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Context. It is well known that the tilt angles of active regions increase with their latitude (Joy's law). It has never been checked before, however, whether the average tilt angles change from one cycle to the next. Flux transport models show the importance of tilt angles for the reversal and build up of magnetic flux at the poles, which is in turn correlated to the strength of the next cycle. Aims. Here we analyse time series of tilt angle measurements and look for a possible relationship of the tilt angles with other solar cycle parameters, in order to glean information on the solar dynamo and to estimate their potential for predicting solar activity. Methods. We employed tilt angle data from Mount Wilson and Kodaikanal observatories covering solar cycles 15 to 21. We analyse the latitudinal distribution of the tilt angles (Joy's law), their variation from cycle to cycle, and their relationship to other solar cycle parameters, such as the strength (or total area covered by sunspots in a cycle), amplitude, and length. Results. The two main results of our analysis follow. 1. We find an anti-correlation between the mean normalised tilt angle of a given cycle and the strength (or amplitude) of that cycle, with a correlation coefficient of r c = −0.95 (99.9% confidence level) and r c = −0.93 (99.76% confidence level) for Mount Wilson and Kodaikanal data, respectively. 2. The product of the cycle's averaged tilt angle and the strength of the same cycle displays a significant correlation with the strength of the next cycle (r c = 0.65 at 89% confidence level and r c = 0.70 at 92% confidence level for Mount Wilson and Kodaikanal data, respectively). An even better correlation is obtained between the source term of the poloidal flux in Babcock-Leighton-type dynamos (which contains the tilt angle) and the amplitude of the next cycle. Further we confirm the linear relationship (Joy's law) between the tilt angle and latitude with slopes of 0.26 and 0.28 for Mount Wilson and Kodaikanal data, respectively. In addition, we obtain good positive correlations between the normalised-areaweighted tilt angle and the length of the following cycle, whereas the strength or the amplitude of the next cycle does not appear to be correlated to the tilt angles of the current cycle alone. Conclusions. The results of this study indicate that, in combination with the cycle strength, the active region tilt angles play an important role in building up the polar fields at cycle minimum.

Sunspots are concentrations of magnetic field on the visible solar surface that strongly affect the convective energy transport in their interior and surroundings. The filamentary outer regions (penumbrae) of sunspots show systematic radial outward flows along channels of nearly horizontal magnetic field. These flows were discovered 100 years ago and are present in all fully developed sunspots. By using a comprehensive numerical simulation of a sunspot pair, we show that penumbral structures with such outflows form when the average magnetic field inclination to the vertical exceeds about 45 degrees. The systematic outflows are a component of the convective flows that provide the upward energy transport and result from anisotropy introduced by the presence of the inclined magnetic field.

Various methods of helioseismology are used to study the subsurface properties of the sunspot in NOAA Active Region 9787. This sunspot was chosen because it is axisymmetric, shows little evolution during 20-28 January 2002, and was observed continuously by the MDI/SOHO instrument. AR 9787 is visible on helioseismic maps of the farside of the Sun from 15 January, i.e. days before it crossed the East limb.Oscillations have reduced amplitudes in the sunspot at all frequencies, whereas a region of enhanced acoustic power above 5.5 mHz (above the quiet-Sun acoustic cutoff) is seen outside the sunspot and the plage region. This enhanced acoustic power has been suggested to be caused by the conversion of acoustic waves into magneto-acoustic waves that are refracted back into the interior and re-emerge as acoustic waves in the quiet Sun. Observations show that the sunspot absorbs a significant fraction of the incoming p and f modes around 3 mHz. A numerical simulation of MHD wave propagation through a simple model of AR 9787 confirmed that wave absorption is likely to be due to the partial conversion of incoming waves into magneto-acoustic waves that propagate down the sunspot. Wave travel times and mode frequencies are affected by the sunspot. In most cases, wave packets that propagate through the sunspot have reduced travel times. At short travel distances, however, the sign of the travel-time shifts appears to depend sensitively on how the data are processed and, in particular, on filtering in frequency-wavenumber space. We carry out two linear inversions for wave speed: one using travel-times and phase-speed filters and the other one using mode frequencies from ring analysis. These two inversions give subsurface wave-speed profiles with opposite signs and different amplitudes.The travel-time measurements also imply different subsurface flow patterns in the surface layer depending on the filtering procedure that is used. Current sensitivity kernels are unable to reconcile these measurements, perhaps because they rely on imperfect models of the power spectrum of solar oscillations. We present a linear inversion for flows of ridge-filtered travel times. This inversion shows a horizontal outflow in the upper 4 Mm that is consistent with the moat flow deduced from the surface motion of moving magnetic features.From this study of AR 9787, we conclude that we are currently unable to provide a unified description of the subsurface structure and dynamics of the sunspot.

