Practical Methods for Continuous Gravitational Wave Detection using Pulsar Timing Data

Gravitational Waves (GWs) are tiny ripples in the fabric of space-time predicted by Einstein's General Relativity. Pulsar timing arrays (PTAs) are well poised to detect low frequency ($10^{-9}$ -- $10^{-7}$ Hz) GWs in the near future. There has been a significant amount of research into the detection of a stochastic background of GWs from supermassive black hole binaries (SMBHBs). Recent work has shown that single continuous sources standing out above the background may be detectable by PTAs operating at a sensitivity sufficient to detect the stochastic background. The most likely sources of continuous GWs in the pulsar timing frequency band are extremely massive and/or nearby SMBHBs. In this paper we present detection strategies including various forms of matched filtering and power spectral summing. We determine the efficacy and computational cost of such strategies. It is shown that it is computationally infeasible to use an optimal matched filter including the poorly constrained pulsar distances with a grid based method. We show that an Earth-term-matched filter constructed using only the correlated signal terms is both computationally viable and highly sensitive to GW signals. This technique is only a factor of two less sensitive than the computationally unrealizable optimal matched filter and a factor of two more sensitive than a power spectral summing technique. We further show that a pairwise matched filter, taking the pulsar distances into account is comparable to the optimal matched filter for the single template case and comparable to the Earth-term-matched filter for many search templates. Finally, using simulated data optimal quality, we place a theoretical minimum detectable strain amplitude of $h>2\times 10^{-15}$ from continuous GWs at frequencies on the order $\sim1/T_{\rm obs}$.Comment: submitted to Ap

Detection, Localization and Characterization of Gravitational Wave Bursts in a Pulsar Timing Array

Efforts to detect gravitational waves by timing an array of pulsars have focused traditionally on stationary gravitational waves: e.g., stochastic or periodic signals. Gravitational wave bursts --- signals whose duration is much shorter than the observation period --- will also arise in the pulsar timing array waveband. Sources that give rise to detectable bursts include the formation or coalescence of supermassive black holes (SMBHs), the periapsis passage of compact objects in highly elliptic or unbound orbits about a SMBH, or cusps on cosmic strings. Here we describe how pulsar timing array data may be analyzed to detect and characterize these bursts. Our analysis addresses, in a mutually consistent manner, a hierarchy of three questions: \emph{i}) What are the odds that a dataset includes the signal from a gravitational wave burst? \emph{ii}) Assuming the presence of a burst, what is the direction to its source? and \emph{iii}) Assuming the burst propagation direction, what is the burst waveform's time dependence in each of its polarization states? Applying our analysis to synthetic data sets we find that we can \emph{detect} gravitational waves even when the radiation is too weak to either localize the source of infer the waveform, and \emph{detect} and \emph{localize} sources even when the radiation amplitude is too weak to permit the waveform to be determined. While the context of our discussion is gravitational wave detection via pulsar timing arrays, the analysis itself is directly applicable to gravitational wave detection using either ground or space-based detector data.Comment: 43 pages, 13 figures, submitted to ApJ

Constraining the coalescence rate of supermassive black-hole binaries using pulsar timing

Pulsar timing observations are used to place constraints on the rate of coalescence of supermassive black-hole (SMBH) binaries as a function of mass and redshift. In contrast to the indirect constraints obtained from other techniques, pulsar timing observations provide a direct constraint on the black-hole merger rate. This is possible since pulsar timing is sensitive to the gravitational waves (GWs) emitted by these sources in the final stages of their evolution. We find that upper bounds calculated from the recently published Parkes Pulsar Timing Array data are just above theoretical predictions for redshifts below 10. In the future, with improved timing precision and longer data spans, we show that a non-detection of GWs will rule out some of the available parameter space in a particular class of SMBH binary merger models. We also show that if we can time a set of pulsars to 10ns timing accuracy, for example, using the proposed Square Kilometre Array, it should be possible to detect one or more individual SMBH binary systems

