No evidence that solar wind turbulence can be described by the critical balance theory

The critical balance theory (GS, Goldreich and Sridhar, 1995) in MHD turbulence seems now to be well accepted in the turbulence community. During recent years, quite a few papers claimed to have provided evidence in support of this theory by solar wind turbulence observations. Here we present new data that result in a different conclusion, namely that the previous observations cannot be considered as evidence for the GS theory. It is based on the critical balance assumption that the parallel Alfven wave propagation time equals the perpendicular cascade time, k⊥v⊥=k//VA. Assuming that the cascading energy flux does not change with scale, a spectral index of -2 is obtained for the parallel power spectrum P(k//). To check this theoretical prediction, small sampling angle (θRB) with the mean magnetic field averaged at the local time and the local scale is used for selecting the local power spectral densities (PSDs). We recovered that the so averaged PSDs at different scales have a nearly -2 slope. However, using 30 days of Ulysses data we discovered that the critical balance assumption was invalid in the corresponding data analysis. The values of δB/B0 corresponding to the selected local PSDs are all found to be much smaller than the required value of tan(θRB). Most of the observations with a small sampling angle may be considered to be rather more perpendicular from the theoretical point of view. We also found that the spectral index of the selected PSDs depends on the selection criterion. If one guarantees constantly small sampling angles in a local time period, the slope of the selected PSD changes to -1.7. Thus our conclusion is that no evidence exists that solar wind turbulence can be described by the GS theory. What is the true origin of the spectral anisotropy of the solar wind turbulence remains an important open question.