Inferences of the deep solar meridional flow

Understanding the solar meridional flow is important for uncovering the origin of the solar activity cycle. Yet, recent helioseismic estimates of this flow have come to conflicting conclusions in deeper layers of the solar interior, i.e., at depths below about 0.9 solar radii.

The aim of this thesis is to contribute to a better understanding of the deep solar meridional flow. Time-distance helioseismology is the major method for investigating this flow. In this method, travel times of waves propagating between pairs of locations on the solar surface are measured. Until now, the travel-time measurements have been modeled using the ray approximation, which assumes that waves travel along infinitely thin ray paths between these locations. In contrast, the scattering of the full wave field in the solar interior due to the flow is modeled in first order by the Born approximation. It is in general a more accurate model of the physics in the solar interior.

In a first step, an existing model for calculating the sensitivity of travel-time measurements to solar interior flows using the Born approximation is extended from Cartesian to spherical geometry. The results are succesfully compared to the Cartesian ones and are tested for self-consistency.

In a second step, the newly developed model is validated using an existing numerical simulation of linear wave propagation in the Sun. An inversion of artificial travel times for meridional flow shows excellent agreement for noiseless data and reproduces many features in the input flow profile in the case of noisy data.

Finally, the new method is used to infer the deep meridional flow. I used Global Oscillation Network Group (GONG) data that were earlier analyzed using the ray approximation and I employed the same Substractive Optimized Local Averaging (SOLA) inversion technique as in the earlier study. Using an existing formula for the covariance of travel-time measurements, it is shown that the assumption of uncorrelated errors from earlier studies leads to errors in the inverted flows being underestimated by a factor of about two to four.

The inverted meridional flow above about 0.85 solar radii confirms the earlier results from ray theory regarding the general pattern of the flow, especially regarding a shallow return flow at about 0.9 solar radii, with some differences in the magnitude of the flow.

Below about 0.85 solar radii, the inversion result depends on the thresholds used in the singular value decomposition. One result is again similar to the original regarding its general single-cell shape. Other results show a multi-cell structure in the southern hemisphere with two or three cells stacked radially. However, both the single-cell and the multi-cell flow profiles are consistent with the measured travel times within the measurement errors.

To reach an unambiguous conclusion on the meridional flow below about 0.85 solar radii, the errors in the measured travel times have to be decreased considerably in future studies. For now, I conclude that the existing controversy of recent measurements of the deep meridional flow is relaxed by properly taking the associated errors into account.