The solar differential rotation in the 18th century

TL;DR

This study analyzes 18th-century sunspot drawings to estimate historical solar differential rotation, finding values consistent with the present Sun and suggesting possible temporal variations.

Contribution

It introduces a Bayesian method to determine solar differential rotation from historical, orientation-unknown sunspot drawings, providing a novel approach for historical solar studies.

Findings

Estimated .048 1 0.025 d for .048 1 0.025 d for .048 1 0.025 d for .048 1 0.025 d for the period.

No significant difference from the current Sun's differential rotation.

Weak, insignificant evidence of change in differential rotation over the 18th century.

Abstract

The sunspot drawings of Johann Staudacher of 1749--1799 were used to determine the solar differential rotation in that period. These drawings of the full disk lack any indication of their orientation. We used a Bayesian estimator to obtain the position angles of the drawings, the corresponding heliographic spot positions, a time offset between the drawings and the differential rotation parameter \delta\Omega, assuming the equatorial rotation period is the same as today. The drawings are grouped in pairs, and the resulting marginal distributions for \delta\Omega were multiplied. We obtain \delta\Omega=-0.048 \pm 0.025 d^-1 (-2.75^o/d) for the entire period. There is no significant difference to the value of the present Sun. We find an (insignificant) indication for a change of \delta\Omega throughout the observing period from strong differential rotation, \delta\Omega\approx -0.07 d^-1, to weaker differential rotation, \delta\Omega\approx-0.04 d^-1.