5 Discussion

To determine the influence of large-scale flows on the inversion results, we use the observed average rotation rate as estimate of the true rotation rate. Observed mode splittings, derived from GONG or MDI time series, represent the solar rotation averaged over 108 days (shifted by 36 days) and 72 days respectively. As a consequence, the results of our numerical experiment represent large-scale flows with a life time of one or more solar rotations. Such a flow can have a maximum sectoral amplitude of about 10 m s^-1. Otherwise, it will lead to a noticeable distortion of the rotation rate in the convection zone in contradiction to the observations. This conclusion relies on the observed smoothness of the a-coefficients and the inferred rotation rate. Any break in the rotation rate introduced by a large scale flow field would be noticeable. Since no such breaks are observed, the "true'' solar rotation would have to precisely counteract the disrupting effect of the flow field which seems unlikely.

Zonal-meridional flows, as expected, have no direct influence on the rotation rate. However, a large zonal meridional flow can disrupt the structure of a multiplet and thus lead to a reduced coverage in the $(l,~\nu)$-diagram. We find that a large-scale flow can have a maximum zonal amplitude of about $u_{\rm char}=100$ m s^-1 without leading to noticeably reduced coverage. However, the even a_s-coefficients show the first indications of the flow field at about $u_{\rm char}= 10$ m s^-1. Thus our methods are similarly sensitive to flows in meridional and rotational direction.

Since the near-surface amplitude is much smaller than the maximum (cf., Fig. 6), this result is comparable to the most stringent constraint provided by previous surface observations which placed an upper limit of a few m s^-1 on the near-surface amplitude of giant cells (for example, LaBonte et al. 1981; Beck et al. 1998). Our results suggest that such long-lived large-scale structures do not exist in the convection zone of the Sun. This conclusion is supported by global simulations of the convection zone. Miesch et al. (2000) found that the convection structure is very time dependent in the turbulent case, making it difficult to identify any persistent features over the course of a full rotation. However, large-scale patterns with velocity amplitudes greater than 10 m s^-1 might exist on time scales of days to a few weeks. Long-lived large-scale patterns with amplitudes lower than 10  m s^-1, which are not ruled out by our result, might allow speculations about the origin of the recently reported dynamic variations with a 1.3  yr period at the base of the convection zone (Howe et al. 2000). There, the peak-to-peak variation of $\delta\Omega/2\pi$in the rotation rate at 0.72R is 6  nHz which corresponds to a variation in the velocity of $\approx$9  m s^-1. As this is of the order of the detectability limit of the inversions, we can speculate whether the physical background for these variations at the base of the convection zone are large-scale flows with a lifetime of 1.3  yr that affected the inversions for rotation rate in the same manner as the model flows did in our experiment.

The final answer about the existence of large-scale flows on the basis of global helioseismology data cannot be given, as long as it is not possible to invert for such flows. The difficulty is that in general the flow component in longitude cannot be disentangled from the rotation. However, we are able to derive some restrictions on the existence of large-scale cells. Only the meridional flows can be clearly separated from the rotation. Therefore our geometry parameterization of the flows was adequate to derive an estimate of the detectability of various large-scale flows. But more complicated flows within a cell impose different maximum amplitudes in different directions. Hence new numerical experiments are necessary to give a more detailed insight into the detectability of the various flow components in the convection zone. For the work presented, the details of the geometry (number of cells) make no difference, but there may be more subtle effects which we will study in a later investigation. Then, in the near future, we might be able to answer the question, whether there exist large-scale flows in the convection zone, e.g., whether there exists a return flow of the meridional surface flow at the base of the convection zone, and whether this return flow can be detected with this method on the basis of global helioseismic data.

Acknowledgements

M. Roth thanks M. Stix for helpful discussion on and interest in this work. M. Roth thanks the NSO/GONG staff for hospitality during the visits in Tucson. This work was supported by DFG Grant STI 65/9 and by NASA Grant S-92698-F. This work utilizes data obtained by the Global Oscillation Network Group (GONG) project, managed by the National Solar Observatory, which is operated by AURA, Inc. under a cooperative agreement with the National Science Foundation. The data were acquired by instruments operated by the Big Bear Solar Observatory, High Altitude Observatory, Learmonth Solar Observatory, Udaipur Solar Observatory, Instituto de Astrofísico de Canarias, and Cerro Tololo Interamerican Observatory.