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Register a new userWhat sets the magnetic field strength and cycle period in solar-type stars?
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Two fundamental properties of stellar magnetic fields have been determined by observations for solar-like stars with different Rossby numbers (Ro), namely, the magnetic field strength and the magnetic cycle period. The field strength exhibits two regimes: 1) for fast rotation it is independent of Ro, 2) for slow rotation it decays with Ro following a power law. For the magnetic cycle period two regimes of activity, the active and inactive branches, also have been identified. For both of them, the longer the rotation period, the longer the activity cycle. Using global dynamo simulations of solar like stars with Rossby numbers between ~0.4 and ~2, this paper explores the relevance of rotational shear layers in determining these observational properties. Our results, consistent with non-linear alpha^2-Omega dynamos, show that the total magnetic field strength is independent of the rotation period. Yet at surface levels, the origin of the magnetic field is determined by Ro. While for Ro<1 it is generated in the convection zone, for Ro>1 strong toroidal fields are generated at the tachocline and rapidly emerge towards the surface. In agreement with the observations, the magnetic cycle period increases with the rotational period. However, a bifurcation is observed for Ro~1, separating a regime where oscillatory dynamos operate mainly in the convection zone, from the regime where the tachocline has a predominant role. In the latter the cycles are believed to result from the periodic energy exchange between the dynamo and the magneto-shear instabilities developing in the tachocline and the radiative interior.
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Parameters of magnetic activity on the solar type stars depend on the properties of the dynamo processes operating in stellar convection zones. We apply nonlinear mean-field axisymmetric $alpha^2Omega$ dynamo models to calculate of the magnetic cycle parameters, such as the dynamo cycle period, the total magnetic flux and the Poynting magnetic energy flux on the surface of solar analogs with the rotation periods from 15 to 30 days. The models take into account the principal nonlinear mechanisms of the large-scale dynamo, such as the magnetic helicity conservation, magnetic buoyancy, and effects of magnetic forces on the angular momentum balance inside the convection zones. Also, we consider two types of the dynamo models. The distributed (D-type) models employ the standard alpha-effect distributed on the whole convection zone. The boundary (B-type) models employ the non-local alpha- effect, which is confined to the boundaries of the convection zone. Both the D- and B-type models show that the dynamo-generated magnetic flux increases with the increase of the stellar rotation rate. {It is found that for the considered range of the rotational periods} the magnetic helicity conservation is the most significant effect for the nonlinear quenching of the dynamo. This quenching is more efficient in the B-type than in the D-type dynamo models. The D-type dynamo reproduces the observed dependence of the cycle period on the rotation rate for the Sun analogs. For the solar analog rotating with a period of 15 days we find nonlinear dynamo regimes with multiply cycles.
We compare spectra of the zonal harmonics of the large-scale magnetic field of the Sun using observation results and solar dynamo models. The main solar activity cycle as recorded in these tracers is a much more complicated phenomenon than the eigen solution of solar dynamo equations with the growth saturated by a back reaction of the dynamo-driven magnetic field on solar hydrodynamics. The nominal 11(22)-year cycle as recorded in each mode has a specific phase shift varying from cycle to cycle; the actual length of the cycle varies from one cycle to another and from tracer to tracer. Both the observation and the dynamo model show an exceptional role of the axisymmetric $ell_{5}$ mode. Its origin seems to be readily connected with the formation and evolution of sunspots on the solar surface. The results of observations and dynamo models show a good agreement for the low $ell_{1}$ and $ell_{3}$ modes. The results for these modes do not differ significantly for the axisymmetric and nonaxisymmetric models. Our findings support the idea that the sources of the solar dynamo arise as a result of both the distributed dynamo processes in the bulk of the convection zone and the surface magnetic activity.
Solar activity undergoes a variation over time scales of several months known as Rieger-type periodicity, which usually occurs near maxima of sunspot cycles. An early analysis showed that the periodicity appears only in some cycles, and is absent in other cycles. But the appearance/absence during different cycles has not been explained. We performed a wavelet analysis of sunspot data from the Greenwich Royal Observatory and the Royal Observatory of Belgium during cycles 14-24. We found that the Rieger-type periods occur in all cycles, but they are cycle-dependent: shorter periods occur during stronger cycles. Our analysis revealed a periodicity of 185-195 days during the weak cycles 14-15 and 24, and a periodicity of 155-165 days during the stronger cycles 16-23. We derived the dispersion relation of the spherical harmonics of the magnetic Rossby waves in the presence of differential rotation and a toroidal magnetic field in the dynamo layer near the base of the convection zone. This showed that the harmonic of fast Rossby waves with m=1 and n=4, where m (n) indicate the toroidal (poloidal) wavenumbers, respectively, perfectly fit with the observed periodicity. The variation of the toroidal field strength from weaker to stronger cycles may lead to the different periods found in those cycles, which explains the observed enigmatic feature of the Rieger-type periodicity. Finally, we used the observed periodicity to estimate the dynamo field strength during cycles 14-24. Our estimations suggest a field strength of 40 kG for the stronger cycles, and 20 kG for the weaker cycles.
According to the scheme of action of the solar dynamo, the poloidal magnetic field can be considered a source of production of the toroidal magnetic field by the solar differential rotation. From the polar magnetic field proxies, it is natural to expect that solar Cycle 25 will be weak as recorded in sunspot data. We suggest that there are parameters of the zonal harmonics of the solar surface magnetic field, such as the magnitude of the $ell$=3 harmonic or the effective multipole index, that can be used as a reasonable addition to the polar magnetic field proxies. We discuss also some specific features of solar activity indices in Cycles 23 and 24.
Using the non-linear mean-field dynamo models we calculate the magnetic cycle parameters, like the dynamo cycle period, the amplitude of the total magnetic energy, and the Poynting flux luminosity from the surface for the solar analogs with rotation periods of range from 1 to 30 days. We do simulations both for the kinematic and non-kinematic dynamo models. The kinematic dynamo models, which take into account the non-linear $alpha$-effect and the loss of the magnetic flux due to magnetic buoyancy, show a decrease of the magnetic cycle with the decrease of the stellar rotation period. The stars with a rotational period of less than 10 days show the non-stationary long-term variations of the magnetic activity. The non-kinematic dynamo models take into account the magnetic field feedback on the large-scale flow and heat transport inside the convection zone. They show the non-monotonic variation of the dynamo period with the rotation rate. The models for the rotational periods fewer than 10 days show the non-stationary evolution with a slight increase in the primary dynamo period with the increase of the rotation rate. The non-kinematic models show the growth of the dynamo generated magnetic flux with the increase of the rotation rate. There is a dynamo saturation for the star rotating with a period of two days and less. The saturation of the magnetic activity parameters is accompanied by depression of the differential rotation.
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