Modeling the uncertainties of solar system ephemerides for robust gravitational-wave searches with pulsar-timing arrays

The regularity of pulsar emissions becomes apparent once we reference the pulses' times of arrivals to the inertial rest frame of the solar system. It follows that errors in the determination of Earth's position with respect to the solar system barycenter can appear as a time-correlated bias in pulsar-timing residual time series, affecting the searches for low-frequency gravitational waves performed with pulsar-timing arrays. Indeed, recent array data sets yield different gravitational-wave background upper limits and detection statistics when analyzed with different solar system ephemerides. Crucially, the ephemerides do not generally provide usable error representations. In this article, we describe the motivation, construction, and application of a physical model of solar system ephemeris uncertainties, which focuses on the degrees of freedom (Jupiter's orbital elements) most relevant to gravitational-wave searches with pulsar-timing arrays. This model, BayesEphem, was used to derive ephemeris-robust results in NANOGrav's 11 yr stochastic-background search, and it provides a foundation for future searches by NANOGrav and other consortia. The analysis and simulations reported here suggest that ephemeris modeling reduces the gravitational-wave sensitivity of the 11 yr data set and that this degeneracy will vanish with improved ephemerides and with pulsar-timing data sets that extend well beyond a single Jovian orbital period

The nightmare scenario: measuring the stochastic gravitational wave background from stalling massive black hole binaries with pulsar timing arrays

Massive black-hole binaries, formed when galaxies merge, are among the primary sources of gravitational waves targeted by ongoing Pulsar Timing Array (PTA) experiments and the upcoming space-based LISA interferometer. However, their formation and merger rates are still highly uncertain. Recent upper limits on the stochastic gravitational-wave background obtained by PTAs are starting being in marginal tension with theoretical models for the pairing and orbital evolution of these systems. This tension can be resolved by assuming that these binaries are more eccentric or interact more strongly with the environment (gas and stars) than expected, or by accounting for possible selection biases in the construction of the theoretical models. However, another (pessimistic) possibility is that these binaries do not merge at all, but stall at large ( 3c pc) separations. We explore this extreme scenario by using a galaxy-formation semi-analytic model including massive black holes (isolated and in binaries), and show that future generations of PTAs will detect the stochastic gravitational-wave background from the massive black-hole binary population within 10 1215 years of observations, even in the "nightmare scenario" in which all binaries stall at the hardening radius. Moreover, we argue that this scenario is too pessimistic, because our model predicts the existence of a sub-population of binaries with small mass ratios (q 7210 123) that should merge within a Hubble time simply as a result of gravitational-wave emission. This sub-population will be observable with large signal-to-noise ratios by future PTAs thanks to next-generation radio telescopes such as SKA or FAST, and possibly by LISA

Post-Newtonian evolution of massive black hole triplets in galactic nuclei II. Survey of the parameter space

Massive black hole binaries (MBHBs) are expected to form at the centre of merging galaxies during the hierarchical assembly of the cosmic structure, and are expected to be the loudest sources of gravitational waves (GWs) in the low frequency domain. However, because of the dearth of energy exchanges with background stars and gas, many of these MBHBs may stall at separations too large for GW emission to drive them to coalescence in less than a Hubble time. Triple MBH systems are then bound to form after a further galaxy merger, triggering a complex and rich dynamics that can eventually lead to MBH coalescence. Here we report on the results of a large set of numerical simulations, where MBH triplets are set in spherical stellar potentials and MBH dynamics is followed through 2.5 post-Newtonian order in the equations of motion. From our full suite of simulated systems we find that a fraction 4320 1230% of the MBH binaries that would otherwise stall are led to coalesce within a Hubble time. The corresponding coalescence timescale peaks around 300 Myr, while the eccentricity close to the plunge, albeit small, is non-negligible ( 720.1). We construct and discuss marginalised probability distributions of the main parameters involved and, in a companion paper of the series, we will use the results presented here to forecast the contribution of MBH triplets to the GW signal in the nHz regime probed by Pulsar Timing Array experiments

Post-Newtonian evolution of massive black hole triplets in galactic nuclei - III. A robust lower limit to the nHz stochastic background of gravitational waves

