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Abstract

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 pericentre passage, however,
the subcluster is decelerated by the gravity of the main cluster, while the shock continues
moving away from the cluster centre. 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 R₅₀₀, gas density profiles are as
steep as, or steeper than, ∼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.