  Results from the UV satellite GALEX revealed large extensions of disks in
some nearby spiral galaxies, extending out to 3 to 4 times the isophotal
radius, r25. M63 is a remarkable example of a spiral galaxy with one of the
most extended UV disks, so it offers the opportunity to search for the
molecular gas and characterize the star formation in outer disk regions as
revealed by the UV emission. We obtained deep CO(1-0) and CO(2-1) observations
on the IRAM 30 m telescope along the major axis of the M63 disk from the center
out to the galactocentric radius rgal = 1.6 r25 and over a bright UV region at
rgal = 1.36 r25. CO(1-0) is detected all along the M63 major axis out to r25,
and CO(2-1) is confined to rgal = 0.68 r25, which may betray lower excitation
temperatures in the outer disk. CO(1-0) is also detected in the external bright
UV region of M63. The radial profiles of the CO emission and of the Halpha, 24
micron, NUV and FUV star formation tracers and HI taken from the literature
show a severe drop with the galactocentric radius, such that beyond r25 they
are all absent with the exception of a faint UV emission and HI. The CO
emission detection in the external UV region, where the UV flux is higher than
the UV flux observed beyond r25, highlights a tight correlation between the CO
and UV fluxes, namely the amount of molecular gas and the intensity of star
formation. This external UV region is dominated by the atomic gas, suggesting
that HI is more likely the precursor of H2 rather than the product of UV
photodissociation. A broken power law needs to be invoked to describe the
Kennicutt-Schmidt (K-S) relation of M63 from the center of the galaxy out to
rgal = 1.36 r25. While all along the major axis out to r25 the K-S relation is
almost linear, in the external UV region the SFR regime is highly nonlinear and
characterized by a steep K-S relation and very low star formation efficiency.
