## 3. The near surface magnetic perturbation determined from BBSO dataLibbrecht and Woodard (1990) extracted the The data of Libbrecht and Woodard went through several preliminary
iterations of which they generously provided us the results. The BBSO
data we use in this paper are from their final iteration. The four
sets of observations were made in the middle of 1986, 1988, 1989 and
1990, respectively. Each of these data sets spans Our purpose here is to derive information about the near surface
perturbation, and use it to evaluate its effect on low- where the describe the contribution of the
second order effect of rotation to the fine structure and next term
describes the near surface perturbation. The The form of the near surface contribution to even- The -coefficients are
-dependent because the radial eigenfunctions are strong functions of
the mode frequency. The angular integral defining the term The where In this limit, contributes only to
coefficient, Goode and Kuhn(1990). This
approximation is applicable to the set of modes we consider. It
doesn't work perfectly for the lowest Our objective is to find the functions, . To this end, we discretize each function by a three term Legendre expansion of argument where and are the maximum and minimum frequencies in the data and . We determine the coefficients by a least squares fitting. The resulting 's are shown in Fig. 3. In the uppermost panel, we show describing the centroid shift relative to 1986. The quantity -the spherically symmetric part of the magnetic perturbation-cannot be observationally determined. We emphasize that only the coefficient differs significantly from zero in the 1986 data, and that this term corresponds to a quadrupole toroidal field geometry for the near surface perturbation.
One may compare the 's for 1986 and 1988 in Fig. 3 to their counterparts in Fig. 1 of Dziembowski and Goode (1991). In doing so, we stress that the 's defined in the latter paper incorporated the factor. Beyond this, there are only slight differences between the two sets of results. The changes in frequency are linked to the activity cycle. Woodard et al. (1991) have observed that the frequency changes are correlated with the surface magnetic activity on a timescale of months. That leaves no room for doubt that the frequencies reflect magnetic changes occuring in the outer layers. Precisely how this occurs is unclear. Whether it is due to a changing fibril structure or whether there is a role for a subsurface velocity field remains to be seen. Henceforth, we denote the near surface perturbation varying with activity as NSPA. We make this distinction not only to emphasize the fact that we are studying this effect, but also that the NSPA is different from any other near surface effect, like that due to vigorous convection. The -dependence of results from the fact that the radial eigenfunctions in the outer layers vary significantly with frequency. The fact that the frequency dependence in all the 's is as weak as it is in Fig. 3 argues for a localization of the perturbing agent very close to the photosphere where the radial eigenfunctions have been uniformly normalized. © European Southern Observatory (ESO) 1997 Online publication: July 8, 1998 |