Red Giant Oscillations: Stellar Models and Mode Frequency Calculations
A. Jendreieck, A. Weiss, V. Silva Aguirre, J. Christensen-Dalsgaard, R. Handberg, G. Ruchti, C. Jiang, A. Thygesen
aa r X i v : . [ a s t r o - ph . S R ] N ov Astron. Nachr. / AN , No. , 1 – 3 () /
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Red Giant Oscillations: Stellar Models and Mode Frequency Calcula-tions
A. Jendreieck ,⋆ , A. Weiss , V. Silva Aguirre , J. Christensen-Dalsgaard , R. Handberg , G. Ruchti ,C. Jiang , and A. Thygesen Max Planck Institute for Astrophysics, Karl-Schwarzschild-Str. 1, 85748, Garching bei M¨unchen, Germany Stellar Astrophysics Centre, Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120,DK-8000 Aarhus C, Denmark Zentrum f¨ur Astronomie der Universit¨at Heidelberg, Landessternwarte, Heidelberg, GermanyReceived 22 August 2012, accepted 18 October 2012Published online ?
Key words stars: oscillations; stars: evolutionWe present preliminary results on modelling KIC 7693833, the so far most metal-poor red-giant star observed by
Kepler .From time series spanning several months, global oscillation parameters and individual frequencies were obtained andcompared to theoretical calculations. Evolution models are calculated taking into account spectroscopic and asteroseismicconstraints. The oscillation frequencies of the models were computed and compared to the
Kepler data. In the range ofmass computed, there is no preferred model, giving an uncertainty of about 30 K in T eff , 0.02 dex in log g , . R ⊙ inradius and of about 2.5 Gyr in age. c (cid:13) WILEY-VCH Verlag GmbH&Co. KGaA, Weinheim
Red giants have a broad spectrum of acoustic oscillationmodes which are excited by an extended convective enve-lope (e.g. Montalb´an et al. 2010; Mosser et al. 2011). Also,as the density in the helium core is quite large, g-modeswith frequencies close to those of the acoustic modes can in-teract with the latter, bringing on the presence of so-calledmixed modes (Di Mauro et al. 2011). Those modes with amore p-mode character, propagating with smaller inertia,can reach the surface where they are observed. As they haveg-mode character in the centre, they provide important in-formation about the deep interior of red giants. The highsensitivity of the
CoRoT and
Kepler space missions madeit possible to observe non-radial oscillations in a large sam-ple of red giants (De Ridder et al., 2009) and the obser-vation of such mixed modes (e.g. Di Mauro et al. 2011).The study of evolved stars is important as it leads to bet-ter constraints on stellar evolution models, since the uncer-tainties in stellar structure properties accumulate with age(De Ridder et al. 2009). Processes not well understood likeconvective overshooting, rotational mixing and diffusionduring the hydrogen-burning phase determines the mass ofthe helium core in the giant phase and also the age of thestar (Aerts et al. 2008). ⋆ Corresponding author: e-mail: [email protected]
Table 1
Basic parameters of KIC 7693833 determinedand used in the present analysis.
Basic Parameters of KIC 7693833 T eff ± Klog g . ± . dex [ Fe/H ] − . ± . dex α -enhancement . dex ν max . ± . µ Hz ∆ ν . ± . µ Hz We have analyzed the red giant KIC 7693833 observed by
Kepler during the Q1-Q10. The frequency spectrum spansa range from µ Hz to µ Hz with 19 modes identified as l = 0 , , with a ν max = 32 . µ Hz and ∆ ν = 4 . µ Hz.The target KIC 7693833 is a metal-poor star classified( [Fe / H] = − . dex) as ascending the red-giant branch ac-cording to the classification given by Bedding et al. (2011).Spectroscopic analysis was performed by Thygesen et al.(2012) and a T eff of about 4800 K was determined. We re-analyzed the spectra considering NLTE effects and found a T eff of about 5100 K. We also found indications of a con-stant α -enhancement of 0.2 dex. From the corrected Kepler lightcurves we extracted the global seismic parameters ∆ ν and ν max , as well as individual frequencies for modes ofdegree l = 0 , , . The basic stellar parameters are summa-rized in Table 1. c (cid:13) WILEY-VCH Verlag GmbH&Co. KGaA, Weinheim
A. Jendreieck et al.: Red Giant Oscillations: Stellar Models and Mode Frequency Calculations
