power), and thenpresent, for a few nearby stars, the comparison between radius and mass determinedusing seismic and non-seismic observational constraints. Once they reach the red-giant phase of their evolution, stars of significantly differentage end up sharing similar photospheric properties. As a consequence, field giantsbelonging to the composite galactic-disk population were so far considered poortracers of age. However, the possibility of determining with asteroseismology themasses of thousands of these objects has unexpectedly reversed this picture.As is well known, the age of RGB and red-clump (RC) stars is largely determinedby their main-sequence lifetime and hence, to a first approximation, by their massand metallicity. The age-mass relation of giant stars predicted by stellar models isillustrated in Fig. 1, where it is compared with that of stars on the main sequence.For the purposes of this comparison, a crude criterion based on the surface gravity g was used to separate giants (log g < .
5) from main-sequence stars (log g > . M ∼ < . M ⊙ the age-mass relation bifurcates due to the significant mass loss ( ∼ . − . M ⊙ ) experienced by low-mass stars near the tip of the RGB . Consequently, RCstars are younger than stars on the RGB with the same actual mass (and metallicitiy).We can, however, remove this degeneracy in the age-mass relation thanks to addi-tional seismic constraints. It is indeed excellent news in this context that the detailedproperties of dipolar oscillation modes allow us to clearly distinguish RGB from RCstars (Montalb´an et al. 2010; Bedding et al. 2011; Mosser et al. 2011; Montalb´an etal, this volume). When applied to the characterisation of stellar populations thisresult can potentially lead to age estimates independent of the uncertain RGB mass-loss rates.As a word of caution we should recall, however, that these age estimates are in-herently model dependent, being affected by uncertainties in predicting, e.g., main-sequence lifetimes. On the other hand, the potential of asteroseismology goes well In the models used in Fig. 1, RGB mass loss is implemented adopting the Reimers (1975) pre-scription (see Girardi et al. 2000 for more details).
Page: 2 job: miglio_roma macro: svmult.cls date/time:4-Oct-2018/20:06 steroseismology of red giants as a tool for studying stellar populations: first steps 3 sun ] l og ( A ge [ y r ] ) log(g) > 3.5 [ F e / H ] −0.6−0.5−0.4−0.3−0.2−0.100.10.20.30.41 1.5 2 2.58.68.899.29.49.69.810 M [M sun ] l og ( A ge [ y r ] ) log(g) < 3.5 [ F e / H ] −0.6−0.5−0.4−0.3−0.2−0.100.10.20.30.4He−BRGBAGB Fig. 1
Age-mass-metallicity relation for main-sequence stars ( upper panel ) and red giants ( lowerpanel ) in a synthetic population representative of thin-disk stars observed by CoRoT in the LRc01field. The evolutionary state of giants is marked with a different symbol: dots (stars in the core-Helium-burning phase), crosses (Asymptotic-Giant-Branch stars), and open circles (stars on theRed Giant Branch). The fraction of AGB stars in the population of giants shown here is ∼ beyond the determination of global stellar parameters using scaling relations. Asfrequencies of individual pulsation modes become available, detailed comparisonsbetween observed and theoretical oscillation spectra promise to improve both theprecision of age estimates (see e.g. Di Mauro et al. 2011), along with their accu-racy, by providing stringent constraints on models of the internal structure of bothmain-sequence and in giant stars. Page: 3 job: miglio_roma macro: svmult.cls date/time:4-Oct-2018/20:06
Andrea Miglio
As a relevant additional constraint that seismology could potentially provide tothe study of stellar populations, we recall that investigations are currently underwayto assess under which conditions a reliable indication of the envelope-helium abun-dance can be derived from the seismic signature of helium ionisation detected inCoRoT and
Kepler giants (see Miglio et al. 2010; Montalb´an et al., this volume).Finally, as discussed during this meeting, it is worth mentioning that Eq. 2 belowprovides a potentially very accurate way of determining the surface gravities ofstars, which could be then used as an input to refine spectroscopic analyses (seee.g. Morel & Miglio 2011) and, eventually, to test model atmospheres of giant stars(Plez, this meeting).
