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Register a new userExtending the Observational Frequency Range for Gravitational Waves in a Pulsar Timing Array
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Chan Park
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We provide an observation method for gravitational waves using a pulsar timing array to extend the observational frequency range up to the rotational frequency of pulsars. For this purpose, we perform an analysis of a perturbed electromagnetic wave in perturbed spacetime from the field perspective. We apply the analysis to the received electromagnetic waves in a radio telescope, which partially composes the periodic electromagnetic pulse emitted by a pulsar. For simple observation, two frequency windows are considered. For each window, we propose gauge-invariant quantities and discuss their observations.
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The maximum frequency of gravitational waves (GWs) detectable with traditional pulsar timing methods is set by the Nyquist frequency ($f_{rm{Ny}}$) of the observation. Beyond this frequency, GWs leave no temporal-correlated signals; instead, they appear as white noise in the timing residuals. The variance of the GW-induced white noise is a function of the position of the pulsars relative to the GW source. By observing this unique functional form in the timing data, we propose that we can detect GWs of frequency $>$ $f_{rm{Ny}}$ (super-Nyquist frequency GWs; SNFGWs). We demonstrate the feasibility of the proposed method with simulated timing data. Using a selected dataset from the Parkes Pulsar Timing Array data release 1 and the North American Nanohertz Observatory for Gravitational Waves publicly available datasets, we try to detect the signals from single SNFGW sources. The result is consistent with no GW detection with 65.5% probability. An all-sky map of the sensitivity of the selected pulsar timing array to single SNFGW sources is generated, and the position of the GW source where the selected pulsar timing array is most sensitive to is $lambda_{rm{s}}=-0.82$, $beta_{rm{s}}=-1.03$ (rad); the corresponding minimum GW strain is $h=6.31times10^{-11}$ at $f=1times10^{-5}$ Hz.
Blazar OJ 287 is a candidate nanoHertz (nHz) gravitational wave (GW) source. In this article, we investigate the GWs generated by OJ 287 and their potential detection through a pulsar timing array (PTA). First, we obtain the orbit and the corresponding GW strain of OJ 287. During the time span of the next 10 years (2019 to 2029), the GW of OJ 287 will be active before 2021, with a peak strain amplitude $8 times 10^{-16}$, and then decay after that. When OJ 287 is silent in the GW channel during 2021 to 2029, the timing residual signals of the PTA will be dominated by the pulsar term of the GW strain and this provides an opportunity to observe this pulsar term. Furthermore, we choose 26 pulsars with white noise below 300 ns to detect the GW signal of OJ 287, evaluating their timing residuals and signal-to-noise ratios (SNRs). The total SNR (with a cadence of 2 weeks in the next 10 years) of the PTA ranges from 1.9 to 2.9, corresponding to a weak GW signal for the current sensitivity level. Subsequently, we investigate the potential measurement of the parameters of OJ 287 using these pulsars. In particular, PSR J0437-4715, with a precisely measured distance, has the potential to constrain the polarization angle with an uncertainty below $8^{deg}$ and this pulsar will play an important role in future PTA observations.
The detection of a stochastic background of low-frequency gravitational waves by pulsar-timing and astrometric surveys will enable tests of gravitational theories beyond general relativity. These theories generally permit gravitational waves with non-Einsteinian polarization modes, which may propagate slower than the speed of light. We use the total-angular-momentum wave formalism to derive the angular correlation patterns of observables relevant for pulsar timing arrays and astrometry that arise from a background of subluminal gravitational waves with scalar, vector, or tensor polarizations. We find that the pulsar timing observables for the scalar longitudinal mode, which diverge with source distance in the luminal limit, are finite in the subluminal case. Furthermore, we apply our results to $f(R)$ gravity, which contains a massive scalar degree of freedom in addition to the standard transverse-traceless modes. The scalar mode in this $f(R)$ theory is a linear combination of the scalar-longitudinal and scalar-transverse modes, exciting only the monopole and dipole for pulsar timing arrays and only the dipole for astrometric surveys.
We study how to probe bispectra of stochastic gravitational waves with pulsar timing arrays. The bispectrum is a key to probe the origin of stochastic gravitational waves. In particular, the shape of the bispectrum carries valuable information of inflation models. We show that an appropriate filter function for three point correlations enables us to extract a specific configuration of momentum triangles in bispectra. We also calculate the overlap reduction functions and discuss strategy for detecting the bispectrum with multiple pulsars.
The physical mechanisms responsible for pulsar timing glitches are thought to excite quasi-normal mode oscillations in their parent neutron star that couple to gravitational wave emission. In August 2006, a timing glitch was observed in the radio emission of PSR B0833-45, the Vela pulsar. At the time of the glitch, the two co-located Hanford gravitational wave detectors of the Laser Interferometer Gravitational-wave observatory (LIGO) were operational and taking data as part of the fifth LIGO science run (S5). We present the first direct search for the gravitational wave emission associated with oscillations of the fundamental quadrupole mode excited by a pulsar timing glitch. No gravitational wave detection candidate was found. We place Bayesian 90% confidence upper limits of 6.3e-21 to 1.4e-20 on the peak intrinsic strain amplitude of gravitational wave ring-down signals, depending on which spherical harmonic mode is excited. The corresponding range of energy upper limits is 5.0e44 to 1.3e45 erg.
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