New Astronomy 13 (2008) 541–548 Contents lists available at ScienceDirect New Astronomy journal homepage: www.elsevier.com/locate/newast Seismic analysis of 70 Ophiuchi A: A new quantity proposed Y.K. Tang a,c,*, S.L. Bi b,a, N. Gai a,c a National Astronomical Observatories/Yunnan Observatory, Chinese Academy of Sciences, Kunming 650011, PR China b Department of Astronomy, Beijing Normal University, Beijing 100875, PR China c Graduate School of the Chinese Academy of Sciences, Beijing 100039, PR China article info abstract Article history: The basic intent of this paper is to model 70 Ophiuchi A using the latest asteroseismic observations as Received 16 July 2007 complementary constraints and to determine the fundamental parameters of the star. Additionally, we Received in revised form 26 February 2008 propose a new quantity to lift the degeneracy between the initial chemical composition and stellar Accepted 26 February 2008 age. Using the Yale stellar evolution code (YREC7), we construct a series of stellar evolutionary tracks Available online 2 March 2008 for the mass range M = 0.85–0.93 M with different composition Y (0.26–0.30) and Z (0.017–0.023). Communicated by W. Soon i i Along these tracks, we select a grid of stellar model candidates that fall within the error box in the HR diagram to calculate the theoretical frequencies, the large- and small-frequency separations using Guen- Keywords: ther’s stellar pulsation code. Following the asymptotic formula of stellar p-modes, we define a quantity Stars: oscillations Stars: evolution r01 which is correlated with stellar age. Also, we test it by theoretical adiabatic frequencies of many mod- Stars: individual: 70 Ophiuchi A els. Many detailed models of 70 Ophiuchi A are listed in Table 3. By combining all non-asteroseismic observations available for 70 Ophiuchi A with these seismological data, we think that Model 60, Model 125 and Model 126, listed in Table 3, are the optimum models presently. Meanwhile, we predict that the radius of this star is about 0.860–0.865 R and the age is about 6.8–7.0 Gyr with mass 0.89–0.90 M . Additionally, we prove that the new quantity r01 can be a useful indicator of stellar age. Ó 2008 Elsevier B.V. All rights reserved. 1. Introduction Recently, Carrier and Eggenberger (2006) detected solar-like oscillations on the K0 V star 70 Ophiuchi A (HD 165341), and iden- The solar 5-min oscillations have led to a wealth of information tified some possible existing frequencies. They obtained the large about the internal structure of the Sun. These results stimulated separation Dm = 161.7 ± 0.3 lHz by observation over six nights with various attempts to detect solar-like oscillations for a handful of HARPS. The spectroscopic visual binary system 70 Ophiuchi is one solar-type stars. Individual p-mode frequencies have been identi- of our nearest neighbors (5 pc) and is among the first discovered fied for a few stars: a Cen A (Bouchy and Carrier, 2002; Bedding binary stars. It was observed first by Herschel in 1779. So 70 et al., 2004), a Cen B (Carrier and Bourban, 2003; Kjeldsen et al., Ophiuchi A is famous as the primary of a visual and spectroscopic 2005), l Arae (Bouchy et al., 2005), HD 49933 (Mosser et al., binary system in the solar neighborhood. Although many observa- 2005), b Vir (Martic´ et al., 2004a; Carrier et al., 2005b), Procyon A tion data have been obtained since 1779, the theoretical analysis of (Martic´ et al., 2004b; Eggenberger et al., 2004a), g Bootis (Kjeldsen 70 Ophiuchi A has only been made by Fernandes et al. (1998).Bya et al., 2003; Carrier et al., 2005a), b Hyi (Bedding et al., 2001; Car- calibration method which takes into account the simultaneous rier et al., 2001) and d Eri (Carrier et al., 2003b). Based on these evolution of the two members of the binary system, they analyzed asteroseismic data, numerous theoretical analyses have been per- 70 Ophiuchi A by means of standard evolutionary stellar models formed in order to determine precise global stellar parameters using the CESAM code (Morel, 1997) without microscopic diffu- and to test the various complicating physical effects on the stellar sion. They found that the metallicity of 70 Ophiuchi A is very close structure and evolutionary theory (Thévenin et al., 2002; Eggen- to the solar one, the values of the mixing-length parameter a and berger et al., 2004b, 2005; Kervella et al., 2004; Miglio and Mont- helium abundance Y are near the Sun. They thought that the star albán, 2005; Provost et al., 2004, 2006). is younger than the Sun and 3 ± 2 Gyr is probably a limit consider- ing the age versus stellar rotation relation with its rotation velocity (vsini 16 km sÀ1). * Corresponding author. Address: National Astronomical Observatories/Yunnan The aim of our paper is to