Radii and masses of solar-like oscillating stars can be estimated from the averageseismic parameters that characterise their oscillation spectra: the so-called averagelarge frequency separation ( Dn ), and the frequency corresponding to the maximumobserved oscillation power ( n max ).The large frequency separation is predicted by theory to scale as the square rootof the mean density of the star (see e.g. Vandakurov, 1967; Tassoul, 1980): Dn ≃ s M / M ⊙ ( R / R ⊙ ) Dn ⊙ , (1)where Dn ⊙ = m Hz. The frequency of maximum power is expected to be pro-portional to the acoustic cutoff frequency (Brown et al., 1991; Kjeldsen & Bedding,1995; Mosser et al., 2010; Belkacem et al., 2011), and therefore: n max ≃ M / M ⊙ ( R / R ⊙ ) p T eff / T eff , ⊙ n max , ⊙ , (2)where n max , ⊙ = m Hz and T eff , ⊙ = Kepler , Eq. 1 and 2 may be solved to derive M and R (seee.g. Kallinger et al., 2010; Mosser et al., 2010): MM ⊙ ≃ (cid:18) n max n max , ⊙ (cid:19) (cid:18) DnDn ⊙ (cid:19) − (cid:18) T eff T eff , ⊙ (cid:19) / (3) RR ⊙ ≃ (cid:18) n max n max , ⊙ (cid:19) (cid:18) DnDn ⊙ (cid:19) − (cid:18) T eff T eff , ⊙ (cid:19) / . (4) Page: 4 job: miglio_roma macro: svmult.cls date/time:4-Oct-2018/20:06 steroseismology of red giants as a tool for studying stellar populations: first steps 5
However, when additional constraints on the distance/luminosity of stars areavailable, M can also be estimated also from Eq. 1 or 2 alone: MM ⊙ ≃ (cid:18) DnDn ⊙ (cid:19) (cid:18) LL ⊙ (cid:19) / (cid:18) T eff T eff , ⊙ (cid:19) − (5) MM ⊙ ≃ (cid:18) n max n max , ⊙ (cid:19) (cid:18) LL ⊙ (cid:19) (cid:18) T eff T eff , ⊙ (cid:19) − / (6)These scaling relations have been widely adopted to estimate masses and radiiof red giants (see e.g. Stello et al., 2008; Kallinger et al., 2010; Mosser et al., 2010),but they are based on simplifying assumptions which must be checked against in-dependent fundamental measurements. Recent advances have been made on pro-viding a theoretical basis for the relation between the acoustic cut-off frequencyand n max (Belkacem et al., 2011), and preliminary investigations with stellar mod-els (Stello et al., 2009) indicate that the scaling relations hold to within ∼
3% on themain sequence and RGB (see also the Supporting Online Material in Chaplin et al.2011). n max and Dn scaling relations To assess the accuracy of the scaling relations, ongoing studies based on models ofstars in different evolutionary phases, and covering a wide range of parameters (seee.g. White et al., 2011; Miglio et al., 2011), must be complemented by calibrationof the n max and Dn relations with independent determinations of masses and radii.As a very first step in this process, we present here a simple comparison betweenradii and masses determined via seismic constraints with those obtained by othermethods (combination of parallax, bolometric flux, effective temperature, angularradius, mass derived from the orbital solution of binary systems).We include in this comparison nearby stars with available seismic constraints,along the lines of the work presented by Bruntt et al. (2010). We consider a total of27 stars with published values of both n max and Dn . The quality of the seismic dataavailable for the stars in this sample is highly heterogeneous, ranging from nearly 6-months long space-based photometric observations with the CoRoT satellite, to fewdays’ single-site radial-velocity monitoring. The methods used to estimate n max and Dn are also not uniform. We therefore decided to adopt a 2% and 5% uncertainty in Dn and n max , respectively, as also suggested in Bruntt et al. (2010).Asteroseismic, spectroscopic, interferometric, and photometric constraints wereeither taken from the Bruntt et al. (2010) compilation (to which we refer for the orig-inal references), or collected from the papers by Ballot et al. (2011); Barban et al.(2009); Bazot et al. (2011); Bruntt (2009); Carrier & Eggenberger (2006); Carrier et al.(2010); Deheuvels et al. (2010); Eggenberger et al. (2008); Gillon & Magain (2006);Kallinger et al. (2010); Mathur et al. (2010); Mazumdar et al. (2009); M´erand et al. Page: 5 job: miglio_roma macro: svmult.cls date/time:4-Oct-2018/20:06
