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Solar wave-field simulation for testing prospects of helioseismic measurements of deep meridional flows

The meridional flow in the Sun is an axisymmetric flow that is generally poleward directed at the surface, and is presumed to be of fundamental importance in the generation and transport of magnetic fields. Its true shape and strength, however, is debated. We present a numerical simulation of helioseismic wave propagation in the whole solar interior in the presence of a prescribed, stationary, single-cell, deep meridional circulation serving as a test-bed for helioseismic measurement techniques. A deep-focusing time-distance helioseismology technique is applied to the artificial data showing that it can in fact be used to measure the effects of the meridional flow very deep in the solar convection zone. It is shown that the ray-approximation which is commonly used for interpretation of helioseismology measurements remains a reasonable approximation even for the very long distances between 12 and 42 degrees corresponding to depths between 52 and 195 Mm considered here. From the measurement noise we extrapolate that on the order of a full solar cycle may be needed to probe the flow all the way to the base of the convection zone.