present the model which can be con- Observatory, Chinese Academy of Sciences, Kunming 650011, PR China. Fax: +86 strained by these seismology data. The observational constraints 3920154. E-mail addresses: [email protected], [email protected] (Y.K. Tang), bisl@ available for 70 Ophiuchi A are summarized in Section 2, while bnu.edu.cn (S.L. Bi). the numerical calculations are presented in Section 3. The seismic 1384-1076/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.newast.2008.02.002 542 Y.K. Tang et al. / New Astronomy 13 (2008) 541–548 analyses are carried out and a new quantity r01 as an indication of large separation of 161.7 lHz, the solution Dm = 172.2 lHz cannot stellar age is proposed in Section 4. Finally, the discussion and con- be ruled out definitely. We refer to these two groups of results in clusions are given in Section 5. the paper and make analyses in Sections 4 and 5. 2. Observational constraints 3. Stellar models 2.1. Non-asteroseismic observation constraints We will construct a grid of stellar evolutionary models by the Yale stellar evolution code (YREC; Guenther et al., 1992) with The mass of this star was investigated by Batten et al. (1984), microscopic diffusion. The initial zero-age main sequence (ZAMS) Heintz (1988), Fernandes et al. (1998) and Pourbaix (2000). In this model used for 70 Ophiuchi A was created from pre-main sequence paper, we adopt the value of the mass deduced from Fernandes evolution calculations. In these computations, we do not consider et al. (1998). The effective temperature was determined by Gray rotation and magnetic field effects. These models are computed and Johanson (1991). So far, the metallicity values obtained by using OPAL equation of state tables EOS2001 (Rogers and Nayfo- observation are [Fe/H] = À0.05 (Peterson, 1978) and [Fe/H] = 0.00 nov, 2002), the opacities interpolated between OPAL GN93 (Igle- (Perrin et al., 1975). We choose [Fe/H] = 0.0 ± 0.1 as a representa- sias and Rogers, 1996) and low temperature tables (Alexander tive value according to Fernandes et al. (1998). and Ferguson, 1994). Using the standard mixing-length theory, The mass fraction of heavy-elements, Z, was derived assuming we set a = 1.7 for all models, close to the value which is required log[Z/X] [Fe/H] + log[Z/X] and [Z/X] = 0.0230 (Grevesse and to reproduce the solar radius under the same physical assumptions Sauval, 1998), for the solar mixture. So we can deduce the [Z/ and stellar evolution code. Meanwhile, it must be emphasized that X]s = 0.0183–0.0290. there are still a number of uncertainties in our analyses, foremost All non-asteroseismic observational constraints are listed in Ta- among which is the still open question of the mixing-length theory ble 1. responsible for the stellar model. The nuclear reaction rates have been updated according to Bahcall et al. (1995). The Krishna- 2.2. Asteroseismic constraints Swamy Atmosphere T–s relation is used for this solar-like star (Guenther and Demarque, 2000). Also, we consider the microscopic Solar-like oscillations of 70 Ophiuchi A have been detected by diffusion effect, by using the diffusion coefficients of Thoul et al. Carrier and Eggenberger (2006) with the HARPS spectrograph. (1994). Since 70 Ophiuchi A, like a Cen B, is less massive than the Fourteen individual modes are identified with amplitudes in the Sun, the mass contained in its convective zone is much larger range 11–14 cm sÀ1. Although they listed two groups of frequen- and, therefore, the effect of microscopic diffusion is much smaller cies by mode identification (see Table 2 in Carrier and Eggenberger, (Miglio and Montalbán, 2005; Morel and Baglin, 1999). However, 2006), one group of frequencies with an average large separation it is necessary to consider this effect as a physical process in stellar Dm = 161.7 lHz was suggested to be more reliable than the other modeling (see Provost et al., 2005; Provost et al., 2006). with an average large separation Dm = 172.2 lHz. The star 70 In general, the determination of parameters (M,t,Yi,Zi) fitting Ophiuchi A is very similar to a Cen B with the same spectral type the observational constraints needs two steps. The first step is to and similar large separation, which has a mean small separation construct a grid of models with position in the HR diagram in of 10 lHz. It is thought that the small separation should be similar. agreement with the observational values of the luminosity, the By inspecting the results of the mode identification, they note that effective temperature and the surface metallicity. The principal the value of the small separation coming from the identification constraints deduced from non-asteroseismic observation are listed with the large separation of 172.2 lHz is significantly different in Table 1.