Andrea Miglio M / M s un b H y i t C e t i H o r d E r i P r o cy on A P up b V i r h B oo a C en A a C en B m A r a 70 O ph A g P a v t P s A n I nd HD HD HD HD HD S c o r p ii HD R / R s un n max + Dn + T eff n max + R + T eff Dn + RM Binary n max + Dn + T eff p + BC + V + T eff p + interf radius Fig. 2
Comparison between masses ( upper panel ) and radii upper panel determined by differentcombinations of the observational constraints available. M / M s un HD A r c t u r u s x H y a e O ph h S e r R / R s un n max + Dn + T eff n max + R + T eff Dn + R n max + Dn + T eff p + BC + V + T eff p + interf radius Fig. 3
Same as Fig. 2, but considering giants with published seismic analysis.
Page: 6 job: miglio_roma macro: svmult.cls date/time:4-Oct-2018/20:06 steroseismology of red giants as a tool for studying stellar populations: first steps 7 (2010); Mosser et al. (2008, 2009, 2010); and Quirion et al. (2010). Parallaxes aretaken from van Leeuwen (2007) and bolometric corrections from Flower (1996).When available, we used T eff determined from the bolometric fluxes and interfero-metric angular radii, in which case we considered the value quoted in Bruntt et al.(2010). Otherwise, we adopted spectroscopic T eff with uncertainties of 100 K, un-less the uncertainty was larger in the original reference. As in Bruntt (2009) weexcluded from the sample HD175726 since its estimated large separation shows anunexplained large modulation with frequency (see Mosser et al., 2009).We then determined radii using Eq. 4 and masses via Eq. 3 or by including con-straints on the luminosity, using Eqs. 5 and 6. The comparisons between different(not always independent) determinations of radius and mass are presented in Figures2 and 3. R/R sun (seismo) R / R s un Fig. 4
Radii determined using seismic constraints (Eq. 4) vs. radii determined from parallax andangular interferometric radius (red), and from apparent magnitude, parallax, BC and T eff (blue).For targets where interferometric measurements are available we also report the comparison withradii determined from apparent magnitude+ parallax+ BC + T eff (black dots). The targets considered span a large domain in radius: from sub-solar radii ( t Cet, 70 Oph A, and a Cen B) to the ∼ R ⊙ of the metal-poor giant Arcturus.The overall agreement found between values determined via Eq. 4 and using clas-sical constraints is remarkable (see Fig. 4 and 5), and the two determinations agreewithin 1- s ( ∼ Page: 7 job: miglio_roma macro: svmult.cls date/time:4-Oct-2018/20:06
Andrea Miglio −0.3−0.2−0.100.10.20.3 ( R − R s e i s m o ) / R R/R sun
Fig. 5
Percentage difference between radii determined using seismic constraints (Eq. 4) and thosederived from the parallax and interferometric angular radius (if available) or the the estimatedbolometric luminosity and T eff . to their errors, we find a mean difference ( R seismo − R ) and standard deviation of-1.5% and 6%, respectively. A significantly larger number of stars (especially gi-ants) should be included to investigate possible trends with stellar properties. Thiscomparison is indeed encouraging and adds strong support to the use of solar-likeoscillators as distance indicators, also when compared to results obtained using ac-curate determinations of radii in eclipsing binaries, as presented in the recent reviewby Torres et al. (2009) (see e.g. their Fig. 1).The expected