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Register a new userPulsar timing array observations of gravitational wave source timing parallax
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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.
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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.
In order to maximize the sensitivity of pulsar timing arrays to a stochastic gravitational wave background, we present computational techniques to optimize observing schedules. The techniques are applicable to both single and multi-telescope experiments. The observing schedule is optimized for each telescope by adjusting the observing time allocated to each pulsar while keeping the total amount of observing time constant. The optimized schedule depends on the timing noise characteristics of each individual pulsar as well as the performance of instrumentation. Several examples are given to illustrate the effects of different types of noise. A method to select the most suitable pulsars to be included in a pulsar timing array project is also presented.
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.
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.
We search for isotropic stochastic gravitational-wave background including non-tensorial polarizations allowed in general metric theories of gravity in the Parkes Pulsar Timing Array (PPTA) second data release (DR2). We find no statistically significant evidence that the common process reported by the PPTA collaboration has the tensor transverse (TT), scalar transverse (ST), vector longitudinal (VL), or scalar longitudinal (SL) correlations in PPTA DR2. Therefore, we place $95%$ upper limit on the amplitude of each polarization mode as $mathcal{A}_{mathrm{TT}} lesssim 3.2times 10^{-15}$, $mathcal{A}_{mathrm{ST}} lesssim 1.8times 10^{-15}$, $mathcal{A}_{mathrm{VL}}lesssim 3.5times 10^{-16}$ and $mathcal{A}_{mathrm{SL}}lesssim 4.2times 10^{-17}$; or equivalently, the $95%$ upper limit on the energy density parameter per logarithm frequency as $Omega_{mathrm{GW}}^{mathrm{TT}} lesssim 1.4times 10^{-8}$, $Omega_{mathrm{GW}}^{mathrm{ST}} lesssim 4.5times 10^{-9}$, $Omega_{mathrm{GW}}^{mathrm{VL}} lesssim 1.7times 10^{-10}$ and $Omega_{mathrm{GW}}^{mathrm{SL}} lesssim 2.4times 10^{-12}$ at frequency of 1/year.
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