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Adopting Schwarzschild's orbit-superposition technique, we construct a seriesof self-consistent galaxy models, embedded in the external field of galaxyclusters in the framework of Milgrom's MOdified Newtonian Dynamics. Thesemodels represent relatively massive ellipticals with a Hernquist radial profileat various distances from the cluster centre. Using $N$-body simulations, weperform a first analysis of these models and their evolution. We find thatself-gravitating axisymmetric density models, even under a weak external field,lose their symmetry by instability and generally evolve to triaxialconfigurations. A kinematic analysis suggests that the instability originatesfrom both box and non-classified orbits with low angular momentum. We alsoconsider a self-consistent isolated system which is then placed in a strongexternal field and allowed to evolve freely. This model, just as thecorresponding equilibrium model in the same external field, eventually settlesto a triaxial equilibrium as well, but has a higher velocity radial anisotropyand is rounder. The presence of an external field in MOND universe genericallypredicts some lopsidedness of galaxy shapes.

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