  Recent X-ray observations have detected a class of very faint X-ray
transients in the Galaxy which probably reveal a previously unrecognised type
of accretion on to neutron stars or black holes. We show that these systems
cannot have descended from binaries with stellar-mass components of normal
composition. Accretion of hydrogen-depleted matter on to stellar-mass black
holes can account for individual systems, but requires that these transients
should be observed to repeat within a few years, and does not explain why the
class is distinctly faint.
  Two other explanations appear to be quite natural. One invokes accretion by
neutron stars or stellar-mass black holes from companions which were already
brown dwarfs or planets when the systems formed, i.e. which did not descend
from low-mass stars. The other possibility is that these systems are the
endpoints of primordial (zero-metallicity) binaries in which the primary was
extremely massive, and collapsed to a black hole of mass > 1000 solar masses.
The (primordial) companion must by now have reached an extremely low mass (<
0.01 solar mass) and be transferring mass at a very low rate to the black hole.
This picture avoids the main difficulty encountered by models invoking
intermediate-mass black hole formation at non-primordial metallicities, and is
a natural consequence of some current ideas about Population III star
formation.
