European Pulsar Timing Array limits on an isotropic stochastic gravitational-wave background

We present new limits on an isotropic stochastic gravitational-wave background (GWB) using a six pulsar data set spanning 18 yr of observations from the 2015 European Pulsar Timing Array data release. Performing a Bayesian analysis, we fit simultaneously for the intrinsic noise parameters for each pulsar, along with common correlated signals including clock, and Solar system ephemeris errors, obtaining a robust 95 per cent upper limit on the dimensionless strain amplitude A of the background of A < 3.0 × 10^(−15) at a reference frequency of 1 yr^(−1) and a spectral index of 13/3, corresponding to a background from inspiralling supermassive black hole binaries, constraining the GW energy density to Ω_(gw)(f)h^2 < 1.1 × 10^(−9) at 2.8 nHz. We also present limits on the correlated power spectrum at a series of discrete frequencies, and show that our sensitivity to a fiducial isotropic GWB is highest at a frequency of ∼5 × 10^(−9) Hz. Finally, we discuss the implications of our analysis for the astrophysics of supermassive black hole binaries, and present 95 per cent upper limits on the string tension, Gμ/c^2, characterizing a background produced by a cosmic string network for a set of possible scenarios, and for a stochastic relic GWB. For a Nambu–Goto field theory cosmic string network, we set a limit Gμ/c^2 < 1.3 × 10^(−7), identical to that set by the Planck Collaboration, when combining Planck and high-ℓ cosmic microwave background data from other experiments. For a stochastic relic background, we set a limit of Ω^(relic)_(gw)(f)h^2 <1.2×10^(−9), a factor of 9 improvement over the most stringent limits previously set by a pulsar timing array

Fisher Formalism For Anisotropic Gravitational-Wave Background Searches With Pulsar Timing Arrays

Pulsar timing arrays (PTAs) are currently the only experiments directly sensitive to gravitational waves with decade-long periods. Within the next five to ten years, PTAs are expected to detect the stochastic gravitational-wave background (SGWB) collectively sourced by inspiraling supermassive black hole binaries. It is expected that this background is mostly isotropic, and current searches focus on the monopole part of the SGWB. Looking ahead, anisotropies in the SGWB may provide a trove of additional information on both known and unknown astrophysical and cosmological sources. In this paper, we build a simple yet realistic Fisher formalism for anisotropic SGWB searches with PTAs. Our formalism is able to accommodate realistic properties of PTAs and allows simple and accurate forecasts. We illustrate our approach with an idealized PTA consisting of identical, isotropically distributed pulsars. In a companion paper, we apply our formalism to current PTAs and show that it can be a powerful tool to guide and optimize real data analysis

Insights Into Searches For Anisotropies In The Nanohertz Gravitational-Wave Background

Within the next several years pulsar timing arrays (PTAs) are positioned to detect the stochastic gravitational-wave background (GWB) likely produced by the collection of inspiralling supermassive black holes binaries, and potentially constrain some exotic physics. So far most of the pulsar timing data analysis has focused on the monopole of the GWB, assuming it is perfectly isotropic. The natural next step is to search for anisotropies in the GWB. In this paper, we use the recently developed PTA Fisher matrix to gain insights into optimal search strategies for GWB anisotropies. For concreteness, we apply our results to the European Pulsar Timing Array (EPTA) data, using realistic noise characteristics of its pulsars. We project the detectability of a GWB whose angular dependence is assumed to be a linear combination of predetermined maps, such as spherical harmonics or coarse pixels. We find that the GWB monopole is always statistically correlated with these maps, implying a loss of sensitivity to the monopole when searching simultaneously for anisotropies. We then derive the angular distributions of the GWB intensity to which a PTA is most sensitive, and illustrate how one may use these “principal maps” to approximately reconstruct the angular dependence of the GWB. Since the principal maps are neither perfectly anisotropic nor uncorrelated with the monopole, we also develop a frequentist criterion to specifically search for anisotropies in the GWB without any prior knowledge about their angular distribution. Lastly, we show how to recover existing EPTA results with our Fisher formalism, and clarify their meaning. The tools presented here will be valuable in guiding and optimizing the computationally demanding analyses of pulsar timing data

From spin noise to systematics: stochastic processes in the first International Pulsar Timing Array data release

We analyse the stochastic properties of the 49 pulsars that comprise the first International Pulsar Timing Array (IPTA) data release. We use Bayesian methodology, performing model selection to determine the optimal description of the stochastic signals present in each pulsar. In addition to spin-noise and dispersion-measure (DM) variations, these models can include timing noise unique to a single observing system, or frequency band. We show the improved radio-frequency coverage and presence of overlapping data from different observing systems in the IPTA data set enables us to separate both system and band-dependent effects with much greater efficacy than in the individual pulsar timing array (PTA) data sets. For example, we show that PSR J1643−1224 has, in addition to DM variations, significant band-dependent noise that is coherent between PTAs which we interpret as coming from time-variable scattering or refraction in the ionized interstellar medium. Failing to model these different contributions appropriately can dramatically alter the astrophysical interpretation of the stochastic signals observed in the residuals. In some cases, the spectral exponent of the spin-noise signal can vary from 1.6 to 4 depending upon the model, which has direct implications for the long-term sensitivity of the pulsar to a stochastic gravitational-wave (GW) background. By using a more appropriate model, however, we can greatly improve a pulsar's sensitivity to GWs. For example, including system and band-dependent signals in the PSR J0437−4715 data set improves the upper limit on a fiducial GW background by ∼60 per cent compared to a model that includes DM variations and spin-noise only

