In this study, we search for large-scale, long-lived structures in the
convection zone by using global helioseismology results combined with
quasi-degenerate perturbation theory and numerical simulations. We
concentrate on changes in the 
coverage, the multiplets,
and the inversion results and derive detectability limits for the
velocity of large-scale structures.
The motivation for this study is two-fold. On the one hand, the internal structure of the Sun has been determined with increasing accuracy within the last few years. Especially with the availability of high-quality helioseismic data the properties of the differential rotation and its depth dependence have been studied in great detail by inverting oscillation data. Because of the improving resolution of the solar interior, it is necessary to know about smaller effects of physical processes in the sun on the solar oscillations and their influences on the inversion results.
One of these processes inside the sun is the possible effect of large-scale convection cells on the solar p-modes. It has been shown by perturbation theory how to solve the forward problem to calculate the influence of toroidal and poloidal velocity fields on the oscillations (Lavely & Ritzwoller 1992). The calculations that deal with the zonal toroidal flows representing the differential rotation have been used to develop inversion methods (Schou et al. 1998). But, so far, there exists no inversion method that based on global helioseismic data is able to determine large-scale poloidal or non-zonal toroidal flow components inside the convection zone. Therefore our investigation might be helpful in developing such inversion methods.
On the other hand the search for large-scale flows, other than solar rotation, in the convection zone has the potential to improve our understanding of the dynamics of the solar convection zone. The hypothesis that convective elements larger than supergranulation exist goes back about 40 years. Simon & Weiss (1968) postulated according to mixing length theory that the largest possible convective pattern extends over the depth of the convection zone, the so-called giant cells. However, such a pattern has not been observed unambiguously despite an extensive search by several groups (for example, Schröter et al. 1978; LaBonte et al. 1981; Cram et al. 1983; Robillot et al. 1984; Bertello & Restaino 1993). Recently, Beck et al. (1998) reported observing long-lived cells elongated in longitude with amplitudes of few m s-1, while Ulrich (2001) interprets a similar pattern as higher-order components of the banded zonal-flow pattern (also known as torsional oscillations). Hathaway et al. (2000) concluded that giant cells do not exist as a distinct mode of convection. Current global simulations of the convection zone (Elliott et al. 2000; Miesch et al. 2000) show large-scale flow patterns that are more complex than simple rolls or banana-shaped cells. Local helioseismology techniques, such as ring diagrams (for example, Haber et al. 2000), are presently limited to near surface layers and cannot be used to determine flows throughout the whole convection zone. Therefore our contribution can help to search for distinct modes of convection, to restrict the parameter space for the numerical simulations and to develop more powerful methods to determine flows within the deeper layers of the convection zone.
In our attempt to detect large-scale flows with global helioseismic data we concentrate on the application of quasi-degenerate perturbation calculations. Following Lavely & Ritzwoller (1992), Roth & Stix (1999) show that poloidal flow components cause small additional frequency shifts compared to the influence of the differential rotation. In order to learn more about the strength of the effect of large-scale flows in the convection zone and their possible detectability, we will use quasi-degenerate perturbation theory to calculate the frequencies of oscillations that are influenced by both differential rotation and large-scale poloidal velocity fields. These artificial frequencies are inverted for differential rotation by the same RLS (Regularized Least Squares) inversion method used for inverting data from the Global Oscillation Network Group (GONG), for example by Howe et al. (2000). This allows us to derive an upper limit for the significance of the poloidal flow field, depending on its amplitude and geometry, which is of the order of 10 m s-1.
Copyright ESO 2002