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The physics of early stellar evolution (e.g. accretion processes) is oftennot properly included in the calculations of pre-main-sequence models, leadingto insufficient model grids and hence systematic errors in the results. We aimto investigate current and improved approaches for the asteroseismic modellingof pre-main-sequence delta Scuti stars. We calculated an extensive grid ofpre-main-sequence models including the early accretion phase and used theresulting equilibrium models as input to calculate theoretical frequencyspectra. These spectra were used to investigate different approaches inmodelling echelle diagrams to find the most reliable methods. By applyingPetersen diagrams, we present a simple algorithm to extract echelle diagramsfrom observed pulsation frequencies. We show that model grids with insufficientinput physics and imperfect modelling approaches lead to underestimateduncertainties and systematic errors in the extracted stellar parameters. Ourre-discussion of HD 139614 leads to different stellar parameters than the onesderived by Murphy et al. (2021). We performed a model comparison between thisprevious investigation and our results by applying the Akaike and Bayesianinformation criteria. While the results with regard to our 10-d model areinconclusive, they show (very) strong evidence of a 6-d model with fixedaccretion parameters (leading to almost identical stellar parameters to thoseof the 10-d model) to be preferred over the model applied by Murphy et al.(2021). In general, our modelling approach can provide narrow constraints onthe stellar parameters (\Delta R ~ 0.05 R_\odot, \Delta log g <~ 0.01, and\Delta M_\star ~ 0.1 M_\odot). The extensively tested modelling approaches andautomatic extraction of echelle diagrams should allow us to study many morepre-main-sequence delta Scuti stars in the future and lead to reliable stellarparameters.

astronomy and astrophysics

Pulsational instability of pre-main-sequence models from accreting  protostars II. Modelling echelle diagrams of $\delta$ Scuti stars without  rotational splitting