Chiara Caprini, Ruth Durrer, Xavier Siemens
If the cosmological QCD phase transition is strongly first order and lasts sufficiently long, it generates a background of gravitational waves which may be detected via pulsar timing experiments. We estimate the amplitude and the spectral shape of such a background and we discuss its detectability prospects.
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We study the observation of stochastic gravitational-wave background (SGWB) made by pulsar-timing arrays in the spherical harmonic space. Instead of using the Shapiro time delay, we keep the Sachs-Wolfe line-of-sight integral for the timing residual of an observed pulsar. We derive the power spectrum of the timing residual, from which the overlap reduction functions and the bipolar spherical harmonics coefficients are constructed for the SGWB intensity and polarization anisotropies. We have reproduced the previous results, noting that we have developed a fast algorithm for computing accurate o…
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 $R\gg2πL^2/λ$, where $L$ is physical extent of the array and $λ$ the radiation wavelength. In the case of pulsar timing arrays (PTAs) the array size is of order the pulsar-Earth distance (kpc) and $λ$ is of order pc. Correspondingly, for point gravitational wave sources closer …
Relic gravitational waves (RGWs) , a background originated during inflation, would give imprints on the pulsar timing residuals. This makes RGWs be one of important sources for detection using the method of pulsar timing. In this paper, we discuss the effects of RGWs on the single pulsar timing, and give quantitively the timing residuals caused by RGWs with different model parameters. In principle, if the RGWs are strong enough today, they can be detected by timing a single millisecond pulsar with high precision after the intrinsic red noise in pulsar timing residuals were understood, even tho…
Pulsar timing observations are used to place constraints on the rate of coalescence of supermassive black-hole (SMBH) binaries as a function of mass and redshift. In contrast to the indirect constraints obtained from other techniques, pulsar timing observations provide a direct constraint on the black-hole merger rate. This is possible since pulsar timing is sensitive to the gravitational waves (GWs) emitted by these sources in the final stages of their evolution. We find that upper bounds calculated from the recently published Parkes Pulsar Timing Array data are just above theoretical predict…
Pulsar timing arrays (PTAs) will be sensitive to a finite number of gravitational wave (GW) "point" sources (e.g. supermassive black hole binaries). N quiet pulsars with accurately known distances d_{pulsar} can characterize up to 2N/7 distant chirping sources per frequency bin Δf_{gw}=1/T, and localize them with "diffraction limited" precision δθ\gtrsim (1/SNR)(λ_{gw}/d_{pulsar}). Even if the pulsar distances are poorly known, a PTA with F frequency bins can still characterize up to (2N/7)[1-(1/2F)] sources per bin, and the quasi-singular pattern of timing residuals in the vicinity of a GW so…
Pulsar timing-array correlation measurements offer an exciting opportunity to test the nature of gravity in the cosmologically novel nanohertz gravitational wave regime. The stochastic gravitational wave background is assumed Gaussian and random, while there are limited pulsar pairs in the sky. This brings theoretical uncertainties to the correlation measurements, namely the pulsar variance due to pulsar samplings and the cosmic variance due to Gaussian signals. We demonstrate a straightforward calculation of the mean and the variances on the Hellings-Downs correlation relying on a power spect…
Pulsar timing experiments are currently searching for gravitational waves, and this dissertation focuses on the development and study of the pulsar timing residual models used for continuous wave searches. The first goal of this work is to re-present much of the fundamental physics and mathematics concepts behind the calculations and theory used in pulsar timing. While there exist many reference sources in the literature, I try to offer a fully self-contained explanation of the fundamentals of this research which I hope the reader will find helpful. The next goal broadly speaking has been to f…
We propose a novel method for observing the gravitational wave signature of super-massive black hole (SMBH) mergers. This method is based on detection of a specific type of gravitational waves, namely gravitational wave burst with memory (BWM), using pulsar timing. We study the unique signature produced by BWM in anomalous pulsar timing residuals. We show that the present day pulsar timing precision allows one to detect BWM due to SMBH mergers from distances up to 1 Gpc (for case of equal mass 10^8 Msun SMBH). Improvements in precision of pulsar timing together with the increase in number of o…
Non-Gaussian timing residual skewness in pulsar timing arrays
受宇宙微波背景非高斯性搜索启发，我们研究脉冲星计时阵列中引力波背景的非高斯偏离，提出偏振框架不变模型，发现归一化偏度极小。
Pulsar Timing Arrays (PTAs) use high accuracy timing of a collection of low timing noise pulsars to search for gravitational waves in the microhertz to nanohertz frequency band. The sensitivity of such a PTA depends on (a) the direction of the gravitational wave source, (b) the timing accuracy of the pulsars in the array and (c) how the available observing time is allocated among those pulsars. Here, we present a simple way to calculate the sensitivity of the PTA as a function of direction of a single GW source, based only on the location and root-mean-square residual of the pulsars in the arr…
We study the ultralight vector dark matter with a mass around $10^{-23}\,\mathrm{eV}$. The vector field oscillating coherently on galactic scales induces oscillations of the spacetime metric with a frequency around nHz, which is detectable by pulsar timing arrays. We find that the pulsar timing signal due to the vector dark matter has nontrivial angular dependence unlike the scalar dark matter and the maximal amplitude is three times larger than that of the scalar dark matter.
