He explained the theory that our Sun may have a twin star moving in an
huge elliptical orbit and may be held responsible for the mass extinction of the dinosaurs.
Here is a very good description of Nemesis which I found on WIKI:
Suppose our Sun was not alone but had a companion star. Suppose that this companion star moved in an elliptical orbit, its solar distance varying between 90,000 a.u. (1.4 light years) and 20,000 a.u., with a period of 30 million years. Also suppose this star is dark or at least very faint, and because of that we haven't noticed it yet.
This would mean that once every 30 million years that hypothetical companion star of the Sun would pass through the Oort cloud (a hypothetical cloud of proto-comets at a great distance from the Sun). During such a passage, the proto-comets in the Oort cloud would be stirred around. Some tens of thousands of years later, here on Earth we would notice a dramatic increase in the the number of comets passing the inner solar system. If the number of comets increases dramatically, so does the risk of the Earth colliding with the nucleus of one of those comets.
When examining the Earth's geological record, it appears that about once every 30 million years a mass extinction of life on Earth has occurred. The most well-known of those mass extinctions is of course the dinosaur extinction some 65 million years ago. About 25 million years from now it's time for the next mass extinction, according to this hypothesis.
This hypothetical "death companion" of the Sun was suggested in 1985 by Daniel P. Whitmire and John J. Matese, Univ of Southern Louisiana. It has even received a name: Nemesis. One awkward fact of the Nemesis hypothesis is that there is no evidence whatever of a companion star of the Sun. It need not be very bright or very massive, a star much smaller and dimmer than the Sun would suffice, even a brown or a black dwarf (a planet-like body insufficiently massive to start "burning hydrogen" like a star). It is possible that this star already exists in one of the catalogues of dim stars without anyone having noted something peculiar, namely the enormous apparent motion of that star against the background of more distant stars (i.e. its parallax). If it should be found, few will doubt that it is the primary cause of periodic mass extinctions on Earth.
Some scientists thought this Nemesis theory was a joke when they first heard of it -- an invisible Sun attacking the Earth with comets sounds like delusion or myth. It deserves an additional dollop of skepticism for that reason: we are always in danger of deceiving ourselves. But even if the theory is speculative, it's serious and respectable, because its main idea is testable: you find the star and examine its properties.
There are programs running where astronomers are searching for the star. If the deamon star exists, we will surely know within the next two years.