Surface layer independent model fitting by phase matching: theory and application to HD49933 an HD177153 (aka Perky)

Aims. To describe the theory of surface layer independent model fitting by phase matching and to apply this to the stars HD49933 observed by CoRoT, and HD177153 (aka Perky), observed by Kepler Methods. We use theoretical analysis, phase shifts, and model fitting. Results. We define the inner and outer phase shifts of a frequency set of a model star and show that the outer phase shifts are (almost) independent of degree $\ell$, and that a function of the inner phase shifts (the phase function) collapses to an $\ell$ independent function of frequency in the outer layers. We then show how to use this result in a model fitting technique to find a best fit model to an observed frequency set by calculating the inner phase shifts of a model using the observed frequencies and determining the extent to which the phase function collapses to a single function of frequency in the outer layers. We give two examples applying this technique to the frequency sets of HD49933 observed by CoRoT and HD177153 (aka Perky) observed by Kepler, and compare our results with those of previous studies and show that they are compatible with those obtained using different techniques. We show that there can be many different models that fit the data within the errors and that better precision on the frequencies is needed to discriminate between the models. We compare this technique to that using the ratios of small to large separations, showing that in principle it is more accurate and avoids the problem of correlated errors in separation ratio fitting.