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Evolution of Magnetic Fields in Corotating Interaction Regions from 1 to 95 AU: Order to Chaos

We discuss the large-scale heliospheric magnetic field strength fluctuations as a function of distance from the Sun during the declining phase of a solar cycle, based on a one-dimensional, MHD, three-fluid model with observations made at 1 AU during 1995 as input. We consider daily averages of the magnetic field strength, B, as a function of time for a ≈1 year interval. The model predicts that B(t) is quasi-periodic, and that the amplitudes of fluctuations in B relative to the yearly average of B (⟨B⟩) are relatively large between 5 and 20 AU ("the corotating merged interaction region zone," or CMIR zone). The model predicts that the fluctuations are aperiodic and that their amplitudes are relatively small between 30 and 95 AU (the "wave interaction region zone"). It predicts a transition between these two zones at ≈25 AU. These results are consistent with a conceptual model proposed by Burlaga in 1983 for the declining phase of the solar cycle. In the CMIR zone, neighboring CMIRs merge in a sequence of events that defines a topological tree. The model predicts the following statistical properties of the fluctuations in B/⟨B⟩ for the declining phase of a solar cycle in the CMIR zone: (1) the power spectrum of B/⟨B⟩ has a prominent peak at 26 days and a secondary peak at 13 days; (2) the distribution of B/⟨B⟩ has no simple form; and (3) the standard deviation (SD) of B/⟨B⟩ is relatively large and has a maximum of 1.2 at 10 AU. In the wave interaction zone, (1) the spectrum has no significant peak, and the power level at 26 days is an order of magnitude smaller than in the CMIR zone; (2) the distribution of B/⟨B⟩ is approximately lognormal; and (3) the SD(B/⟨B⟩) is nearly constant, ≈0.48. The SD(B/⟨B⟩) versus R shows that the transition between the CMIR and the wave interaction zones is at ≈25 ± 5 AU. The results of the model are consistent with the Voyager 1 (V1) observations near 15 and 55 AU during 1983 and 1994, respectively. During the declining phase of solar cycle 23, in ≈2003-2005, Voyager 2 (V2) will move from 69 to 76 AU while V1 moves from 87 to 95 AU. The model makes the following predictions for the properties of B between 65 and 95 AU: (1) B(t) will be aperiodic, with relatively low amplitude fluctuations similar to those observed at 55 AU; (2) the power spectra will resemble those observed near 55 AU, and there will be little radial variation in the power at the solar rotation period, 26 days; (3) the distribution of B will be approximately lognormal; (4) the SD(B) of the daily averages of B will be ≈0.48⟨B⟩; and (5) the tail of the distribution of B will be exponential.