Constraining gas motions in the Centaurus cluster using X-ray surface
  brightness fluctuations and metal diffusion
  We compare two different methods of constraining the characteristic velocity
and spatial scales of gas motions in the X-ray bright, nearby Centaurus
cluster, using new deep (760ks) Chandra observations. The power spectrum of
excess surface brightness fluctuations in the 0.5-6.0 keV band in a sector to
the west is measured and compared to theoretical expectations for Kolmogorov
index fluctuations. The observed power spectrum is flatter than these
expectations, and the surface brightness fluctuations are around the 8 percent
level on length scales of 2 kpc. We convert the 2D power spectrum of
fluctuations into a 3D power spectrum using the method of Churazov et al., and
then convert this into constraints on the one-component velocity of the gas
motions as a function of their length scale. We find one-component velocities
in the range 100-150 km/s on spatial scales of 4-10 kpc. An independent
constraint on the characteristic velocity and length scales of the gas motions
is then found by considering the diffusion coefficient needed to explain the
distribution of metals in the Centaurus cluster, combined with the need to
balance the rate of gas cooling with the rate of heat dissipated by the gas
motions. We find that these two methods of constraining the velocity and length
scales of the gas motions are in good agreement.
