The NANOGrav 11-Year Data Set: Limits on Gravitational Waves from Individual Supermassive Black Hole Binaries

Observations indicate that nearly all galaxies contain supermassive black holes (SMBHs) at their centers. When galaxies merge, their component black holes form SMBH binaries (SMBHBs), which emit low-frequency gravitational waves (GWs) that can be detected by pulsar timing arrays (PTAs). We have searched the recently-released North American Nanohertz Observatory for Gravitational Waves (NANOGrav) 11-year data set for GWs from individual SMBHBs in circular orbits. As we did not find strong evidence for GWs in our data, we placed 95\% upper limits on the strength of GWs from such sources as a function of GW frequency and sky location. We placed a sky-averaged upper limit on the GW strain of $h_0 < 7.3(3) \times 10^{-15}$ at $f_\mathrm{gw}= 8$ nHz. We also developed a technique to determine the significance of a particular signal in each pulsar using ``dropout' parameters as a way of identifying spurious signals in measurements from individual pulsars. We used our upper limits on the GW strain to place lower limits on the distances to individual SMBHBs. At the most-sensitive sky location, we ruled out SMBHBs emitting GWs with $f_\mathrm{gw}= 8$ nHz within 120 Mpc for $\mathcal{M} = 10^9 \, M_\odot$, and within 5.5 Gpc for $\mathcal{M} = 10^{10} \, M_\odot$. We also determined that there are no SMBHBs with $\mathcal{M} > 1.6 \times 10^9 \, M_\odot$ emitting GWs in the Virgo Cluster. Finally, we estimated the number of potentially detectable sources given our current strain upper limits based on galaxies in Two Micron All-Sky Survey (2MASS) and merger rates from the Illustris cosmological simulation project. Only 34 out of 75,000 realizations of the local Universe contained a detectable source, from which we concluded it was unsurprising that we did not detect any individual sources given our current sensitivity to GWs.Comment: 10 pages, 11 figures. Accepted by Astrophysical Journal. Please send any comments/questions to S. J. Vigeland ([email protected]

Testing Theories of Gravitation Using 21-Year Timing of Pulsar Binary J1713+0747

We report 21-year timing of one of the most precise pulsars: PSR J1713+0747. Its pulse times of arrival are well modeled by a comprehensive pulsar binary model including its three-dimensional orbit and a noise model that incorporates short-and long-timescale correlated noise such as jitter and red noise. Its timing residuals have weighted root mean square similar to 92 ns. The new data set allows us to update and improve previous measurements of the system properties, including the masses of the neutron star (1.31 +/- 0.11 M-circle dot) and the companion white dwarf (0.286 +/- 0.012 M-circle dot) as well as their parallax distance 1.15 +/- 0.03 kpc. We measured the intrinsic change in orbital period, (P) over dot(b)(Int), is -0.20 +/- 0.17 ps s(-1), which is not distinguishable from zero. This result, combined with the measured (P) over dot(b)(Int) of other pulsars, can place a generic limit on potential changes in the gravitational constant G. We found that (G) over dot/G is consistent with zero [(-0.6 +/- 1.1) x 10(-12) yr(-1), 95% confidence] and changes at least a factor of 31 (99.7% confidence) more slowly than the average expansion rate of the universe. This is the best (G) over dot/G limit from pulsar binary systems. The (P) over dot(b)(Int) of pulsar binaries can also place limits on the putative coupling constant for dipole gravitational radiation kappa(D) = (-0.9 +/- 3.3) 10(-4) (95% confidence). Finally, the nearly circular orbit of this pulsar binary allows us to constrain statistically the strong-field post-Newtonian parameters Delta, which describes the violation of strong equivalence principle, and (alpha) over cap (3), which describes a breaking of both Lorentz invariance in gravitation and conservation of momentum. We found, at 95% confidence, Delta <0.01 and (3) <2 x 10(-20) based on PSR J1713+0747

The NANOGrav Nine-year Data Set: Measurement and Analysis of Variations in Dispersion Measures

