On the relationship between coronal heating, magnetic flux, and the density of the solar wind

The stark differences between the current solar minimum and the previous one offer a unique opportunity to develop new constraints on mechanisms for heating and acceleration of the solar wind. We have used a combination of numerical simulations and analysis of remote solar and in situ observations to infer that the coronal heating rate, H, scales with the average magnetic field strength within a coronal hole, B-ch. This was accomplished in three steps. First, we analyzed Ulysses measurements made during its first and third orbit southern and northern polar passes (i.e., during near-solar minimum conditions) to deduce a linear relationship between proton number density (n(p)) and radial magnetic field strength (B-r) in the high-speed quiescent solar wind, consistent with the results of McComas et al. (2008) and Ebert et al. (2009). Second, we used Wilcox Solar Observatory measurements of the photospheric magnetic field to show that the magnetic field strength within coronal holes (B-ch) is approximately correlated with the strength of the interplanetary field at the location of Ulysses. Third, we used hydrodynamic simulations to show that n(p) in the solar wind scales linearly with H. Taken together, these results imply the chain: H proportional to n(p) proportional to B-r proportional to B-ch. We also explored ideas that the correlation between n(p) and B-r could have resulted from interplanetary processes, or from the superradial expansion of the coronal magnetic field close to the Sun, but find that neither possibility can produce the observed relationship. The derived heating relationship is consistent with (1) empirical heating laws derived for closed-field line regions and (2) theoretical models aimed at understanding both the heating and acceleration of the solar wind.