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Time-distance helioseismology: A new averaging scheme for measuring flow vorticity

Time-distance helioseismology provides information about vector flows in the near-surface layers of the Sun by measuring wave travel times between points on the solar surface. Specific spatial averages of travel times have been proposed for distinguishing between flows in the east-west and north-south directions and measuring the horizontal divergence of the flows. No specific measurement technique has, however, been developed to measure flow vorticity. Here we propose a new measurement technique tailored to measuring the vertical component of vorticity. Fluid vorticity is a fundamental property of solar convection zone dynamics and of rotating turbulent convection in particular. The method consists of measuring the travel time of waves along a closed contour on the solar surface in order to approximate the circulation of the flow along this contour. Vertical vorticity is related to the difference between clockwise and counter-clockwise travel times. We applied the method to characterize the vortical motions of solar convection using helioseismic data from the Helioseismic and Magnetic Imager onboard the Solar Dynamics Observatory (SDO/HMI) and from the Michelson Doppler Imager onboard the Solar and Heliospheric Observatory (SOHO/MDI). Away from the equator, a clear correlation between vertical vorticity and horizontal divergence is detected. Horizontal outflows are associated with negative vorticity in the northern hemisphere and positive vorticity in the southern hemisphere. The signal is much stronger for HMI than for MDI observations. We characterize the spatial power spectrum of the signal by comparison with a noise model. Vertical vorticity at horizontal wavenumbers below 250/R_Sun can be probed with this helioseismic technique.