Lopsidedness of self-consistent galaxies by the external field effect of clusters

Adopting Schwarzschild's orbit-superposition technique, we construct a series of self-consistent galaxy models, embedded in the external field of galaxy clusters in the framework of Milgrom's MOdified Newtonian Dynamics. These models represent relatively massive ellipticals with a Hernquist radial profile at various distances from the cluster centre. Using $N$-body simulations, we perform a first analysis of these models and their evolution. We find that self-gravitating axisymmetric density models, even under a weak external field, lose their symmetry by instability and generally evolve to triaxial configurations. A kinematic analysis suggests that the instability originates from both box and non-classified orbits with low angular momentum. We also consider a self-consistent isolated system which is then placed in a strong external field and allowed to evolve freely. This model, just as the corresponding equilibrium model in the same external field, eventually settles to a triaxial equilibrium as well, but has a higher velocity radial anisotropy and is rounder. The presence of an external field in MOND universe generically predicts some lopsidedness of galaxy shapes.