Ubiquitous cold and massive filaments in cool core clusters
  Multi-phase filamentary structures around Brightest Cluster Galaxies are
likely a key step of AGN-feedback. We observed molecular gas in 3 cool cluster
cores: Centaurus, Abell S1101, and RXJ1539.5 and gathered ALMA and MUSE data
for 12 other clusters. Those observations show clumpy, massive and long, 3--25
kpc, molecular filaments, preferentially located around the radio bubbles
inflated by the AGN (Active Galactic Nucleus). Two objects show nuclear
molecular disks. The optical nebula is certainly tracing the warm envelopes of
cold molecular filaments. Surprisingly, the radial profile of the H$\alpha$/CO
flux ratio is roughly constant for most of the objects, suggesting that (i)
between 1.2 to 7 times more cold gas could be present and (ii) local processes
must be responsible for the excitation. Projected velocities are between
100--400 km s$^{-1}$, with disturbed kinematics and sometimes coherent
gradients. This is likely due to the mixing in projection of several thin
unresolved filaments. The velocity fields may be stirred by turbulence induced
by bubbles, jets or merger-induced sloshing. Velocity and dispersions are low,
below the escape velocity. Cold clouds should eventually fall back and fuel the
AGN. We compare the filament's radial extent, r$_{fil}$, with the region where
the X-ray gas can become thermally unstable. The filaments are always inside
the low-entropy and short cooling time region, where t$_{cool}$/t$_{ff}$<20 (9
of 13 sources). The range t$_{cool}$/t$_{ff}$, 8-23 at r$_{fil}$, is likely due
to (i) a more complex gravitational potential affecting the free-fall time
(e.g., sloshing, mergers); (ii) the presence of inhomogeneities or uplifted gas
in the ICM, affecting the cooling time. For some of the sources, r$_{fil}$ lies
where the ratio of the cooling time to the eddy-turnover time,
t$_{cool}$/t$_{eddy}$, is approximately unity.
