Observational Analysis and Numerical Modeling of the Solar Wind Fluctuation Spectra during Intervals of Plasma Instability

We perform a statistical analysis of observed magnetic spectra in the solar wind at 1 au with localized power elevations above the level of the ambient turbulent fluctuations. We show that the elevations are seen only when the intensity of the ambient fluctuations is sufficiently low. Assuming that the spectral elevations are caused by thermal-ion instabilities, this suggests that on average the effect of the solar wind background is strong enough to suppress the instability or obscure it or both. We then carry out nonlinear numerical simulations with particle ions and an electron fluid to model a thermal-ion instability coexisting with an ambient turbulence. The parameters of the simulation are taken from a known solar wind interval where an instability was assumed to exist based on the linear theory and a bi-Maxwellian fit of the observed distribution with core and secondary-beam protons. The numerical model closely matches the position of the observed spectral elevation in the wavenumber space. This confirms that the thermal-ion instability is responsible for the elevation. At the same time, the magnitude of the elevation turns out to be smaller than in the real solar wind. When higher intensity of the turbulence is used in the simulation, which is typical of solar wind in general, the power elevation is no longer seen. This is in agreement with the reduced observability of the elevations at higher intensities. However, the simulations show that the turbulence does not simply obscure the instability but also lowers its saturation level.