  The unexpected temperature evolution of the neutron star in the Cassiopeia A
supernova remnant (Cas A, for short) has renewed tremendous interest in the
cooling mechanisms of neutron stars. In particular, the formation of
superconducting protons and superfluid neutrons deep inside the cores of
neutron stars have become focal points of the discussion. The purpose of this
letter is to add a new aspect to this discussion, which focuses on the
connection between proton superconductivity and the masses of neutron stars.
  Assuming (as is currently the case) that the temperature evolution of Cas A
is largely controlled by superconducting protons, we study a series of
phenomenological proton-pairing models to determine how deep into the stellar
core superconducting protons actually penetrate. This allows us to establish a
heretofore unknown relationship between the mass of the neutron star in Cas A
and the penetration depth of the superconducting proton phase. This
relationship can be used to either predict the depth of the superconducting
proton phase, or, conversely, determine the mass of Cas A from a reliable
calculation of the size of the proton superconducting phase in superdense
neutron star matter. We emphasize that the strategy outlined in this paper can
be applied to any other neutron star of similar age, whose temperature might be
reliably monitored over a several years period. High-mass neutron stars, such
as the recently discovered neutron stars J1614-2230 ($1.97 \pm 0.04\, \msun$)
and J0348+0432 ($2.01 \pm 0.04 \, \msun$), appear particularly appealing as a
significant fraction of the protons in their cores may be superconducting.
