Context. Space-based observations of solar-like oscillations present an opportunity to constrain stellar models using individual mode frequencies. However, current stellar models are inaccurate near ...the surface, which introduces a systematic difference that must be corrected. Aims. We introduce and evaluate two parametrizations of the surface corrections based on formulae given by Gough (1990, LNP, 367, 283). The first we call a cubic term proportional to ν3/ ℐ and the second has an additional inverse term proportional to ν-1/ ℐ, where ν and ℐ are the frequency and inertia of an oscillation mode. Methods. We first show that these formulae accurately correct model frequencies of two different solar models (Model S and a calibrated MESA model) when compared to observed BiSON frequencies. In particular, even the cubic form alone fits significantly better than a power law. We then incorporate the parametrizations into a modelling pipeline that simultaneously fits the surface effects and the underlying stellar model parameters. We apply this pipeline to synthetic observations of a Sun-like stellar model, solar observations degraded to typical asteroseismic uncertainties, and observations of the well-studied CoRoT target HD 52265. For comparison, we also run the pipeline with the scaled power-law correction proposed by Kjeldsen et al. (2008, ApJ, 683, L175). Results. The fits to synthetic and degraded solar data show that the method is unbiased and produces best-fit parameters that are consistent with the input models and known parameters of the Sun. Our results for HD 52265 are consistent with previous modelling efforts and the magnitude of the surface correction is similar to that of the Sun. The fit using a scaled power-law correction is significantly worse but yields consistent parameters, suggesting that HD 52265 is sufficiently Sun-like for the same power-law to be applicable. Conclusions. We find that the cubic term alone is suitable for asteroseismic applications and it is easy to implement in an existing pipeline. It reproduces the frequency dependence of the surface correction better than a power-law fit, both when comparing calibrated solar models to BiSON observations and when fitting stellar models using the individual frequencies. This parametrization is thus a useful new way to correct model frequencies so that observations of individual mode frequencies can be exploited.
Cool main-sequence, subgiant, and red giant stars all show solar-like oscillations, pulsations that are excited and intrinsically damped by near-surface convection. Many overtones are typically ...excited to observable amplitudes, giving a rich spectrum of detectable modes. These modes provide a wealth of information on fundamental stellar properties. However, the radial velocity (RV) shifts induced by these oscillations can also be problematic when searching for low-mass, long-period planets; this is because their amplitudes are large enough to completely mask such minute planetary signals. Here we show how fine-tuning exposure times to the stellar parameters can help efficiently average out the solar-like, oscillation-induced shifts. To reduce the oscillation signal to the RV precision commensurate with an Earth analog, we find that for cool, low-mass stars (near spectral type K), the necessary exposure times may be as short as ∼4 minutes, while for hotter, higher-mass stars (near spectral type F, or slightly evolved), the required exposure times can be longer than 100 minutes. We provide guideline exposure durations required to suppress the total observed amplitude due to oscillations to a level of 0.1 m s−1, and a level corresponding to the Earth-analog reflex amplitude for the star. Owing to the intrinsic stochastic variability of the oscillations, we recommend in practice choosing short exposure durations at the telescope and then averaging over those exposures later, as guided by our predictions. To summarize, as we enter an era of 0.1 m s−1 instrumental precision, it is critical to tailor our observing strategies to the stellar properties.
Context. Accurate modelling of solar-like oscillators requires that modelled mode frequencies are corrected for the systematic shift caused by improper modelling of the near-surface layers, known as ...the surface effect. Several parametrizations of the surface effect are now available but they have not yet been systematically compared with observations of stars showing modes with mixed g- and p-mode character. Aims. We investigate how much additional uncertainty is introduced to stellar model parameters by our uncertainty about the functional form of the surface effect. At the same time, we test whether any of the parametrizations is significantly better or worse at modelling observed subgiants and low-luminosity red giants. Methods. We model six stars observed by Kepler that show clear mixed modes. We fix the input physics of the stellar models and vary the choice of surface correction between five parametrizations. Results. Models using a solar-calibrated power law correction consistently fit the observations more poorly than the other four corrections. Models with the remaining four corrections generally fit the observations about equally well, with the combined surface correction by Ball & Gizon perhaps being marginally superior. The fits broadly agree on the model parameters within about the 2σ uncertainties, with discrepancies between the modified Lorentzian and free power law corrections occasionally exceeding the 3σ level. Relative to the best-fitting values, the total uncertainties on the masses, radii and ages of the stars are all less than 2, 1 and 6 per cent, respectively. Conclusions. A solar-calibrated power law, as formulated by Kjeldsen et al., appears unsuitable for use with more evolved solar-like oscillators. Among the remaining surface corrections, the uncertainty in the model parameters introduced by the surface effects is about twice as large as the uncertainty in the individual fits for these six stars. Though the fits are thus somewhat less certain because of our uncertainty of how to manage the surface effect, these results also demonstrate that it is feasible to model the individual mode frequencies of subgiants and low-luminosity red giants, and hence also use these individual stars to help to constrain stellar models.
We use asteroseismic data obtained by the NASA Kepler mission to estimate the fundamental properties of more than 500 main-sequence and sub-giant stars. Data obtained during the first 10 months of ...Kepler science operations were used for this work, when these solar-type targets were observed for one month each in survey mode. Stellar properties have been estimated using two global asteroseismic parameters and complementary photometric and spectroscopic data. Homogeneous sets of effective temperatures, Tsubeff , were available for the entire ensemble from complementary photometry; spectroscopic estimates of Tsubeff and Fe/H were available from a homogeneous analysis of ground-based data on a subset of 87 stars. We adopt a grid-based analysis, coupling six pipeline codes to 11 stellar evolutionary grids. Future analyses using individual oscillation frequencies will offer significant improvements on up to 150 stars, in particular for estimates of the ages, where having the individual frequency data is most important.
