Asymmetric supernova explosions and the formation of short period low-mass X-ray binaries

We consider the formation of short period low-mass X-ray binaries using standard evolutionary scenario which involves a common envelope phase and a supernova explosion. We consider three models of systems and assume several values of the efficiency factor for the common envelope evolution (alpha_ {CE). In most cases the systems can only be formed if the neutron stars in the systems receive a kick velocity at their birth. We determine the lower and upper limits of the required kick velocity as a function of alpha_ {CE. Larger kicks are required to form shorter orbital period systems. Higher alpha_ {CE also requires larger kicks. In general, the required kick velocity is of the order of a few hundred kms(-1) with a maximum of ~ 1000 kms(-1) . The range of the required kick velocity is narrower for higher alpha_ {CE.