Inferring the Solar Meridional Circulation Flow Profile by Applying Bayesian Methods to Time-Distance Helioseismology

Mapping the large-scale subsurface plasma flow profile within the Sun has been attempted using various methods for several decades. One such flow in particular is the meridional circulation, for which numerous studies have been published. However, such studies often show disagreement in structure. In an effort to constrain the flow profile from the data, a Bayesian Markov chain Monte Carlo framework has been developed to take advantage of the advances in computing power that allow for the efficient exploration of high-dimensional parameter spaces. This study utilizes helioseismic travel-time difference data covering a span of 21 years and a parameterized model of the meridional circulation to find the most likely flow profiles. Tests were carried out on artificial data to determine the ability of this method to recover expected solar-like flow profiles, as well as a few extreme cases. We find that this method is capable of recovering the input flows of both single- and double-cell flow structures. Some inversion results indicate potential differences in meridional circulation between the two solar cycles in terms of both magnitude and morphology, in particular in the mid-convection zone. Of these, the most likely solutions show that solar cycle 23 has a large single-celled profile, while cycle 24 shows weaker flows in general and hints toward a double-celled structure.