The fundamental plane of elliptical galaxies with modified Newtonian dynamics

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 M ∝ σ. This is consistent with the observed Faber-Jackson relation for elliptical galaxies. 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, 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 global 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 similar to that implied by the traditional virial theorem. Spherically symmetric N-body calculations demonstrate that objects resembling these idealized models would form naturally and early within the framework of a hypothetical MOND cosmology.