Efficient Gravitational Wave Searches with Pulsar Timing Arrays using Hamiltonian Monte Carlo

Pulsar timing arrays (PTAs) detect low-frequency gravitational waves (GWs) bylooking for correlated deviations in pulse arrival times. Current Bayesiansearches use Markov Chain Monte Carlo (MCMC) methods, which struggle to samplethe large number of parameters needed to model the PTA and GW signals. As thedata span and number of pulsars increase, this problem will only worsen. Analternative Monte Carlo sampling method, Hamiltonian Monte Carlo (HMC),utilizes Hamiltonian dynamics to produce sample proposals informed byfirst-order gradients of the model likelihood. This in turn allows it toconverge faster to high dimensional distributions. We implement HMC as analternative sampling method in our search for an isotropic stochastic GWbackground, and show that this method produces equivalent statistical resultsto similar analyses run with standard MCMC techniques, while requiring 100-200times fewer samples. We show that the speed of HMC sample generation scales as$\mathcal{O}(N_\mathrm{psr}^{5/4})$ where $N_\mathrm{psr}$ is the number ofpulsars, compared to $\mathcal{O}(N_\mathrm{psr}^2)$ for MCMC methods. Thesefactors offset the increased time required to generate a sample using HMC,demonstrating the value of adopting HMC techniques for PTAs.<br

Microarcsecond VLBI pulsar astrometry with PSRPI I. Two binary millisecond pulsars with white dwarf companions

Model-independent distance constraints to binary millisecond pulsars (MSPs) are of great value to both the timing observations of the radio pulsars, and multiwavelength observations of their companion stars. Very Long Baseline Interferometry (VLBI) astrometry can be employed to provide these model-independent distances with very high precision via the detection of annual geometric parallax. Using the Very Long Baseline Array, we have observed two binary millisecond pulsars, PSR J1022+1001 and J2145-0750, over a two-year period and measured their distances to be 700 +14 -10 pc and 613 +16 -14 pc respectively. We use the well-calibrated distance in conjunction with revised analysis of optical photometry to tightly constrain the nature of their massive (M ~ 0.85 Msun) white dwarf companions. Finally, we show that several measurements of their parallax and proper motion of PSR J1022+1001 and PSR J2145-0750 obtained by pulsar timing array projects are incorrect, differing from the more precise VLBI values by up to 5 sigma. We investigate possible causes for the discrepancy, and find that imperfect modeling of the solar wind is a likely candidate for the timing model errors given the low ecliptic latitude of these two pulsars.Comment: 14 pages, 9 figures, 6 tables; minor revisions in response to referee comments to match version accepted by Ap

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]

The scientific potential of space-based gravitational wave detectors

The millihertz gravitational wave band can only be accessed with a space-based interferometer, but it is one of the richest in potential sources. Observations in this band have amazing scientific potential. The mergers between massive black holes with mass in the range 10 thousand to 10 million solar masses, which are expected to occur following the mergers of their host galaxies, produce strong millihertz gravitational radiation. Observations of these systems will trace the hierarchical assembly of structure in the Universe in a mass range that is very difficult to probe electromagnetically. Stellar mass compact objects falling into such black holes in the centres of galaxies generate detectable gravitational radiation for several years prior to the final plunge and merger with the central black hole. Measurements of these systems offer an unprecedented opportunity to probe the predictions of general relativity in the strong-field and dynamical regime. Millihertz gravitational waves are also generated by millions of ultra-compact binaries in the Milky Way, providing a new way to probe galactic stellar populations. ESA has recognised this great scientific potential by selecting The Gravitational Universe as its theme for the L3 large satellite mission, scheduled for launch in ~2034. In this article we will review the likely sources for millihertz gravitational wave detectors and describe the wide applications that observations of these sources could have for astrophysics, cosmology and fundamental physics.Comment: 18 pages, 2 figures, contribution to Gravitational Wave Astrophysics, the proceedings of the 2014 Sant Cugat Forum on Astrophysics; v2 includes one additional referenc

Evidence for alignment of the rotation and velocity vectors in pulsars

We present strong observational evidence for a relationship between the direction of a pulsar's motion and its rotation axis. We show carefully calibrated polarization data for 25 pulsars, 20 of which display linearly polarized emission from the pulse longitude at closest approach to the magnetic pole. Such data allow determination of the position angle of the linear polarisation which in turn reflects the position angle of the rotation axis. Of these 20 pulsars, 10 show an offset between the velocity vector and the polarisation position angle which is either less than 10\degr or more than 80\degr, a fraction which is very unlikely by random chance. We believe that the bimodal nature of the distribution arises from the presence of orthogonal polarisation modes in the pulsar radio emission. In some cases this orthogonal ambiguity is resolved by observations at other wavelengths so that we conclude that the velocity vector and the rotation axis are aligned at birth. Strengthening the case is the fact that 4 of the 5 pulsars with ages less than 3 Myr show this relationship, including the Vela pulsar. We discuss the implications of these findings in the context of the Spruit & Phinney (1998)\nocite{sp98} model of pulsar birth-kicks. We point out that, contrary to claims in the literature, observations of double neutron star systems do not rule out aligned kick models and describe a possible observational test involving the double pulsar system.Comment: MNRAS, In Pres

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

Compact Binary Coalescences in the Band of Ground-based Gravitational-Wave Detectors

As the ground-based gravitational-wave telescopes LIGO, Virgo, and GEO 600 approach the era of first detections, we review the current knowledge of the coalescence rates and the mass and spin distributions of merging neutron-star and black-hole binaries. We emphasize the bi-directional connection between gravitational-wave astronomy and conventional astrophysics. Astrophysical input will make possible informed decisions about optimal detector configurations and search techniques. Meanwhile, rate upper limits, detected merger rates, and the distribution of masses and spins measured by gravitational-wave searches will constrain astrophysical parameters through comparisons with astrophysical models. Future developments necessary to the success of gravitational-wave astronomy are discussed.Comment: Replaced with version accepted by CQG