  Canopus, the brightest and closest yellow supergiant to our Solar System,
offers a unique laboratory for understanding the physics of evolved massive
stars. The accurate and precise PIONIER data allowed us to simultaneously
measure the angular diameter and the limb darkening (LD) profile using
different analytical laws. We found that the power-law LD, being also in
agreement with predictions from stellar atmosphere models, reproduces the
interferometric data well. For this model we measured an angular diameter of
$7.184 \pm 0.0017 \pm 0.029$ mas and an LD coefficient of $0.1438 \pm 0.0015$,
which are respectively $\gtrsim 5$ and $\sim15-25$ more precise than in our
previous A\&A paper on Canopus from 2008. From a dedicated analysis of the
interferometric data, we also provide new constraints on the putative presence
of weak surface inhomogeneities. Additionally, we analyzed the SED in a
innovative way by simultaneously fitting the reddening-related parameters and
the stellar effective temperature and gravity. We find that a model based on
two effective temperatures is much better at reproducing the whole SED, from
which we derived several parameters, including a new bolometric flux estimate.
The Canopus angular diameter and LD measured in this work with PIONIER are the
most precise to date, with a direct impact on several related fundamental
parameters. Moreover, thanks to our joint analysis, we were able to determine a
set of fundamental parameters that simultaneously reproduces both
high-precision interferometric data and a good quality SED and, at the same
time, agrees with stellar evolution models.
