Inversions for Deep Solar Meridional Flow Using Spherical Born Kernels

Abstract

The solar meridional flow is a crucial ingredient in modern dynamo theory. Seismic estimates of this flow have, however, been contradictory in deeper layers below about 0.9 R . Results from timedistance helioseismology have so far been obtained using the ray approximation. Here, we perform inversions using the Born approximation. The initial result is similar to the result previously obtained by Jackiewicz et al. (2015) using ray kernels while using the same set of GONG data and the SOLA inversion technique. However, we show that the assumption of uncorrelated measurements used in earlier studies may lead to inversion errors being underestimated by a factor of about two to four. In a second step, refined inversions are performed using the full covariance matrix and a regularization for cross-talk. As the results are found to depend on the threshold used in the singular value decomposition, they were obtained for a medium threshold (10 −7 − 10 −5 , about 50% of the values used) and a threshold lower by a factor of 10 (about 70% of the values used). The result obtained with the medium threshold is again similar to the original, with less latitudinal variation. However, using the lower threshold, the inverted flow in the southern hemisphere shows two or three cells stacked radially depending on the associated radial flows. Both the single-cell and the multi-cell profiles are consistent with the measured travel times. All our results confirm a shallow return flow at about 0.9 R .

Nonkinematic solar dynamo models with double-cell meridional circulation

“…It is important no mention that the current results of the helioseismic inversions for the meridional circulation remains controversial For example, Rajaguru and Antia [72] found that the meridional circulation can be approximated by a single-cell structure with the return flow deeper than 0.77R . However, their results indicate an additional weak cell in the equatorial region, and contradict to the recent results of Böning et al [5] who confirmed a shallow return flow at 0.9R . Also, their results indicated that the upper meridional circulation cell extends close to the solar pole.…”

Solar meridional circulation from twenty-one years of SOHO/MDI and SDO/HMI observations

“…On closer inspection, this may incur an uncertainty of 0.01-0.03 s, for short distances in particular (see Appendix D). In this regard, a sophisticated inversion with kernels that take into account finite-wavelength effects (e.g., Böning et al 2017;Gizon et al 2017;Fournier et al 2018;Mandal et al 2018) is needed to correctly decipher the meaning of the measured traveltime shifts. It would be preferable to study the north-south asymmetry and other fine structures of meridional circulation by inversion instead of forward modeling.…”

“…Recently, a number of inconsistent helioseismic results were reported (Zhao et al 2013;Schad et al 2013;Jackiewicz et al 2015;Rajaguru & Antia 2015;Böning et al 2017;Chen & Zhao 2017;Lin & Chou 2018). The main reason is that helioseismic measurements suffer from a variety of systematic errors such as instrumental misalignment, the center-to-limb variation, and the influence of the surface magnetic field (e.g., Beck & Giles 2005;Zhao et al 2012;Liang & Chou 2015a).…”

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

“…In that case, we can only obtain an average meridional flow profile for the time period of the analysis. Improvements such as including full covariance matrix as Böning et al (2017) have suggested and accounting for line-of-sight effects (latter is only possible in wave-theoretic approach) is reserved for our future studies.…”