The pulsar timing residuals induced by gravitational waves from non-evolving single binary sources are affected by many parameters related to the relative positions of the pulsar and the gravitational wave sources. We will fully analyze the effects due to different parameters one by one. The standard deviations of the timing residuals will be calculated with a variable parameter fixing a set of other parameters. The orbits of the binary sources will be generally assumed to be elliptical. The influences of different eccentricities on the pulsar timing residuals will also studied in detail. We f…
Detecting Chiral Gravitational Wave Background with a Dipole Pulsar Timing Array
本文提出双极脉冲星定时阵列系统，通过交叉相关信号推导重叠减少函数，发现其对纳赫兹范围的手性引力波背景具有灵敏度，并扩展了引力波背景探测的频率范围。
We constrain the cosmological density of cosmic string loops using two observational signatures -- gravitational microlensing and the Kaiser-Stebbins effect. Photometry from RXTE and CoRoT space missions and pulsar timing from Parkes Pulsar Timing Array, Arecibo and Green Bank radio telescopes allow us to probe cosmic strings in a wide range of tensions $Gμ/c^2=10^{-16}\div10^{-10}$. We find that pulsar timing data provide the most stringent constraints on the abundance of light strings at the level $Ω_s \sim 10^{-3}$. Future observational facilities such as the Square Kilometer Array will all…
One of the open questions of modern cosmology is the nature and properties of the Dark Matter halo and its substructures. In this work we study the gravitational effect of dark matter substructures on pulsar timing observations. Since millisecond pulsars are stable and accurate emitters, they have been proposed as plausible astrophysical tools to probe the gravitational effects of dark matter structures. We study this effect on pulsar timing through Shapiro time delay (or Integrated Sachs-Wolfe (ISW) effect) and Doppler effects statistically, showing that the latter dominates the signal. For t…
Gravitational waves provide a new probe of the Universe which can reveal a number of cosmological and astrophysical phenomena that cannot be observed by electromagnetic waves. Different frequencies of gravitational waves are detected by different means. Among them, precision measurements of pulsar timing provides a natural detector for gravitational waves with light-year scale wavelengths. In this review, first a basic framework to detect a stochastic gravitational wave background using pulsar timing array is introduced, and then possible interpretations of the latest observational result of 1…
Pulsar timing array sensitivity to anisotropies in the gravitational wave background
本研究利用脉冲星计时延迟的全协方差矩阵评估PTA对引力波背景各向异性的灵敏度，发现未来可实现低多极矩百分比级精度，且各向异性与Hellings-Downs角相关性可独立重建。
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.
