On the Particle Acceleration Mechanisms in a Double Radio Relic Galaxy Cluster, Abell 1240

We present a 368 ks deep Chandra observation of Abell 1240, a binary merging galaxy cluster at a redshift of 0.195 with two brightest cluster galaxies that may have passed each other 0.3 Gyr ago. Building upon previous investigations involving Giant Metrewave Radio Telescope, Very Large Array, and LOFAR data, our study focuses on two prominent extended radio relics at the northwest (NW) and southeast (SE) of the cluster core. By leveraging the high-resolution Chandra imaging, we have identified two distinct surface-brightness edges at similar to 1 Mpc and 1.2 Mpc NW and SE of the cluster center, respectively, coinciding with the outer edges of both relics. Our temperature measurements suggest the edges to be shock front edges. The Mach numbers, derived from the gas density jumps, yield MSE = 1.49-0.24+0.22 for the SE shock and MNW = 1.41-0.19+0.17 for the NW shock. Our estimated Mach numbers are remarkably smaller compared to those derived from radio observations ( MSE = 2.3 and MNW = 2.4), highlighting the prevalence of a reacceleration scenario over direct acceleration of electrons from the thermal pool. Furthermore, we compare the observed temperature profiles across both shocks with those of predictions from collisional versus collisionless models. Both shocks favor the Coulomb collisional model, but we could not rule out a purely collisionless model due to pre-shock temperature uncertainties.