Latitudinal Differential Rotation Research Articles

Modeling the effects of starspots on stellar magnetic cycles

Context. Observations show that faster rotating stars tend to have stronger magnetic activity and shorter magnetic cycles. The cyclical magnetic activity of the Sun and stars is believed to be driven by the dynamo process. The success of the Babcock-Leighton (BL) dynamo in explaining the solar cycle suggests that starspots could play an important role in stellar magnetic cycles. Aims. We aim to extend the BL mechanism to solar-mass stars with various rotation rates and explore the effects of emergence properties of starspots in latitudes and tilt angles on stellar magnetic cycles. Methods. We adopt a kinematic BL-type dynamo model operating in the bulk of the convection zone. The profiles of the large-scale flow fields are from the mean-field hydrodynamical model for various rotators. The BL source term in the model is constructed based on the rotation dependence of starspot emergence; that is, faster rotators have starspots at higher latitudes with larger tilt angles. Results. Faster rotators have poloidal flux appearing closer to about ±55° latitudes, where the toroidal field generation efficiency is the strongest because of the peak in the strength of the latitudinal differential rotation there. It takes a shorter time for faster rotators to transport the surface poloidal field from their emergence latitude to the ±55° latitudes of efficient Ω-effect, which shortens their magnetic cycles. The faster rotators operate in a more supercritical regime because of a stronger BL α-effect relating to the tilt angles, which leads to stronger saturated magnetic fields and makes the coupling of the poloidal field between two hemispheres more difficult. The magnetic field parity therefore shifts from the hemispherically asymmetric mixed mode to quadrupole, and further to dipole when a star spins down. Conclusions. The emergence of starspots plays an essential role in the large-scale stellar dynamo.

The Sun's differential rotation is controlled by high-latitude baroclinically unstable inertial modes.

Rapidly rotating fluids have a rotation profile that depends only on the distance from the rotation axis, in accordance with the Taylor-Proudman theorem. Although the Sun was expected to be such a body, helioseismology showed that the rotation rate in the convection zone is closer to constant on radii. It has been postulated that this deviation is due to the poles being warmer than the equator by a few degrees. Using numerical simulations, we show that the pole-to-equator temperature difference cannot exceed 7 kelvin as a result of the back-reaction of the high-latitude baroclinically unstable inertial modes. The observed amplitudes of the modes further indicate that this maximum temperature difference is reached in the Sun. We conclude that the Sun's latitudinal differential rotation reaches its maximum allowed value.

Toroidal Magnetic Flux Budget in Mean-field Dynamo Model of Solar Cycles 23 and 24

We study the toroidal magnetic flux budget of the axisymmetric part of a data-driven 3D mean-field dynamo model of Solar Cycles 23 and 24. The model simulates the global solar dynamo that includes the effects of the formation and evolution of bipolar magnetic regions (BMRs) emerging on the solar surface. By applying Stokes’s theorem to the dynamo induction equation, we show that the hemispheric magnitude of the net axisymmetric toroidal magnetic field generation rate in the bulk of the convection zone can only partially be estimated from the surface parameters of the differential rotation and the axisymmetric radial magnetic field. The contribution of the radial integral along the equator, which is mostly due to the rotational radial shear at the bottom of the convection zone, has the same magnitude and is nearly in phase with the effect of the surface latitudinal differential rotation. Also, the toroidal field generation rate estimate strongly depends on the latitudinal profile of the surface radial magnetic field near the poles. This profile in our dynamo models significantly deviates from the polar magnetic field distribution observed during the minima of Solar Cycles 22, 23, and 24. The cause of this discrepancy requires further observational and theoretical studies. Comparing the 2D axisymmetric and the 3D nonaxisymmetric dynamo models, we find an increase in the toroidal field generation rate in the 3D model due to the surface effects of BMRs, resulting in an increase in the axisymmetric poloidal magnetic field magnitude.

