Asteroseismic modelling of Procyon A: Preliminary results
Gülnur Doğan, Alfio Bonanno, Tim R. Bedding, Tiago L. Campante, Jørgen Christensen-Dalsgaard, Hans Kjeldsen
aa r X i v : . [ a s t r o - ph . S R ] J un Astron. Nachr. / AN , No. 000, 1 – 3 (2010) /
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Asteroseismic modelling of Procyon A: Preliminary results
G. Do˘gan ,⋆ A. Bonanno T. R. Bedding T. L. Campante , J. Christensen-Dalsgaard and H. Kjeldsen Department of Physics and Astronomy, Aarhus University, Ny Munkegade, DK-8000, Aarhus C, Denmark Catania Astrophysical Observatory, Via S.Sofia 78, 95123, Catania, Italy School of Physics A29, University of Sydney, NSW 2006, Sydney, Australia Centro de Astrof´ısica da Universidade do Porto, Rua das Estrelas, 4150-762 Porto, PortugalReceived XX, accepted XX
Key words stars: individual (Procyon A) – stars: oscillations – stars: evolutionWe present our preliminary results of the modelling of the F5 star Procyon A. The frequencies predicted by our models arecompared with the frequencies extracted through a global fit to the power spectrum obtained by the latest ground-basedobservations, which provides two different mode identification scenarios. c (cid:13) Procyon A is a member of a binary system with a whitedwarf companion, Procyon B. It is one of the very brightstars to the naked eye, and hence it has been very attrac-tive for the observers. The observational constraints whichwe adopted are summarized in Section 2. It has also beenof asteroseismic interest for a long while (see Arentoftet al. 2008, for a summary), with a solar-like power ex-cess in its spectrum first reported by Brown et al. (1991).However, there has been no agreement on the individ-ual oscillation frequencies. Several authors have investi-gated the structure and evolution of Procyon A throughan asteroseismic approach (e.g., Guenther & Demarque1993; Barban et al. 1999; Chaboyer et al. 1999; Di Mauro& Christensen-Dalsgaard 2001; Eggenberger et al. 2005;Provost et al. 2006, Bonanno et al. 2007), but there hasbeen a need for more accurate frequencies. Recently, the starwas observed through a multi-site campaign by eleven tele-scopes for more than three weeks (Arentoft et al. 2008). Thefrequency analysis is described by Bedding et al. (2010).They presented results from different approaches of fre-quency extraction: Iterative sine-wave fitting and global fit-ting to the power spectrum. In the former method, a sinewave is fitted to each mode one after the other while thecorresponding sinusoid is subtracted from the time seriesat each step. This is repeated until the signal to noise ra-tio of the remaining power is lower than a given threshold.This method was used for frequency extraction of ground-based radial velocity data before (see, e.g., the analysis onsolar-like star β Hyi by Bedding et al. (2007)). In the lattermethod, the goal is to find an overall fit to the power spec-trum for all the frequencies, mode heights, and linewidthssimultaneously, using some prior knowledge of oscillation ⋆ e-mail: [email protected] properties as constraints. A similar implementation of thismethod was previously applied to space-based data (see,e.g., frequency analysis of CoRoT star HD 49933 by Beno-mar et al. (2009)). In this work, we adopted this Bayesianapproach which provided us with two mode identificationscenarios, referred to as Scenario A and B, with differentposterior odds (for a detailed discussion, see Bedding etal. 2010). We chose the output of this analysis in order totest both scenarios. Note that Scenario B was favoured byBedding et al. (2010; see that paper for a discussion), buthere we test both scenarios. We have adopted the following properties for the position ofthe star in the H-R Diagram: T eff = 6530 ±
90 K (Fuhrmannet al. 1997) and log(
L/L ⊙ ) =0.85 ± ( L/L ⊙ ) =0.840 ± ± ρ ⊙ , obtained from the mea-sured radius using the angular diameter 5.404 ± .
031 mas (Aufdenberg et al. 2005) and the revised Hipparcos parallax( . ± .
26 mas , van Leeuwen 2007), together with theadopted mass . ± . M ⊙ , which is the mean of thetwo different astrometric determinations (Girard et al. 2000, Note that there is an error in Bedding et al. 2010 (Section 9); the valuethey give for the revised parallax is actually the original one. We also notethat the uncertainty on the revised parallax is larger than the original but ispresumably more reliable. c (cid:13) G. Do˘gan et al.: Modelling Procyon A
Gatewood and Han 2006). For the metallicity of the star, weallowed a wide range covering the .
