Analysis of 51 Peg : Large and Small Spacings from Standard Models Eric

We present a preliminary theoretical seismic study of the astronomically famous star 51 Peg. This is done by first performing a detailed analysis within the Hertzsprung-Russell diagram (HRD). Using the Yale stellar evolution code (YREC), a grid of stellar evolutionary tracks has been constructed for the masses 1.00M ⊙ , 1.05M ⊙ and 1.10M ⊙ , in the metallicity range Z = 0.024 − 0.044, and for values of the Galactic helium enrichment ratio (∆Y /∆Z) in the range 0-2.5. Along these evolutionary tracks, we select 75 stellar model candidates that fall within the 51 Peg observational error box in the HRD (all turn out to have masses of 1.05M ⊙ and 1.10M ⊙). The corresponding allowable age range for these models, which depends sensitively on the parameters of the model, is relatively large and is ∼2.5-5.5 Gyr. For each of the 75 models, a non-radial pulsation analysis is carried out, and the large and small frequency spacings are calculated. The results show that just measuring the large and small frequency spacings will greatly reduce the present uncertainties in the derived physical parameters and in the age of 51 Peg. Finally we discuss briefly refinements in the physics of the models and in the method of analysis which will have to be included in future models to make the best of the precise frequency determinations expected from space observations.