  We characterized the population of galaxy clusters detected with the SZ
effect with Planck, by measuring the cool core state of the objects in a
well-defined subsample of the Planck catalogue. We used as indicator the
concentration parameter Santos et al. (2008). The fraction of cool core
clusters is $29 \pm 4 \%$ and does not show significant indications of
evolution in the redshift range covered by our sample. We compare the
distribution of the concentration parameter in the Planck sample with the one
of the X-ray selected sample MACS (Mann & Ebeling, 2011): the distributions are
significantly different and the cool core fraction in MACS is much higher ($59
\pm 5 \%$). Since X-ray selected samples are known to be biased towards cool
cores due to the presence of their prominent surface brightness peak, we
simulated the impact of the "cool core bias" following Eckert et al. (2011). We
found that it plays a large role in the difference between the fractions of
cool cores in the two samples. We examined other selection effects that could
in principle bias SZ-surveys against cool cores but we found that their impact
is not sufficient to explain the difference between Planck and MACS. The
population of X-ray under-luminous objects, which are found in SZ-surveys but
missing in X-ray samples (Planck Collaboration 2016), could possibly contribute
to the difference, as we found most of them to be non cool cores, but this
hypothesis deserves further investigation.
