  The ATLAS collaboration has recently observed that the variance of the
transverse momentum per particle ($[ p_t ]$), when measured as a function of
the collision multiplicity ($N_{ch}$) in Pb+Pb collisions, decreases by a
factor $2$ for the largest values of $N_{ch}$, corresponding to ultra-central
collisions. We show that this phenomenon is naturally explained by invoking
impact parameter ($b$) fluctuations, which contribute to the variance, and
gradually disappear in ultra-central collisions. It implies that $N_{ch}$ and
$[ p_t ]$ are strongly correlated at fixed $b$, which is explained by the local
thermalization of the QGP medium.
