• gravitation;
  • galaxies: elliptical and lenticular, cD;
  • galaxies: fundamental parameters;
  • galaxies: kinematics and dynamics;
  • dark matter

The modified Newtonian dynamics (MOND), suggested by Milgrom as an alternative to dark matter, implies that isothermal spheres with a fixed anisotropy parameter should exhibit a near-perfect relation between the mass and velocity dispersion of the form Mσ 4. This is consistent with the observed Faber–Jackson relation for elliptical galaxies: a luminosity–velocity dispersion relation with large scatter. However, the observable global properties of elliptical galaxies comprise a three-parameter family; they lie on a ‘fundamental plane’ in a logarithmic space consisting of central velocity dispersion, effective radius (re) and luminosity. The scatter perpendicular to this plane is significantly less than that about the Faber–Jackson relation. I show here that, in order to match the observed properties of elliptical galaxies with MOND, models must deviate from being strictly isothermal and isotropic; such objects can be approximated by high-order polytropic spheres with a radial orbit anisotropy in the outer regions. MOND imposes boundary conditions on the inner Newtonian regions which restrict these models to a dynamical fundamental plane of the form where the exponents may differ from the Newtonian expectations (α=2, γ=1). Scatter about this plane is relatively insensitive to the necessary deviations from homology.