We analyze dispersion measure (DM) variations of 37 millisecond pulsars in the nine-year North American Nanohertz Observatory for Gravitational Waves (NANOGrav) data release and constrain the sources of these variations. DM variations can result from a changing distance between Earth and the pulsar, inhomogeneities in the interstellar medium, and solar effects. Variations are significant for nearly all pulsars, with characteristic timescales comparable to or even shorter than the average spacing between observations. Five pulsars have periodic annual variations, 14 pulsars have monotonically increasing or decreasing trends, and 14 pulsars show both effects. Of the four pulsars with linear trends that have line-of-sight velocity measurements, three are consistent with a changing distance and require an overdensity of free electrons local to the pulsar. Several pulsars show correlations between DM excesses and lines of sight that pass close to the Sun. Mapping of the DM variations as a function of the pulsar trajectory can identify localized interstellar medium features and, in one case, an upper limit to the size of the dispersing region of 4 au. Four pulsars show roughly Kolmogorov structure functions (SFs), and another four show SFs less steep than Kolmogorov. One pulsar has too large an uncertainty to allow comparisons. We discuss explanations for apparent departures from a Kolmogorov-like spectrum, and we show that the presence of other trends and localized features or gradients in the interstellar medium is the most likely cause

Multi-Messenger Gravitational Wave Searches with Pulsar Timing Arrays: Application to 3C66B Using the NANOGrav 11-year Data Set

When galaxies merge, the supermassive black holes in their centers may form binaries and, during the process of merger, emit low-frequency gravitational radiation in the process. In this paper we consider the galaxy 3C66B, which was used as the target of the first multi-messenger search for gravitational waves. Due to the observed periodicities present in the photometric and astrometric data of the source of the source, it has been theorized to contain a supermassive black hole binary. Its apparent 1.05-year orbital period would place the gravitational wave emission directly in the pulsar timing band. Since the first pulsar timing array study of 3C66B, revised models of the source have been published, and timing array sensitivities and techniques have improved dramatically. With these advances, we further constrain the chirp mass of the potential supermassive black hole binary in 3C66B to less than $(1.65\pm0.02) \times 10^9~{M_\odot}$ using data from the NANOGrav 11-year data set. This upper limit provides a factor of 1.6 improvement over previous limits, and a factor of 4.3 over the first search done. Nevertheless, the most recent orbital model for the source is still consistent with our limit from pulsar timing array data. In addition, we are able to quantify the improvement made by the inclusion of source properties gleaned from electromagnetic data to `blind' pulsar timing array searches. With these methods, it is apparent that it is not necessary to obtain exact a priori knowledge of the period of a binary to gain meaningful astrophysical inferences.Comment: 14 pages, 6 figures. Accepted by Ap

The NANOGrav Nine-year Data Set:Noise Budget for Pulsar Arrival Times on Intraday Timescales

The use of pulsars as astrophysical clocks for gravitational wave (GW) experiments demands the highest possible timing precision. Pulse times of arrival (TOAs) are limited by stochastic processes that occur in the pulsar itself, along the line of sight through the interstellar medium, and in the measurement process. On timescales of seconds to hours, the TOA variance exceeds that from template-fitting errors due to additive noise. We assess contributions to the total variance from two additional effects: amplitude and phase jitter intrinsic to single pulses and changes in the interstellar impulse response from scattering. The three effects have different dependencies on time, frequency, and pulse signal-to-noise ratio. We use data on 37 pulsars from the North American Nanohertz Observatory for GWs to assess the individual contributions to the overall intraday noise budget for each pulsar. We detect jitter in 22 pulsars and estimate the average value of rms jitter in our pulsars to be $\sim 1\%$ of pulse phase. We examine how jitter evolves as a function of frequency and find evidence for evolution. Finally, we compare our measurements with previous noise parameter estimates and discuss methods to improve GW detection pipelines

A Second Chromatic Timing Event of Interstellar Origin toward PSR J1713+0747

The frequency dependence of radio pulse arrival times provides a probe of structures in the intervening media. Demorest et al. was the first to show a short-term (~100–200 days) reduction in the electron content along the line of sight to PSR J1713+0747 in data from 2008 (approximately MJD 54750) based on an apparent dip in the dispersion measure of the pulsar. We report on a similar event in 2016 (approximately MJD 57510), with average residual pulse-arrival times ≈−3.0, −1.3, and −0.7 μs at 820, 1400, and 2300 MHz, respectively. Timing analyses indicate possible departures from the standard ν −2 dispersive-delay dependence. We discuss and rule out a wide variety of potential interpretations. We find the likeliest scenario to be lensing of the radio emission by some structure in the interstellar medium, which causes multiple frequency-dependent pulse arrival-time delays

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 Agw \u3c 1.5 × 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, Ωgw(f)h2 \u3c 4.2 × 10-10. Our limit on the cosmic string GWB, Ωgw(f)h2 \u3c 2.2 × 10-10, translates to a conservative limit on the cosmic string tension with Gμ \u3c 3.3 × 10-8, a factor of four better than the joint Planck and high-l cosmic microwave background data from other experiments