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Astron. Astrophys. 323, 231-234 (1997)

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2. Comparison of LOWL and BBSO data on the Sun's asymmetry

The most complete set of even-a coefficients are from BBSO data, Libbrecht & Woodard (1990) and Woodard and Libbrecht (1991). These data are observations from the 1986 activity minimum, as well as the years of 1988, 1989, and 1990 during which the Sun's activity climbed to its most recent maximum. Very large changes in these coefficients were detected among the four sets. The new data discussed in this paper are the even-a coefficients from the LOWL instrument, Tomczyk et al. (1995). The data were taken between Feb. 1994 and Feb. 1995-a period of low solar activity.

Libbrecht & Woodard (1990) showed that the l -dependence of the [FORMULA] coefficients is given by [FORMULA], where I denotes mode inertia which is evaluated assuming constant values of the radial displacement at the base of the photosphere. They noted that the inverse proportionality to the inertia implies that the perturbation giving rise to the frequency shifts described by the even-a coefficients must be located well above the lower turning point for nearly all modes in their data set, which means the outer layers of the Sun spanning at most a few percent of the radius.

Here we represent the even-a coefficients in the form


where the [FORMULA] describe the contribution of the second order effect of rotation to the fine structure and the [FORMULA] are functions which we determine. The same form was used by Dziembowski & Goode (1996), who analysed the full set of the BBSO data, and our form differs from that used by Libbrecht & Woodard (1990) in two respects. Firstly, the effect of centrifugal distortion, which is significant only for [FORMULA], is taken into account. Secondly, a [FORMULA] dependence in the [FORMULA] 's is allowed. If [FORMULA], each [FORMULA] -coefficient arises almost solely from the [FORMULA] component of the perturbation (e.g. Gough, 1988).

The centroid frequencies from the LOWL instrument were used by Basu et al. (1996) to infer the internal structure. The odd-a 's were used by Tomczyk, Schou and Thompson (1995) to determine the rotation in the Sun's deep interior. Here we determine the [FORMULA] 's for the LOWL data and compare them in Fig. 1 to those obtained from the BBSO data by Dziembowski and Goode (1996). The LOWL data contain modes ranging from l =5 to 99. while the BBSO data range from 5 to 140.

[FIGURE] Fig. 1. From top panel to bottom [FORMULA], [FORMULA] and [FORMULA] are shown as a function of mode frequency for the 1986, 1988, 1989 and 1990 BBSO data. [FORMULA] and [FORMULA] for the LOWL data are shown in the top two panels. The normalization of the radial displacement amplitude at the base of the photosphere was chosen to be 3 [FORMULA]. With such a normalization, the mode inertia in Eq. (2) is of order unity for modes of frequency near 3 mHz. The least-square error bars are shown for the BBSO 89 data.

The important thing to notice in Fig. 1 is that the LOWL [FORMULA] 's nearly co-incide with those from the 1986 BBSO data, and that only [FORMULA] differs significantly from zero. These two data sets are from periods of low solar activity. We see a drastically different pattern in the [FORMULA] 's from years of high activity.

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© European Southern Observatory (ESO) 1997

Online publication: June 5, 1998