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

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 $(14.296\pm 0.006)+(-1.847\pm 0.056){\sin }^{2}b+(-2.615\pm 0.093){\sin }^{4}b$, with units of ${\text{ deg d}}^{-1}$, and a large covariance ${\sigma }_{BC}^2=-4.87\times 10^{-3}({\text{ deg d}}^{-1}{)}^2$. 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 $16.7\pm 0.6{\text{ m s}}^{-1}$ 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.

Accepted by ApJ. 24 pages, 9 figures

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