Mapping the Gas Turbulence in the Coma Cluster: Predictions for Astro-H
  Astro-H will be able for the first time to map gas velocities and detect
turbulence in galaxy clusters. One of the best targets for turbulence studies
is the Coma cluster, due to its proximity, absence of a cool core, and lack of
a central active galactic nucleus. To determine what constraints Astro-H will
be able to place on the Coma velocity field, we construct simulated maps of the
projected gas velocity and compute the second-order structure function, an
analog of the velocity power spectrum. We vary the injection scale, dissipation
scale, slope, and normalization of the turbulent power spectrum, and apply
measurement errors and finite sampling to the velocity field. We find that even
with sparse coverage of the cluster, Astro-H will be able to measure the Mach
number and the injection scale of the turbulent power spectrum--the quantities
determining the energy flux down the turbulent cascade and the diffusion rate
for everything that is advected by the gas (metals, cosmic rays, etc.). Astro-H
will not be sensitive to the dissipation scale or the slope of the power
spectrum in its inertial range, unless they are outside physically motivated
intervals. We give the expected confidence intervals for the injection scale
and the normalization of the power spectrum for a number of possible pointing
configurations, combining the structure function and velocity dispersion data.
Importantly, we also determine that measurement errors on the line shift will
bias the velocity structure function upward, and show how to correct this bias.
