  When a planet transits its host star, it blocks regions of the stellar
surface from view; this causes a distortion of the spectral lines and a change
in the line-of-sight (LOS) velocities, known as the Rossiter-McLaughlin (RM)
effect. Since the LOS velocities depend, in part, on the stellar rotation, the
RM waveform is sensitive to the star-planet alignment (which provides
information on the system's dynamical history). We present a new RM modelling
technique that directly measures the spatially-resolved stellar spectrum behind
the planet. This is done by scaling the continuum flux of the (HARPS) spectra
by the transit light curve, and then subtracting the in- from the
out-of-transit spectra to isolate the starlight behind the planet. This
technique does not assume any shape for the intrinsic local profiles. In it, we
also allow for differential stellar rotation and centre-to-limb variations in
the convective blueshift. We apply this technique to HD189733 and compare to 3D
magnetohydrodynamic (MHD) simulations. We reject rigid body rotation with high
confidence (> 99% probability), which allows us to determine the occulted
stellar latitudes and measure the stellar inclination. In turn, we determine
both the sky-projected (lambda ~ -0.4 +/- 0.2 degrees) and true 3D obliquity
(psi ~ 7^+12_-4 degrees). We also find good agreement with the MHD simulations,
with no significant centre-to-limb variations detectable in the local profiles.
Hence, this technique provides a new powerful tool that can probe stellar
photospheres, differential rotation, determine 3D obliquities, and remove
sky-projection biases in planet migration theories. This technique can be
implemented with existing instrumentation, but will become even more powerful
with the next generation of high-precision radial velocity spectrographs.
