A study of the gravitational wave form from pulsars

Abstract

We present analytical and numerical studies of the Fourier transform (FT) of the gravitational wave (GW) signal from a pulsar, taking into account the rotation and orbital motion of the Earth. We also briefly discuss the Zak–Gelfand integral transform and a special class of the generalized hypergeometric function of potential relevance. The Zak–Gelfand integral transform that arises in our analytic approach has also been useful for Schrödinger operators in periodic potentials in condensed matter physics (Bloch wavefunctions) and holds promise for the study of periodic GW signals for long integration times.

A study of the gravitational wave pulsar signal with orbital and spindown effects

“…The contribution of a perturbation to the phase of the GW signal (in radians), crucial in determining search templates for the GW forms, is given by (t) = 2πf 0 (R i (t) ·n/c), where R i (t) is the contributing vector for the perturbation [2]. Our numerical estimates of the phase contributions for the Earth's circular and elliptical orbital and rotational motions, as well as those from the Jovian and Lunar perturbations, are shown as functions of θ (the angle of the pulsar from the orbital plane normal) and φ (the angle of the pulsar from the x-axis in the orbital plane), for t = 6 lunar months (6 × 29.5 d), α = π/2 and f 0 = 1 kHz (see Fig.…”

“…In recent works [1,2], we have implemented the Fourier transform (FT) of the Doppler-shifted GW signal from a pulsar with the plane wave expansion in spherical harmonics (PWESH). It turns out that the consequent analysis of the FT of the GW signal from a pulsar has a very interesting and convenient development in terms of the resulting spherical Bessel, generalized hypergeometric, Gamma and Legendre functions.…”

“…The intensity of the signal, h (f ) 2 , can be expressed in analytic form from (13). A detailed numerical analysis of this expression for the variety of parameters, which can take huge values (> 50 000), present in the GW signal is a challenge for high-performance parallel computation [8].…”

Global parameter-space correlations of coherent searches for continuous gravitational waves

“…However, following an approach first used in [6,10], it is more advantageous to use the Jacobi-Anger expansion, which allows one to expand an oscillatory exponent in terms of the Bessel functions J n (z), namely…”

“…Except for very short observation times T ≪ 1 day, which are not relevant for searches for continuous waves, the phase modulation Φ spin due to the spin-motion of the earth is oscillatory, and can therefore not be treated using a Taylor-expansion. However, following an approach first used in [6,10], it is more advantageous to use the Jacobi-Anger expansion, which allows one to expand an oscillatory exponent in terms of the Bessel-functions J n (z), namely…”