Authors: Jiaming Wang (University of Delaware), Francesco Pecora (University of Delaware), Rohit Chhiber (NASA Goddard Space Flight Center), William H. Matthaeus (University of Delaware)

The scale-invariant 1/f spectrum, first identified in voltage fluctuations of vacuum tubes, has since been observed across a wide range of systems, including heart rate fluctuations and loudness patterns in musical compositions. In the solar wind at 1 au, the interplanetary magnetic field trace spectrum is known to exhibit 1/f scaling at frequencies below approximately 1e-3 Hz. We present a comprehensive analysis of the 1 au magnetic field correlation and power spectrum, using 12 years of continuous observations (1998-2009) from the Advanced Composition Explorer (ACE) mission, covering a full solar cycle. Autocorrelation functions are computed with sufficient statistical weight for lags up to 3.6 years, allowing detailed examination of the ultra-low-frequency regime of the magnetic power spectrum. We find that the radial and tangential magnetic field components exhibit persistent oscillations with an approximately 27-day periodicity, corresponding to the synodic solar rotation period at the equator. The normal component, in contrast, shows no clear periodic behavior. The resulting trace spectrum reveals a clear 1/f region, extending from below the solar rotation frequency to approximately 1e-4 Hz, which then gradually transitions into the Kolmogorov -5/3 inertial range turbulence spectrum. Additional analyses are performed for different solar wind regimes – including slow wind, fast wind, solar minimum, and solar maximum – revealing substantial differences in their respective correlation and spectral characteristics. The generation mechanism and place of origin of the interplanetary 1/f noise have been longstanding subjects of debate. Our results suggest that the low-frequency 1/f signals cannot be readily explained by local interplanetary dynamics, and therefore likely originate below the solar corona and possibly in the solar dynamo.