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

Abstract

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, δτ CtoL , and meridional-flow-induced travel-time shifts, δτ 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 δτ CtoL and δτ MF , which can be disentangled through solving the linear equation set. The δτ CtoL is found isotropic relative to the azimuthal angle, and the δτ 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 ⊙ for low latitude areas and between about 0.85 and 0.91 R ⊙ for higher latitude areas. Poleward flows are found below and above the equatorward flow zones, indicating a double-cell circulation in each hemisphere.

Helioseismic Inversion to Infer the Depth Profile of Solar Meridional Flow Using Spherical Born Kernels

“…Using 2 years of GONG data, Jackiewicz et al (2015) obtained results that agreed with Zhao et al (2013) about the shallow return flow but could not find the second cell in the deeper convection zone. Recently, Chen & Zhao (2017) using 7 years of SDO/HMI data covering 2010 May 1 to 2017 April 30 found qualitatively similar profile as Zhao et al (2013). These studies did not apply the mass conservation constraint.…”

“…Liang & Chou (2015) have demonstrated that not removing surface magnetic regions affects the travel time measurements. We have accounted for local mass conservation and also employed Born kernels, whereas Chen & Zhao (2017) have not considered mass conservation and used ray kernels. Braun & Birch (2008) have shown that in order to infer the depth profile of a weak signal like the solar meridional flow in the entire convection zone, many years of data are needed.…”

“…These W-E travel times are estimated from the central W-E equatorial belt spanning 15 degrees on either side of the equator. Recently, Chen & Zhao (2017) have proposed a new empirical method to remove the systematics. They measure travel-time shifts between two points located on the solar disk for many different azimuthal angles and skip distances, followed by solving a system of linear equations containing both center-to-limb systematics and travel-time shifts due to meridional flow.…”

“…They measure travel-time shifts between two points located on the solar disk for many different azimuthal angles and skip distances, followed by solving a system of linear equations containing both center-to-limb systematics and travel-time shifts due to meridional flow. In addition, Chen & Zhao (2017) have removed data pixels containing fields stronger than a threshold of 10 G, following a method suggested by Liang & Chou (2015). In our travel-time measurement process, we have not removed the oscillation signals over the strongly magnetized surface regions.…”

Effect of Magnetic Field Strength on Solar Differential Rotation and Meridional Circulation

“…The same can be said of the meridional circulation. Chen & Zhao (2017) studied the internal meridional flow profiles. They found that the flow velocity decreases linearly by 30% with depth around 0.975 R sun and is almost constant from 0.975 to 0.95R sun .…”