TESS photometry of the pulsating hot subdwarf star V585 Peg

ABSTRACT We report on the first space-based observations of the bright, high-amplitude hybrid pulsator V585 Peg (Balloon 090100001). TESS observed V585 Peg for 28 d during Sector 56 from which we detect 14 g-mode pulsations, 20 p-mode pulsations, and 26 combination frequencies. These pulsations are unusual and interesting in a number of ways; V585 Peg is a rare hybrid pulsator where both regions have many (>10) pulsations, the p-mode pulsations have clear frequency multiplets and overtone spacings while the g-mode pulsations do not, its multiplets have shown changes in splittings between years, and it appears to have two stochastic pulsations while most are stable. From p-mode multiplets, we find an average rotation period of 6.91 ± 0.83 d in which the different ℓ and m indices indicate latitudinal differential rotation. Unresolved g-mode multiplets limit rotation periods to be longer then 9.3 d for dipole modes, indicating V585 Peg to also be a radially differential rotator. We detect one secure p-mode overtone of 950 $\mu$Hz and four less sure ones of 314, 410, 440, and 554 $\mu$Hz. Two frequencies show stochastic properties indicating mode lifetimes of 3.5 and 6.2 h, which would be the shortest yet discovered.

Linear and non-linear properties of the Goldreich–Schubert–Fricke instability in stellar interiors with arbitrary local radial and latitudinal differential rotation

ABSTRACT We investigate the linear and non-linear properties of the Goldreich–Schubert–Fricke (GSF) instability in stellar radiative zones with arbitrary local (radial and latitudinal) differential rotation. This instability may lead to turbulence that contributes to the redistribution of angular momentum and chemical composition in stars. In our local Boussinesq model, we investigate varying the orientation of the shear with respect to the ‘effective gravity’, which we describe using the angle ϕ. We first perform an axisymmetric linear analysis to explore the effects of varying ϕ on the local stability of arbitrary differential rotations. We then explore the non-linear hydrodynamical evolution in three dimensions using a modified shearing box. The model exhibits both diffusive GSF instability and a non-diffusive instability that occurs when the Solberg-Høiland criteria are violated. We observe the non-linear development of strong zonal jets (‘layering’ in the angular momentum) with a preferred orientation in both cases, which can considerably enhance turbulent transport. By varying ϕ, we find instability with mixed radial and latitudinal shears transports angular momentum more efficiently (particularly if adiabatically unstable) than cases with purely radial shear (ϕ = 0). By exploring the dependence on box size, we find the transport properties of the GSF instability to be largely insensitive to this, implying we can meaningfully extrapolate our results to stars. However, there is no preferred length-scale for adiabatic instability, which therefore exhibits strong box-size dependence. These instabilities may contribute to the missing angular momentum transport required in red giant and subgiant stars and drive turbulence in the solar tachocline.

Optical and near-infrared stellar activity characterization of the early M dwarf Gl 205 with SOPHIE and SPIRou

Context. The stellar activity of M dwarfs is the main limiting factor in the discovery and characterization of the exoplanets orbiting them, because it induces quasi-periodic radial velocity (RV) variations. Aims. We aim to characterize the magnetic field and stellar activity of the early, moderately active M dwarf Gl 205 in the optical and near-infrared (NIR) domains. Methods. We obtained high-precision quasi-simultaneous spectra in the optical and NIR with the SOPHIE spectrograph and SPIRou spectropolarimeter between 2019 and 2022. We computed the RVs from both instruments and the SPIRou Stokes V profiles. We used Zeeman–Doppler imaging (ZDI) to map the large-scale magnetic field over the time span of the observations. We studied the temporal behavior of optical and NIR RVs and activity indicators with the Lomb-Scargle periodogram and a quasi-periodic Gaussian process regression (GPR). In the NIR, we studied the equivalent width of Al I, Ti I, K I, Fe I, and He I. We modeled the activity-induced RV jitter using a multi-dimensional GPR with activity indicators as ancillary time series. Results. The optical and NIR RVs show similar scatter but NIR shows a more complex temporal evolution. We observe an evolution of the magnetic field topology from a poloidal dipolar field in 2019 to a dominantly toroidal field in 2022. We measured a stellar rotation period of Prot = 34.4 ± 0.5 days in the longitudinal magnetic field. Using ZDI, we measure the amount of latitudinal differential rotation (DR) shearing the stellar surface, yielding rotation periods of Peq = 32.0 ± 1.8 days at the stellar equator and Ppol = 45.5 ± 0.3 days at the poles. We observed inconsistencies in the periodicities of the activity indicators that could be explained by these DR values. The multi-dimensional GP modeling yields an RMS of the RV residuals down to the noise level of 3 m s−1 for both instruments while using Hα and the BIS in the optical and the full width at half maximum (FWHM) in the NIR as ancillary time series. Conclusions. The RV variations observed in Gl 205 are due to stellar activity, with a complex evolution and different expressions in the optical and NIR revealed thanks to an extensive follow-up. Spectropolarimetry remains the best technique to constrain the stellar rotation period over standard activity indicators, particularly for moderately active M dwarfs.