We study the origin of the predictive skill of some methods to forecast the strength of solar activity cycles. A simple flux transport model for the azimuthally averaged radial magnetic field at the solar surface is used, which contains a source term describing the emergence of new flux based on observational sunspot data. We consider the magnetic flux diffusing over the equator as a predictor, since this quantity is directly related to the global dipole field from which a Babcock-Leighton dynamo generates the toroidal field for the next activity cycle. If the source is represented schematically by a narrow activity belt drifting with constant speed over a fixed range of latitudes between activity minima, our predictor shows considerable predictive skill with correlation coefficients up to 0.95 for past cycles. However, the predictive skill is completely lost when the actually observed emergence latitudes are used. This result originates from the fact that the precursor amplitude is determined by the sunspot activity a few years before solar minimum. Since stronger cycles tend to rise faster to their maximum activity (known as the Waldmeier effect), the temporal overlapping of cycles leads to a shift of the minimum epochs that depends on the strength of the following cycle. This information is picked up by precursor methods and also by our flux transport model with a schematic source. Therefore, their predictive skill does not require a memory, i.e., a physical connection between the surface manifestations of subsequent activity cycles.

Context. Chromospheric activity monitoring of a wide range of cool stars can provide valuable information on stellar magnetic activity and its dependence on fundamental stellar parameters such as effective temperature and rotation. Aims. We compile a chromospheric activity catalogue of 4454 cool stars from a combination of archival HARPS spectra and multiple other surveys, including the Mount Wilson data that have recently been released by the NSO. We explore the variation in chromospheric activity of cool stars along the main sequence for stars with different effective temperatures. Additionally, we also perform an activity-cycle period search and investigate its relation with rotation. Methods. The chromospheric activity index, S-index, was measured for 304 main-sequence stars from archived high-resolution HARPS spectra. Additionally, the measured and archived S-indices were converted into the chromospheric flux ratio log RHK'. The activity-cycle periods were determined using the generalised Lomb-Scargle periodogram to study the active and inactive branches on the rotation – activity-cycle period plane. Results. The global sample shows that the bimodality of chromospheric activity, known as the Vaughan-Preston gap, is not prominent, with a significant percentage of the stars at an intermediate-activity level around R'HK = −4.75. Independently, the cycle period search shows that stars can lie in the region intermediate between the active and inactive branch, which means that the active branch is not as clearly distinct as previously thought. Conclusions. The weakening of the Vaughan-Preston gap indicates that cool stars spin down from a higher activity level and settle at a lower activity level without a sudden break at intermediate activity. Some cycle periods are close to the solar value between the active and inactive branch, which suggests that the solar dynamo is most likely a common case of the stellar dynamo.

We model the surface magnetic field and open flux of the Sun from 1913 to 1986 using a surface flux transport model, which includes the observed cycleto-cycle variation of sunspot group tilts. The model reproduces the empirically derived time evolution of the solar open magnetic flux, and the reversal times of the polar fields. We find that both the polar field and the axial dipole moment resulting from this model around cycle minimum correlate with the strength of the following cycle.Subject headings:

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