# Comparison of acoustic travel-time measurement of solar meridional circulation from SDO/HMI and SOHO/MDI

## TL;DR

This study compares solar meridional circulation measurements from SDO/HMI and SOHO/MDI, addressing systematic errors like P-angle offsets and center-to-limb effects to ensure consistent travel-time measurements across the solar convection zone.

## Contribution

It demonstrates that correcting for P-angle and center-to-limb effects aligns travel-time measurements from both instruments, highlighting the importance of systematic error correction in helioseismology.

## Key findings

- Corrected travel times from MDI and HMI are consistent within errors.
- P-angle offsets decrease with travel distance but affect deep measurements.
- Solar-origin fluctuations dominate the travel-time variations.

## Abstract

Time-distance helioseismology is one of the primary tools for studying the solar meridional circulation. However, travel-time measurements of the subsurface meridional flow suffer from a variety of systematic errors, such as a center-to-limb variation and an offset due to the P-angle uncertainty of solar images. Here we apply the time-distance technique to contemporaneous medium-degree Dopplergrams produced by SOHO/MDI and SDO/HMI to obtain the travel-time difference caused by meridional circulation throughout the solar convection zone. The P-angle offset in MDI images is measured by cross-correlating MDI and HMI images. The travel-time measurements in the south-north and east-west directions are averaged over the same observation period for the two data sets and then compared to examine the consistency of MDI and HMI travel times after correcting the systematic errors. The offsets in the south-north travel-time difference from MDI data induced by the P-angle error gradually diminish with increasing travel distance. However, these offsets become noisy for travel distances corresponding to waves that reach the base of the convection zone. This suggests that a careful treatment of the P-angle problem is required when studying a deep meridional flow. After correcting the P-angle and the removal of the center-to-limb effect, the travel-time measurements from MDI and HMI are consistent within the error bars for meridional circulation covering the entire convection zone. The fluctuations observed in both data sets are highly correlated and thus indicate their solar origin rather than an instrumental origin. Although our results demonstrate that the ad hoc correction is capable of reducing the wide discrepancy in the travel-time measurements from MDI and HMI, we cannot exclude the possibility that there exist other systematic effects acting on the two data sets in the same way.