The covariance of latitudinal and longitudinal motions of small magnetic features

Abstract

We study the covariance of longitudinal and latitudinal motions of small magnetic features after subtracting long-term averages of differential rotation and meridional flow. The covariance is generally interpreted as Reynolds stress and linked to the equatorward transport of angular momentum. Using high-resolution magnetograms taken daily with the NSO Vacuum Telescope on Kitt Peak, we determine large-scale motions by a two-dimensional crosscorrelation analysis of pairs of consecutive daily observations from which active regions are excluded, i.e., we analyze the motions of small magnetic features. In the present work, we focus on 107 day pairs obtained during the year 1988 and on 472 day pairs taken in selected intervals from 1978 to 1990. We find that all covariance values are very small (below 250 m² s⁻²), which is about one to two orders of magnitude smaller than the values from sunspot measurements derived by other authors. At active region latitudes, the masking process increases the noise, which increases the chance that the covariances at these latitudes are not significantly different from zero. We find that the results depend strongly on the temporal averaging involved. Daily unaveraged crosscorrelations lead to no apparent correlation between the residual velocities, while in the monthly averages of the 1988 data, we find a covariance of −37 ± 15 m² s⁻² at 45° with a linear correlation of −0.59, which is significantly different from zero and has the right sign for an equatorial transport of angular momentum. When we average over longer time periods, the covariance values decrease again. The annual averages of the 1978–1990 data show both no significant covariances and the smallest errors. These small covariances imply that the motions of small magnetic features do not reflect the transport of angular momentum via the mechanism of Reynolds stress.