Inspiraling massive black hole binaries (MBHBs) forming in the aftermath of galaxy mergers are expected to be the loudest gravitational-wave (GW) sources relevant for pulsar-timing arrays (PTAs) at nHz frequencies. The incoherent overlap of signals from a cosmic population of MBHBs gives rise to a stochastic GW background (GWB) with characteristic strain around h c ~ 10 -15 at a reference frequency of 1 yr -1 , although uncertainties around this value are large. Current PTAs are piercing into theGWamplitude range predicted by MBHB-population models, but no detection has been reported so far. To assess the future success prospects of PTA experiments, it is therefore important to estimate the minimum GWB level consistent with our current understanding of the formation and evolution of galaxies and massive black holes (MBHs). To this purpose, we couple a semi-analytic model of galaxy evolution and an extensive study of the statistical outcome of triple MBH interactions. We show that even in the most pessimistic scenario where all MBHBs stall before entering the GW-dominated regime, triple interactions resulting from subsequent galaxy mergers inevitably drive a considerable fraction of the MBHB population to coalescence. At frequencies relevant for PTA, the resulting GWB is only a factor of 2-3 suppressed compared to a fiducial model where binaries are allowed to merge over Gyr time-scales. Coupled with current estimates of the expected GWB amplitude range, our findings suggest that the minimum GWB from cosmic MBHBs is unlikely to be lower than h c ~ 10 -16 (at f = 1 yr -1 ), well within the expected sensitivity of projected PTAs based on future observations with FAST, MeerKAT, and SKA. \ua9 2018 The Author(s)

Detecting eccentric supermassive black hole binaries with pulsar timing arrays: Resolvable source strategies

The couplings between supermassive black-hole binaries and their environments within galactic nuclei have been well studied as part of the search for solutions to the final parsec problem. The scattering of stars by the binary or the interaction with a circumbinary disk may efficiently drive the system to sub-parsec separations, allowing the binary to enter a regime where the emission of gravitational waves can drive it to merger within a Hubble time. However, these interactions can also affect the orbital parameters of the binary. In particular, they may drive an increase in binary eccentricity which survives until the system's gravitational-wave signal enters the pulsar-timing array band. Therefore, if we can measure the eccentricity from observed signals, we can potentially deduce some of the properties of the binary environment. To this end, we build on previous techniques to present a general Bayesian pipeline with which we can detect and estimate the parameters of an eccentric supermassive black-hole binary system with pulsar-timing arrays. Additionally, we generalize the pulsar-timing array $\mathcal{F}_e$-statistic to eccentric systems, and show that both this statistic and the Bayesian pipeline are robust when studying circular or arbitrarily eccentric systems. We explore how eccentricity influences the detection prospects of single gravitational-wave sources, as well as the detection penalty incurred by employing a circular waveform template to search for eccentric signals, and conclude by identifying important avenues for future study.Comment: 15 pages, 13 figures, 1 table. Accepted for publication in ApJ. New results on expected binary measurement precisions as a function of signal-to-noise (Fig 9

Timing of Five PALFA-Discovered Millisecond Pulsars

We report the discovery and timing results for five millisecond pulsars (MSPs) from the Arecibo PALFA survey: PSRs J1906+0055, J1914+0659, J1933+1726, J1938+2516, and J1957+2516. Timing observations of the five pulsars were conducted with the Arecibo and Lovell telescopes for time spans ranging from 1.5 to 3.3 years. All of the MSPs except one (PSR J1914+0659) are in binary systems with low eccentricities. PSR J1957+2516 is likely a redback pulsar, with a $\sim 0.1\,{M}_{\odot }$ companion and possible eclipses that last ~10% of the orbit. The position of PSR J1957+2516 is also coincident with a near-infrared source. All five MSPs are distant ($\gt 3.1$ kpc) as determined from their dispersion measures, and none of them show evidence of γ-ray pulsations in a fold of Fermi Gamma-Ray Space Telescope data. These five MSPs bring the total number of MSPs discovered by the PALFA survey to 26 and further demonstrate the power of this survey in finding distant, highly dispersed MSPs deep in the Galactic plane

Multi-Messenger Astrophysics with Pulsar Timing Arrays

Pulsar timing arrays (PTAs) are on the verge of detecting low-frequency gravitational waves (GWs) from supermassive black hole binaries (SMBHBs). With continued observations of a large sample of millisecond pulsars, PTAs will reach this major milestone within the next decade. Already, SMBHB candidates are being identified by electromagnetic surveys in ever-increasing numbers; upcoming surveys will enhance our ability to detect and verify candidates, and will be instrumental in identifying the host galaxies of GW sources. Multi-messenger (GW and electromagnetic) observations of SMBHBs will revolutionize our understanding of the co-evolution of SMBHs with their host galaxies, the dynamical interactions between binaries and their galactic environments, and the fundamental physics of accretion. Multi-messenger observations can also make SMBHBs 'standard sirens' for cosmological distance measurements out to $z\simeq0.5$. LIGO has already ushered in breakthrough insights in our knowledge of black holes. The multi-messenger detection of SMBHBs with PTAs will be a breakthrough in the years $2020-2030$ and beyond, and prepare us for LISA to help complete our views of black hole demographics and evolution at higher redshifts