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 (BCGs) may have passed each other 0.3 Gyr ago. Building upon previous investigations involving GMRT, VLA, and LOFAR data, our study focuses on two prominent extended radio relics at the north-west (NW) and south-east (SE) of the cluster core. By leveraging the high-resolution Chandra imaging, we have identified two distinct surface brightness edges at $\sim$ 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 hint the edges to be shock front edges. The Mach numbers, derived from the gas density jumps, yield $\cal{M}_{\rm SE}$ = 1.49$^{+0.22}_{-0.24}$ for the South Eastern shock and $\cal{M}_{\rm NW}$ = 1.41$^{+0.17}_{-0.19}$ for the North Western shock. Our estimated Mach numbers are remarkably smaller compared to those derived from radio observations ($\cal{M}_{\rm SE}$ = 2.3 and $\cal{M}_{\rm NW}$ = 2.4), highlighting the prevalence of a re-acceleration scenario over direct acceleration of electrons from the thermal pool. Furthermore, we compare the observed temperature profiles across both shocks with that of predictions from collisional vs. 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.