Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Constraints on the ICM velocity power spectrum from the X-ray lines
  width and shift   Future X-ray observations of galaxy clusters by high spectral resolution
missions will provide spatially resolved measurements of the energy and width
for the brightest emission lines in the intracluster medium (ICM) spectrum. In
this paper we discuss various ways of using these high resolution data to
constrain velocity power spectrum in galaxy clusters. We argue that variations
of these quantities with the projected distance R in cool core clusters contain
important information on the velocity field length scales in the ICM. The
effective length $l_{\rm eff}$ along the line of sight, which provides dominant
contribution to the line flux, increases with R, allowing one to probe the
amplitude of the velocity variations at different spatial scales. In
particular, we show that the width of the line as a function of R is closely
linked to the structure function of the 3D velocity field. Yet another easily
obtainable proxy of the velocity field length scales is the ratio of the
amplitude of the projected velocity field (line energy) variations to the
dispersion of the velocity along the line of sight (line width). Finally the
projected velocity field can be easily converted into 3D velocity field,
especially for clusters like Coma with an extended flat core in the surface
brightness. Under assumption of a homogeneous isotropic Gaussian 3D velocity
field we derived simple expressions relating the power spectrum of the 3D
velocity field (or structure function) and the observables. The uncertainties
in the observables, caused by stochastic nature of the velocity field, are
estimated by making multiple realizations of the random Gaussian velocity field
and evaluating the scatter in observables. If large scale motions are present
in the ICM these uncertainties may dominate the statistical errors of line
width and shift measurements.

11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
2
The categories of this paper are: math
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
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The categories of this paper are: stat
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The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
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The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
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The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph