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Long vs short: Quantifying uncertainties in modelling gravity mode period spacing patterns

Pedersen, May Gade

Abstract

A unique property of gravity mode oscillations is that they form period spacing patterns, where all included oscillations share the same degree and azimuthal order, and are consecutive in radial order. The exact morphology of the patterns depends on the mass, age, rotation, and mixing history of the stars and can therefore be used to probe these exact stellar quantities. The variations in the morphology of the period spacing patterns depend on which radial orders are observed and generally decrease for increasing radial orders. We therefore expect that the asteroseismically determined stellar parameters will have some dependence on not only the number of modes in the pattern (i.e. the pattern length), but also which radial orders are observed. We present the first systematic study of the impact on the asteroseismically derived stellar parameters of Slowly Pulsating B stars arising from varying the length and observed radial orders of their period spacing patterns. These stars have previously been found to have period spacing patterns that include five to 36 gravity mode oscillations. We show that increasing the number of radial orders in the patterns significantly improves the precision on the derived asteroseismic masses, convective core masses, and ages of the stars by a factor of two to four. Furthermore, we show that varying which radial orders are included in a period spacing pattern with fifteen gravity modes causes variations in the estimated masses, convective core masses, and ages of at least 3-5%.

Full text

Long vs short: Quantifying uncertainties in modelling gravity mode period spacing patterns May Gade Pedersen ([email protected], University of Sydney, Australia) Introduction Gravity mode oscillations form period spacing patterns, where all included oscillations share the same and are consecutive in radial order, . The exact morphology of the patterns depends on the mass, age, rotation, and mixing history of the stars and can therefore be used to probe these quantities. ! .! Here we present the first systematic study of the impact on the derived stellar parameters of SPB stars arising from varying the number of observed modes in the pattern and which radial orders are observed. We do so by selecting a number of reference stellar models with known parameters and model their corresponding theoretical period spacing patterns. (ℓ,m) n X Relative differences in derived stellar parameters Estimated parameter uncertainties versus pattern length SPB stars have been found to have observed period spacing patterns consisting of 5 to 36 frequencies.! .! The density distributions show the relative differences between the estimated parameters and known reference model values for two pattern lengths across all MS ages and radial order ranges. Stellar models The grid contains >106 stellar models with 2000 unique combinations of M, Z, fov, and Denv. ! .! Seven reference models with different (M, Z, fov, Denv) values are selected for modelling. X Nfreq = 5 Nfreq = 12 Right: Period spacing pattern of a reference model (Xc/Xini = 0.50)! .! Left: Relative differences between estimated parameters (fit) and ! the known reference values. ! Grey: All fit results for fixed Nfreq but varying range in n.! .! Nfreq = # of included g-mode frequencies in pattern, i.e. pattern length Varying pattern length and observed n Future work ❖Increase number of reference models to 500. .! ❖Make a statistical model and neural network representation of the model grid. .! ❖Include rotation .! ❖Investigate if the accuracy depends on the reference model mass, metallicity, mixing parameters, age, or rotation Relative differences in estimated parameters for all main-sequence ages of the seven reference models. Biggest improvements towards longer pattern lengths are seen for mcc, fov and Xc/Xini. 16-84th percentile 25-75th percentile Median M: stellar mass! .! Z: metallicity! .! fov: convective core overshoot! .! Denv: envelope mixing! .! mcc/M: convective core mass! .! Xc/Xini: current to initial core ! hydrogen mass fraction 10M ⊙ 3M ⊙