  We comparatively studied the long-term variation (1992-2017) in polar
brightening observed with the Nobeyama Radioheliograph, the polar solar wind
velocity with interplanetary scintillation observations at the Institute for
Space-Earth Environmental Research, and the coronal hole distribution computed
by potential field calculations of the solar corona using synoptic magnetogram
data obtained at Kitt Peak National Solar Observatory. First, by comparing the
solar wind velocity (V) and the brightness temperature (T_b) in the polar
region, we found good correlation coefficients (CCs) between V and T_b in the
polar regions, CC = 0.91 (0.83) for the northern (southern) polar region, and
we obtained the V-T_b relationship as V =12.6 (T_b-10,667)^{1/2}+432. We also
confirmed that the CC of V-T_b is higher than those of V-B and V-B/f, where B
and f are the polar magnetic field strength and magnetic flux expansion rate,
respectively. These results indicate that T_b is a more direct parameter than B
or B/f for expressing solar wind velocity. Next, we analyzed the long-term
variation of the polar brightening and its relation to the area of the polar
coronal hole (A). As a result, we found that the polar brightening matches the
probability distribution of the predicted coronal hole and that the CC between
T_b and A is remarkably high, CC = 0.97. This result indicates that the polar
brightening is strongly coupled to the size of the polar coronal hole.
Therefore, the reasonable correlation of V-T_b is explained by V-A. In
addition, by considering the anti-correlation between A and f found in a
previous study, we suggest that the V-T_b relationship is another expression of
the Wang-Sheeley relationship (V-1/f) in the polar regions.
