A coherent method for the detection and estimation of continuous gravitational wave signals using a pulsar timing array

The use of a high precision pulsar timing array is a promising approach to detecting gravitational waves in the very low frequency regime ($10^{-6} -10^{-9}$ Hz) that is complementary to the ground-based efforts (e.g., LIGO, Virgo) at high frequencies ($\sim 10 -10^3$ Hz) and space-based ones (e.g., LISA) at low frequencies ($10^{-4} -10^{-1}$ Hz). One of the target sources for pulsar timing arrays are individual supermassive black hole binaries that are expected to form in galactic mergers. In this paper, a likelihood based method for detection and estimation is presented for a monochromatic continuous gravitational wave signal emitted by such a source. The so-called pulsar terms in the signal that arise due to the breakdown of the long-wavelength approximation are explicitly taken into account in this method. In addition, the method accounts for equality and inequality constraints involved in the semi-analytical maximization of the likelihood over a subset of the parameters. The remaining parameters are maximized over numerically using Particle Swarm Optimization. Thus, the method presented here solves the monochromatic continuous wave detection and estimation problem without invoking some of the approximations that have been used in earlier studies.Comment: 33 pages, 10 figures, submitted to Ap

Coherent network analysis for continuous gravitational wave signals in a pulsar timing array: Pulsar phases as extrinsic parameters

Supermassive black hole binaries are one of the primary targets for gravitational wave searches using pulsar timing arrays. Gravitational wave signals from such systems are well represented by parametrized models, allowing the standard Generalized Likelihood Ratio Test (GLRT) to be used for their detection and estimation. However, there is a dichotomy in how the GLRT can be implemented for pulsar timing arrays: there are two possible ways in which one can split the set of signal parameters for semi-analytical and numerical extremization. The straightforward extension of the method used for continuous signals in ground-based gravitational wave searches, where the so-called pulsar phase parameters are maximized numerically, was addressed in an earlier paper (Wang et al. 2014). In this paper, we report the first study of the performance of the second approach where the pulsar phases are maximized semi-analytically. This approach is scalable since the number of parameters left over for numerical optimization does not depend on the size of the pulsar timing array. Our results show that, for the same array size (9 pulsars), the new method performs somewhat worse in parameter estimation, but not in detection, than the previous method where the pulsar phases were maximized numerically. The origin of the performance discrepancy is likely to be in the ill-posedness that is intrinsic to any network analysis method. However, scalability of the new method allows the ill-posedness to be mitigated by simply adding more pulsars to the array. This is shown explicitly by taking a larger array of pulsars.Comment: 30 pages, 11 figures, revised version, published in Ap

The Arecibo Observatory as an Instrument for Investigating Orbital Debris: Legacy and Next Generation Performance

In this paper, we investigate the ability of the Arecibo Observatory to characterize the orbital debris environment and compare it to the primary instrument used by NASA\u27s Orbital Debris Program Office, the Haystack Ultra-Wideband Satellite Imaging Radar (HUSIR). Arecibo\u27s location (183 N) increases the percentage of observable orbits (relative to HUSIR) by 27%, which gives Arecibo access to a much larger and previously unmeasured portion of the environment. Due to the recent collapse of the Arecibo dish, in addition to exploring historic capabilities of the Legacy Arecibo Telescope, estimates of the performance of the proposed Next Generation Arecibo Telescope (NGAT) are explored. We show that the current NGAT design could have a sensitivity comparable to the Goldstone Orbital Debris Radar, currently NASA\u27s most sensitive orbital debris radar. Additionally, design suggestions are presented that would significantly improve the capabilities of the NGAT for orbital debris investigations. We show that, with appropriate hardware upgrades, it would be possible to achieve a minimum-detectable debris size as small as 1 mm. These capabilities would allow data from Arecibo to significantly improve short-term debris environment models, which are used to inform spacecraft design and operations, particularly for orbital debris smaller than 3 mm, which pose the highest penetration risk to most spacecraft

The intrinsic intensity modulation of PSR B1937+21 at 1410 MHz

The single-pulse properties of the millisecond radio pulsar PSR B1937+21 are studied in the 1410 MHz radio band. Aside from occasional ``giant pulses'' occurring in restricted regions of pulse phase, the emission appears to be remarkably stable, showing no pulse-to-pulse fluctuations other then those induced by propagation through the interstellar medium. This type of behavior has not been seen in any other pulsar although it was seen in previous 430 MHz observations of this source. The stability of PSR B1937+21 can be understood in the context of the sparking gap model of radio pulsar emission. Given the emission properties of this source at 430 MHz, this model predicts that the emission at all higher frequencies will be just as stable. Since the stability depends on the outflow velocity of the emitting plasma, an upper bound may be placed on its Lorentz factor.Comment: submitted to ApJ

Understanding the gravitational-wave Hellings and Downs curve for pulsar timing arrays in terms of sound and electromagnetic waves