Transition of latitudinal differential rotation as a possible cause of weakened magnetic braking of solar-type stars

ABSTRACTWe investigate the role of latitudinal differential rotation (DR) in the spin evolution of solar-type stars. Recent asteroseismic observation detected the strong equator-fast DR in some solar-type stars. Numerical simulations show that the strong equator-fast DR is a typical feature of young fast-rotating stars and that this tendency is gradually reduced with stellar age. Incorporating these properties, we develop a model for the long-term evolution of stellar rotation. The magnetic braking is assumed to be regulated dominantly by the rotation rate in the low-latitude region. Therefore, in our model, stars with the equator-fast DR spin down more efficiently than those with the rigid-body rotation. We calculate the evolution of stellar rotation in ranges of stellar mass, $0.9 \, \mathrm{M}_{\odot } \le M \le 1.2\, \mathrm{M}_{\odot }$, and metallicity, $0.5\, \mathrm{Z}_{\odot } \le Z \le 2\, \mathrm{Z}_{\odot }$, where M⊙ and Z⊙ are the solar mass and metallicity, respectively. Our model, using the observed torque in the present solar wind, nicely explains both the current solar rotation and the average trend of the rotation of solar-type stars, including the dependence on metallicity. In addition, our model naturally reproduces the observed trend of the weakened magnetic braking in old slowly rotating solar-type stars because strong equator-fast DR becomes reduced. Our results indicate that latitudinal DR and its transition are essential factors that control the stellar spin down.

Meta-analysis of Photometric and Asteroseismic Measurements of Stellar Rotation Periods: The Lomb–Scargle Periodogram, Autocorrelation Function, and Wavelet and Rotational Splitting Analysis for 92 Kepler Asteroseismic Targets

We perform intensity variability analyses (photometric analyses: the Lomb–Scargle periodogram, autocorrelation, and wavelet) and asteroseismic analysis of 92 Kepler solar-like main-sequence stars to understand the reliability of the measured stellar rotation periods. We focus on the 70 stars without reported stellar companions, and classify them into four groups according to the quarter-to-quarter variance of the Lomb–Scargle period and the precision of the asteroseismic period. We present detailed individual comparison among photometric and asteroseismic constraints for these stars. We find that most of our targets exhibit significant quarter-to-quarter variances in the photometric periods, suggesting that the photometrically estimated period should be regarded as a simplified characterization of the true stellar rotation period, especially under the presence of the latitudinal differential rotation. On the other hand, there are a fraction of stars with a relatively small quarter-to-quarter variance in the photometric periods, most of which have consistent values for asteroseismically and photometrically estimated rotation periods. We also identify over 10 stars whose photometric and asteroseismic periods significantly disagree, which would be potentially interesting targets for further individual investigations.

The white dwarf binary pathways survey – VIII. A post-common envelope binary with a massive white dwarf and an active G-type secondary star

ABSTRACT The white dwarf binary pathways survey is dedicated to studying the origin and evolution of binaries containing a white dwarf and an intermediate-mass secondary star of the spectral type A, F, G, or K (WD + AFGK). Here, we present CPD-65 264, a new post-common envelope binary with an orbital period of 1.37 d that contains a massive white dwarf ($0.86\pm 0.06\, \mathrm{M}_{\odot }$) and an intermediate-mass ($1.00\pm 0.05\, \mathrm{M}_{\odot }$) main-sequence secondary star. We characterized the secondary star and measured the orbital period using high-resolution optical spectroscopy. The white dwarf parameters are determined from HST spectroscopy. In addition, TESS observations revealed that up to 19 per cent of the surface of the secondary is covered with starspots. Small period changes found in the light curve indicate that the secondary is the second example of a G-type secondary star in a post-common envelope binary with latitudinal differential rotation. Given the relatively large mass of the white dwarf and the short orbital period, future mass transfer will be dynamically and thermally stable and the system will evolve into a cataclysmic variable. The formation of the system can be understood assuming common envelope evolution without contributions from energy sources besides orbital energy. CPD-65 264 is the seventh post-common envelope binaries with intermediate-mass secondaries that can be understood assuming a small efficiency in the common envelope energy equation, in agreement with findings for post-common envelope binaries with M-dwarf or substellar companions.

