  In this paper, we present two observations about static spherically symmetric
solutions of the Einstein-Klein-Gordon equations. The first is a comment
extending the well-known result of the existence of static states (i.e.
standing wave solutions) of the Einstein-Klein-Gordon equations. The second
more important observation shows that, in the low field limit, the mass
profiles of these static states lie along hyperbolas of constant $\Upsilon$,
the fundamental constant of the Einstein-Klein-Gordon equations.
