Runaway Merger Shocks in Galaxy Cluster Outskirts and Radio Relics
  Moderately strong shocks arise naturally when two subclusters merge. For
instance, when a smaller subcluster falls into the gravitational potential of a
more massive cluster, a bow shock is formed and moves together with the
subcluster. After pericenter passage, however, the subcluster is decelerated by
the gravity of the main cluster, while the shock continues moving away from the
cluster center. These shocks are considered as promising candidates for
powering radio relics found in many clusters. The aim of this paper is to
explore the fate of such shocks when they travel to the cluster outskirts, far
from the place where the shocks were initiated. In a uniform medium, such a
"runaway" shock should weaken with distance. However, as shocks move to large
radii in galaxy clusters, the shock is moving down a steep density gradient
that helps the shock to maintain its strength over a large distance.
Observations and numerical simulations show that, beyond $R_{500}$, gas density
profiles are as steep as, or steeper than, $\sim r^{-3}$, suggesting that there
exists a "Habitable zone" for moderately strong shocks in cluster outskirts
where the shock strength can be maintained or even amplified. A characteristic
feature of runaway shocks is that the strong compression, relative to the
initial state, is confined to a narrow region just behind the shock. Therefore,
if such a shock runs over a region with a pre-existing population of
relativistic particles, then the boost in radio emissivity, due to pure
adiabatic compression, will also be confined to a narrow radial shell.
