A Systematic Study of Hale and Anti-Hale Sunspot Physical Parameters

We present a systematic study of sunspot physical parameters using full disk magnetograms from MDI/SoHO and HMI/SDO. Our aim is to use uniform datasets and analysis procedures to characterize the sunspots, paying particular attention to the differences and similarities between "Hale" and "anti-Hale" spots. Included are measurements of the magnetic tilt angles, areas, fluxes and polarity pole separations for 4385 sunspot groups in Cycles 23 and 24 each measured, on average, at $\sim$66 epochs centered on meridian-crossing. The sunspots are classified as either "Hale" or "anti-Hale", depending on whether their polarities align or anti-align with Hale's hemispheric polarity rule. We find that (1) The "anti-Hale" sunspots constitute a fraction ($8.1\pm0.4$)\% of all sunspots, and this fraction is the same in both hemispheres and cycles, (2) "Hale" sunspots obey Joy's law in both hemispheres and cycles but "anti-Hale" sunspots do not. Three equivalent forms of Joy's law are derived, $\sin\gamma=(0.38\pm0.05)\sin\phi$, $\gamma=(0.39\pm0.06)\phi$, and $\gamma=(23.80\pm3.51)\sin\phi$, where $\gamma$ is the tilt angle and $\phi$ is the heliospheric latitude, (3) The average Hale sunspot tilt angle is $\overline{\gamma} = 5.49^\circ\pm0.09$, (4) The tilt angles, magnetic fluxes and pole separations of sunspots are interrelated, with larger fluxes correlated with larger pole separations and smaller tilt angles. We present empirical relations between these quantities. Cycle 24 is a much weaker cycle than Cycle 23 in sunspot numbers, cumulative magnetic flux, and average sunspot magnetic flux. The "anti-Hale" sunspots are also much weaker than "Hale" sunspots in those parameters, but they share similar magnetic flux distributions and average latitudes. We characterize the two populations, and aim to shed light on the origin of "anti-Hale" sunspots.