Clusters of galaxies are the most massive gravitationally-bound objects in
the Universe and are still forming. They are thus important probes of
cosmological parameters and a host of astrophysical processes. Knowledge of the
dynamics of the pervasive hot gas, which dominates in mass over stars in a
cluster, is a crucial missing ingredient. It can enable new insights into
mechanical energy injection by the central supermassive black hole and the use
of hydrostatic equilibrium for the determination of cluster masses. X-rays from
the core of the Perseus cluster are emitted by the 50 million K diffuse hot
plasma filling its gravitational potential well. The Active Galactic Nucleus of
the central galaxy NGC1275 is pumping jetted energy into the surrounding
intracluster medium, creating buoyant bubbles filled with relativistic plasma.
These likely induce motions in the intracluster medium and heat the inner gas
preventing runaway radiative cooling; a process known as Active Galactic
Nucleus Feedback. Here we report on Hitomi X-ray observations of the Perseus
cluster core, which reveal a remarkably quiescent atmosphere where the gas has
a line-of-sight velocity dispersion of 164+/-10 km/s in a region 30-60 kpc from
the central nucleus. A gradient in the line-of-sight velocity of 150+/-70 km/s
is found across the 60 kpc image of the cluster core. Turbulent pressure
support in the gas is 4% or less of the thermodynamic pressure, with large
scale shear at most doubling that estimate. We infer that total cluster masses
determined from hydrostatic equilibrium in the central regions need little
correction for turbulent pressure.