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Register a new userEffect of latitudinal differential rotation on solar Rossby waves: Critical layers, eigenfunctions, and momentum fluxes in the equatorial $beta$ plane
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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 $20^circ$-$30^circ$, and decrease at higher latitudes. We search for an explanation that takes into account solar latitudinal differential rotation. In the equatorial $beta$ plane, we study the propagation of linear Rossby waves (phase speed $c <0$) in a parabolic zonal shear flow, $U = - overline{U} xi^2<0$, where $overline{U} = 244$ m/s and $xi$ is the sine of latitude. 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 in the problem to account for wave attenuation. In the viscous case, the stream functions are solution of 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 $100 le Re le 700$), all modes are stable. At fixed longitudinal wavenumber, the least damped mode is a symmetric mode with a real frequency close to that of the classical Rossby mode, which we call the R mode. For $Re approx 300$, 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. Conclusion: 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 towards the equator.
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Asteroseismology has undergone a profound transformation as a scientific field following the CoRoT and Kepler space missions. The latter is now yielding the first measurements of latitudinal differential rotation obtained directly from oscillation frequencies. Differential rotation is a fundamental mechanism of the stellar dynamo effect. Our goal is to measure the amount of differential rotation in the solar analogues 16 Cyg A and B, which are the components of a binary system. These stars are the brightest observed by Kepler and have therefore been extensively observed, with exquisite precision on their oscillation frequencies. We modelled the acoustic power spectrum of 16 Cyg A and B using a model that takes into account the contribution of differential rotation to the rotational frequency splitting. The estimation was carried out in a Bayesian setting. We then inverted these results to obtain the rotation profile of both stars under the assumption of a solar-like functional form. We observe that the magnitude of latitudinal differential rotation has a strong chance of being solar-like for both stars, their rotation rates being higher at the equator than at the pole. The measured latitudinal differential rotation, defined as the difference of rotation rate between the equator and the pole, is $320pm269$ nHz and $440^{+363}_{-383}$ nHz for 16 Cyg A and B, respectively, confirming that the rotation rates of these stars are almost solar-like. Their equatorial rotation rates are $535pm75$ nHz and $565_{-129}^{+150}$ nHz. Our results are in good agreement with measurements obtained from spectropolarimetry, spectroscopy, and photometry. We present the first conclusive measurement of latitudinal differential rotation for solar analogues. Their rotational profiles are very close to those of the Sun. These results depend weakly on the uncertainties of the stellar parameters.
Floquet theory is used to describe the unstable spectrum at large scales of the beta-plane equation linearized about Rossby waves. Base flows consisting of one to three Rossby wave are considered analytically using continued fractions and the method of multiple scales, while base flow with more than three Rossby waves are studied numerically. It is demonstrated that the mechanism for instability changes from inflectional to triad resonance at an O(1) transition Rhines number Rh, independent of the Reynolds number. For a single Rossby wave base flow, the critical Reynolds number Re^c for instability is found in various limits. In the limits Rh --> infinity and k --> 0, the classical value Re^c = sqrt(2) is recovered. For Rh --> 0 and all orientations of the Rossby wave except zonal and meridional, the base flow is unstable for all Reynolds numbers; a zonal Rossby wave is stable, while a meridional Rossby wave has critical Reynolds number Re^c = sqrt(2). For more isotropic base flows consisting of many Rossby waves (up to forty), the most unstable mode is purely zonal for 2 <= Rh < infinity and is nearly zonal for Rh = 1/2, where the transition Rhines number is again O(1), independent of the Reynolds number and consistent with a change in the mechanism for instability from inflectional to triad resonance.
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 of latitudinal differential rotation in the convection zones of 40 Sun-like stars using asteroseismology. For the most significant detections, the stars equators rotate approximately twice as fast as their mid-latitudes. The latitudinal shear inferred from asteroseismology is much larger than predictions from numerical simulations.
We studied the solar surface flows (differential rotation and meridional circulation) using a magnetic element feature tracking technique by which the surface velocity is obtained using magnetic field data. We used the line-of-sight magnetograms obtained by the Helioseismic and Magnetic Imager aboard the Solar Dynamics Observatory from 01 May 2010 to 16 August 2017 (Carrington rotations 2096 to 2193) and tracked the magnetic element features every hour. Using our method, we estimated the differential rotation velocity profile. We found rotation velocities of $sim$ 30 and -170 m s$^{-1}$ at latitudes of 0$^{circ}$ and 60$^{circ}$ in the Carrington rotation frame, respectively. Our results are consistent with previous results obtained by other methods, such as direct Doppler, time-distance helioseismology, or cross correlation analyses. We also estimated the meridional circulation velocity profile and found that it peaked at $sim$12 m s$^{-1}$ at a latitude of 45$^{circ}$, which is also consistent with previous results. The dependence of the surface flow velocity on the magnetic field strength was also studied. In our analysis, the magnetic elements having stronger and weaker magnetic fields largely represent the characteristics of the active region remnants and solar magnetic networks, respectively. We found that magnetic elements having a strong (weak) magnetic field show faster (slower) rotation speed. On the other hand, magnetic elements having a strong (weak) magnetic field show slower (faster) meridional circulation velocity. These results might be related to the Suns internal dynamics.
Annual oscillations have been detected in many indices of solar activity during many cycles. Recent multi spacecraft observations of coronal bright points revealed slow retrograde toroidal phase drift (with the speed of 3 m/s of 1 yr oscillations, which naturally suggested their connection with Rossby-type waves in the interior. We have studied from a theoretical point of view the dynamics of global magneto-Kelvin and magneto-Rossby waves in the solar tachocline with toroidal magnetic field. Using spherical coordinates, the dispersion relations of the waves and latitudinal structure of solutions were obtained analytically. We have also obtained the spectrum of unstable magneto-Rossby wave harmonics in the presence of the latitudinal differential rotation. Estimated periods and phase speeds show that the magneto-Rossby waves rather than the Kelvin waves match with the observations of 1 yr oscillations. On the other hand, Morlet wavelet analysis of Greenwich Royal Observatory sunspot areas for the solar cycle 23 has revealed multiple periodicities with periods of 450-460 days, 370-380 days, 310-320 days, 240-270 days, and 150-175 days in hemispheric and full disk data. Comparison of theoretical results with the observations allow us to conclude that the global magneto-Kelvin waves in the upper overshoot tachocline may be responsible for the periodicity of 450-460 days (1.3 yrs), while the remaining periods can be connected with different harmonics of global fast magneto-Rossby waves.
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