Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New Coordinates for the Amplitude Parameter Space of Continuous
  Gravitational Waves   The parameter space for continuous gravitational waves (GWs) can be divided
into amplitude parameters (signal amplitude, inclination and polarization
angles describing the orientation of the source, and an initial phase) and
phase-evolution parameters. The division is useful in part because the
Jaranowski-Krolak-Schutz (JKS) coordinates on the four-dimensional amplitude
parameter space allow the GW signal to be written as a linear combination of
four template waveforms with the JKS coordinates as coefficients. We define a
new set of coordinates on the amplitude parameter space, with the same
properties, which is more closely connected to the physical amplitude
parameters. These naturally divide into two pairs of Cartesian-like coordinates
on two-dimensional subspaces, one corresponding to left- and the other to
right-circular polarization. We thus refer to these as CPF (circular
polarization factored) coordinates. The corresponding two sets of polar
coordinates (known as CPF-polar) can be related in a simple way to the physical
parameters. We illustrate some simplifying applications for these various
coordinate systems, such as: a calculation of Jacobians between various
coordinate systems; an illustration of the signal coordinate singularities
associated with left- and right-circular polarization, which correspond to the
origins of the two two-dimensional subspaces; and an elucidation of the form of
the log-likelihood ratio between hypotheses of Gaussian noise with and without
a continuous GW signal. These are used to illustrate some of the prospects for
approximate evaluation of a Bayesian detection statistic defined by
marginalization over the physical parameter space. Additionally, in the
presence of simplifying assumptions about the observing geometry, we are able
to explicitly evaluate the integral for the Bayesian detection statistic, and
compare it to the approximate results.

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The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: chem-ph
2
The categories of this paper are: math
7
The categories of this paper are: hep-th
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an