  The Sun is the only star whose surface can be directly resolved at high
resolution, and therefore constitutes an excellent test case to explore the
physical origin of stellar radial-velocity (RV) variability. We present HARPS
observations of sunlight scattered off the bright asteroid 4/Vesta, from which
we deduced the Sun's activity-driven RV variations. In parallel, the HMI
instrument onboard the Solar Dynamics Observatory provided us with simultaneous
high spatial resolution magnetograms, Dopplergrams, and continuum images of the
Sun in the Fe I 6173A line. We determine the RV modulation arising from the
suppression of granular blueshift in magnetised regions and the flux imbalance
induced by dark spots and bright faculae. The rms velocity amplitudes of these
contributions are 2.40 m/s and 0.41 m/s, respectively, which confirms that the
inhibition of convection is the dominant source of activity-induced RV
variations at play, in accordance with previous studies. We find the Doppler
imbalances of spot and plage regions to be only weakly anticorrelated.
Lightcurves can thus only give incomplete predictions of convective blueshift
suppression. We must instead seek proxies that track the plage coverage on the
visible stellar hemisphere directly. The chromospheric flux index R'_HK derived
from the HARPS spectra performs poorly in this respect, possibly because of the
differences in limb brightening/darkening in the chromosphere and photosphere.
We also find that the activity-driven RV variations of the Sun are strongly
correlated with its full-disc magnetic flux density, which may become a useful
proxy for activity-related RV noise.
