1,104 research outputs found
Full analytic expression of overlap reduction function for gravitational wave background with pulsar timing arrays
Pulsar timing array (PTA) is expected to detect gravitational wave background
(GWB) in the nanohertz band within the next decade. This provides an
opportunity to test the gravity theory and cosmology. A typical data analysis
method to detect GWB is cross-correlation analysis. The overlap reduction
function (ORF) plays an important role in the correlation data analysis of GWB.
The present approach to dealing with the intricate integration in ORF is to use
short-wave approximation to drop out the tricky terms. In this paper, we
provide the full analytic expression of the ORF for PTA without any
approximation for all possible polarizations allowed by modifications of
general relativity. Compared with the numerical simulation and short-wave
approximation, our results are more efficient and widely applicable. Especially
for the scalar-longitudinal mode where the short-wave approximation is not
available, our analytical expression is particularly significant
Revisitation of algebraic approach for time delay interferometry
Time Delay Interferometry (TDI) is often utilized in the data pre-processing
of space-based gravitational wave detectors, primarily for suppressing laser
frequency noise. About twenty years ago, assuming armlengths remain constant
over time, researchers presented comprehensive mathematical descriptions for
the first-generation and modified first-generation TDI. However, maintaining a
steady distance between satellites is pragmatically challenging. Hence, the
operator equation that neutralizes laser frequency noise, though provided, was
deemed difficult to resolve. In this paper, we solve this equation in the
context of a non-static scenario where distances between spacecrafts vary over
time. Surprisingly, contrary to what previous researchers thought, the study
reveals that the equation has only the zero solution, which suggests that no
nonzero TDI combination can entirely suppress laser frequency noise under
time-varying armlengths. This necessitates the persistent search for
second-generation TDI combinations through alternative methods besides directly
solving the operator equation. We establish the connections between TDI
combinations of different generations and propose a search strategy for finding
higher-generation TDI combinations by using generators of lower-generation TDI.
The findings contribute to the ongoing discussion on gravitational waves and
provide a novel insight into the hurdles faced in space-based gravitational
wave detection.Comment: accepted by Physical Review
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