Constraining cosmological topology via highly luminous X-ray clusters

The topology of the observable Universe is not yet known. The most significant observational sign of a non-trivial topology would be multiple images (``ghosts'') of a single object at (in general) different sky positions and redshifts. It is pointed out that the previous search by Gott (1980) for ghost images of the Coma cluster can be extended by using highly X-ray luminous clusters of galaxies. This is likely to be more efficient than with other astrophysical objects viewable on these scales since (1) X-ray clusters would be at least as easy to identify if viewed from other angles as any other objects and (2) the X-ray emitting thermally heated gas is likely to be simpler than for other objects. Possibilities that the highly luminous cluster RXJ~1347.5-1145 ($z=0\.45$) has a ``ghost image'' at lower redshift are analysed. It is noted that RXJ~1347.5-1145, the Coma cluster and the cluster CL~09104+4109 form nearly a right angle ($\approx 88\deg$) with arms of nearly identical length ($970h^{-1}$ and $960h^{-1}$ Mpc respectively) for $\Omega_0=1, \lambda_0=0$ curvature ($h\equiv H_0/100 kms^{-1} Mpc^{-1}$). This is a clue that the three clusters could be ghost images of one and the same cluster, for a hypertoroidal topology. However, several arguments are presented that this relation is not physical.