The low-frequency power spectrum of slow solar wind turbulence

An important challenge in the accurate estimation of power spectra of plasma fluctuations in the solar wind at very low frequencies is that it requires extremely long signals, which will necessarily contain a mixture of qualitatively different solar wind streams, such as fast and slow winds, different magnetic polarities, or a mixture of compressible and incompressible fluctuations, along with other transient structures. This mixture of streams with qualitatively different properties unavoidably affects the structure of the power spectra by conflating all these different properties into a single power spectrum. In this work, we present a conditional statistical analysis that allows us to accurately estimate the power spectrum, at arbitrarily low frequencies, for ``pure'' slow solar wind streams, defined as those for which the solar wind speed is below $500 The conditional analysis is based on the estimation of autocorrelation functions (ACF) of arbitrarily long but discontiguous signals, which result from excluding portions of the signal that do not satisfy the required properties. We use numerical simulations of magnetohydrodynamic (MHD) turbulence and magnetic field signals from the spacecraft to test the estimator's convergence to its true ensemble-averaged counterpart. Finally, we use this methodology on a fourteen-year-long data interval to obtain the magnetic power spectrum of slow wind at extremely low frequencies. We show, for the first time, a full $1/f$ range in the slow wind, with a low-frequency spectral break below which the spectrum flattens and exhibits a well-defined peak at the solar rotation frequency.