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.
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.
The differentially rotating outer layers of stars are thought to play a role in driving their magnetic activity, but the underlying mechanisms that generate and sustain differential rotation are ...poorly understood. We report the measurement using asteroseismology of latitudinal differential rotation in the convection zones of 40 Sun-like stars. For the most significant detections, the stars' equators rotate approximately twice as fast as their midlatitudes. The latitudinal shear inferred from asteroseismology is much larger than predictions from numerical simulations.
Aims. We aim to measure the starspot rotation periods of active stars in the Kepler field as a function of spectral type and to extend reliable rotation measurements from F-, G-, and K-type to M-type ...stars. Methods. Using the Lomb-Scargle periodogram we searched more than 150 000 stellar light curves for periodic brightness variations. We analyzed periods between 1 and 30 days in eight consecutive Kepler quarters, where 30 days is an estimated maximum for the validity of the PDC_MAP data correction pipeline. We selected stable rotation periods, i.e., periods that do not vary from the median by more than one day in at least six of the eight quarters. We averaged the periods for each stellar spectral class according to B − V color and compared the results to archival vsini data, using stellar radii estimates from the Kepler Input Catalog. Results. We report on the stable starspot rotation periods of 12 151 Kepler stars. We find good agreement between starspot velocities and vsini data for all F-, G- and early K-type stars. The 795 M-type stars in our sample have a median rotation period of 15.4 days. We find an excess of M-type stars with periods less than 7.5 days that are potentially fast-rotating and fully convective. Measuring photometric variability in multiple Kepler quarters appears to be a straightforward and reliable way to determine the rotation periods of a large sample of active stars, including late-type stars.
Context.
Retrograde-propagating waves of vertical vorticity with longitudinal wavenumbers between 3 and 15 have been observed on the Sun with a dispersion relation close to that of classical sectoral ...Rossby waves. The observed vorticity eigenfunctions are symmetric in latitude, peak at the equator, switch sign near 20°–30°, and decrease at higher latitudes.
Aims.
We search for an explanation that takes solar latitudinal differential rotation into account.
Methods.
In the equatorial
β
plane, we studied the propagation of linear Rossby waves (phase speed
c
< 0) in a parabolic zonal shear flow,
U
= −
U̅
ξ
2
< 0, where
U̅
= 244 m s
−1
, and
ξ
is the sine of latitude.
Results.
In the inviscid case, the eigenvalue spectrum is real and continuous, and the velocity stream functions are singular at the critical latitudes where
U
=
c
. We add eddy viscosity to the problem to account for wave attenuation. In the viscous case, the stream functions solve a fourth-order modified Orr-Sommerfeld equation. Eigenvalues are complex and discrete. For reasonable values of the eddy viscosity corresponding to supergranular scales and above (Reynolds number 100 ≤
Re
≤ 700), all modes are stable. At fixed longitudinal wavenumber, the least damped mode is a symmetric mode whose real frequency is close to that of the classical Rossby mode, which we call the R mode. For
Re
≈ 300, the attenuation and the real part of the eigenfunction is in qualitative agreement with the observations (unlike the imaginary part of the eigenfunction, which has a larger amplitude in the model).
Conclusions.
Each longitudinal wavenumber is associated with a latitudinally symmetric R mode trapped at low latitudes by solar differential rotation. In the viscous model, R modes transport significant angular momentum from the dissipation layers toward the equator.
Context.
Retrograde Rossby waves, measured to have significant amplitudes in the Sun, likely have notable implications for various solar phenomena.
Aims.
Rossby waves create small-amplitude, very-low ...frequency motions, on the order of the rotation rate and lower, which in turn shift the resonant frequencies and eigenfunctions of the acoustic modes of the Sun. The detection of even azimuthal orders Rossby modes using mode coupling presents additional challenges and prior work therefore only focused on odd orders. Here, we successfully extend the methodology to measure even azimuthal orders as well.
Methods.
We analyze 4 and 8 years of Helioseismic and Magnetic Imager (HMI) data and consider coupling between different-degree acoustic modes (of separations 1 and 3 in the harmonic degree). The technique uses couplings between different frequency bins to capture the temporal variability of the Rossby modes.
Results.
We observe significant power close to the theoretical dispersion relation for sectoral Rossby modes, where the azimuthal order is the same as the harmonic degree,
s
= |
t
|. Our results are consistent with prior measurements of Rossby modes with azimuthal orders over the range
t
= 4 to 16 with maximum power occurring at mode
t
= 8. The amplitudes of these modes vary from 1 to 2 m s
−1
. We place an upper bound of 0.2 m s
−1
on the sectoral
t
= 2 mode, which we do not detect in our measurements.
Conclusions.
This effort adds credence to the mode-coupling methodology in helioseismology.
On the uncertain nature of the core of α Cen A Bazot, M.; Christensen-Dalsgaard, J.; Gizon, L. ...
