ON THE RELAXATION OF SUPERSTRING AXION MINI-CLUSTERS

Abstract

The cosmological axion theory leads to the prediction of axionic mini-clusters of mass M ~ 10-9M⊙, which form at the time t e of equipartition of matter and radiation. By applying the two-body relaxation formula of Spitzer and Hart, we show, for the heterotic superstring theory of Gross et al., that these mini-clusters, considered as point masses, themselves cluster into axion mini-stars of mass [Formula: see text] within the age of the Universe t0 only if they are located within a distance R ~ 0.1 pc of the Galactic Center. Here, λ ≡ fB/fA is the ratio of the second to model-independent axion decay constants, assuming the QCD decay constant to be in the range [Formula: see text], and [Formula: see text] is the strong-interaction coupling parameter. Thus, if axion mini-stars are to explain the microlensing observations by the EROS and MACHO groups towards the Galactic Bulge and the Large and Small Magellanic Clouds, then a collisionless relaxation mechanism is required, as proposed by Seidel and Suen (essentially the violent relaxation of Lynden–Bell), or the four-axion self-interaction effect considered by Tkachev.