Making use of the observed constraints on the asteroseismicparameters and the effective temperature, we first estimateda preliminary mass using the asteroseismic scaling relation(Brown et al. 1991; Kjeldsen & Bedding 1995): MM ⊙ = (cid:18) ∆ ν ∆ ν ⊙ (cid:19) − (cid:18) ν max ν max , ⊙ (cid:19) (cid:18) T eff T eff , ⊙ (cid:19) / , (1)resulting in a mass of . M ⊙ . With this information, agrid of models was calculated for masses from . − . M ⊙ in steps of . M ⊙ with the GARSTEC evolutionarycode (Weiss & Schlattl 2008).All the models were computed with the same inputparameters. OPAL 2005 (Rogers & Nayfonov 2002) equa-tion of state were used together with NACRE (Angulo et al.1999) reaction rates. The metallicity was calculated consid-ering the α -enhancement according to Salaris et al. (1997),giving a Z = 1 . × − . We used the He primordialcontent Y = 0 . derived by Steigman (2010). Convec-tion is treated according to the mixing-length theory (MLT)(B¨ohm-Vitense 1958) and with the parameter α MLT =1 . calibrated for the Sun.The oscillation frequencies were calculated with theADIPLS package (Christensen-Dalsgaard 2008) for modesof angular degree l = 0 , and 2 for all models that satisfied ∆ ν observed according to the scaling relation: ∆ ν ∆ ν ⊙ = (cid:18) MM ⊙ (cid:19) / (cid:18) LL ⊙ (cid:19) − . (cid:18) T eff T eff , ⊙ (cid:19) . (2)Afterwards, a thinner time step was set to find the modelsthat matched the lowest l = 0 mode observed within theerror bars. We compared the calculated and observed frequencies. Asthe calculated frequency spectrum is heavily populated,only the frequencies with minimum mode inertia were cho-sen to be compared because these modes have the highestamplitudes at the surface and hence are the most proba-ble to be observed (e.g. Christensen-Dalsgaard et al. 1995;Dupret et al. 2009). Figure 1 shows mode inertia plottedversus frequency for a model with 1 M ⊙ . Radial modes arerepresented as diamonds, l = 1 modes as triangles and l = 2 modes as squares.Figure 2 shows the difference between calculated andobserved frequencies, for some of the models with masses . and . M ⊙ . The error bars are representing the errorsfrom the observational data. The frequency differences aresmaller than . µ Hz for all models considered up to now,having no preferred model. Figure 3 shows the ´echelle dia-grams for the same models. Open symbols are the frequen-cies computed from models and filled circles are represent-ing the observational data. Both models show good agree-ment with data, showing again no preferred model.
Fig. 1
Mode inertia as function of frequency for modes l = 0 (diamonds), l = 1 (triangles) and l = 2 (squares).The modes with lowest inertia are the ones with higher am-plitudes at the surface and hence are easier to observe. Table 2
Differences in the basic parameters for the mod-els with 1.00 M ⊙ and 1.20 M ⊙ Mass 1.00 M ⊙ ⊙ T eff K K log g . dex . dex R/R ⊙ . . Age . Gyr 3.2 Gyr
In the range of masses investigated by now, the dis-crepancies in the determination of the basic parameters areshowed in Table 2.We also tried to investigate the asymptotic period spac-ing of the models to see if it would be a good way todisentangle between the mass. However the difference be-tween 1.00 and 1.20 M ⊙ are of a few seconds, both about60 s. Bedding et al. (2011) found a value of observed periodspacing of 80 s giving an even larger asymptotic value. Thediscrepancies in period spacing might be solved with highermass and is being investigated. KIC 7693833 is the so far most metal-poor red giant and itwas observed by
Kepler during Q1-Q10. From its frequencyspectrum, 19 modes of oscillation were identified as l =0 , , with a ν max = 32 . µ Hz and ∆ ν = 4 . µ Hz.Models within 1.00-1.20 M ⊙ were computed to matchthe observational constraints using the scaling relations asstarting point. The frequencies computed for all modelsagree within . µ Hz, having no preferred model. This givesan uncertainty of about 30 K in T eff , 0.02 dex in log g , 0.7 R ⊙ in radius, corresponding to 7%, and of about 2.5 Gyr inage. The period spacing of the models computed are smallerthan the observed one and the possibility to resolve the dis-crepancies by possible higher masses is currently investi- c (cid:13) WILEY-VCH Verlag GmbH&Co. KGaA, Weinheim stron. Nachr. / AN () 3
Fig. 2
Frequency difference between model and observational values for models with 1.00 (left) and 1.20 (right) M ⊙ .Both models agree within a range of . µ Hz with the data. There is no preferred model.
Fig. 3 ´Echelle diagram for the models with 1.00 M ⊙ (left) and 1.20 M ⊙ (right). Open symbols show the frequenciescomputed for the models and filled symbols show the observed ones. Diamonds are for l = 0 modes, triangles for l = 1 modes and squares for l = 2 .gated. This would make the star even younger and quite pe-culiar for a metal-poor star.For a more detailed modeling, it is important to inves-tigate different physics inputs and see how the oscillationfrequencies change. This way, we might find a way to dis-tinguish between models of different masses and differentphysics. Currently, we still have no good diagnosis to dis-entangle models of red giants. Acknowledgements.
Funding for the
Kepler
Discovery mission isprovided by NASA’s Science Mission Directorate. Funding for theStellar Astrophysics Centre is provided by The Danish NationalResearch Foundation. The research is supported by the ASTER-ISK project (ASTERoseismic Investigations with SONG and Ke-pler) funded by the European Research Council (Grant agreementno.: 267864).
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