Differential rotation and meridional flow in the solar convection zone and beneath

The influence of the basic rotation on anisotropic and inhomogeneous turbulence is discussed in the context of differential rotation theory. An improved representation for the original turbulence leads to a Λ‐effect which complies with the results of 3D numerical simulations. The resulting rotation law and meridional flow agree well with both the surface observations (∂Ω/∂r < 0 and meridional flow towards the poles) and with the findings of helioseismology. The computed equatorward flow at the bottom of convection zone has an amplitude of about 10 m/s and may be significant for the solar dynamo. The depth of the meridional flow penetration into the radiative zone is proportional to ν^0.5_core, where ν_core is the viscosity beneath the convection zone. The penetration is very small if the tachocline is laminar. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Signature of differential rotation in solar disk‐integrated chromospheric line emission

UARS SOLSTICE data have been subjected to Fourier and wavelet analyses in order to search for the signature of the solar rotation law in the disk‐integrated irradiance of UV lines. Lyman‐α, Mg II, and Ca II data show a different behaviour. In the SOLSTICE data there are significant temporal variations of the rotation rate of the UV tracers over 5—6 years. Often several distinct rotation periods appear almost simultaneously. Beside the basic period around 27 days there are signals at 32—35 days corresponding to the rotation rate at very high latitudes. For more than 5 years during another period of the solar cycle the rotational behaviour is quite different; there is an indication of differential rotation of active regions in these Ca II ground‐based data. The data contain a wealth of information about the solar differential rotation, but it proves difficult to disentangle the effects of the different emitting sources.     

Sounding stellar cycles with Kepler – I. Strategy for selecting targets

The long-term monitoring and high photometric precision of the Kepler satellite will provide a unique opportunity to sound the stellar cycles of many solar-type stars using asteroseismology. This can be achieved by studying periodic changes in the amplitudes and frequencies of the oscillation modes observed in these stars. By comparing these measurements with conventional ground-based chromospheric activity indices, we can improve our understanding of the relationship between chromospheric changes and those taking place deep in the interior throughout the stellar activity cycle. In addition, asteroseismic measurements of the convection zone depth and differential rotation may help us determine whether stellar cycles are driven at the top or at the base of the convection zone. In this paper, we analyse the precision that will be possible using Kepler to measure stellar cycles, convection zone depths and differential rotation. Based on this analysis, we describe a strategy for selecting specific targets to be observed by the Kepler Asteroseismic Investigation for the full length of the mission, to optimize their suitability for probing stellar cycles in a wide variety of solar-type stars.     

On the solar rotation and activity

The interaction between differential rotation and magnetic fields in the solar convection zone was recently modelled by Brun (2004). One consequence of that model is that the Maxwell stresses can oppose the Reynolds stresses, and thus contribute to the transport of the angular momentum towards the solar poles, leading to a reduced differential rotation. So, when magnetic fields are weaker, a more pronounced differential rotation can be expected, yielding a higher rotation velocity at low latitudes taken on the average. This hypothesis is consistent with the behaviour of the solar rotation during the Maunder minimum. In this work we search for similar signatures of the relationship between the solar activity and rotation determined tracing sunspot groups and coronal bright points. We use the extended Greenwich data set (1878–1981) and a series of full-disc solar images taken at 28.4 nm with the EIT instrument on the SOHO spacecraft (1998–2000). We investigate the dependence of the solar rotation on the solar activity (described by the relative sunspot number) and the interplanetary magnetic field (calculated from the interdiurnal variability index). Possible rotational signatures of two weak solar activity cycles at the beginning of the 20th century (Gleissberg minimum) are discussed. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Meridional circulation in the radiation zones of rotating stars: Origins,behaviors and consequences on stellar evolution

Stellar radiation zones are the seat of meridional currents. This circulation has a strong impact on the transport of angular momentum and the mixing of chemicals that modify the evolution of stars. First, we recall in details the dynamical processes that are taking place in differentially rotating stellar radiation zones and the assumptions which are adopted for their modelling in stellar evolution. Then, we present our new results of numerical simulations which allow us to follow in 2D the secular hydrodynamics of rotating stars, assuming that anisotropic turbulence enforces a shellular rotation law and taking into account the transport of angular momentum by internal gravity waves. The different behaviors of the meridional circulation in function of the type of stars which is studied are discussed with their physical origin and their consequences on the transport of angular momentum and of chemicals. Finally, we show how this work is leading to a dynamical vision of the evolution of rotating stars from their birth to their death. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Differential rotation in F stars

