Scaled models, scaled frequencies, and model fitting

摘要

I show that given a model star of mass M, radius R, and density profile ρ(x) [x = r/R], there exists a two parameter family of models with masses Mk, radii Rk, density profile ρk(x) = λρ(x) and frequencies νkn? = λ1/2νn?, where λ,Rk/RA are scaling factors. These models have different internal structures, but all have the same value of separation ratios calculated at given radial orders n, and all exactly satisfy a frequency matching algorithm with an offset function determined as part of the fitting procedure. But they do not satisfy ratio matching at given frequencies nor phase shift matching. This illustrates that erroneous results may be obtained when model fitting with ratios at given n values or frequency matching. I give examples from scaled models and from non scaled evolutionary models.