  Contact binaries are close binary systems in which both components fill their
inner Roche lobes so that the stars are in direct contact and in potential mass
and energy exchange. The most common such systems of low-mass are the so-called
W UMa-type. In the last few years, there is a growing interest of the
astronomical community in stellar mergers, primarily due to the detection of
gravitational waves (mergers of black holes and neutron stars), but also
because of an alternative model for type Ia supernovae (merger of two white
dwarfs), which are again particularly important in cosmology where they played
an important role in the discovery of dark energy and the accelerated expansion
of the Universe. In that sense, contact systems of W UMa-type with extremely
low mass ratio are especially interesting because there are indications that in
their case, too, stars can merge and possible form fast-rotating stars such as
FC Com stars and the blue-stragglers, and (luminous) red novae such as V1309
Sco. Namely, previous theoretical research has shown that in the cases when the
orbital angular momentum of the system is only about three times larger than
the rotational angular momentum of the primary, a tidal Darwin's instability
occurs, the components can no longer remain in synchronous rotation, orbit
continue to shrink fast and they finally merge into a single star. The above
stability condition for contact systems can be linked to some critical mass
ratio below which we expect a system to be unstable. We give an overview of
this condition and show how it can be used to identify potential mergers.
Finally, we discuss a number of known extreme mass ratio binaries from the
literature and prospect for future research on this topic.
