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

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 1 month of SDO/HMI line-of-sight magnetic field observations, combined with the Southwest Automatic Magnetic Identification Suite magnetic feature-tracking code 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-resolution (2° bins) differential rotation measurements with well-characterized variances and covariances of the fit parameters. I find a sidereal rotational profile of (14.296 ± 0.006) + (−1.847 ± 0.056)sin² b + (−2.615 ± 0.093) sin⁴ b, with units of deg day⁻¹, and a large covariance σ _BC ² = −4.87 × 10⁻³(deg day⁻¹)². I also produce measurements of the much weaker meridional flow that are broadly consistent with previous results. These measurements exhibit a peak flow of 16.7 ± 0.6 m s⁻¹ at latitude b = 45° but are insufficiently characterized at higher latitudes to ascertain whether the chosen functional form $2\cos b\sin b$ is appropriate. This work demonstrates 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.