Differential rotation can be detected in single line profiles of stars rotating more rapidly than about v sin i = 10km s-1 with the Fourier transform technique. This allows to search for differential rotation in large samples to look for correlations between differential rotation and other stellar parameters. I analyze the fraction of differentially rotating stars as a function of color, rotation, and activity in a large sample of F-type stars. Color and rotation exhibit a correlation with differential rotation in the sense that more stars are rotating differentially in the cooler, less rapidly rotating stars. Effects of rotation and color, however, cannot be disentangled in the underlying sample. No trend with activity is found. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the possibility of a bimodal solar dynamo

A simple way to couple an interface dynamo model to a fast tachocline model is presented, under the assumption that the dynamo saturation is due to a quadratic process and that the effect of finite shear layer thickness on the dynamo wave frequency is analogous to the effect of finite water depth on surface gravity waves. The model contains one free parameter which is fixed by the requirement that a solution should reproduce the helioseismically determined thickness of the tachocline. In this case it is found that, in addition to this solution, another steady solution exists, characterized by a four times thicker tachocline and 4–5 times weaker magnetic fields. It is tempting to relate the existence of this second solution to the occurrence of grand minima in solar activity. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Destabilization of hydrodynamically stable rotation laws by azimuthal magnetic fields

We consider the effect of toroidal magnetic fields on hydrodynamically stable Taylor–Couette differential rotation flows. For current-free magnetic fields a non-axisymmetric   m = 1  magnetorotational instability arises when the magnetic Reynolds number exceeds   O (100)  . We then consider how this 'azimuthal magnetorotational instability' (AMRI) is modified if the magnetic field is not current-free, but also has an associated electric current throughout the fluid. This gives rise to current-driven Tayler instabilities (TIs) that exist even without any differential rotation at all. The interaction of the AMRI and the TI is then considered when both electric currents and differential rotation are present simultaneously. The magnetic Prandtl number Pm turns out to be crucial in this case. Large Pm have a destabilizing influence, and lead to a smooth transition between the AMRI and the TI. In contrast, small Pm have a stabilizing influence, with a broad stable zone separating the AMRI and the TI. In this region the differential rotation is acting to stabilize the TIs, with possible astrophysical applications (Ap stars). The growth rates of both the AMRI and the TI are largely independent of Pm , with the TI acting on the time-scale of a single rotation period, and the AMRI slightly slower, but still on the basic rotational time-scale. The azimuthal drift time-scale is ∼20 rotations, and may thus be a (flip-flop) time-scale of stellar activity between the rotation period and the diffusion time.     

Intermittent Behaviour in Axisymmetric Mean-Field Dynamo Models in Spherical Shells

Axisymmetric mean-field dynamo models in spherical shells are shown to be capable of producing temporally intermittent behaviour. This is of potential importance since (i) it is, as far as we are aware, the first time such behaviour has been produced internally by a mean-field dynamo model in a spherical shell, without requiring any additional assumptions or truncations, and (ii) it may be characteristic of the type of behaviour observed in the long-term record of solar activity, such as Maunder minima. We also show that these types of behaviour persist when the functional form of the alpha quenching is altered and also occur over intervals of the shell thickness and the dynamo number.     

27‐day variations of solar indices and cosmic ray neutron monitor intensities

Solar activity indices (coronal, chromospheric as well as photospheric) and cosmic ray neutron monitor rates (different cut‐off rigidity) have been used to study 27‐day variations in the years from 1957 to 2004. Daily data were employed for this purpose, analysed by the FFT and wavelet techniques. To work with a continuous data set for the cosmic rays (CR), the ‘Composite Cosmic Ray’ (CCR) set was first created from the observations carried out at different neutron monitor stations. The CCR frequency analysis shows significant 27‐day variations in the intensity of CR, with its amplitude's values very sensitive to the sign of the quantity qA. The most significant 27‐day variations of CR were found not to correlate with those of other solar indices. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Rotation speed and stellar axis inclination from p modes: how CoRoT would see other suns

In the context of future space-based asteroseismic missions, we have studied the problem of extracting the rotation speed and the rotation-axis inclination of solar-like stars from the expected data. We have focused on slow rotators (at most twice solar rotation speed), first, because they constitute the most difficult case and, secondly, because some of the Convection Rotation and planetary Transits ( CoRoT ) main targets are expected to have slow rotation rates. Our study of the likelihood function has shown a correlation between the estimates of inclination of the rotation axis i and the rotational splitting δν of the star. By using the parameters, i and  δν^⋆=δν sin  i   , we propose and discuss new fitting strategies. Monte Carlo simulations have shown that we can extract a mean splitting and the rotation-axis inclination down to solar rotation rates. However, at the solar rotation rate we are not able to correctly recover the angle i , although we are still able to measure a correct  δν^⋆  with a dispersion less than 40 nHz.     

