An analysis of the solar differential rotation in solar cycle No. 19 (1954-1964) determined using Kanzelhoehe sunspot group positions

TL;DR

The paper analyzes solar differential rotation during solar cycle No. 19 (1954–1964) by tracing sunspot groups on Kanzelhoehe Observatory drawings, extending a prior KSO DR catalog to pre-1964 data. It employs two velocity methods, the daily-shift (DS) and robust linear least-squares (rLSQ), to derive synodic velocities, converts them to sidereal values, and fits the DR law $\omega(b) = A + B \sin^2 b$ to obtain $A$ and $B$ for the whole Sun and for each hemisphere. The study finds that $A$ is around 14.3–14.4 deg/day and $B$ around −2.1 to −2.9 deg/day, with KSO/KoSO/YNAO results largely in agreement, but GPR results showing significant differences in $A$; it also reports no statistically significant north–south asymmetry in cycle No. 19. These findings support consistent DR characterization across multiple independent datasets and demonstrate the value of filling long-term data gaps to inform solar dynamo studies, while suggesting further investigation into GPR inconsistencies. The work also highlights plans to complete a comprehensive KSO sunspot catalog (1944–today) for extended long-term analyses.

Abstract

We study solar differential rotation (DR) for solar cycle No. 19 (1954-1964) by tracing sunspot groups on the sunspot drawings of Kanzelhoehe Observatory for Solar and Environmental Research (KSO). Our aim is to extend previous DR analysis from the KSO data (1964-2016) to the years prior to 1964 to create a catalog of sunspot group positions and DR parameters from KSO sunspot drawings and white light images. Synodic angular rotation velocities were first determined using the daily shift (DS) and robust linear least-squares fit (rLSQ) methods, then converted to sidereal velocities, and used to derive solar DR parameters. We compare the DR parameters obtained from different sources and analyse the north-south asymmetry of rotation for solar cycle No. 19. It has been shown that our results for the equatorial rotation velocity (parameter A) and the gradient of DR (parameter B) coincide with earlier results from the KSO data (performed with a different method), as well as with results from the Kodaikanal Solar Observatory (KoSO) and the Yunnan Observatories (YNAO). In contrast, the values of parameter A from three different earlier studies based on the Greenwich Photoheliographic Results (GPR) exhibit statistically significant differences when compared to the values of parameter A derived from KSO, KoSO and YNAO. These findings suggest that the GPR data have the largest inconsistency compared to the other three data sources, highlighting the need for further analysis to identify the causes of these discrepancies. The analysis of the north-south asymmetry in the solar rotation profile using two different methods shows that the DR parameters of the hemispheres coincide, indicating a rotational symmetry around the equator. This is consistent with previous results from KSO and YNAO data. However, all sources indicate slightly higher equatorial rotation velocities in the southern hemisphere.

Figures (11)

• Figure 1: Example of the determination of the center of sunspot group 19134. The red dot indicates the determined position of the sunspot group's center.
• Figure 2: Part of the KSO sunspot drawing from November 26, 1958, with marked KSO (green) and GPR (blue) positions of the sunspot groups, that are measured only 8 minutes apart.
• Figure 3: Residuals of the DS sidereal rotation velocities against the explanatory variable - heliographic latitude $b$.
• Figure 4: A Q–Q plot of a sample of data (vertical axis) versus a Normal distribution (horizontal axis).
• Figure 5: Solar differential rotation profiles (black lines) from KSO sunspot groups data for solar cycle No. 19 (1954 – 1964), determined by: a) DS method (Table \ref{['table1']}, row 1) and b) rLSQ method (Table \ref{['table1']}, row 4). The mean values and standard deviations of the sidereal rotation rates within 2-degree bins are represented by the dots and error bars. Box-and-whisker plots show interquartile ranges for bins of unequal heliographic latitude “interval widths”, while keeping the number of sidereal velocities unchanged. The median values are marked with orange lines. Boxplots are scaled to 80% of the full width for clarity.