A Comprehensive Method to Measure Solar Meridional Circulation and Center-to-Limb Effect Using Time-Distance Helioseismology

Meridional circulation is a crucial component of the Sun's internal dynamics, but its inference in the deep interior is complicated by a systematic center-to-limb effect in helioseismic measurement techniques. Previously, an empirical method, removing travel-time shifts measured for east-west traveling waves in the equatorial area from those measured for north-south traveling waves in the central meridian area, was used, but its validity and accuracy need to be assessed. Here we develop a new method to separate the center-to-limb effect, \delta\tau_CtoL, and meridional-flow-induced travel-time shifts, \delta\tau_MF, in a more robust way. Using 7-yr observations of the SDO/HMI, we exhaustively measure travel-time shifts between two surface locations along the solar disk's radial direction for all azimuthal angles and all skip distances. The measured travel-time shifts are a linear combination of \delta\tau_CtoL and \delta\tau_MF, which can be disentangled through solving the linear equation set. The \delta\tau_CtoL is found isotropic relative to the azimuthal angle, and the \delta\tau_MF are then inverted for the meridional circulation. Our inversion results show a three-layer flow structure, with equatorward flow found between about 0.82 and 0.91 R_sun for low latitude areas and between about 0.85 and 0.91 R_sun for higher latitude areas. Poleward flows are found below and above the equatorward flow zones, indicating a double-cell circulation in each hemisphere.