  We accurately determine the fundamental system parameters of the neutron-star
X-ray transient Cen X-4 solely using phase-resolved high-resolution UVES
spectroscopy. We first determine the radial-velocity curve of the secondary
star and then model the shape of the phase-resolved absorption line profiles
using an X-ray binary model. The model computes the exact rotationally
broadened phase-resolved spectrum and does not depend on assumptions about the
rotation profile, limb-darkening coefficients and the effects of contamination
from an accretion disk. We determine the secondary star-to-neutron star binary
mass ratio to be 0.1755+/-0.0025, which is an order of magnitude more accurate
than previous estimates. We also constrain the inclination angle to be 32 (+8;
-2) degrees, Combining these values with the results of the radial velocity
study gives a neutron star mass of 1.94 (+0.37; -0.85) Msun consistent with
previous estimates. Finally, we perform the first Roche tomography
reconstruction of the secondary star in an X-ray binary. The tomogram reveals
surface inhomogeneities that are due to the presence of cool starspots. A large
cool polar spot, similar to that seen in Doppler images of rapidly-rotating
isolated stars is present on the Northern hemisphere of the K7 secondary star
and we estimate that about 4 per cent of the total surface area of the donor
star is covered with spots. This evidence for starspots supports the idea that
magnetic braking plays an important role in the evolution of low-mass X-ray
binaries.
