Thermal SZ fluctuations in the ICM: probing turbulence and
  thermodynamics in Coma cluster with ${\it Planck}$
  We report the detection of thermal Sunyaev-Zeldovich effect (SZ) fluctuations
in the intracluster medium (ICM) of Coma cluster observed with ${\it Planck}$.
The SZ data links the maximum observable X-ray scale to the large Mpc scale,
extending our knowledge of the power spectrum of ICM fluctuations. Deprojecting
the 2-d SZ perturbations into 3-d pressure fluctuations, we find an amplitude
spectrum which peaks at $\delta P/P = 33\pm 12\%$ and $74\pm19\%$ in the $15'$
and $40'$ radius region, respectively. We perform tests to ensure fluctuations
are intrinsic to the cluster and not due to noise contamination. By using
high-resolution hydrodynamical models, we improve the ICM turbulence
constraints in Coma, finding 3-d Mach number ${\rm Ma_{3d}}= 0.8\pm0.3$ (15'
region), increasing to supersonic values at larger radii (40'), and an
injection scale $L_{\rm inj}\approx 500$ kpc. Such properties are consistent
with driving due to mergers, in particular tied to internal galaxy groups. The
large pressure fluctuations show that Coma is in adiabatic mode (mediated by
sound waves), rather than isobaric mode (mediated by buoyancy waves). As
predicted by turbulence models, the distribution of SZ fluctuations is
log-normal with mild non-Gaussianities (heavy tails). The substantial
non-thermal pressure support implies hydrostatic mass bias $b_M=-15\%$ to
$-45\%$ from the core to the outskirt region, respectively. While total SZ
power probes the thermal energy content, the SZ fluctuations constrain the
non-thermal deviations important for precision cosmology. The proposed, novel
approach can be exploited by multifrequency observations using ground based
interferometers and future space CMB missions.