Meteor radiant activity mapping using single-station radar observations

In this paper, we present a study of the general physical and chemical properties and radial velocity monitoring of young active stars. We derive temperatures, log  g , [Fe/H], v sin  i and R _spec values for eight stars. The detailed analysis reveals that the stars are not homogeneous in their principal physical parameters or in the age distribution. In 4/5, we found a periodic radial velocity signal which originates in surface features; the fifth is surprisingly inactive and shows little variation.     

Differential rotation of cool active stars: the case of intermediate rotators

In this paper, we present a new method for measuring the surface differential rotation of cool stars with rotation periods of a few days, for which the sparse phase coverage achievable from single-site observations generally prevents the use of more conventional techniques. The basic idea underlying this new analysis is to obtain the surface differential rotation pattern that minimizes the information content of the reconstructed Doppler image through a simultaneous fit of all available data.
Simulations demonstrate that the performance of this new method in the case of cool stars is satisfactory for a variety of observing strategies. Differential rotation parameters can be recovered reliably as long as the total data set spans at least 4 per cent of the time for the equator to lap the pole by approximately one complete cycle. We find in particular that these results hold for potentially complex spot distributions (as long as they include a mixture of low- and high-latitude features), and for various stellar inclination angles and rotation velocities. Such measurements can be obtained from either unpolarized or polarized data sets, provided their signal-to-noise ratio is larger than approximately 500 and 5000 per 2 km s⁻¹ spectral bin, respectively.
This method should therefore be very useful for investigating differential rotation in a much larger sample of objects than what has been possible up to now, and should hence give us the opportunity of studying how differential rotation reacts to various phenomena operating in stellar convective zones, such as tidal effects or dynamo magnetic field generation.     

A new look at the relationship between activity, dynamo number and Rossby number in late-type stars

The correlation between stellar activity, as measured by the indicator Δ R _HK, and the Rossby number Ro in late-type stars is revisited in light of recent developments in solar dynamo theory. Different stellar interior models, based on both mixing-length theory and the full spectrum of turbulence, are used in order to see to what extent the correlation of activity with Rossby number is model dependent, or otherwise can be considered universal. Although we find some modest model dependence, we find that the correlation of activity with Rossby number is significantly better than with rotation period alone for all the models we consider. Dynamo theory suggests that activity should scale with the dynamo number. A current model of the solar dynamo, the so-called interface dynamo, proposes that the amplification of the toroidal magnetic field by differential rotation (the ω -effect) and the production of the poloidal magnetic field from toroidal by helical turbulence (the α -effect) take place in different, adjacent layers near the base of the convection zone. A new scale analysis based on the interface dynamo shows that the appropriate dynamo number does not depend on the Rossby number alone, but also depends on an additional dimensionless factor related to the differential rotation. This leads to a new interpretation of the correlation between activity and Rossby number, which in turn leads to some conclusions about the magnitude of differential rotation in the dynamo layers of late-type main-sequence stars.     

Differential rotation on rapidly rotating stars

Theories of meridional circulation and differential rotation in stellar convective zones predict trends in surface flow patterns on main-sequence stars that are amenable to direct observational testing. Here I summarise progress made in the last few years in determining surface differential rotation patterns on rapidly-rotating young main-sequence stars of spectral types F, G, K and M. Differential rotation increases strongly with increasing effective temperature along the main sequence. The shear rate appears to increase with depth in the sub-photospheric layers. Tidal locking in close binaries appears to suppress differential rotation, but better statistics are needed before this conclusion can be trusted. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dynamics of the solar magnetic field from SOHO/MDI

The investigation of the dynamics of magnetic fields from small scales to the large scales is very important for the understanding of the nature of solar activity. It is also the base for producing adequate models of the solar cycle with the purpose to predict the level of solar activity. Since December 1995 the Michelson Doppler Imager (MDI) on board of the Solar and Heliospheric Observatory (SOHO) provides full disk magnetograms and synoptic maps which cover the period of solar cycle 23 and the current minimum. In this paper, I review the following important topics with a focus on the dynamics of the solar magnetic field. The synoptic structure of the solar cycle; the birth of the solar cycle (overlapping cycles 23 and 24); the relationship of the photospheric magnetic activity and the EUV solar corona, polar magnetic fields and dynamo theory (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)