The enigmatic pair of dwarf galaxies Leo IV and Leo V: coincidence or
  common origin?
  We have obtained deep photometry in two 1x1 degree fields covering the close
pair of dwarf spheroidal galaxies (dSph) Leo IV and Leo V and part of the area
in between. We find that both systems are significantly larger than indicated
by previous measurements based on shallower data and also significantly
elongated. With half-light radii of r_h=4'.6 +- 0'.8 (206 +- 36 pc) and
r_h=2'.6 +- 0'.6 (133 +- 31 pc), respectively, they are now well within the
physical size bracket of typical Milky Way dSph satellites. Their ellipticities
of epsilon ~0.5 are shared by many faint (M_V>-8) Milky Way dSphs. The large
spatial extent of our survey allows us to search for extra-tidal features with
unprecedented sensitivity. The spatial distribution of candidate red giant
branch and horizontal branch stars is found to be non-uniform at the ~3 sigma
level. This substructure is aligned along the direction connecting the two
systems, indicative of a possible `bridge' of extra-tidal material. Fitting the
stellar distribution with a linear Gaussian model yields a significance of 4
sigma for this overdensity, a most likely FWHM of ~16 arcmin and a central
surface brightness of ~32 mag arcsec^{-2}. We investigate different scenarios
to explain the close proximity of Leo IV and Leo V and the possible tidal
bridge between them. Orbit calculations demonstrate that they are unlikely to
be remnants of a single disrupted progenitor, while a comparison with
cosmological simulations shows that a chance collision between unrelated
subhalos is negligibly small. Leo IV and Leo V could, however, be a bound
`tumbling pair' if their combined mass exceeds 8 +- 4 x 10^9 M_sun. The
scenario of an internally interacting pair appears to be the most viable
explanation for this close celestial companionship. (abridged)
