  We present a Chandra study of surface brightness fluctuations in the diffuse
intracluster medium of the Perseus Cluster. Our study utilizes deep, archival
imaging of the cluster core as well as a new mosaic of 29 short 5 ks
observations extending in 8 different directions out to radii of r_500 ~
2.2r_2500. Under the assumption that the distribution of densities at a given
radius is log-normally distributed, two important quantities can be derived
from the width of the log-normal density distribution on a given spatial scale:
the density bias, which is equal to the square root of the clumping factor C;
and the one-component turbulent velocity, v_(k, 1D). We forward-model all
contributions to the measured surface brightness, including astrophysical and
particle background components, and account for the Poisson nature of the
measured signal. Measuring the distribution of surface brightness fluctuations
in 1 arcmin^2 regions, spanning the radial range 0.3-2.2 r_2500 (7.8-57.3
arcmin), we find a small to moderate average density bias of around 3% at radii
below 1.6r_2500. We also infer an average turbulent velocity at these radii of
v_1D <400 km s^-1. Direct confirmation of our results on turbulent velocities
inferred from surface brightness fluctuations should be possible using the
X-ray calorimeter spectrometers to be flown aboard the XRISM and Athena.
observatories.
