774 research outputs found
Elimination of Clock Jitter Noise in Spaceborn Laser Interferometers
Space gravitational wave detectors employing laser interferometry between
free-flying spacecraft differ in many ways from their laboratory counterparts.
Among these differences is the fact that, in space, the end-masses will be
moving relative to each other. This creates a problem by inducing a Doppler
shift between the incoming and outgoing frequencies. The resulting beat
frequency is so high that its phase cannot be read to sufficient accuracy when
referenced to state-of-the-art space-qualified clocks. This is the problem that
is addressed in this paper. We introduce a set of time-domain algorithms in
which the effects of clock jitter are exactly canceled. The method employs the
two-color laser approach that has been previously proposed, but avoids the
singularities that arise in the previous frequency-domain algorithms. In
addition, several practical aspects of the laser and clock noise cancellation
schemes are addressed.Comment: 20 pages, 5 figure
Unequal arm space-borne gravitational wave detectors
Unlike ground-based interferometric gravitational wave detectors, large
space-based systems will not be rigid structures. When the end-stations of the
laser interferometer are freely flying spacecraft, the armlengths will change
due to variations in the spacecraft positions along their orbital trajectories,
so the precise equality of the arms that is required in a laboratory
interferometer to cancel laser phase noise is not possible. However, using a
method discovered by Tinto and Armstrong, a signal can be constructed in which
laser phase noise exactly cancels out, even in an unequal arm interferometer.
We examine the case where the ratio of the armlengths is a variable parameter,
and compute the averaged gravitational wave transfer function as a function of
that parameter. Example sensitivity curve calculations are presented for the
expected design parameters of the proposed LISA interferometer, comparing it to
a similar instrument with one arm shortened by a factor of 100, showing how the
ratio of the armlengths will affect the overall sensitivity of the instrument.Comment: 14 pages, 7 figures, REVTeX
The Angular Resolution of Space-Based Gravitational Wave Detectors
Proposed space-based gravitational wave antennas involve satellites arrayed
either in an equilateral triangle around the earth in the ecliptic plane (the
ecliptic-plane option) or in an equilateral triangle orbiting the sun in such a
way that the plane of the triangle is tilted at 60 degrees relative to the
ecliptic (the precessing-plane option). In this paper, we explore the angular
resolution of these two classes of detectors for two kinds of sources
(essentially monochromatic compact binaries and coalescing massive-black-hole
binaries) using time-domain expressions for the gravitational waveform that are
accurate to 4/2 PN order. Our results display an interesting effect not
previously reported in the literature, and underline the importance of
including the higher-order PN terms in the waveform when predicting the angular
resolution of ecliptic-plane detector arrays.Comment: 13 pages, 6 figures, submitted to Phys Rev D. The current version
corrects an error in our original paper and adds some clarifying language.
The error also required correction of the graphs now shown in Figures 3
through
The information content of gravitational wave harmonics in compact binary inspiral
The nonlinear aspect of gravitational wave generation that produces power at
harmonics of the orbital frequency, above the fundamental quadrupole frequency,
is examined to see what information about the source is contained in these
higher harmonics. We use an order (4/2) post-Newtonian expansion of the
gravitational wave waveform of a binary system to model the signal seen in a
spaceborne gravitational wave detector such as the proposed LISA detector.
