Pulsar timing analysis in the presence of correlated noise

Pulsar timing observations are usually analysed with least-square-fitting procedures under the assumption that the timing residuals are uncorrelated (statistically "white"). Pulsar observers are well aware that this assumption often breaks down and causes severe errors in estimating the parameters of the timing model and their uncertainties. Ad hoc methods for minimizing these errors have been developed, but we show that they are far from optimal. Compensation for temporal correlation can be done optimally if the covariance matrix of the residuals is known using a linear transformation that whitens both the residuals and the timing model. We adopt a transformation based on the Cholesky decomposition of the covariance matrix, but the transformation is not unique. We show how to estimate the covariance matrix with sufficient accuracy to optimize the pulsar timing analysis. We also show how to apply this procedure to estimate the spectrum of any time series with a steep red power-law spectrum, including those with irregular sampling and variable error bars, which are otherwise very difficult to analyse.Comment: Accepted by MNRA

Fabrication of comb-drive actuators for straining nanostructured suspended graphene

We report on the fabrication and characterization of an optimized comb-drive actuator design for strain-dependent transport measurements on suspended graphene. We fabricate devices from highly p-doped silicon using deep reactive ion etching with a chromium mask. Crucially, we implement a gold layer to reduce the device resistance from $\approx51.6$ k$\mathrm{\Omega}$ to $\approx236$ $\mathrm{\Omega}$ at room temperature in order to allow for strain-dependent transport measurements. The graphene is integrated by mechanically transferring it directly onto the actuator using a polymethylmethacrylate membrane. Importantly, the integrated graphene can be nanostructured afterwards to optimize device functionality. The minimum feature size of the structured suspended graphene is 30 nm, which allows for interesting device concepts such as mechanically-tunable nanoconstrictions. Finally, we characterize the fabricated devices by measuring the Raman spectrum as well as the a mechanical resonance frequency of an integrated graphene sheet for different strain values.Comment: 10 pages, 9 figure

Tunable mechanical coupling between driven microelectromechanical resonators

We present a microelectromechanical system, in which a silicon beam is attached to a comb-drive actuator, that is used to tune the tension in the silicon beam, and thus its resonance frequency. By measuring the resonance frequencies of the system, we show that the comb-drive actuator and the silicon beam behave as two strongly coupled resonators. Interestingly, the effective coupling rate (~ 1.5 MHz) is tunable with the comb-drive actuator (+10%) as well as with a side-gate (-10%) placed close to the silicon beam. In contrast, the effective spring constant of the system is insensitive to either of them and changes only by $\pm$ 0.5%. Finally, we show that the comb-drive actuator can be used to switch between different coupling rates with a frequency of at least 10 kHz.Comment: 5 pages, 4 figures, 1 tabl

Optimizing Pulsar Timing Arrays to Maximize Gravitational Wave Single Source Detection: a First Cut

Pulsar Timing Arrays (PTAs) use high accuracy timing of a collection of low timing noise pulsars to search for gravitational waves in the microhertz to nanohertz frequency band. The sensitivity of such a PTA depends on (a) the direction of the gravitational wave source, (b) the timing accuracy of the pulsars in the array and (c) how the available observing time is allocated among those pulsars. Here, we present a simple way to calculate the sensitivity of the PTA as a function of direction of a single GW source, based only on the location and root-mean-square residual of the pulsars in the array. We use this calculation to suggest future strategies for the current North American Nanohertz Observatory for Gravitational Waves (NANOGrav) PTA in its goal of detecting single GW sources. We also investigate the affects of an additional pulsar on the array sensitivity, with the goal of suggesting where PTA pulsar searches might be best directed. We demonstrate that, in the case of single GW sources, if we are interested in maximizing the volume of space to which PTAs are sensitive, there exists a slight advantage to finding a new pulsar near where the array is already most sensitive. Further, the study suggests that more observing time should be dedicated to the already low noise pulsars in order to have the greatest positive effect on the PTA sensitivity. We have made a web-based sensitivity mapping tool available at http://gwastro.psu.edu/ptasm.Comment: 14 pages, 3 figures, accepted by Ap

On detection of the stochastic gravitational-wave background using the Parkes pulsar timing array

We search for the signature of an isotropic stochastic gravitational-wave background in pulsar timing observations using a frequency-domain correlation technique. These observations, which span roughly 12 yr, were obtained with the 64-m Parkes radio telescope augmented by public domain observations from the Arecibo Observatory. A wide range of signal processing issues unique to pulsar timing and not previously presented in the literature are discussed. These include the effects of quadratic removal, irregular sampling, and variable errors which exacerbate the spectral leakage inherent in estimating the steep red spectrum of the gravitational-wave background. These observations are found to be consistent with the null hypothesis, that no gravitational-wave background is present, with 76 percent confidence. We show that the detection statistic is dominated by the contributions of only a few pulsars because of the inhomogeneity of this data set. The issues of detecting the signature of a gravitational-wave background with future observations are discussed.Comment: 12 pages, 8 figures, 7 tables, accepted for publication in MNRA

The Sensitivity of the Parkes Pulsar Timing Array to Individual Sources of Gravitational Waves

We present the sensitivity of the Parkes Pulsar Timing Array to gravitational waves emitted by individual super-massive black-hole binary systems in the early phases of coalescing at the cores of merged galaxies. Our analysis includes a detailed study of the effects of fitting a pulsar timing model to non-white timing residuals. Pulsar timing is sensitive at nanoHertz frequencies and hence complementary to LIGO and LISA. We place a sky-averaged constraint on the merger rate of nearby ($z < 0.6$) black-hole binaries in the early phases of coalescence with a chirp mass of 10^{10}\,\rmn{M}_\odot of less than one merger every seven years. The prospects for future gravitational-wave astronomy of this type with the proposed Square Kilometre Array telescope are discussed.Comment: fixed error in equation (4). [13 pages, 6 figures, 1 table, published in MNRAS

A possible signature of cosmic neutrino decoupling in the nHz region of the spectrum of primordial gravitational waves

In this paper we study the effect of cosmic neutrino decoupling on the spectrum of cosmological gravitational waves (GWs). At temperatures T>>1 MeV, neutrinos constitute a perfect fluid and do not hinder GW propagation, while for T<<1 MeV they free-stream and have an effective viscosity that damps cosmological GWs by a constant amount. In the intermediate regime, corresponding to neutrino decoupling, the damping is frequency-dependent. GWs entering the horizon during neutrino decoupling have a frequency f ~ 1 nHz, corresponding to a frequency region that will be probed by Pulsar Timing Arrays (PTAs). In particular, we show how neutrino decoupling induces a spectral feature in the spectrum of cosmological GWs just below 1 nHz. We briefly discuss the conditions for a detection of this feature and conclude that it is unlikely to be observed by PTAs.Comment: 11 pages, 2 figures. V2: References Adde

Status Update of the Parkes Pulsar Timing Array

The Parkes Pulsar Timing Array project aims to make a direct detection of a gravitational-wave background through timing of millisecond pulsars. In this article, the main requirements for that endeavour are described and recent and ongoing progress is outlined. We demonstrate that the timing properties of millisecond pulsars are adequate and that technological progress is timely to expect a successful detection of gravitational waves within a decade, or alternatively to rule out all current predictions for gravitational wave backgrounds formed by supermassive black-hole mergers.Comment: 10 pages, 3 figures, Amaldi 8 conference proceedings, accepted by Classical & Quantum Gravit