Issue 
A&A
Volume 569, September 2014



Article Number  A21  
Number of page(s)  24  
Section  Stellar structure and evolution  
DOI  https://doi.org/10.1051/00046361/201423797  
Published online  11 September 2014 
Online material
Appendix A: Models with different input physics or optimization details
Specifications of additional optimized models assuming different prescriptions for the modelling.
Appendix A.1: Optimization of set A models with alternate prescriptions
In the following, we present other optimization models, all based on the reference physics of set A (Table 2). These models were optimized following Table 3, but with different approaches or choices of free parameters, as described below and listed in Table A.1. The results of the models are listed in Tables A.2 and A.3.

1.
Cases 1− Y/2 − YAs explained in the main text, in cases 1 and 2a, b, and c, the initial helium content Y could not be adjusted because of the lack of observational constraints. Here we investigate the consequence of not deriving Y from the ΔY/ ΔZ = 2 enrichment law (as was done in cases 1 and 2 of Table 3). We sought a solution with the lowest possible initial helium content, never lower than the primordial abundance. These choices have an important impact on the results and are therefore discussed in the main text. We point out that in case A1Y it was possible to find a solution with a primordial helium abundance. This is because no seismic constraints were used in this case. On the other hand, in cases A2a− Y, b− Y, and c− Y, we had to increase the helium abundance above the primordial one because of the seismic constraints introduced, to find a solution that agreed with both the seismic and the classical observational constraints (we found that models with low Y either have a too low temperature or a too high luminosity).

2.
Cases 1α0.550, 1α0.826 In case 1, α_{conv} could not be adjusted because of the lack of observational constraints and, as often seen in papers, the solar value α_{conv, ⊙} was used. Here, we investigated the impact of other choices and we sought a solution for acceptable, extreme values of α_{conv}. Numerical 2D simulations of convection suggest that α_{conv} might differ by a few tenths of dex from the solar value (see e.g. Ludwig et al. 1999). We investigated changes of α_{conv} of 20 per cent around the solar value that correspond to α_{conv,min} = 0.550 and α_{conv,max} = 0.826. These choices have an important impact on the results and are therefore discussed in the main text.

3.
Cases 1ov30 No overshooting was assumed in the reference models of case 1. Here, to estimate its impact, we chose a rather high value, i.e. α_{ov} = 0.30. The impact on case 1 results is discussed in the main text.

4.
Cases 1, 2, 7νrad In these models, the impact of mixing that results from the radiative diffusivity associated with the kinematic radiative viscosity is investigated. Following Morel & Thévenin (2002), we added an extra mixing diffusion coefficient d_{rad} = D_{R} × ν_{rad} with D_{R} = 1 that limits gravitational settling in the outer stellar layers of stars with thin convective envelopes. As can be seen in Tables A.2 and A.3, the impact is weak and is not discussed further.

5.
Case 5allfreq In the list of frequencies extracted by Ballot et al. (2011), 31 frequencies were given, of which 28 were flagged as secure. In this model, we considered the 31 values and found that the impact is weak and that the results remain inside the uncertainty range we gave in the main text.

6.
Case 6YM, 7YM For each optimization case, there are a range of initial heliummass doublets (Y_{0}, M) that provide seismically equivalent optimized models. We investigated the Y_{0} − M degeneracy by searching for optimized models with different values of Y_{0} and M. As discussed in the main text, the impact on age is weak but a range of possible masses of HD 52265 is found.

7.
Case 6nocorrel As explained in the main text, in case 6, we took into account the correlations between the frequency separation ratios and calculated the χ^{2} from Eq. (13). In this model the correlations are not considered and the χ^{2} is evaluated from Eq. (14). The impact is weak and is not discussed further.

8.
Case 6interr Roxburgh & Vorontsov (2013) recently claimed that modelfitting by searching for a best fit of observed and model separation ratios at the same radial orders n is incorrect, and that the correct procedure is to compare the model ratios interpolated to the observed frequencies. We followed this recommendation here. The impact is weak and the results remain in the uncertainty range we gave in the main text.

9.
Case 7rot As explained in the main text, rotation and its effects on the transport of angular momentum and chemicals was treated as in Marques et al. (2013), and we tuned the K_{w} coefficient that enters the treatment of magnetic braking by winds to match the observed rotation period. The impact on age and mass is weak for this rather evolved star. A thorough study of the effects of rotation on HD 52265 will be presented in a forthcoming paper.

10.
Case 7noSE and case 7bSE4.9. As explained in the main text, in case 7, we corrected the individual frequencies for the surface effects with the Kjeldsen et al. (2008) empirical prescription and calibrated the b_{SE} parameter in Eq. (12) to achieve the best match between observed and modelled frequencies. In model 7bSE4.9, we used the solar value of b_{SE} calibrated by Kjeldsen et al. (2008) and found that the impact on the results is weak. In model 7noSE, we did not correct frequencies for the surface effects. The impact is strong, in particular on age. This is discussed in the main text.

11.
Case 7pms. The main models were calculated by starting the computation at the zeroage main sequence. This model was evolved from the premain sequence. The impact is weak.

12.
Cases 6 and 7ov. In the models presented in the main text, overshooting was either neglected (sets A − H, K) or fixed (sets I, J). Since there are enough observational constraints to add overshooting and convective penetration as additional free parameters in cases 6 and 7, we considered this possibility here. We therefore also optimized the values of α_{ov} and ξ_{PC}. As also discussed in the main text, we found that low values of α_{ov} are favoured (range 0.00− 0.04) and rather high values of ξ_{PC} (range 0.90−1.25). This latter result, related to the oscillatory behaviour of the frequencies, close to the convective envelope agrees with the conclusions of Lebreton & Goupil (2012).
Appendix A.2: Optimization with different input physics
In the following, we present optimization models based on the different choices of input physics listed in Table 2. These models were optimized following Table 3. The results are listed in Tables A.4 and A.5. Discussions are found in the main text.
© ESO, 2014
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