A model for spin–orbit commensurability and synchronous starspot activity in stars with close-by planets

Context. The rotation period of some planet-hosting stars appears to be in close commensurability with the orbital period of their close-by planets. In some cases, starspots rotating with a commensurable period have been detected, while the star displays latitudinal differential rotation. Aims. A model is proposed to interpret such a phenomenon based on the excitation of resonant oscillations in the interior magnetic field of the star by a component of the tidal potential with a very low frequency in the reference frame rotating with the star. Methods. A magnetic flux tube located in the overshoot layer of the star is assumed in order to study the excitation of the resonant oscillations in the magnetostrophic regime. The model considers a planet on a circular oblique orbit, and the growth timescale of the oscillations is estimated. To keep the system in resonance with the exciting potential despite the variations in the magnetic field or tidal frequency, a self-regulating mechanism is proposed. Results. The model is applied to ten systems and proves capable of accounting for the observed close commensurability in eight of them by assuming a magnetic field between 102 and 104 G. Systems with distant low-mass planets, such as AU Mic and HAT-P-11, cannot be interpreted by the proposed model. Conclusions. Consequences for the spin–orbit evolution of the systems, including the dynamical tides and gyrochronology of planet-hosting stars, are discussed together with the effects on the chromospheric features produced by star–planet magnetic interactions.

Spot and Facula Activity Variations of the Eccentric Detached Eclipsing Binary KIC 8098300 Based on the Time-series Orbital Solutions

The LAMOST spectra and Kepler light curves are combined to investigate the detached eclipsing binary KIC 8098300, which shows the O’Connell effect caused by spot/facula modulation. The radial velocity (RV) measurements are derived by using the tomographic spectra disentangling technology. The mass ratio q = K 1/K 2 = 0.812 ± 0.007, and the orbital semimajor axis are obtained by fitting the RV curves. We optimize the binary model concerning the spot/facula activity with the code PHOEBE and obtain precise parameters of the orbit including the eccentricity e = 0.0217 ± 0.0008, the inclination i = 87.°71 ± 0.°04, and the angle of periastron ω = 284.°1 ± 0.°5. The masses and radii of the primary and secondary star are determined as M 1 = 1.3467 ± 0.0001 M ⊙, R 1 = 1.569 ± 0.003 R ⊙, and M 2 = 1.0940 ± 0.0001 M ⊙, R 2 = 1.078 ± 0.002 R ⊙, respectively. The ratio of temperatures of the two component stars is r teff = 0.924 ± 0.001. We also obtain the periastron precession speed of 0.000024 ± 0.000001 day cycle−1. The residuals of out-of-eclipse are analyzed using the auto-correlation function and the discrete Fourier transform. The spot/facula activity is relatively weaker, but the lifetime is longer than that of most single main sequence stars in the same temperature range. The average rotation period of the spots P rot = 4.32 days is slightly longer than the orbital period, which may be caused by either the migration of spots/faculae along the longitude or the latitudinal differential rotation. The activity may be spot-dominated for the secondary star and facula-dominated for the primary star. The method of this work can be used to analyze more eclipsing binaries with the O’Connell effect in the Kepler field to obtain the precise parameters and investigate the difference of spot behavior between binaries and single stars. It is helpful for a deeper understanding of the stellar magnetic activity and dynamo theory.

Disentangling the stellar inclination of transiting planetary systems: Fully analytic approach to the Rossiter–McLaughlin effect incorporating the stellar differential rotation

Abstract The Rossiter–McLaughlin (RM) effect has been widely used to estimate the sky-projected spin-orbit angle, λ, of transiting planetary systems. Most of the previous analysis assumes that the host stars are rigid rotators in which the amplitude of the RM velocity anomaly is proportional to v⋆ sin i⋆. When their latitudinal differential rotation is taken into account, one can break the degeneracy, and determine separately the equatorial rotation velocity v⋆ and the inclination i⋆ of the host star. We derive a fully analytic approximate formula for the RM effect adopting a parametrized model for the stellar differential rotation. For those stars that exhibit a differential rotation similar to that of the Sun, the corresponding RM velocity modulation amounts to several m s−1. We conclude that the latitudinal differential rotation offers a method to estimate i⋆, and thus the full spin-orbit angle ψ, from the RM data analysis alone.

