Rossby waves play a fundamental role in angular momentum processes in rotating fluids. In addition to the potential to shed light on physical mechanisms operating in the solar convection zone, the recent detection of Rossby waves in the Sun (Löptien et al. 2018;Liang et al. 2018) also serves as a means of comparison between different helioseismic methods. Time-distance helioseismology, ring-diagram analysis and other techniques have all proven successful in recovering the Rossby-wave dispersion relation from analyses of Helioseismic and Magnetic Imager data (HMI;Schou et al. 2012). In this article, we demonstrate that analyses of two years of HMI global-mode-oscillation data using the technique of normal-mode coupling also show signatures of Rossby waves. In addition to providing an independent means of inferring Rossby waves, this detection lends credence to the methodology of mode coupling and encourages a more complete exploration of its possibilities.

Rossby waves play an important role in mediating the angular momentum of rotating spherical fluids, creating weather on Earth and tuning exoplanet orbits in distant stellar systems (Ogilvie 2014). Their recent discovery in the solar convection zone provides an exciting opportunity to appreciate the detailed astrophysics of Rossby waves. Large-scale Rossby waves create subtle drifts in acoustic oscillations in the convection zone, which we measure using helioseismology to image properties of Rossby waves in the interior. We analyze 20 years of space-based observations, from 1999 to 2018, to measure Rossbymode frequencies, line-widths and amplitudes. Spatial leakage affects the measurements of normal model coupling and complicates the analysis of separating out specific harmonic degree and azimuthal number of features on the Sun. Here we demonstrate a novel approach to overcome this difficulty and test it by performing synthetic tests. We find that the root-mean-square velocity of the modes is of the order of 0.5 m/s at the surface.

Accurate inference of solar meridional flow is of crucial importance for the understanding of solar dynamo process. Wave travel times, as measured on the surface, will change if the waves encounter perturbations e.g. in the sound speed or flows, as they propagate through the solar interior. Using functions called sensitivity kernels, we may image the underlying anomalies that cause measured shifts in travel times. The inference of large-scale structures e.g meridional circulation requires computing sensitivity kernels in spherical geometry. Mandal et al.(2017) have computed such spherical kernels in the limit of the first-Born approximation. In this work, we perform an inversion for meridional circulation using travel-time measurements obtained from 6 years of SDO/HMI data and those sensitivity kernels. We enforce mass conservation by inverting for a stream function. The number of free parameters is reduced by projecting the solution on to cubic B-splines in radius and derivatives of the Legendre-polynomial basis in latitude, thereby improving the condition number of the inverse problem. We validate our approach for synthetic observations before performing the actual inversion. The inversion suggests a single-cell profile with the return-flow occurring at depths below 0.78 R ⊙ .

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.

The inference of internal properties of the Sun from surface measurements of wave travel times is the goal of time-distance helioseismology. A critical step toward the accurate interpretation of travel-time shifts is the computation of sensitivity functions linking seismic measurements to internal structure. Here we calculate finite-frequency sensitivity kernels in spherical geometry for two-point travel-time measurements. We numerically build Green's function by solving for it at each frequency and spherical-harmonic degree and summing over all these pieces. These computations are performed in parallel ("embarrassingly"), thereby achieving significant speedup in wall-clock time. Kernels are calculated by invoking the first-order Born approximation connecting deviations in the wavefield to perturbations in the operator. Validated flow kernels are shown to produce travel-times within 0.47% of the true value for uniform flows up to 750 m/s. We find that travel-time can be obtained with errors of 1 millisecond or less for flows having magnitudes similar to meridional circulation. Alongside flows, we also compute and validate sensitivity kernel for sound-speed perturbations. These accurate sensitivity kernels might improve the current inferences of sub-surface flows significantly.