The NANOGrav Nine-year Data Set: Limits on the Isotropic Stochastic Gravitational Wave Background

We compute upper limits on the nanohertz-frequency isotropic stochastic gravitational wave background (GWB) using the 9 year data set from the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) collaboration. Well-tested Bayesian techniques are used to set upper limits on the dimensionless strain amplitude (at a frequency of 1 yr^(−1) for a GWB from supermassive black hole binaries of A_(gw) < 1.5 x 10^(-15). We also parameterize the GWB spectrum with a broken power-law model by placing priors on the strain amplitude derived from simulations of Sesana and McWilliams et al. Using Bayesian model selection we find that the data favor a broken power law to a pure power law with odds ratios of 2.2 and 22 to one for the Sesana and McWilliams prior models, respectively. Using the broken power-law analysis we construct posterior distributions on environmental factors that drive the binary to the GW-driven regime including the stellar mass density for stellar-scattering, mass accretion rate for circumbinary disk interaction, and orbital eccentricity for eccentric binaries, marking the first time that the shape of the GWB spectrum has been used to make astrophysical inferences. Returning to a power-law model, we place stringent limits on the energy density of relic GWs, Ω_(gw)(f)h^2 < 4.2 x 10^(-10). Our limit on the cosmic string GWB, Ω_(gw)(f)h^2 < 2.2 x 10^(-10), translates to a conservative limit on the cosmic string tension with Gµ < 3.3 x 10^(-8), a factor of four better than the joint Planck and high-l cosmic microwave background data from other experiments

High-precision timing of 42 millisecond pulsars with the European Pulsar Timing Array

We report on the high-precision timing of 42 radio millisecond pulsars (MSPs) observed by the European Pulsar Timing Array (EPTA). This EPTA Data Release 1.0 extends up to mid-2014 and baselines range from 7–18 yr. It forms the basis for the stochastic gravitational-wave background, anisotropic background, and continuous-wave limits recently presented by the EPTA elsewhere. The Bayesian timing analysis performed with temponest yields the detection of several new parameters: seven parallaxes, nine proper motions and, in the case of six binary pulsars, an apparent change of the semimajor axis. We find the NE2001 Galactic electron density model to be a better match to our parallax distances (after correction from the Lutz–Kelker bias) than the M2 and M3 models by Schnitzeler. However, we measure an average uncertainty of 80 per cent (fractional) for NE2001, three times larger than what is typically assumed in the literature. We revisit the transverse velocity distribution for a set of 19 isolated and 57 binary MSPs and find no statistical difference between these two populations. We detect Shapiro delay in the timing residuals of PSRs J1600−3053 and J1918−0642, implying pulsar and companion masses m_p=1.22^(+0.5)_(−0.35) M_⊙, m_c=0.21^(+0.06)_(−0.04) M_⊙ and m_p=1.25^(+0.6)_(−0.4) M_⊙, m_c=0.23^(+0.07)_(−0.05) M_⊙, respectively. Finally, we use the measurement of the orbital period derivative to set a stringent constraint on the distance to PSRs J1012+5307 and J1909−3744, and set limits on the longitude of ascending node through the search of the annual-orbital parallax for PSRs J1600−3053 and J1909−3744

European Pulsar Timing Array limits on an isotropic stochastic gravitational-wave background

We present new limits on an isotropic stochastic gravitational-wave background (GWB) using a six pulsar data set spanning 18 yr of observations from the 2015 European Pulsar Timing Array data release. Performing a Bayesian analysis, we fit simultaneously for the intrinsic noise parameters for each pulsar, along with common correlated signals including clock, and Solar system ephemeris errors, obtaining a robust 95 per cent upper limit on the dimensionless strain amplitude A of the background of A < 3.0 × 10^(−15) at a reference frequency of 1 yr^(−1) and a spectral index of 13/3, corresponding to a background from inspiralling supermassive black hole binaries, constraining the GW energy density to Ω_(gw)(f)h^2 < 1.1 × 10^(−9) at 2.8 nHz. We also present limits on the correlated power spectrum at a series of discrete frequencies, and show that our sensitivity to a fiducial isotropic GWB is highest at a frequency of ∼5 × 10^(−9) Hz. Finally, we discuss the implications of our analysis for the astrophysics of supermassive black hole binaries, and present 95 per cent upper limits on the string tension, Gμ/c^2, characterizing a background produced by a cosmic string network for a set of possible scenarios, and for a stochastic relic GWB. For a Nambu–Goto field theory cosmic string network, we set a limit Gμ/c^2 < 1.3 × 10^(−7), identical to that set by the Planck Collaboration, when combining Planck and high-ℓ cosmic microwave background data from other experiments. For a stochastic relic background, we set a limit of Ω^(relic)_(gw)(f)h^2 <1.2×10^(−9), a factor of 9 improvement over the most stringent limits previously set by a pulsar timing array

Limits on Anisotropy in the Nanohertz Stochastic Gravitational Wave Background

The paucity of observed supermassive black hole binaries (SMBHBs) may imply that the gravitational wave background (GWB) from this population is anisotropic, rendering existing analyses suboptimal. We present the first constraints on the angular distribution of a nanohertz stochastic GWB from circular, inspiral-driven SMBHBs using the 2015 European Pulsar Timing Array data. Our analysis of the GWB in the ∼2–90  nHz band shows consistency with isotropy, with the strain amplitude in l>0 spherical harmonic multipoles ≲40% of the monopole value. We expect that these more general techniques will become standard tools to probe the angular distribution of source populations