# Measurements of Solar Differential Rotation and Meridional Circulation from Tracking of Photospheric Magnetic Features

## TL;DR

This study uses magnetic feature tracking in SDO/HMI data to accurately measure solar differential rotation and meridional flow, providing high-fidelity insights into solar surface dynamics over a short observational period.

## Contribution

It introduces a method combining magnetic feature tracking with control for short-lived flow perturbations to produce precise measurements of solar surface flows.

## Key findings

- Measured solar differential rotation profile with high precision.
- Detected broad meridional flow consistent with previous studies.
- Demonstrated the effectiveness of feature tracking for short-term flow analysis.

## Abstract

Long-lived rotational and meridional flows are important ingredients of the solar cycle. Magnetic field images have typically been used to measure these flows on the solar surface by cross-correlating thin longitudinal strips or square patches across sufficiently long time gaps. Here, I use one month of SDO/HMI line-of-sight magnetic field observations, combined with the SWAMIS magnetic feature tracking algorithm to measure the motion of individual features in these magnetograms. By controlling for perturbations due to short-lived flows and due to false motions from feature interactions, I effectively isolate the long-lived flows traced by the magnetic features. This allows me to produce high-fidelity differential rotation measurements with well-characterized variances and covariances of the fit parameters.I find a sidereal rotational profile of $(14.296\pm0.006)+(-1.847\pm0.056)\sin^{2}b+(-2.615\pm0.093)\sin^{4}b$, with units of $\textrm{ deg d}^{-1}$, and a large covariance $\sigma_{BC}^{2}=-4.87\times10^{-3}(\textrm{ deg d}^{-1})^{2}$. I also produce medium-fidelity measurements of the much weaker meridional flow that is broadly consistent with previous results. This measurement shows a peak flow of $16.7\pm0.6\text{ m s}^{-1}$ at latitude $b=45^\circ$ but is insufficiently characterized at higher latitudes to ascertain whether the chosen functional form $2\cos b\sin b$ is appropriate. This work shows that measuring the motions of individual features in photospheric magnetograms can produce high precision results in relatively short time spans, and suggests that high resolution non-longitudinally averaged photospheric velocity residual measurements could be produced to compare with coronal results, and to provide other diagnostics of the solar dynamo.