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Register a new userMixed Modes and Asteroseismic Surface Effects: II. Subgiant Systematics
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J. M. Joel Ong
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Models of solar-like oscillators yield acoustic modes at different frequencies than would be seen in actual stars possessing identical interior structure, due to modelling error near the surface. This asteroseismic surface term must be corrected when mode frequencies are used to infer stellar structure. Subgiants exhibit oscillations of mixed acoustic ($p$-mode) and gravity ($g$-mode) character, which defy description by the traditional $p$-mode asymptotic relation. Since nonparametric diagnostics of the surface term rely on this description, they cannot be applied to subgiants directly. In Paper I, we generalised such nonparametric methods to mixed modes, and showed that traditional surface-term corrections only account for mixed-mode coupling to, at best, first order in a perturbative expansion. Here, we apply those results, modelling subgiants using asteroseismic data. We demonstrate that, for grid-based inference of subgiant properties using individual mode frequencies, neglecting higher-order effects of mode coupling in the surface term results in significant systematic differences in the inferred stellar masses, and measurable systematics in other fundamental properties. While these systematics are smaller than those resulting from other choices of model construction, they persist for both parametric and nonparametric formulations of the surface term. This suggests that mode coupling should be fully accounted for when correcting for the surface term in seismic modelling with mixed modes, irrespective of the choice of correction used. The inferred properties of subgiants, in particular masses and ages, also depend on the choice of surface-term correction, in a different manner from both main-sequence and red giant stars.
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Normal-mode oscillation frequencies computed from stellar models differ from those which would be measured from stars with identical interior structures, because of modelling errors in the near-surface layers. These frequency differences are referred to as the asteroseismic surface term. The vast majority of solar-like oscillators which have been observed, and which are expected to be observed in the near future, are evolved stars which exhibit mixed modes. For these evolved stars, the inference of stellar properties from these mode frequencies has been shown to depend on how this surface term is corrected for. We show that existing parametrisations of the surface term account for mode mixing only to first order in perturbation theory, if at all, and therefore may not be adequate for evolved stars. Moreover, existing nonparametric treatments of the surface term do not account for mode mixing. We derive both a first-order construction, and a more general approach, for one particular class of nonparametric methods. We illustrate the limits of first-order approximations from both analytic considerations and using numerical injection-recovery tests on stellar models. First-order corrections for the surface term are strictly only applicable where the size of the surface term is much smaller than both the coupling strength between the mixed p- and g-modes, as well as the local g-mode spacing. Our more general matrix construction may be applied to evolved stars, where perturbation theory cannot be relied upon.
Localised modelling error in the near-surface layers of evolutionary stellar models causes the frequencies of their normal modes of oscillation to differ from those of actual stars with matching interior structures. These frequency differences are referred to as the asteroseismic surface term. Global stellar properties estimated via detailed constraints on individual mode frequencies have previously been shown to be robust with respect to different parameterisations of this surface term. It has also been suggested that this may be true of a broader class of nonparametric treatments. We examine systematic differences in inferred stellar properties with respect to different surface-term treatments, both for a statistically large sample of main-sequence stars, as well as for a sample of red giants, for which no such characterisation has previously been done. For main-sequence stars, we demonstrate that while masses and radii, and hence ages, are indeed robust to the choice of surface term, the inferred initial helium abundance $Y_0$ is sensitive to the choice of surface correction. This implies that helium-abundance estimates returned from detailed asteroseismology are methodology-dependent. On the other hand, for our red giant sample, nonparametric surface corrections return dramatically different inferred stellar properties than parametric ones. The nature of these differences suggests that such nonparametric methods should be preferred for evolved stars; this should be verified on a larger sample.
Since few decades, asteroseismology, the study of stellar oscillations, enables us to probe the interiors of stars with great precision. It allows stringent tests of stellar models and can provide accurate radii, masses and ages for individual stars. Of particular interest are the mixed modes that occur in subgiant solar-like stars since they can place very strong constraints on stellar ages. Here we measure the characteristics of the mixed modes, particularly the coupling strength, using a grid of stellar models for stars with masses between 0.9 and 1.5 M_{odot}. We show that the coupling strength of the $ell = 1$ mixed modes is predominantly a function of stellar mass and appears to be independent of metallicity. This should allow an accurate mass evaluation, further increasing the usefulness of mixed modes in subgiants as asteroseismic tools.
The existence of mixed modes in stars is a marker of stellar evolution. Their detection serves for a better determination of stellar age. The goal of this paper is to identify the dipole modes in an automatic manner without human intervention. I use the power spectra obtained by the Kepler mission for the application of the method. I compute asymptotic dipole mode frequencies as a function of coupling factor and dipole period spacing, and other parameters. For each star, I collapse the power in an echelle diagramme aligned onto the monopole and dipole mixed modes. The power at the null frequency is used as a figure of merit. Using a genetic algorithm, I then optimise the figure of merit by adjusting the location of the dipole frequencies in the power spectrum}. Using published frequencies, I compare the asymptotic dipole mode frequencies with published frequencies. I also used published frequencies for deriving coupling factor and dipole period spacing using a non-linear least squares fit. I use Monte-Carlo simulations of the non-linear least square fit for deriving error bars for each parameters. From the 44 subgiants studied, the automatic identification allows to retrieve within 3 $mu$Hz at least 80% of the modes for 32 stars, and within 6 $mu$Hz at least 90% of the modes for 37 stars. The optimised and fitted gravity-mode period spacing and coupling factor agree with previous measurements. Random errors for the mixed-mode parameters deduced from Monte-Carlo simulation are about 30-50 times smaller than previously determined errors, which are in fact systematic errors. The period spacing and coupling factors of mixed modes in subgiants are confirmed. The current automated procedure will need to be improved using a more accurate asymptotic model and/or proper statistical tests.
Asteroseismic forward modelling techniques are being used to determine fundamental properties (e.g. mass, radius, and age) of solar-type stars. The need to take into account all possible sources of error is of paramount importance towards a robust determination of stellar properties. We present a study of 34 solar-type stars for which high signal-to-noise asteroseismic data is available from multi-year Kepler photometry. We explore the internal systematics on the stellar properties, that is, associated with the uncertainty in the input physics used to construct the stellar models. In particular, we explore the systematics arising from: (i) the inclusion of the diffusion of helium and heavy elements; and (ii) the uncertainty in solar metallicity mixture. We also assess the systematics arising from (iii) different surface correction methods used in optimisation/fitting procedures. The systematics arising from comparing results of models with and without diffusion are found to be 0.5%, 0.8%, 2.1%, and 16% in mean density, radius, mass, and age, respectively. The internal systematics in age are significantly larger than the statistical uncertainties. We find the internal systematics resulting from the uncertainty in solar metallicity mixture to be 0.7% in mean density, 0.5% in radius, 1.4% in mass, and 6.7% in age. The surface correction method by Sonoi et al. and Ball & Gizons two-term correction produce the lowest internal systematics among the different correction methods, namely, ~1%, ~1%, ~2%, and ~8% in mean density, radius, mass, and age, respectively. Stellar masses obtained using the surface correction methods by Kjeldsen et al. and Ball & Gizons one-term correction are systematically higher than those obtained using frequency ratios.
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