To: International Workshop on Aspects of Dark Matter in Astro- and Particle Physics. Organizers: Prof. H. V. Klapdor-Kleingrothaus, Dr. A. Mueller, Y. Ramachers; Max-Planck-Institut Kernphysik, Postfach 103 980, 69029 Heidelberg, Germany; Email:,; Tel.: (49) 6221-516-262, (49) 6221-516-259; Fax: (49) 6221-516-540.

From: Carl H. Gibson, Professor of Engineering Physics and Oceanography, Departments of Applied Mechanics and Scripps Institution of Oceanography, MC 0411, University of California at San Diego, La Jolla, CA, 92093-0411, USA, Tel: 619 534-3184, Fax: 619 534-7599, Email:, WWW:

Subject: Abstract submitted for International Dark Matter Workshop, Sept. 16-20, 1996.

Abstract Title: Evidence for self-gravitational condensation at the viscous-gravitational length scale rather than the Jeans acoustic-gravitational length scale, forming two classes of dark matter.

It is suggested that the acoustic Jeans self-gravitational condensation criterion is incomplete and misleading. Condensation on non-acoustic nuclei is limited by either viscous forces at the viscous Schwarz radius L_SV = ( gamma nu / rho G)^1/2 or by turbulence forces at the turbulent Schwarz radius L_ST = ( epsilon )^1/2 / ( rho G)^3/4 , depending on the Reynolds number, where gamma is the rate-of-strain, nu is the kinematic viscosity, rho is the density of the condensing fluid, G is Newton's gravitational constant, and epsilon is the viscous dissipation rate. By these new criteria, condensation of baryonic matter begins early (30,000 y) at 10^47 kg when L_SV = ct in the super-viscous plasma epoch, where c is the velocity of light and t is time, and decreases with further expansion and cooling. Upon plasma neutralization (300,000 years), the entire universe of relatively inviscid, weakly-turbulent gas condenses to form 10^22 kg "primordial fog particles" (PFPs). Most PFPs should persist as cold, compact, "black-dwarf" dark matter in galaxy halos, separated by 10^14 m from each other and 10^16 m from stars. The enormous effective diffusivity of WIMP (weakly interacting massive particle) fluid results in large L_SV scales, so that such material should condense very slowly, only on the largest structures, to form "superhalos" and "clusterhalos". Recent Hubble space telescope photographs support this model (see for Figures and References).