Stable higher order finite-difference schemes for stellar pulsation calculations

Context: Calculating stellar pulsations requires a sufficient accuracy to match the quality of the observations. Many current pulsation codes apply a second order finite-difference scheme, combined with Richardson extrapolation to reach fourth order accuracy on eigenfunctions. Although this is a simple and robust approach, a number of drawbacks exist thus making fourth order schemes desirable. A robust and simple finite-difference scheme, which can easily be implemented in either 1D or 2D stellar pulsation codes is therefore required. Aims: One of the difficulties in setting up higher order finite-difference schemes for stellar pulsations is the so-called mesh-drift instability. Current ways of dealing with this defect include introducing artificial viscosity or applying a staggered grids approach. However these remedies are not well-suited to eigenvalue problems, especially those involving non-dissipative systems, because they unduly change the spectrum of the operator, introduce supplementary free parameters, or lead to complications when applying boundary conditions. Methods: We propose here a new method, inspired from the staggered grids strategy, which removes this instability while bypassing the above difficulties. Furthermore, this approach lends itself to superconvergence, a process in which the accuracy of the finite differences is boosted by one order. Results: This new approach is shown to be accurate, flexible with respect to the underlying grid, and able to remove mesh-drift.Comment: 15 pages, 11 figures, accepted for publication in A&

Inequalities on stellar rotational splittings derived from assumptions on the rotation profile

Context: A number of pulsating stars with rotational splittings have been observed thanks to the CoRoT and Kepler missions. This is particularly true of evolved (sub-giant and giant) stars, and has led various groups to investigate their rotation profiles via different methods. Aims: We would like to set up some criteria which will help us to know whether a decreasing rotation profile, or one which satisfies Rayleigh's stability criterion, is compatible with a set of observed rotational splittings for a given reference model. Methods: We derive inequalities on the rotational splittings using a reformulated version of the equation which relates the splittings to the rotation profile and kernels. Results: These inequalities are tested out on some simple examples. The first examples show how they are able to reveal when a rotation profile is increasing somewhere or inconsistent with Rayleigh's criterion in a main sequence star, depending on the profile and the $\ell$ values of the splittings. The next example illustrates how a slight mismatch between an observed evolved star and a reference model can lead to erroneous conclusions about the rotation profile. We also show how frequency differences between the star and the model, which should normally reveal this mismatch, can be masked by frequency corrections for near-surface effects.Comment: 15 pages, 19 figures, accepted for publication in A&

Using seismic inversions to obtain an internal mixing processes indicator for main-sequence solar-like stars

Determining accurate and precise stellar ages is a major problem in astrophysics. These determinations are either obtained through empirical relations or model-dependent approaches. Currently, seismic modelling is one of the best ways of providing accurate ages. However, current methods are affected by simplifying assumptions concerning mixing processes. In this context, providing new structural indicators which are less model-dependent and more sensitive to such processes is crucial. We build a new indicator for core conditions on the main sequence, which should be more sensitive to structural differences and applicable to older stars than the indicator t presented in a previous paper. We also wish to analyse the importance of the number and type of modes for the inversion, as well as the impact of various constraints and levels of accuracy in the forward modelling process that is used to obtain reference models for the inversion. First, we present a method to obtain new structural kernels and use them to build an indicator of central conditions in stars and test it for various effects including atomic diffusion, various initial helium abundances and metallicities, following the seismic inversion method presented in our previous paper. We then study its accuracy for 7 different pulsation spectra including those of 16CygA and 16CygB and analyse its dependence on the reference model by using different constraints and levels of accuracy for its selection We observe that the inversion of the new indicator using the SOLA method provides a good diagnostic for additional mixing processes in central regions of stars. Its sensitivity allows us to test for diffusive processes and chemical composition mismatch. We also observe that octupole modes can improve the accuracy of the results, as well as modes of low radial order.Comment: Accepted for publication in Astronomy and Astrophysic

