Possible signature of solar oblateness in the Sun's oscillation frequency splittings

Departures from spherical symmetry split the frequencies of the Sun's normal oscillation modes. In addition to the well-studied, dominant splitting of the mode frequencies, due to the first-order advection of internal wave motion, a number of second-order effects of rotation on the frequency splittings, predominantly the solar oblateness, are expected. Whereas the largest rotational frequency splittings have an odd dependence on the azimuthal order, m, of the modes, the second-order effects should have an even dependence. The biggest, and thus far the only well-studied, even-m effect on splittings, is due to the solar-cycle variations in magnetic activity near the Sun's surface, which need to be modeled with some care to bring out the signature of solar oblateness. A crude analysis of the even mode-frequency splittings, obtained from approximately 15 years of SOHO/MDI spherical-harmonic time series, was undertaken. To extract the small even-m splittings of interest from the dominant, solar-cycle effects, which have a strong mode-frequency dependence, the former were assumed to depend only weakly on mode frequency and to have no time dependence. Perhaps the most important finding of the study is that the MDI data are capable of yielding statistically significant estimates of solar oblateness. Indeed the oblateness estimates obtained from the analysis presented here appear to be roughly consistent with both theoretical expectations and with direct measurements of the oblateness. There is also a hint of a pole-equator temperature difference in the seismic measurements, at the level recently suggested by Miesch and Hindman.