Gao, J. JACoW Publishing Geneva, Switzerland In this paper, we will discuss analytical estimation of the beam beam limited dynamic aperture and lifetimes, which are very important for modern electron positron designs and operations, such as CEPC and FCCee, super Tau Charm factories, Super KEK B and BEPC-II, etc. This dicussion is in complementary to the beam beam limit discussion from the beam beam heating induced diffussion effect. The combination of the two effects from beam-beam interaction, i.e. nonlinear beam beam induced dynamic aperture limitation effect and the heating induced diffusion effect, makes the discussion of beam beam effect complete.