Constraints on the structure of 16 Cyg A and 16 Cyg B using inversion techniques

Constraining mixing processes and chemical composition is a central problem in stellar physics as their impact on stellar age determinations leads to biases in our studies of stellar evolution, galactic history and exoplanetary systems. In two previous papers, we showed how seismic inversion techniques could offer strong constraints on such processes by pointing out weaknesses in theoretical models. We now apply our technique to the solar analogues 16CygA and 16CygB, being amongst the best targets in the Kepler field to test the diagnostic potential of seismic inversions. The combination of various seismic indicators helps to provide more constrained and accurate fundamendal parameters for these stars. We use the latest seismic, spectroscopic and interferometric observational constraints in the litterature for this system to determine reference models independently for both stars. We carry out seismic inversions of the acoustic radius, the mean density and a core conditions indicator. We note that a degeneracy exists for the reference models. Namely, changing the diffusion coefficient or the chemical composition within the observational values leads to 5% changes in mass, 3% changes in radius and up to 8% changes in age. We use acoustic radius and mean density inversions to improve our reference models then carry out inversions for a core conditions indicator. Thanks to its sensitivity to microscopic diffusion and chemical composition mismatches, we are able to reduce the mass dispersion to 2%, namely [0.96, 1.0] M_sun, the radius dispersion to 1%, namely [1.188, 1.200] R_sun and the age dispersion to 3%, namely [7.0, 7.4] Gy, for 16CygA. For 16CygB, we can check the consistency of the models but not reduce independently the age dispersion. Nonetheless, assuming consistency with the age of 16CygA helps to further constrain its mass and radius.Comment: Submitted to Astronomy and Astrophysic

Regular Oscillation Sub-spectrum of Rapidly Rotating Stars

We present an asymptotic theory that describes regular frequency spacings of pressure modes in rapidly rotating stars. We use an asymptotic method based on an approximate solution of the pressure wave equation constructed from a stable periodic solution of the ray limit. The approximate solution has a Gaussian envelope around the stable ray, and its quantization yields the frequency spectrum. We construct semi-analytical formulas for regular frequency spacings and mode spatial distributions of a subclass of pressure modes in rapidly rotating stars. The results of these formulas are in good agreement with numerical data for oscillations in polytropic stellar models. The regular frequency spacings depend explicitly on internal properties of the star, and their computation for different rotation rates gives new insights on the evolution of mode frequencies with rotation.Comment: 14 pages, 10 figure

Mode identification in rapidly rotating stars

Context: Recent calculations of pulsation modes in rapidly rotating polytropic models and models based on the Self-Consistent Field method have shown that the frequency spectrum of low degree pulsation modes can be described by an empirical formula similar to Tassoul's asymptotic formula, provided that the underlying rotation profile is not too differential. Aims: Given the simplicity of this asymptotic formula, we investigate whether it can provide a means by which to identify pulsation modes in rapidly rotating stars. Methods: We develop a new mode identification scheme which consists in scanning a multidimensional parameter space for the formula coefficients which yield the best-fitting asymptotic spectra. This mode identification scheme is then tested on artificial spectra based on the asymptotic formula, on random frequencies and on spectra based on full numerical eigenmode calculations for which the mode identification is known beforehand. We also investigate the effects of adding random frequencies to mimic the effects of chaotic modes which are also expected to show up in such stars. Results: In the absence of chaotic modes, it is possible to accurately find a correct mode identification for most of the observed frequencies provided these frequencies are sufficiently close to their asymptotic values. The addition of random frequencies can very quickly become problematic and hinder correct mode identification. Modifying the mode identification scheme to reject the worst fitting modes can bring some improvement but the results still remain poorer than in the case without chaotic modes

Insect (Arthropoda: Insecta) Composition in the Diet of Ornate Box Turtles (Terrapene ornata ornata) in Two Western Illinois Sand Prairies, with a New State Record for Cyclocephala (Coleoptera: Scarabaeidae)

A study of fecal samples collected over a two-year period from juvenile ornate box turtles (Terrapene ornata ornata Agassiz) revealed diets consisting of six orders of insects representing 19 families. Turtles were reared in captivity from eggs harvested from local, wild populations, and released at two remnant prairies. Identifiable insect fragments were found in 94% of samples in 2013 (n=33) and 96% in 2014 (n=25). Frequency of occurrence of insects in turtle feces is similar to results reported in previous studies of midwestern Terrapene species. A comparison of insect composition presented no significant difference between release sites. There is no significant difference in consumed insect species between turtles released into or outside of a fenced enclosure at the same site. Specimens of Cyclocephala longula LeConte collected during this study represent a new state record for Illinois