Solar differential rotation in the period 1964 - 2016 determined by the Kanzelh\"ohe data set

The main aim of this work is to determine the solar differential rotation by tracing sunspot groups during the period 1964-2016, using the Kanzelh\"ohe Observatory for Solar and Environmental Research (KSO) sunspot drawings and white light images. Two procedures for the determination of the heliographic positions were applied: an interactive procedure on the KSO sunspot drawings (1964 - 2008, solar cycles nos. 20 - 23) and an automatic procedure on the KSO white light images (2009 - 2016, solar cycle no. 24). For the determination of the synodic angular rotation velocities two different methods have been used: a daily shift (DS) method and a robust linear least-squares fit (rLSQ) method. Afterwards, the rotation velocities had to be converted from synodic to sidereal, which were then used in the least-squares fitting for the solar differential rotation law. For the test data from 2014, we found the rLSQ method for calculating rotational velocities to be more reliable than the DS method. The best fit solar differential rotation profile for the whole time period is $\omega(b)$ = (14.47 $\pm$ 0.01) - (2.66 $\pm$ 0.10) $\sin^2b$ (deg/day) for the DS method and $\omega(b)$ = (14.50 $\pm$ 0.01) - (2.87 $\pm$ 0.12) $\sin^2b$ (deg/day) for the rLSQ method. A barely noticeable north - south asymmetry is observed for the whole time period 1964 - 2016 in the present paper. Rotation profiles, using different data sets (e.g. Debrecen Photoheliographic Data, Greenwich Photoheliographic Results), presented by other authors for the same time periods and the same tracer types, are in good agreement with our results. Therefore, the KSO data set is suitable for the investigation of the long-term variabilities in the solar rotation profile

Variation in solar differential rotation and activity in the period 1964–2016 determined by the Kanzelhöhe data set

Aims. Theoretical calculations predict an increased equatorial rotation and more pronounced differential rotation (DR) during the minimum of solar magnetic activity. However, the results of observational studies vary, some showing less and some more pronounced DR during the minimum of solar magnetic activity. Our study aims to gain more insight into these discrepancies. Methods. We determined the DR parameters A and B (corresponding to the equatorial rotation velocity and the gradient of the solar DR, respectively) by tracing sunspot groups in sunspot drawings of the Kanzelhöhe Observatory for Solar and Environmental Research (KSO; 1964–2008, for solar cycles 20–23) and KSO white-light images (2009–2016, for solar cycle 24). We used different statistical methods and approaches to analyse variations in DR parameters related to the cycle and to the phase of the solar cycle, together with long-term related variations. Results. The comparison of the DR parameters for individual cycles obtained from the KSO and from other sources yield statistically insignificant differences for the years after 1980, meaning that the KSO sunspot group data set is well suited for long-term cycle to cycle studies. The DR parameters A and B show statistically significant periodic variability. The periodicity corresponds to the solar cycle and is correlated with the solar activity. The changes in A related to solar cycle phase are in accordance with previously reported theoretical and experimental results (higher A during solar minimum, lower A during the maximum of activity), while changes in B differ from the theoretical predictions as we observe more negative values of B, that is, a more pronounced differential rotation during activity maximum. The main result of this paper for the long-term variations in A is the detection of a phase shift between the activity flip (in the 1970s) and the equatorial rotation velocity flip (in the early 1990s), during which both A and activity show a secular decreasing trend. This indicates that the two quantities are correlated in between 1970 and 1990. Therefore, the theoretical model fails in the phase-shift time period that occurs after the modern Gleissberg maximum, while in the time period thereafter (after the 1990s), theoretical and experimental results are consistent. The long-term variations in B in general yield an anticorrelation of B and activity, as a rise of B is observed during the entire time period (1964–2016) we analysed, during which activity decreased, with the exception of the end of solar cycle 22 and the beginning of solar cycle 23. Conclusions. We study for the first time the variation in solar DR and activity based on 53 years of KSO data. Our results agree well with the results related to the solar cycle phase from corona observations. The disagreement of the observational results for B and theoretical studies may be due to the fact that we analysed the period immediately after the modern Gleissberg maximum, where for the phase-shift period, A versus activity also entails a result that differs from theoretical predictions. Therefore, studies of rotation versus activity with data sets encompassing the Gleissberg extremes should include separate analyses of the parts of the data set in between different flips (e.g., before the activity flip, between the activity and the rotation flip, and after the rotation flip)

Variation in solar differential rotation and activity in the period 1964-2016 determined by the Kanzelh\"ohe data set

We determined the differential rotation (DR) parameters $A$ and $B$ (corresponding to the equatorial rotation velocity and the gradient of the solar DR) by tracing sunspot groups in sunspot drawings of the Kanzelh\"ohe Observatory for Solar and Environmental Research (KSO; 1964-2008, for solar cycles (SC) 20-23) and KSO white-light images (2009-2016, for SC 24). We used different statistical methods and approaches to analyse cycle related variations, solar cycle phase-related variations and long-term variations of the DR. $A$ and $B$ show statistically significant periodic variability. The changes in $A$ related to solar cycle phase are in accordance with previously reported theoretical and experimental results (higher $A$ during solar minimum, lower $A$ during the maximum of activity), while changes in $B$ differ from the theoretical predictions as we observe more negative values of $B$, that is, a more pronounced DR during activity maximum. The main result of this paper for the long-term variations in $A$ is the detection of a phase shift between the activity flip (in the 1970s) and the equatorial rotation velocity flip (in the early 1990s). During this time period both $A$ and activity show a secular decreasing trend, indicating their correlation. Therefore, the theoretical model fails in the phase-shift time period that occurs after the modern Gleissberg maximum, while in the time period thereafter (after the 1990s), theoretical and experimental results are consistent. The long-term variations in $B$ in general yield an anticorrelation of $B$ and activity, as a rise of $B$ is observed during the entire time period (1964-2016) we analysed, during which activity decreased. We study for the first time the variation in solar DR and activity based on 53 years of KSO data. Our results agree well with the results related to the solar cycle phase from corona observations