Short-term variations of surface magnetism and prominences of the young Sun-like star V530 Per

Aims. We investigate magnetic tracers in the photosphere and the chromosphere of the ultra-rapid rotator (P ~ 0.32 d) V530 Per, a cool member of the open cluster α Persei, to characterize the short-term variability of the magnetic activity and large-scale magnetic field of this prototypical young, rapidly rotating solar-like star. Methods. With time-resolved spectropolarimetric observations spread over four close-by nights, we reconstructed the brightness distribution and large-scale magnetic field geometry of V530 Per through Zeeman-Doppler imaging. Simultaneously, we estimated the short-term variability of the surface through latitudinal differential rotation. Using the same data set, we also mapped the spatial distribution of prominences through tomography of Hα emission. Results. As in our previous study, a large dark spot occupies the polar region of V530 Per with smaller, dark, and bright spots at lower latitudes. The large-scale magnetic field is dominated by a toroidal, mostly axisymmetric component. The maximal radial field strength is equal to ~1 kG. The surface differential rotation is consistent with a smooth Sun-like shear dΩ = 0.053 ± 0.004 rad d−1, close to the solar shear level. The prominence pattern displays a stable component that is confined close to the corotation radius. We also observe rapidly evolving Hα emitting structures, over timescales ranging from minutes to days. The fast Hα evolution was not linked to any detected photospheric changes in the spot or magnetic coverage.

The Fine Structure of the Quasi-Biennial Oscillations of Sunspot Areas and the Double Magnetic Cycle of the Sun

One of the basic features of solar activity is the quasi-biennial oscillations (QBOs)—variations with a period of about two years. The nature of the QBO remains unclear and the most puzzling is the high instability of the QBO period. We investigated a fine structure of the QBO period variability as manifested in sunspot area variations in Solar Cycles 19 – 23 using the wavelet transform with a real mother wavelet, Daubechies 10, that provided a high temporal resolution. We found that within every 11-yr solar cycle the QBO period varies not randomly, as it is widely accepted now, but it gradually decreases from the beginning of the solar cycle till the end, in phase with the shift of the average sunspots latitude to the equator. We have analyzed in a similar way the time series which were simulated using a combination of sine waves with different periods (constant and variable one) and red noise with a standard deviation as large as 40% of the sine amplitude. The analysis has shown that noise does not distort significantly the initial signal and noise itself does not form the structures with the properties which were observed in the case of the natural time series. We suppose that the revealed modification of the QBO period with the development of the solar cycle may be related to the latitudinal differential rotation in the solar convection zone and the possible influence of the rotational velocity in the region of the QBO generation on the QBO period value. Under this assumption, the process responsible for the QBO generation should operate in a layer with a substantial latitudinal shear which according to the helioseismology analysis is observed in the bulk of the convection zone and is getting smaller in the vicinity of the tachocline.

Magnetic field and prominences of the young, solar-like, ultra-rapid rotator V530 Persei

Context. Young solar analogs reaching the main sequence experience very strong magnetic activity, generating angular momentum losses through wind and mass ejections. Aims. We investigate signatures of magnetic fields and activity at the surface and in the prominence system of the ultra-rapid rotator V530 Per, a G-type solar-like member of the young open cluster α Persei. This object has a rotation period that is shorter than all stars with available magnetic maps. Methods. With a time-series of spectropolarimetric observations gathered with ESPaDOnS over two nights on the Canada-France-Hawaii Telescope, we reconstructed the surface brightness and large-scale magnetic field of V530 Per using the Zeeman-Doppler imaging method, assuming an oblate stellar surface. We also estimated the short term evolution of the brightness distribution through latitudinal differential rotation. Using the same data set, we finally mapped the spatial distribution of prominences through tomography of the Hα emission. Results. The brightness map is dominated by a large, dark spot near the pole, accompanied by a complex distribution of bright and dark features at lower latitudes. Taking the brightness map into account, the magnetic field map is reconstructed as well. Most of the large-scale magnetic field energy is stored in the toroidal field component. The main radial field structure is a positive region of about 500 G, at the location of the dark polar spot. The brightness map of V530 Per is sheared by solar-like differential rotation, with roughly a solar value for the difference in rotation rate between the pole and equator. It is important to note that Hα is observed in emission and it is mostly modulated by the stellar rotation period over one night. The prominence system is organized in a ring at the approximate location of the corotation radius, and displays significant evolution between the two observing nights. Conclusions. V530 Per is the first example of a solar-type star to have its surface magnetic field and prominences mapped together, which will bring important observational constraints to better understand the role of slingshot prominences in the angular momentum evolution of the most active stars.

