We present a new 400ks Chandra X-ray observation and a GMRT radio observation at 325MHz of the merging galaxy cluster Abell 2146. The Chandra observation reveals detailed structure associated with the major merger event including the Mach M=2.1+/-0.2 bow shock located ahead of the dense subcluster core and the first known example of an upstream shock (M=1.6+/-0.1). Surprisingly, the deep GMRT observation at 325MHz does not detect any extended radio emission associated with either shock front. All other merging galaxy clusters with X-ray detected shock fronts, including the Bullet cluster, Abell 520, Abell 754 and Abell 2744, and clusters with candidate shock fronts have detected radio relics or radio halo edges coincident with the shocks. We consider several possible factors which could affect the formation of radio relics, including the shock strength and the presence of a pre-existing electron population, but do not find a favourable explanation for this result. We calculate a 3sigma upper limit of 13mJy on extended radio emission, which is significantly below the radio power expected by the observed P_{radio}-L_{X} correlation for merging systems. The lack of an extended radio halo in Abell 2146 maybe due to the low cluster mass relative to the majority of merging galaxy clusters with detected radio halos.
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