AAS 200th meeting, Albuquerque, NM, June 2002
Session 41. Clusters of Galaxies, Large Scale Structure
Display, Tuesday, June 4, 2002, 10:00am-6:30pm, SW Exhibit Hall

## [41.13] Are Massive Photons Needed to Bind the Coma Cluster?

D. F. Bartlett (University of Colorado at Boulder)

For believers in dark matter, the answer is clearly no. Zwicky (1933) postulated dark matter specifically to bind the Coma cluster with Newtonian gravitational forces. At the 199th Meeting I introduced a sinusoidal potential that alleviates the need for dark matter, particularly in spiral galaxies such as the Milky Way. This non-Newtonian potential satisfies the equation \nabla2\phi+k2\phi=4\pi\rho. The new potential excels in producing strong tidal forces but is inadequate to bind a large amorphous collection of galaxies. Here I make a complementary "non-Coulombic" proposal. The electrostatic potential satisfies \nabla2\phi -k2\phi=-4\pi\rho. The putative k's for the two potentials are identical. They are both k=2\pi/(Ro/20) =0.015 pc-1.

The proposed binding for Coma is not electric but magnetic. Maxwell's equations can be extended to accomodate a finite k and consequently a massive photon m\gamma=(h/2\pi)(k/c) (Goldhaber & Nieto 1971). The familiar expression for the magnetic energy density gains a new term: \Delta W/\Delta V =B2/8\pi + k2A2/8\pi =(B2/8\pi)(1+k2l2). Here A is the vector potential and l is the scale length for coherent magnetic fields. Maxwell's stress tensor is modified so that the added term gives a negative, and hence attractive, pressure (Chibisov 1976). Felten (1996) suggested that B should be about 10 times bigger than observed for [conventional] magnetic pressures to equal thermal. This factor may be provided instead by k and the length l = 1 kpc as observed by Feretti et al (1995).

This naive proposal is incompatible with both general relativity and gauge invariance. A complete quantized field theory is yet to be developed (Bartlett 2001). In the meantime the proposal offers astronomers the opportunity to make a variety of tests. Some will be discussed here.