Covariance studies are then performed to determine the ultimate accuracy to be
expected when the parameters of the source are fit to the received signal. We
find three areas where the higher harmonics contribute crucial information that
breaks degeneracies in the model and allows otherwise badly-correlated
parameters to be separated and determined. First, we find that the position of
a coalescing massive black hole binary in an ecliptic plane detector, such as
OMEGA, is well-determined with the help of these harmonics. Second, we find
that the individual masses of the stars in a chirping neutron star binary can
be separated because of the mass dependence of the harmonic contributions to
the wave. Finally, we note that supermassive black hole binaries, whose
frequencies are too low to be seen in the detector sensitivity window for long,
may still have their masses, distances, and positions determined since the
information content of the higher harmonics compensates for the information
lost when the orbit-induced modulation of the signal does not last long enough
to be apparent in the data.Comment: 13 pages, 5 figure
Sensitivity curves for spaceborne gravitational wave interferometers
To determine whether particular sources of gravitational radiation will be
detectable by a specific gravitational wave detector, it is necessary to know
the sensitivity limits of the instrument. These instrumental sensitivities are
often depicted (after averaging over source position and polarization) by
graphing the minimal values of the gravitational wave amplitude detectable by
the instrument versus the frequency of the gravitational wave. This paper
describes in detail how to compute such a sensitivity curve given a set of
specifications for a spaceborne laser interferometer gravitational wave
observatory. Minor errors in the prior literature are corrected, and the first
(mostly) analytic calculation of the gravitational wave transfer function is
presented. Example sensitivity curve calculations are presented for the
proposed LISA interferometer. We find that previous treatments of LISA have
underestimated its sensitivity by a factor of .Comment: 27 pages + 5 figures, REVTeX, accepted for publication in Phys Rev D;
Update reflects referees comments, figure 3 clarified, figure 5 corrected for
LISA baselin
I/O efficient bisimulation partitioning on very large directed acyclic graphs
In this paper we introduce the first efficient external-memory algorithm to
compute the bisimilarity equivalence classes of a directed acyclic graph (DAG).
DAGs are commonly used to model data in a wide variety of practical
applications, ranging from XML documents and data provenance models, to web
taxonomies and scientific workflows. In the study of efficient reasoning over
massive graphs, the notion of node bisimilarity plays a central role. For
example, grouping together bisimilar nodes in an XML data set is the first step
in many sophisticated approaches to building indexing data structures for
efficient XPath query evaluation. To date, however, only internal-memory
bisimulation algorithms have been investigated. As the size of real-world DAG
data sets often exceeds available main memory, storage in external memory
becomes necessary. Hence, there is a practical need for an efficient approach
to computing bisimulation in external memory.
Our general algorithm has a worst-case IO-complexity of O(Sort(|N| + |E|)),
where |N| and |E| are the numbers of nodes and edges, resp., in the data graph
and Sort(n) is the number of accesses to external memory needed to sort an
input of size n. We also study specializations of this algorithm to common
variations of bisimulation for tree-structured XML data sets. We empirically
verify efficient performance of the algorithms on graphs and XML documents
having billions of nodes and edges, and find that the algorithms can process
such graphs efficiently even when very limited internal memory is available.
The proposed algorithms are simple enough for practical implementation and use,
and open the door for further study of external-memory bisimulation algorithms.
To this end, the full open-source C++ implementation has been made freely
available
LATOR Covariance Analysis
We present results from a covariance study for the proposed Laser Astrometric
Test of Relativity (LATOR) mission. This mission would send two
laser-transmitter spacecraft behind the Sun and measure the relative
gravitational light bending of their signals using a hundred-meter-baseline
optical interferometer to be constructed on the International Space Station. We
assume that each spacecraft is equipped with a drag-free system and assume
approximately one year of data. We conclude that the observations allow a
simultaneous determination of the orbit parameters of the spacecraft and of the
Parametrized Post-Newtonian (PPN) parameter with an uncertainty of
. We also find a determination of the
solar quadrupole moment, , as well as the first measurement of the
second-order post-PPN parameter to an accuracy of about .Comment: 9 pages, 3 figures. first revision: minor changes to results. Second
revision: additional discussion of orbit modelling and LATOR drag-free system
requirement feasibility. Added references to tables I and V (which list PPN
parameter uncertainties), removed word from sentence in Section III. 3rd
revision: removed 2 incorrect text fragments (referring to impact parameter
as distance of closest approach) and reference to upcoming publication of
ref. 2, removed spurious gamma from eq. 1 - Last error is still in cqg
published versio
LISA data analysis I: Doppler demodulation
The orbital motion of the Laser Interferometer Space Antenna (LISA) produces
amplitude, phase and frequency modulation of a gravitational wave signal. The
modulations have the effect of spreading a monochromatic gravitational wave
signal across a range of frequencies. The modulations encode useful information
about the source location and orientation, but they also have the deleterious
affect of spreading a signal across a wide bandwidth, thereby reducing the
strength of the signal relative to the instrument noise. We describe a simple
method for removing the dominant, Doppler, component of the signal modulation.
The demodulation reassembles the power from a monochromatic source into a
narrow spike, and provides a quick way to determine the sky locations and
frequencies of the brightest gravitational wave sources.Comment: 5 pages, 7 figures. References and new comments adde
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