Solar meridional circulation from twenty-one years of SOHO/MDI and SDO/HMI observations: Helioseismic travel times and forward modeling in the ray approximation

Context. The solar meridional flow is an essential ingredient in flux-transport dynamo models. However, no consensus on its subsurface structure has been reached. Aims. We merge the data sets from SOHO/MDI and SDO/HMI with the aim of achieving a greater precision on helioseismic measurements of the subsurface meridional flow. Methods. The south-north travel-time differences are measured by applying time-distance helioseismology to the MDI and HMI medium-degree Dopplergrams covering May 1996-April 2017. Our data analysis corrects for several sources of systematic effects: P-angle error, surface magnetic field effects, and center-to-limb variations. For HMI data, we used the P-angle correction provided by the HMI team based on the Venus and Mercury transits. For MDI data, we used a P-angle correction estimated from the correlation of MDI and HMI data during the period of overlap. The center-to-limb effect is estimated from the east-west travel-time differences and is different for MDI and HMI observations. An interpretation of the travel-time measurements is obtained using a forward-modeling approach in the ray approximation. Results. In the latitude range 20°-35°, the travel-time differences are similar in the southern hemisphere for cycles 23 and 24. However, they differ in the northern hemisphere between cycles 23 and 24. Except for cycle 24's northern hemisphere, the measurements favor a single-cell meridional circulation model where the poleward flows persist down to ∼0.8 R, accompanied by local inflows toward the activity belts in the near-surface layers. Cycle 24's northern hemisphere is anomalous: Travel-time differences are significantly smaller when travel distances are greater than 20°. This asymmetry between northern and southern hemispheres during cycle 24 was not present in previous measurements, which assumed a different P-angle error correction where south-north travel-time differences are shifted to zero at the equator for all travel distances. In our measurements, the travel-time differences at the equator are zero for travel distances less than ∼30°, but they do not vanish for larger travel distances. This equatorial offset for large travel distances need not be interpreted as a deep cross-equator flow; it could be due to the presence of asymmetrical local flows at the surface near the end points of the acoustic ray paths. Conclusions. The combined MDI and HMI helioseismic measurements presented here contain a wealth of information about the subsurface structure and the temporal evolution of the meridional circulation over 21 years. To infer the deep meridional flow, it will be necessary to model the contribution from the complex time-varying flows in the near-surface layers.