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Register a new userDetection of Rossby modes with even azimuthal orders using helioseismic normal-mode coupling
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Retrograde Rossby waves, measured to have significant amplitudes in the Sun, likely have notable implications for various solar phenomena. 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. 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 harmonic degree). The technique uses couplings between different frequency bins to capture the temporal variability of the Rossby modes. We observe significant power close to the theoretical dispersion relation for sectoral Rossby modes (where the azimuthal order is same as 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. We place an upper bound of 0.2 m/s on the sectoral t = 2 mode, which we do not detect in our measurements. This effort adds credence to the mode-coupling methodology in helioseismology
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Normal-mode coupling is a technique applied to probe the solar interior using surface observations of oscillations. The technique, which is straightforward to implement, makes more use of the seismic information in the wavefield than other comparable local imaging techniques and therefore has the potential to significantly improve current capabilities. Here, we examine supergranulation power spectra using mode-coupling analyses of intermediate-to-high-degree modes by invoking a Cartesian-geometric description of wave propagation under the assumption that the localized patches are much smaller in size than the solar radius. We extract the supergranular power spectrum and compare the results with prior helioseismic studies. Measurements of the dispersion relation and life times of supergranulation, obtained using near surface modes (f and p$_1$), are in accord with the literature. We show that the cross-coupling between the p$_2$ and p$_3$ acoustic modes, which are capable of probing greater depths, are also sensitive to supergranulation.
Large-scale Rossby waves have recently been discovered from measurements of horizontal surface and near-surface solar flows (Loptien at al. 2018). We are interested in understanding why only the sectoral modes are seen in the observations and also in modelling the radial structure of the observed modes. To do so, we characterise here the radial eigenfunctions of r modes for slowly-rotating polytropes in uniform rotation. We find that for free-surface boundary conditions on a spheroid of non-vanishing surface density, r modes can only exist for $ell=m$ spherical harmonics in the inviscid case, and we compute their depth dependence and frequencies to leading order. For quasi-adiabatic stratification the sectoral modes with no radial nodes are the only modes which are almost toroidal and the depth dependence of the corresponding horizontal motion scales as $r^m$. For all r modes except the zero radial order sectoral ones, non-adiabatic stratification plays a crucial role in the radial force balance. The lack of quasi-toroidal solutions when stratification is close to neutral, except for the sectoral modes without nodes in radius, follows from the statement that the system needs to be in both horizontal and radial force balance. In the absence of super- or subadiabatic stratification and viscosity, both the horizontal and radial force balances independently determine the pressure perturbation. The only quasi-toroidal cases in which the two determinations of the pressure perturbation are consistent are the special cases where $ell=m$, and the horizontal displacement scales with $r^m$.
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.
Nonlinear growth of the bar-mode deformation is studied for a differentially rotating star with supercritical rotational energy. In particular, the growth mechanism of some azimuthal modes with odd wave numbers is examined by comparing a simplified mathematical model with a realistic simulation. Mode coupling to even modes, i.e., the bar mode and higher harmonics, significantly enhances the amplitudes of odd modes, unless they are exactly zero initially. Therefore, other modes which are not axially symmetric cannot be neglected at late times in the growth of the unstable bar-mode even when starting from an almost axially symmetric state.
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