Surface effects on the red giant branch Ball, W H; Themeßl, N; Hekker, S
Monthly notices of the Royal Astronomical Society,
08/2018, Letnik:
478, Številka:
4
Journal Article
Context. Rotational shear in Sun-like stars is thought to be an important ingredient in models of stellar dynamos. Thanks to helioseismology, rotation in the Sun is characterized well, but the ...interior rotation profiles of other Sun-like stars are not so well constrained. Until recently, measurements of rotation in Sun-like stars have focused on the mean rotation, but little progress has been made on measuring or even placing limits on differential rotation. Aims. Using asteroseismic measurements of rotation we aim to constrain the radial shear in five Sun-like stars observed by the NASA Kepler mission: KIC 004914923, KIC 005184732, KIC 006116048, KIC 006933899, and KIC 010963065. Methods. We used stellar structure models for these five stars from previous works. These models provide the mass density, mode eigenfunctions, and the convection zone depth, which we used to compute the sensitivity kernels for the rotational frequency splitting of the modes. We used these kernels as weights in a parametric model of the stellar rotation profile of each star, where we allowed different rotation rates for the radiative interior and the convective envelope. This parametric model was incorporated into a fit to the oscillation power spectrum of each of the five Kepler stars. This fit included a prior on the rotation of the envelope, estimated from the rotation of surface magnetic activity measured from the photometric variability. Results. The asteroseismic measurements without the application of priors are unable to place meaningful limits on the radial shear. Using a prior on the envelope rotation enables us to constrain the interior rotation rate and thus the radial shear. In the five cases that we studied, the interior rotation rate does not differ from the envelope by more than approximately ± 30%. Uncertainties in the rotational splittings are too large to unambiguously determine the sign of the radial shear.
In previous work, we identified six Sun-like stars observed by Kepler with exceptionally clear asteroseismic signatures of rotation. Here, we show that five of these stars exhibit surface variability ...suitable for measuring rotation. We compare the rotation periods obtained from light-curve variability with those from asteroseismology in order to further constrain differential rotation. The two rotation measurement methods are found to agree within uncertainties, suggesting that radial differential rotation is weak, as is the case for the Sun. Furthermore, we find significant discrepancies between ages from asteroseismology and from three different gyrochronology relations, implying that stellar age estimation is problematic even for Sun-like stars.
Aims. We quantify the effect of observational spectroscopic and asteroseismic uncertainties on regularised least squares (RLS) inversions for the radial differential rotation of Sun-like and subgiant ...stars. Methods. We first solved the forward problem to model rotational splittings plus the observed uncertainties for models of a Sun-like star, HD 52265, and a subgiant star, KIC 7341231. We randomly perturbed the parameters of the stellar models within the uncertainties of the spectroscopic and asteroseismic constraints and used these perturbed stellar models to compute rotational splittings. We experimented with three rotation profiles: solid body rotation, a step function, and a smooth rotation profile decreasing with radius. We then solved the inverse problem to infer the radial differential rotation profile using a RLS inversion and kernels from the best-fit stellar model. We also compared RLS, optimally localised average (OLA) and direct functional fitting inversion techniques. Results. We found that the inversions for Sun-like stars with solar-like radial differential rotation profiles are insensitive to the uncertainties in the stellar models. The uncertainties in the splittings dominate the uncertainties in the inversions and solid body rotation is not excluded. We found that when the rotation rate below the convection zone is increased to six times that of the surface rotation rate the inferred rotation profile excluded solid body rotation. We showed that when we reduced the uncertainties in the splittings by a factor of about 100, the inversion is sensitive to the uncertainties in the stellar model. With the current observational uncertainties, we found that inversions of subgiant stars are sensitive to the uncertainties in the stellar model. Conclusions. Our findings suggest that inversions for the radial differential rotation of subgiant stars would benefit from more tightly constrained stellar models. We conclude that current observational uncertainties make it difficult to infer radially resolved features of the rotation profile in a Sun-like star using inversions with regularisation. In Sun-like stars, the insensitivity of the inversions to stellar model uncertainties suggests that it may be possible to perform ensemble inversions for the average radial differential rotation of many stars with a range of stellar types to better constrain the inversions.
ABSTRACT
Asteroseismology is a powerful tool to infer fundamental stellar properties. The use of these asteroseismic-inferred properties in a growing number of astrophysical contexts makes it vital ...to understand their accuracy. Consequently, we performed a hare-and-hounds exercise where the hares simulated data for six artificial main-sequence stars and the hounds inferred their properties based on different inference procedures. To mimic a pipeline such as that planned for the PLATO mission, all hounds used the same model grid. Some stars were simulated using the physics adopted in the grid, others a different one. The maximum relative differences found (in absolute value) between the inferred and true values of the mass, radius, and age were 4.32, 1.33, and 11.25 per cent, respectively. The largest systematic differences in radius and age were found for a star simulated assuming gravitational settling, not accounted for in the model grid, with biases of −0.88 per cent (radius) and 8.66 per cent (age). For the mass, the most significant bias (−3.16 per cent) was found for a star with a helium enrichment ratio outside the grid range. Moreover, an ∼7 per cent dispersion in age was found when adopting different prescriptions for the surface corrections or shifting the classical observations by ±1σ. The choice of the relative weight given to the classical and seismic constraints also impacted significantly the accuracy and precision of the results. Interestingly, only a few frequencies were required to achieve accurate results on the mass and radius. For the age the same was true when at least one l = 2 mode was considered.
PDF