05 dex iron deficiencysuggested by Allende Prieto et al. (2002), and we used thesolar mixture from Grevesse & Noels (1993).We have computed stellar models with two differ-ent evolutionary codes: ASTEC (Aarhus STellar Evolu-tion Code) (Christensen-Dalsgaard 2008a) and GARSTEC(Garching Stellar Evolution Code) (Weiss & Schlattl 2008).The method we used is to compute several grids of stan-dard models scanning through a parameter space formed byvarying the mass, the initial metallicity at the stellar sur-face, Z i /X i , and the mixing-length parameter, α , where themixing length is defined as ℓ = αH p , H p being the pressurescale height. So far, we have searched within the follow-ing ranges: M = 1.42 – 1.52 M ⊙ , Z i /X i = 0.0204 – 0.0245, Y i = 0.26 – 0.31, and α = 1.6 – 1.9. Here X i , Y i , and Z i , arethe initial mass fractions of hydrogen, helium, and the ele-ments heavier than helium, respectively. We have computedthe models without taking into account diffusion, convectiveovershooting, or rotation.The Aarhus adiabatic pulsation package (ADIPLS)(Christensen-Dalsgaard 2008b) has been used to calculatethe frequencies of the models having properties that are inagreement with the observations. We have then comparedthe model frequencies with the observed frequencies. Weselected the models that minimize the following χ : χ = X n,l (cid:18) ν obs l ( n ) − ν model l ( n ) σ ( ν obs l ( n )) (cid:19) , where ν obs l ( n ) , and ν model l ( n ) are the model, and the ob-served, frequencies with spherical degree l and radial order n , and σ ( ν obs l ( n )) represents the uncertainties in the ob-served frequencies. The results from the two different stellar evolution codesare similar; hence we present some of the selected modelscomputed with ASTEC. The so-called ´echelle diagrams ofthe best models for both of the scenarios, chosen withoutapplying any near-surface corrections are shown in Figs 1and 2, with their parameters summarized in Table 1. Oneplots the ´echelle diagrams using the frequency modulo thelarge frequency separation, ∆ ν , in the horizontal axis. Inorder to allow easy comparison with the diagrams shown byBedding et al. (2010), we use the same value, ∆ ν = µ Hz,in our diagrams.The behaviour of the frequency differences between themodels and the observations (shown in Figs 3 and 4) arequite different from that in the Sun. Kjeldsen et al. (2008)showed that the difference between observed and model fre-quencies of the Sun can be fitted by a power law, which canalso be employed to correct the model frequencies for near-surface effects in other solar-like stars, such as β Hyi and
Fig. 1 ´Echelle diagram of the selected model for ScenarioA. Open symbols represent the model frequencies, while thefilled symbols with the uncertainties correspond to the fre-quencies extracted from the observations. Circles, triangles,and diamonds are used for the modes with spherical degree l = 0, 1, and 2, respectively. The vertical dot-dashed line cor-responds to the value of ∆ ν . Fig. 2 ´Echelle diagram of the selected model for ScenarioB. Symbols are used in the same way as in Fig. 1. α Cen A. However, in Procyon, we cannot justify the ap-plication of such a surface correction to yield a significantimprovement in the fit, since the frequency differences donot follow the power-law behaviour (see also Figs 16 and17 of Bedding et al. 2010).
We can argue, if Scenario A is the correct one, that the pre-dictions of the stellar evolutionary models match the ob-servations quite well; however, a surface correction for themodel frequencies seems not to be needed, unlike in thesolar case. Therefore, the effects of different near-surfaceproperties on the high frequencies might be cancelling outin Procyon; this deserves further investigation.If, on the other hand, Scenario B is correct, there seemsto be no good agreement between the models and the ob- c (cid:13) stron. Nachr. / AN (2010) 3 Table 1
Parameters of the best models
Parameter Scenario A Scenario B
M/M ⊙ Z i /X i Y i R/R ⊙ ρ/ρ ⊙ L/L ⊙ T eff (K) 6446 6603 α X ∗ c χ ∗ Mass fraction of hydrogen remaining in the centre of the star
Fig. 3
The difference between the radial ( l = 0 ) frequen-cies from the observations and the selected model for Sce-nario A. The indicated uncertainties are those from the dataanalysis.servations, even in the low-frequency region, which meansthat there is something incompatible in the structure of themodels.We have presented preliminary results from our on-going work. To come to a conclusion we need to extendour analysis. Effects of inclusion of overshooting and useof different treatments of convection should be analysed. Inaddition, the suspected mixed mode reported by Bedding etal. (2010) could help us distinguish between the two scenar-ios, and put further constraints on the age, and the chemicalcomposition.Although from the point of view of modelling, ScenarioA seems to be less problematic, we cannot yet stronglyfavour either of the scenarios; therefore, it is difficult to setaccurate constraints on the stellar properties. Nevertheless,either of the cases suggests that Procyon is quite differentfrom the Sun, which provides a very good opportunity totest our understanding of stellar structure and evolution. Acknowledgements.
This work was supported by the EuropeanHelio- and Asteroseismology Network (HELAS), a major interna-tional collaboration funded by the European Commission’s SixthFramework Programme. GD, JC-D, and HK acknowledge finan-cial support from the Danish Natural Science Research Council.
Fig. 4
Same as Fig. 3, but for Scenario B
GD would like to thank Pierre-Olivier Quirion for providing aparallel-programming code for faster evolution computation.
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