Effect of latitudinal differential rotation on solar Rossby waves: Critical layers, eigenfunctions, and momentum fluxes in the equatorialβplane

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 equatorialβplane, we studied the propagation of linear Rossby waves (phase speedc < 0) in a parabolic zonal shear flow,U= −U̅ξ2< 0, whereU̅= 244 m s−1, andξis 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 whereU = 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. ForRe ≈ 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.

Stellar activity and rotation of the planet host Kepler-17 from long-term space-borne photometry

Context. The study of young Sun-like stars is fundamental to understanding the magnetic activity and rotational evolution of the Sun. Space-borne photometry by the Kepler telescope provides unprecedented datasets to investigate these phenomena in Sun-like stars. Aims. We present a new analysis of the entire Kepler photometric time series of the moderately young Sun-like star Kepler-17 accompanied by a transiting hot Jupiter. Methods. We applied a maximum-entropy spot model to the long-cadence out-of-transit photometry of the target to derive maps of the starspot filling factor versus the longitude and the time. These maps are compared to the spots occulted during transits to validate our reconstruction and derive information on the latitudes of the starspots. Results. We find two main active longitudes on the photosphere of Kepler-17, one of which has a lifetime of at least ∼1400 days although with a varying level of activity. The latitudinal differential rotation is of solar type, that is, with the equator rotating faster than the poles. We estimate a minimum relative amplitude ΔΩ/Ω between ∼0.08 ± 0.05 and 0.14 ± 0.05, our determination being affected by the finite lifetime of individual starspots and depending on the adopted spot model parameters. We find marginal evidence of a short-term intermittent activity cycle of ∼48 days and an indication of a longer cycle of 400−600 days characterized by an equatorward migration of the mean latitude of the spots as in the Sun. The rotation of Kepler-17 is likely to be significantly affected by the tides raised by its massive close-by planet. Conclusion. We confirm the reliability of maximum-entropy spot models to map starspots in young active stars and characterize the activity and differential rotation of this young Sun-like planetary host.

Magneto-Rossby Waves in the Solar Tachocline and the Annual Variations in Solar Activity

Abstract 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−1) 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, 370–380, 310–320, 240–270, 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 yr), while the remaining periods can be connected with different harmonics of global fast magneto-Rossby waves.

Latitudinal differential rotation in the solar analogues 16 Cygni A and B

Context.Asteroseismology has undergone a profound transformation as a scientific field following the CoRoT andKeplerspace 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.Aims.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 byKeplerand have therefore been extensively observed, with exquisite precision on their oscillation frequencies.Methods.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.Results.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 320 ± 269 nHz and 440−383+363nHz for 16 Cyg A and B, respectively, confirming that the rotation rates of these stars are almost solar-like. Their equatorial rotation rates are 535 ± 75 nHz and 565−129+150nHz. Our results are in good agreement with measurements obtained from spectropolarimetry, spectroscopy, and photometry.Conclusions.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.

Starspot rotation rates versus activity cycle phase: Butterfly diagrams ofKeplerstars are unlike that of the Sun

Context. During the solar magnetic activity cycle the emergence latitudes of sunspots change, leading to the well-known butterfly diagram. This phenomenon is poorly understood for other stars since starspot latitudes are generally unknown. The related changes in starspot rotation rates caused by latitudinal differential rotation can, however, be measured.Aims. Using the set of 3093Keplerstars with measured activity cycles, we aim to study the temporal change in starspot rotation rates over magnetic activity cycles, and how this relates to the activity level, the mean rotation rate of the star, and its effective temperature.Methods. We measured the photometric variability as a proxy for the magnetic activity and the spot rotation rate in each quarter over the duration of theKeplermission. We phase-folded these measurements with the cycle period. To reduce random errors, we performed averages over stars with comparable mean rotation rates and effective temperature at fixed activity-cycle phases.Results. We detect a clear correlation between the variation of activity level and the variation of the starspot rotation rate. The sign and amplitude of this correlation depends on the mean stellar rotation and – to a lesser extent – on the effective temperature. For slowly rotating stars (rotation periods between 15 − 28 days), the starspot rotation rates are clearly anti-correlated with the level of activity during the activity cycles. A transition is observed around rotation periods of 10 − 15 days, where stars with an effective temperature above 4200 K instead show positive correlation.Conclusions. Our measurements can be interpreted in terms of a stellar “butterfly diagram”, but these appear different from that of the Sun since the starspot rotation rates are either in phase or anti-phase with the activity level. Alternatively, the activity cycle periods observed byKeplerare short (around 2.5 years) and may therefore be secondary cycles, perhaps analogous to the solar quasi-biennial oscillations.