Machian MOND: a variable a ₀ in galaxy clusters

Modified Newtonian Dynamics (MOND) generally resolves the need for dark matter in galaxy rotation curves introducing a single new constant of acceleration [Formula: see text]. It is well known that increasing [Formula: see text] by a factor of a few can alleviate the residual mass discrepancies that MOND leaves in galaxy clusters. Within a parameter-free Machian interpretation of MOND, in which [Formula: see text] arises from the scalar sum of inverse-square distance gravitational mass contributions in the universe, we promote [Formula: see text] to a variable influenced by mass external to a locally enclosed region in the spherically symmetric case. Instead of a boost of [Formula: see text] in terms of gravitational potentials as in EMOND, we show that a boost in terms of this directionless inverse-square field roughly amounts to the boost needed to accommodate the mass discrepancies of MOND in galaxy clusters. We conclude by beginning to generalize the proposed formulation beyond spherical symmetry.