Monthly Notices of the Royal Astronomical Society,
08/2016, Letnik:
460, Številka:
2
Journal Article
Flow vorticity is a fundamental property of turbulent convection in rotating systems. Solar supergranules exhibit a preferred sense of rotation, which depends on the hemisphere. This is due to the ...Coriolis force acting on the diverging horizontal flows. We aim to spatially resolve the vertical flow vorticity of the average supergranule at different latitudes, both for outflow and inflow regions. To measure the vertical vorticity, we use two independent techniques: time-distance helioseismology (TD) and local correlation tracking of granules in intensity images (LCT) using data from the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO). Both maps are corrected for center-to-limb systematic errors. We find that 8 h TD and LCT maps of vertical vorticity are highly correlated at large spatial scales. Associated with the average supergranule outflow, we find tangential (vortical) flows that reach about 10 m s-1 in the clockwise direction at 40° latitude. In average inflow regions, the tangential flow reaches the same magnitude, but in the anticlockwise direction. These tangential velocities are much smaller than the radial (diverging) flow component (300 m s-1 for the average outflow and 200 m s-1 for the average inflow). The results for TD and LCT as measured from HMI are in excellent agreement for latitudes between −60° and 60°. From HMI LCT, we measure the vorticity peak of the average supergranule to have a full width at half maximum of about 13 Mm for outflows and 8 Mm for inflows. This is larger than the spatial resolution of the LCT measurements (about 3 Mm). On the other hand, the vorticity peak in outflows is about half the value measured at inflows (e.g., 4 × 10-6 s-1 clockwise compared to 8 × 10-6 s-1 anticlockwise at 40° latitude). Results from the Michelson Doppler Imager (MDI) on board the Solar and Heliospheric Observatory (SOHO) obtained in 2010 are biased compared to the HMI/SDO results for the same period.
The Sunrise balloon-borne solar observatory, consisting of a 1 m aperture telescope that provides a stabilized image to a UV filter imager and an imaging vector polarimeter, carried out its second ...science flight in 2013 June. It provided observations of parts of active regions at high spatial resolution, including the first high-resolution images in the Mg ii k line. The obtained data are of very high quality, with the best UV images reaching the diffraction limit of the telescope at 3000 after Multi-Frame Blind Deconvolution reconstruction accounting for phase-diversity information. Here a brief update is given of the instruments and the data reduction techniques, which includes an inversion of the polarimetric data. Mainly those aspects that evolved compared with the first flight are described. A tabular overview of the observations is given. In addition, an example time series of a part of the emerging active region NOAA AR 11768 observed relatively close to disk center is described and discussed in some detail. The observations cover the pores in the trailing polarity of the active region, as well as the polarity inversion line where flux emergence was ongoing and a small flare-like brightening occurred in the course of the time series. The pores are found to contain magnetic field strengths ranging up to 2500 G, and while large pores are clearly darker and cooler than the quiet Sun in all layers of the photosphere, the temperature and brightness of small pores approach or even exceed those of the quiet Sun in the upper photosphere.
Context.
Helioseismology is the study of the Sun’s interior using observations of oscillations at the surface. It suffers from systematic errors, for instance a center-to-limb error in travel-time ...measurements. Understanding these errors requires an adequate understanding of the nontrivial relationship between wave displacement and helioseismic observables (intensity or velocity).
Aims.
The wave displacement causes perturbations in the atmospheric thermodynamical quantities which, in turn, perturb the opacity, the optical depth, the source function, and the local ray geometry, thus affecting the emergent intensity. We aim to establish the most complete relationship achieved to date between the wave displacement and the emergent intensity perturbation by solving the radiative transfer problem in the perturbed atmosphere.
Methods.
We derived an expression for the emergent intensity perturbation caused by acoustic oscillations at any point on the solar disk by applying a first-order perturbation theory. As input perturbations, we considerd adiabatic modes of oscillation of different degrees in a spherically-symmetric solar model. The background and the perturbed intensities are computed by solving the radiative transfer equation considering the main sources of opacity in the continuum (absorption and scattering).
Results.
We find that for all modes, the perturbations to the thermodynamical quantities are not sufficient to model the intensity perturbations: the geometrical effects due to the wave displacement must always be taken into account as they lead to a difference in amplitude and a phase shift between temperature perturbations at the surface and emergent intensity perturbations. The closer to the limb, the greater the differences. For modes with eigenfrequencies around 3 mHz, we found that the radial and horizontal components of the wave displacement are important, in particular, for high-degree modes.
Conclusions.
This work presents improvements for the computation of the intensity perturbations, in particular, for high-degree modes. Here, we explain the differences in intensity computations seen in earlier works. The phase shifts and amplitude differences between the temperature and intensity perturbations increase toward the limb. This should prove helpful when interpreting some of the systematic centre-to-limb effects observed in local helioseismology. The computations are fast (3 s for 2000 positions and one frequency for one core) and can be parallelised. This work can be extended to models of the line-of-sight velocity observable.
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