  In recent years, a phenomenological solar wind heating model based on a
turbulent energy cascade prescribed by the Kolmogorov theory has produced
reasonably good agreement with observations on proton temperatures out to
distances around 70 AU, provided the effect of turbulence generation due to
pickup ions is included in the model. In a recent study [Ng et al., J. Geophys.
Res., 115, A02101 (2010)], we have incorporated in the heating model the energy
cascade rate based on Iroshnikov-Kraichnan (IK) scaling. We showed that the IK
cascade rate can also produce good agreement with observations, with or without
the inclusion of pickup ions. This effect was confirmed both by integrating the
model using average boundary conditions at 1 AU, and by applying a method
[Smith et al., Astrophys. J., 638, 508 (2006)] that uses directly observed
values as boundary conditions. The effects due to pickup ions is found to be
less important for the IK spectrum, which is shallower than the Kolmogorov
spectrum. In this paper, we will present calculations of the pickup ions effect
in more details, and discuss the physical reason why a shallower spectrum
generates less waves and turbulence.