Searches for stochastic gravitational-wave backgrounds using pulsar timing arrays look for correlations in the timing residuals induced by the background across the pulsars in the array. The correlation signature of an isotropic, unpolarized gravitational-wave background predicted by general relativity follows the so-called Hellings and Downs curve, which is a relatively simple function of the angle between a pair of Earth-pulsar baselines. In this paper, we give a pedagogical discussion of the Hellings and Downs curve for pulsar timing arrays, considering simpler analogous scenarios involving sound and electromagnetic waves. We calculate Hellings-and-Downs-type functions for these two scenarios and develop a framework suitable for doing more general correlation calculations.Comment: 15 pages, 6 figures. The revised version has been expanded in several places based on referee comments. To appear in American Journal of Physic

A method for calculating lateral surface area of bistatic radar beam overlap

It has been shown that bistatic radars using radio telescopes as receivers can be used to increase the sensitivity of orbital debris measurements over traditional terrestrial monostatic radar. A method to calculate the lateral surface area of a bistatic radar is needed to evaluate the efficacy of a proposed bistatic radar configuration for orbital debris measurements. For over three decades, models of the orbital debris (OD) environment in low Earth orbit (LEO) have been developed to assess the risk posed by OD to spacecraft. While terrestrial radar measures debris 3 mm and larger and in situ measurements provide data for debris smaller than 1 mm, no good data sources exist for debris between 1 mm and 3 mm in size. This results in large variations between competing OD models. It also happens to be the size regime which poses the highest mission-ending risk to spacecraft. It is, therefore, of interest to investigate potential new data sources for this under-sampled size regime. There are many radars and radio telescopes that could be combined to create sensitive bistatic radars that could potentially bridge the size gap. In addition to sensitivity, it is necessary to predict the expected count rate of a candidate sensor to evaluate its performance. NASA’s Orbital Debris Engineering Model (ORDEM) can be used to predict the flux of debris passing through the line of sight of a radar or telescope. This flux is related to a count rate through the calculation of the lateral surface area of the sensor. While this can be done easily for monostatic radars, a method for calculating the lateral surface area of a bistatic radar is needed. This new method of calculation has been developed and is described. The new method maps the radar beam overlap in 3D space, calculating the area of the complex surface formed by the gain product of the two antennas. Comparisons of the monostatic and new bistatic lateral surface area calculation methods for the monostatic case are presented. Results of a sample lateral surface area calculation for a bistatic radar observation configuration currently employed by NASA are shown. Finally, a guide for total error as a function of baseline and target altitude is established

Fundamental Emission via Wave Advection from a Collapsing Wave Packet in Electromagnetic Strong Plasma Turbulence

Zakharov simulations of nonlinear wave collapse in continuously driven two-dimensional, electromagnetic strong plasma turbulence with electron thermal speeds v⩾0.01c show that for v≲0.1c, dipole radiation occurs near the plasma frequency, mainly near arrest, but for v≳0.1c, a new mechanism applies in which energy oscillates between trapped Langmuir and transverse modes until collapse is arrested, after which trapped transverse waves are advected into incoherent interpacket turbulence by an expanding annular density well, where they detrap. The multipole structure, Poynting flux, source current, and radiation angular momentum are computed

Pulsar Timing Sensitivity to Very-Low-Frequency Gravitational Waves

At nanohertz frequencies gravitational waves (GWs) cause variations in time-of-arrival of pulsar signals potentially measurable via precision timing observations. Here we compute very-low-frequency GW sensitivity constrained by instrumental, propagation, and other noises fundamentally limiting pulsar timing observations. Reaching expected GW signal strengths will require estimation and removal of $\simeq$99% of time-of-arrival fluctuations caused by typical interstellar plasma turbulence and a reduction of white rms timing noise to $\sim$100 nsec or less. If these were achieved, single-pulsar signal-to-noise ratio (SNR) = 1 sensitivity is then limited by the best current terrestrial time standards at $h_{rms} \sim$2 $\times 10^{-16}$ [f/(1 cycle/year)]$^{-1/2}$ for $f < 3 \times 10^{-8}$ Hz, where f is Fourier frequency and a bandwidth of 1 cycle/(10 years) is assumed. This sensitivity envelope may be optimistic in that it assumes negligible intrinsic pulsar rotational noise, perfect time transfer from time standard to observatory, and stable pulse profiles. Nonetheless it can be compared to predicted signal levels for a broadband astrophysical GW background from supermassive black hole binaries. Such a background is comparable to timekeeping-noise only for frequencies lower than about 1 cycle/(10 years), indicating that reliable detections will require substantial improvements in signal-to-noise ratio through pulsar array signal processing.Comment: 8 pages, 1 figure. Submitted to Physical Revie

Constraining the properties of supermassive black hole systems using pulsar timing: Application to 3C 66B

General expressions for the expected timing residuals induced by gravitational wave (G-wave) emission from a slowly evolving, eccentric, binary black hole system are derived here for the first time. These expressions are used to search for the signature of G-waves emitted by the proposed supermassive binary black hole system in 3C 66B. We use data from long-term timing observations of the radio pulsar PSR B1855+09. For the case of a circular orbit, the emitted G-waves should generate clearly detectable fluctuations in the pulse-arrival times of PSR B1855+09. Since no G-waves are detected, the waveforms are used in a Monte Carlo analysis in order to place limits on the mass and eccentricity of the proposed black hole system. The analysis presented here rules out the adopted system with 95% confidence. The reported analysis also demonstrates several interesting features of a G-wave detector based on pulsar timing