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Register a new userGravitational wave astronomy of single sources with a pulsar timing array
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Abbreviated: We investigate the potential of detecting the gravitational wave from individual binary black hole systems using pulsar timing arrays (PTAs) and calculate the accuracy for determining the GW properties. This is done in a consistent analysis, which at the same time accounts for the measurement of the pulsar distances via the timing parallax. We find that, at low redshift, a PTA is able to detect the nano-Hertz GW from super massive black hole binary systems with masses of $sim10^8 - 10^{10},M_{sun}$ less than $sim10^5$,years before the final merger, and those with less than $sim10^3 - 10^4$ years before merger may allow us to detect the evolution of binaries. We derive an analytical expression to describe the accuracy of a pulsar distance measurement via timing parallax. We consider five years of bi-weekly observations at a precision of 15,ns for close-by ($sim 0.5 - 1$,kpc) pulsars. Timing twenty pulsars would allow us to detect a GW source with an amplitude larger than $5times 10^{-17}$. We calculate the corresponding GW and binary orbital parameters and their measurement precision. The accuracy of measuring the binary orbital inclination angle, the sky position, and the GW frequency are calculated as functions of the GW amplitude. We note that the pulsar term, which is commonly regarded as noise, is essential for obtaining an accurate measurement for the GW source location. We also show that utilizing the information encoded in the GW signal passing the Earth also increases the accuracy of pulsar distance measurements. If the gravitational wave is strong enough, one can achieve sub-parsec distance measurements for nearby pulsars with distance less than $sim 0.5 - 1$,kpc.
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Pulsar timing arrays act to detect gravitational waves by observing the small, correlated effect the waves have on pulse arrival times at Earth. This effect has conventionally been evaluated assuming the gravitational wave phasefronts are planar across the array, an assumption that is valid only for sources at distances $Rgg2pi{}L^2/lambda$, where $L$ is physical extent of the array and $lambda$ the radiation wavelength. In the case of pulsar timing arrays (PTAs) the array size is of order the pulsar-Earth distance (kpc) and $lambda$ is of order pc. Correspondingly, for point gravitational wave sources closer than $sim100$~Mpc the PTA response is sensitive to the source parallax across the pulsar-Earth baseline. Here we evaluate the PTA response to gravitational wave point sources including the important wavefront curvature effects. Taking the wavefront curvature into account the relative amplitude and phase of the timing residuals associated with a collection of pulsars allows us to measure the distance to, and sky position of, the source.
Merging supermassive black hole binaries produce low-frequency gravitational waves, which pulsar timing experiments are searching for. Much of the current theory is developed within the plane-wave formalism, and here we develop the more general Fresnel formalism. We show that Fresnel corrections to gravitational wave timing residual models allow novel measurements to be made, such as direct measurements of the source distance from the timing residual phase and frequency, as well as direct measurements of chirp mass from a monochromatic source. Probing the Fresnel corrections in these models will require future pulsar timing arrays with more distant pulsars across our Galaxy (ideally at the distance of the Magellanic Clouds), timed with precisions less than $100$ ns, with distance uncertainties reduced to the order of the gravitational wavelength. We find that sources with chirp mass of order $10^9 mathrm{M}_odot$ and orbital frequency $omega_0 > 10$ nHz are good candidates for probing Fresnel corrections. With these conditions met, the measured source distance uncertainty can be made less than 10 per cent of the distance to the source for sources out to $sim 100$ Mpc, source sky localization can be reduced to sub-arcminute precision, and source volume localization can be made to less than $1 text{Mpc}^3$ for sources out to 1-Gpc distances.
The NANOGrav Collaboration reported strong Bayesian evidence for a common-spectrum stochastic process in its 12.5-yr pulsar timing array dataset, with median characteristic strain amplitude at periods of a year of $A_{rm yr} = 1.92^{+0.75}_{-0.55} times 10^{-15}$. However, evidence for the quadrupolar Hellings & Downs interpulsar correlations, which are characteristic of gravitational wave signals, was not yet significant. We emulate and extend the NANOGrav dataset, injecting a wide range of stochastic gravitational wave background (GWB) signals that encompass a variety of amplitudes and spectral shapes, and quantify three key milestones: (I) Given the amplitude measured in the 12.5 yr analysis and assuming this signal is a GWB, we expect to accumulate robust evidence of an interpulsar-correlated GWB signal with 15--17 yrs of data, i.e., an additional 2--5 yrs from the 12.5 yr dataset; (II) At the initial detection, we expect a fractional uncertainty of $40%$ on the power-law strain spectrum slope, which is sufficient to distinguish a GWB of supermassive black-hole binary origin from some models predicting more exotic origins;(III) Similarly, the measured GWB amplitude will have an uncertainty of $44%$ upon initial detection, allowing us to arbitrate between some population models of supermassive black-hole binaries. In addition, power-law models are distinguishable from those having low-frequency spectral turnovers once 20~yrs of data are reached. Even though our study is based on the NANOGrav data, we also derive relations that allow for a generalization to other pulsar-timing array datasets. Most notably, by combining the data of individual arrays into the International Pulsar Timing Array, all of these milestones can be reached significantly earlier.
We explore opportunities for multi-messenger astronomy using gravitational waves (GWs) and prompt, transient low-frequency radio emission to study highly energetic astrophysical events. We review the literature on possible sources of correlated emission of gravitational waves and radio transients, highlighting proposed mechanisms that lead to a short-duration, high-flux radio pulse originating from the merger of two neutron stars or from a superconducting cosmic string cusp. We discuss the detection prospects for each of these mechanisms by low-frequency dipole array instruments such as LWA1, LOFAR and MWA. We find that a broad range of models may be tested by searching for radio pulses that, when de-dispersed, are temporally and spatially coincident with a LIGO/Virgo GW trigger within a $usim 30$ second time window and $usim 200 mendash 500 punits{deg}^{2}$ sky region. We consider various possible observing strategies and discuss their advantages and disadvantages. Uniquely, for low-frequency radio arrays, dispersion can delay the radio pulse until after low-latency GW data analysis has identified and reported an event candidate, enabling a emph{prompt} radio signal to be captured by a deliberately targeted beam. If neutron star mergers do have detectable prompt radio emissions, a coincident search with the GW detector network and low-frequency radio arrays could increase the LIGO/Virgo effective search volume by up to a factor of $usim 2$. For some models, we also map the parameter space that may be constrained by non-detections.
We search for isotropic stochastic gravitational-wave background (SGWB) in the International Pulsar Timing Array second data release. By modeling the SGWB as a power-law, we find very strong Bayesian evidence for a common-spectrum process, and further this process has scalar transverse (ST) correlations allowed in general metric theory of gravity as the Bayes factor in favor of the ST-correlated process versus the spatially uncorrelated common-spectrum process is $30pm 2$. The median and the $90%$ equal-tail amplitudes of ST mode are $mathcal{A}_{mathrm{ST}}= 1.29^{+0.51}_{-0.44} times 10^{-15}$, or equivalently the energy density parameter per logarithm frequency is $Omega_{mathrm{GW}}^{mathrm{ST}} = 2.31^{+2.19}_{-1.30} times 10^{-9}$, at frequency of 1/year. However, we do not find any statistically significant evidence for the tensor transverse (TT) mode and then place the $95%$ upper limits as $mathcal{A}_{mathrm{TT}}< 3.95 times 10^{-15}$, or equivalently $Omega_{mathrm{GW}}^{mathrm{TT}}< 2.16 times 10^{-9}$, at frequency of 1/year.
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