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

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 2011). However, the data reduction procedure (in simple analogy with the stellar case) adopted therein was not necessarily adequate, because a 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 (\(v_{\mathrm{obs}}\)) in a consistent manner as shown in the study of solar gravitational redshift (Takeda and Ueno 2012). Likewise, instead of converting \(v_{\mathrm{obs}}\) into \(\omega \) (angular velocity) at each disk point, which suffers considerable errors especially near the central meridian, \(\omega \) is derived this time by applying the least squares analysis to a dataset comprising \(v_{\mathrm{obs}}\) values at many points. This new analysis resulted in \(\omega \) (deg day⁻¹) = \(13.92 (\pm 0.03) -1.69(\pm 0.34)\sin ^{2}\psi -2.37(\pm 0.62) \sin ^{4}\psi \) (\(\psi \): the heliographic latitude) along with the gravitational redshift of 675 m s⁻¹, 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.