  (To appear in the Astrophysical Journal) Holdom and Malaney (1994) have
suggested a mechanism for gamma-ray bursts which requires that stars be
captured by a neutrino ball. Neutrino balls would be, for the most part, denser
than main sequence stars, but their density would decrease as their mass
increased. We show that small neutrino balls would subject stars to tidal
forces sufficient to disrupt them. We thus argue that if neutrino balls existed
at the centres of galaxies, only the largest would be able to act as a source
of gamma-ray bursts. Such neutrino balls would have a mass of order
$10^7\Msun$. Tidal capture of stars by a neutrino ball would not be important,
but dynamical friction against the neutrinos or star-disc interactions could
both be important capture mechanisms. We find that a gamma-ray burst would
occur in a galaxy containing such a neutrino ball roughly every $10^2\y$, and
the fraction of all galaxies contributing to the gamma-ray burst flux would be
$\sim 10^{-4}$, assuming that this was the mechanism of all gamma-ray bursts.
These numbers have implications for neutrino ball models of active galaxies,
assuming that all gamma-ray bursts and all AGN come from neutrino balls. Either
a small fraction $\sim 10^{-2}$ of the lifetime of such an object could be
spent as an AGN, or that the probability of a neutrino ball becoming an AGN
would be $10^{-2}$. It is not possible to rule out the possibility that
neutrino balls might exist at the centres of galaxies through direct
ground-based observation of stellar kinematics.
