Wavelet analysis of stellar differential rotation

Abstract

Among the several methods to study differential rotation on stellar surfaces the observation of a stellar butterfly diagram, i.e. monitoring the rotation period over a complete activity cycle, is the only method which canbe applied to stars rotating as slow as the Sun. However, the method requires active belts on the stellar surface which are moving continously in stellar latitude during a cycle. In addition, an appropriate activity tracer showing rotational modulation is needed. Tracers which even work for slowly rotating, i.e. weakly active, stars are the emission cores of certain spectral lines. However, the question is whether surface differential rotation can be determined from this kind of observations and furthermore, which method of analysis is best suited to yield a correct result. We investigate observations of the Sun as a star, i.e. disk-integrated measurements, to answer these questions. In a Paper I it was demonstrated that time-frequency analysis using the wavelet transform is possibly a suitable method for monitoring the stellar butterfly diagram. It was also shown that - in comparison with Fourier analysis - wavelet analysis of disk-integrated solar Ca II K line core emission measures yield a much more realistic pattern of the solar differential rotation. In this Paper II disk-integrated solar measures in Mg II h+k and Lyman a taken from public UARLS Solstice data are analysed using the same methods as in Paper I. In these data solar rotational modulation is much more pronounced than in earlier Ca II K time-series. Wavelet analysis yields the following results: from the beginning of the time-series in 1991 until the end of solar cycle 22 the period of rotational modulation remains stable at 26.9-27.0 days. It is followed by a jump to 27.6 days when the new cycle 23 starts. Then the period rapidly decreases to 26.9 days again until the end of the time-series in 1999. However, the analysis is hampered by frequent period splitting into two modes. It can be shown that this kind of splitting results from phase jumps in the time-series coming from active region growth and decay at 180° shifted solar longitudes.