We investigate the capability of pulsar timing arrays (PTAs) as a probe of primordial black holes (PBHs), which might constitute the Galactic dark matter. A PBH passing nearby the Earth or a pulsar gives an impulse acceleration and induces residuals on otherwise orderly pulsar timing data. We show that the timing residuals induced at pulsars are optimal for searching heavier PBHs than those at the Earth, and the two probes are highly complemental. Future facilities like SKA could detect PBHs with masses around 10^(22-28) g even if only a small fraction (< 1%) of the Galactic dark matter consis…
The coherent oscillation of ultralight dark matter in the mass regime around $10^{-23}$ eV induces changes in gravitational potential with the frequency in the nanohertz range. This effect is known to produce a monochromatic signal in the pulsar timing residuals. Here we discuss a multifield scenario that produces a wide spectrum of frequencies, such that the ultralight particle oscillation can mimic the pulsar timing signal of stochastic common spectrum process. We discuss how ultralight dark matter with various spins produces such a wide band spectrum on pulsar timing residuals and perform t…
Pulsar timing and polarimetry: results and perspectives
本文全面综述了脉冲星计时与偏振测量领域的研究现状，重点介绍了多个国际PTA合作组织在探测nHz引力波随机背景方面的最新进展，并回顾了基于脉冲星数据对标量超轻物质的约束，探讨了其在基础物理和宇宙学中的应用前景。
Astrophysical neutrino oscillations after pulsar timing array analyses
本文研究脉冲星计时阵列合作组报告的引力波背景对中微子味振荡的影响，并探讨近未来中微子探测器如何揭示这些效应以帮助区分nHz以下的不同引力波背景模型。
Pulsar timing provides a sensitive probe of small-scale structure. Gravitational perturbations arising from an inhomogeneous environment could manifest as detectable perturbations in the pulsation phase. Consequently, pulsar timing arrays have been proposed as a probe of dark matter substructure on mass scales as small as $10^{-11} M_\odot$. Since the small-scale mass distribution is connected to early-Universe physics, pulsar timing can therefore constrain the thermal history prior to Big Bang nucleosynthesis (BBN), a period that remains largely unprobed. We explore here the prospects for pul…
We derive scaling laws for the signal-to-noise ratio of the optimal cross-correlation statistic, and show that the large power-law increase of the signal-to-noise ratio as a function of the the observation time $T$ that is usually assumed holds only at early times. After enough time has elapsed, pulsar timing arrays enter a new regime where the signal to noise only scales as $\sqrt{T}$. In addition, in this regime the quality of the pulsar timing data and the cadence become relatively un-important. This occurs because the lowest frequencies of the pulsar timing residuals become gravitational-w…
Nancay radiotelescope is involved in high precision timing since 20 years. Since 2004, a coherent dedispersion instrumentation enables numerous routine observations on more than 200 pulsars using half of the time if this 100-meters class radiotelescope. Two main programs are currently conducted. A large set of young and old pulsars is timed for a multi-wavelength approach, complementary to the very successful high energy observations of pulsars done by FERMI. A set of highly stable millisecond pulsars is monitored as our contribution to the European Pulsar Timing Array in order to probe the co…
Any unambiguous detection of a stochastic gravitational wave background by a pulsar timing array will rest on the measurement of a characteristic angular correlation between pulsars. The ability to measure this correlation will depend on the geometry of the array. However, spatially correlated sources of noise, such as errors in the planetary ephemeris or clock errors, can produce false-positive correlations. The severity of this contamination will also depend on the geometry of the array. This paper quantifies these geometric effects with a spherical harmonic analysis of the pulsar timing res…
Ultra-light Dark Matter (ULDM) models are suitable candidates for the cosmological Dark Matter that may leave characteristic imprints in many observables. Among other probes, signatures of ULDM can be searched for in pulsar timing data. In this work we describe the effects of spin-2 ULDM on pulsar timing arrays, extending previous results on lower spins. Spin-2 ULDM is universally coupled to standard matter with dimensionless strength $α$. We estimate that current data could constrain this coupling in the mass range $m\lesssim4\times10^{-22}$ eV at the $10^{-5}$ to $10^{-6}$ level, which is th…
The sensitivity of Pulsar Timing Arrays to gravitational waves depends on the noise present in the individual pulsar timing data. Noise may be either intrinsic or extrinsic to the pulsar. Intrinsic sources of noise will include rotational instabilities, for example. Extrinsic sources of noise include contributions from physical processes which are not sufficiently well modelled, for example, dispersion and scattering effects, analysis errors and instrumental instabilities. We present the results from a noise analysis for 42 millisecond pulsars (MSPs) observed with the European Pulsar Timing Ar…
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