Divergence and Vorticity of Subsurface Flows During Solar Cycles 23 and 24

We study the solar-cycle variation of the divergence and vorticity of subsurface horizontal flows from the surface to a depth of 16 Mm. The flows were derived with ringdiagram analysis applied to Michelson Doppler Imager (MDI) Dynamics Program, Global Oscillation Network Group (GONG), and Helioseismic and Magnetic Imager (HMI) Dopplergrams. We study their variation for the complete data set and for two subsets representing active and quiet regions. All three data sets show alternating bands of diverging and converging flows and bands of cyclonic and anticyclonic flows moving from mid-latitudes toward the equator during a solar cycle. For Solar Cycle 24, these bands are precursors of the magnetic activity appearing several years before magnetic activity is present at a given latitude even leading the fast bands of the flows. The amplitude differences between the cyclonic and anticyclonic and the converging and diverging bands during a solar cycle agree within the error bars between the complete data set and the two subsets. For Solar Cycle 24, the amplitude differences are 6.0 +/- 0.7 10(-8) s(-1) for the bands of vorticity and -4.9 +/- 0.6 10(-8) s(-1) for those of divergence averaged over 2.0 - 11.6 Mm using the complete data set. The amplitude differences of Solar Cycle 23 are 26 +/- 3% smaller than those of Solar Cycle 24. The flows of the active-region subset are more converging and cyclonic than those of the quiet-region subset with an extra vorticity of 1.3 +/- 0.1 10(-8) s(-1) and an extra divergence of -6.7 +/- 0.3 10(-8) s(-1) averaged over 7.5 degrees-30 degrees and all depths and epochs. The amplitude of the extra divergence of active regions is about a factor of 1.3 larger at depths shallower than 6 Mm and decreases with increasing depth, while the extra vorticity is nearly constant with depth.