uncertainty in the mass determined using Eq. 3 and the availabledata is ∼ − a Cen A and B, Procyon A, and 70 Oph A) could we testthe mass determined using n max and/or Dn with the independent estimate based onthe orbital solution. In these cases we find a 1- s agreement, except for 70 Oph Awhich has an observed n max larger than expected (still within 2 s of the predictedvalue). This is clear from the direct comparison between n max and Dn observed andpredicted by scaling relations is shown in Fig. 6.The quality of seismic constraints obtained from space-based data exceeds thatavailable for most of the stars considered in this comparison. Consequently, whileradii and masses can be estimated with greater precision, this demands more strin-gent tests of the accuracy of the scaling relations. In this respect nearby Kepler andCoRoT targets, and in particular high-duty cycle ground-based observations (e.g.with SONG, see Grundahl et al. 2009) will play a crucial role in testing n max and Dn in well constrained systems. Moreover, the detection with Kepler of solar-like os-cillations in red giants members of open clusters provides additional means for test-ing the accuracy of scaling relations, particularly when largely model-independentconstraints are available for cluster members (see the encouraging results reportedin Stello et al. 2010; Basu et al. 2011; Miglio et al. 2011). Eclipsing binaries withsolar-like pulsating components observed by
Kepler and CoRoT are also promisingand privileged targets for this purpose (see e.g. Hekker et al., 2010).
Page: 8 job: miglio_roma macro: svmult.cls date/time:4-Oct-2018/20:06 steroseismology of red giants as a tool for studying stellar populations: first steps 9 n max Scaling law [ m Hz] n m a x O b s [ m H z ] Procyon A a Cen A a Cen B70 Oph A
Sun 10 Dn Scaling law [ m Hz] Dn O b s [ m H z ] Procyon A a Cen A a Cen B70 Oph A
Sun
Fig. 6
Left panel : Comparison between n max observed vs. n max predicted using independent mea-surements of mass and radius. Right panel : as left panel, but for Dn . Thanks to the interpretation of solar-like oscillation spectra detected by CoRoT and
Kepler , we can now determine the mass and radius of thousands of stars belongingto the composite population of the Milky Way’s disk. These truly innovative con-straints will allow precise age estimates for giants, and will inform studies of galac-tic formation and evolution with observational constraints which were not availableprior to asteroseismology. To fully exploit the potential of these observations, how-ever, it will be crucial to combine them with spectroscopic constraints, which shouldbecome available in the near future thanks to large spectroscopic surveys such asSDSS-APOGEE and the GAIA-ESO spectroscopic survey. Further efforts shouldalso be devoted to assess the validity of the n max and Dn scaling relations, bothin terms of their theoretical foundation, and through calibration with independentmeasurements of radius and mass.In the future, the pioneering observations of CoRoT and Kepler could be ex-tended to significantly wider areas of the sky by the candidate ESA mission PLATO ,providing observational constraints that will be complementary to the accurate dis-tance and proper motions measured by GAIA in the coming years. Acknowledgements
The author acknowledges FNRS for financial support, M. Barbieri, L. Gi-rardi, J. Montalb´an, T. Morel, B. Mosser, and A. Noels for enlightening discussions about seismol-ogy and stellar populations. Additional thanks are due to M. Barbieri and L. Girardi for their kindhelp with the code TRILEGAL, and to W.J. Chaplin for reading the manuscript. http://sci.esa.int/plato http://gaia.esa.int/ Page: 9 job: miglio_roma macro: svmult.cls date/time:4-Oct-2018/20:06
References