Measurement of Solar Differential Rotation by Absolutely Calibrated Iodine-Cell Spectroscopy

TL;DR

This study refines the measurement of solar differential rotation using iodine-cell spectroscopy by applying theoretical spectrum fitting and least squares analysis to improve accuracy and account for observational biases.

Contribution

It introduces a new analysis method that yields more precise heliocentric velocities and rotation parameters, addressing previous data reduction limitations.

Findings

Derived solar rotation law with specific coefficients

Confirmed gravitational redshift of 675 m/s

Highlighted impact of observation point distribution on results

Abstract

The iodine-cell technique, which is known to be efficient in precisely establishing Doppler velocity shifts, was once applied by the author to measuring the solar differential rotation based on full-disk spectroscopic observations (Takeda and Ueno, Sol. Phys. 270, 447, 2011). However, the data reduction procedure (in simple analogy with the stellar case) adopted therein was not necessarily adequate, because specific characteristic involved with the disk-resolved Sun (i.e., center-limb variation of line strengths) was not properly taken into consideration. Therefore, this problem is revisited based on the same data but with an application to theoretical spectrum fitting, which can yield absolute heliocentric radial velocities (v_obs) in a consistent manner as shown in the study of solar gravitational redshift (Takeda and Ueno, Sol. Phys. 281, 551, 2012). Likewise, instead of converting v_obs into omega (angular velocity) at each disk point, which suffers considerable errors especially near the central meridian, omega was derived this time by applying the least squares analysis to a dataset comprising v_obs values at many points. This new analysis resulted in omega (deg/day) = 13.92 (+/- 0.03) -1.69(+/- 0.34)(sin psi)^2 -2.37(+/- 0.62) (sin psi)^4 (psi: the heliographic latitude) along with the gravitational redshift of 675 m/s, which are favorably compared with previous publications. In addition, how the distribution of observing points on the disk affects the result is also examined, which reveals that rotation parameters may suffer appreciable errors depending on cases.