The effect of Poisson statistics on studies of turbulence in the solar wind

Abstract

Studies of Alfvén turbulence in the solar wind require the use of magnetic field and particle data. However, particle data is subject to a source of noise not present in magnetic field data, i.e. statistical noise because the bulk parameters of the plasma are calculated from a finite number of counts. The derivation of bulk parameters is unavoidably affected by Poisson statistics which add variance to the real value. The magnitude of the effects of Poisson noise on the frequency spectrum of Alfvén waves in the solar wind has been calculated by numerical simulation for the case of cometary pickup ion turbulence observed at comet Halley. The results show that Poisson noise is “white” and flattens the frequency spectrum at high frequencies, where its power spectral density exceeds the solar wind turbulence. If a power law is fitted to the spectrum, the power law index can be reduced significantly even if the flattening is not obvious in the spectrum, and the effect can be significant even when the particle count rates seem high. In Elsässer variable studies the influence of Poisson noise is seen as a tendency to equality of the two spectra at high frequencies since each contains uncorrelated noise. The simulations show that Poisson noise effects must be taken into account in the interpretation of Alfvén wave observations. A concrete result is that the difference between the spectral indices obtained separately from magnetic and particle data at comet Halley can be explained quantitatively by Poisson noise.