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We present LOFAR $120-168$ MHz images of the merging galaxy cluster Abell1240 that hosts double radio relics. In combination with the GMRT $595-629$ MHzand VLA $2-4$ GHz data, we characterised the spectral and polarimetricproperties of the radio emission. The spectral indices for the relics steepenfrom their outer edges towards the cluster centre and the electric fieldvectors are approximately perpendicular to the major axes of the relics. Theresults are consistent with the picture that these relics trace large-scaleshocks propagating outwards during the merger. Assuming diffusive shockacceleration (DSA), we obtain shock Mach numbers of $\mathcal{M}=2.4$ and $2.3$for the northern and southern shocks, respectively. For $\mathcal{M}\lesssim3$shocks, a pre-existing population of mildly relativistic electrons is requiredto explain the brightness of the relics due to the high ($>10$ per cent)particle acceleration efficiency required. However, for $\mathcal{M}\gtrsim4$shocks the required efficiency is $\gtrsim1\%$ and $\gtrsim0.5\%$,respectively, which is low enough for shock acceleration directly from thethermal pool. We used the fractional polarization to constrain the viewingangle to $\geqslant(53\pm3)^\circ$ and $\geqslant(39\pm5)^\circ$ for thenorthern and southern shocks, respectively. We found no evidence for diffuseemission in the cluster central region. If the halo spans the entire regionbetween the relics ($\sim1.8\,\text{Mpc}$) our upper limit on the power is$P_\text{1.4 GHz}=(1.4\pm0.6)\times10^{23}\,\text{W}\text{Hz}^{-1}$ which isapproximately equal to the anticipated flux from a cluster of this mass.However, if the halo is smaller than this, our constraints on the power implythat the halo is underluminous.

Radio observations of the double-relic galaxy cluster Abell 1240