Detection of variable frequency signals using a fast chirp transform

The detection of signals with varying frequency is important in many areas of physics and astrophysics. The current work was motivated by a desire to detect gravitational waves from the binary inspiral of neutron stars and black holes, a topic of significant interest for the new generation of interferometric gravitational wave detectors such as LIGO. However, this work has significant generality beyond gravitational wave signal detection. We define a Fast Chirp Transform (FCT) analogous to the Fast Fourier Transform (FFT). Use of the FCT provides a simple and powerful formalism for detection of signals with variable frequency just as Fourier transform techniques provide a formalism for the detection of signals of constant frequency. In particular, use of the FCT can alleviate the requirement of generating complicated families of filter functions typically required in the conventional matched filtering process. We briefly discuss the application of the FCT to several signal detection problems of current interest

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

Minimum Requirements for Detecting a Stochastic Gravitational Wave Background Using Pulsars

We assess the detectability of a nanohertz gravitational wave (GW) background with respect to additive red and white noise in the timing of millisecond pulsars. We develop detection criteria based on the cross-correlation function summed over pulsar pairs in a pulsar timing array. The distribution of correlation amplitudes is found to be non-Gaussian and highly skewed, which significantly influences detection and false-alarm probabilities. When only white noise and GWs contribute, our detection results are consistent with those found by others. Red noise, however, drastically alters the results. We discuss methods to meet the challenge of GW detection ("climbing mount significance") by distinguishing between GW-dominated and red or white-noise limited regimes. We characterize detection regimes by evaluating the number of millisecond pulsars that must be monitored in a high-cadence, 5-year timing program for a GW background spectrum $h_c(f) = A f^{-2/3}$ with $A = 10^{-15}$ yr$^{-2/3}$. Unless a sample of 20 super-stable millisecond pulsars can be found --- those with timing residuals from red-noise contributions $\sigma_r \lesssim 20$ ns --- a much larger timing program on $\gtrsim 50 - 100$ MSPs will be needed. For other values of $A$, the constraint is $\sigma_r \lesssim 20 {\rm ns} (A/10^{-15} {\rm yr}^{-2/3})$. Identification of suitable MSPs itself requires an aggressive survey campaign followed by characterization of the level of spin noise in the timing residuals of each object. The search and timing programs will likely require substantial fractions of time on new array telescopes in the southern hemisphere as well as on existing ones.Comment: Submitted to the Astrophysical Journa

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

Pengaruh Covid-19 Terhadap Gaya Hidup Masyarakat Usia "Remaja Akhir' di Kelurahan Bukit Duri, Manggarai

Pandemi covid-19 ini tentunya membuat masyarakat di belahan bumi menjadi khawatir.  Sehingga, pemerintah di berbagai negara membuat peraturan yang beragam dan mengajak masyarakat untuk turut bekerjasama dalam rangka memutus mata rantai penyebaran covid-19.  Pandemi ini membuat situasi tidak menentu dan mengharuskan masyarakat untuk memulai gaya hidup yang baru, yaitu gaya hidup yang lebih sehat.  Jurnal ini menuliskan tentang bagaimana dampak protokol kesehatan yang diberikan kepada masyarkat Indonesia.  Dengan menggunakan metode kuantitatif dengan menggunakan teknologi Google Form sebagai kuisioner, dan penelitian ini dikhususkan untuk masyarakat usia “remaja akhir” di kelurahan Bukit Duri, Manggarai Jakarta Selatan.  Penelitian ini dilakukan dengan menggunakan metode cross sectional study dan menghasilkan sebanyak 33 responden.

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

Drawing with and without models: An examination of drawing behavior in children and adults

Research in drawing development has indicated that individuals’ drawing behavior changes with age. Preschoolers, six, nine, twelve year-olds, and adults participated in the present study since these ages corresponded to the most prominent stages noted in the literature. Part one of this study examined drawing behavior in three drawing conditions: a model-absent condition (C1) in which drawing took place following a brief verbal description, a model briefly-present condition (C2) in which the model on which the verbal description was based was examined and drawn when removed from sight, and a model continuously present-condition (C3) in which drawings were made while the model remained present. All participants created such drawings with two familiar drawing topics: a flower and a dog. Further empirical support for the literature was derived from results which indicated that the two youngest age groups drew the most elaborate, colourful and unrealistic drawings, and that technical skill and realism first became apparent in nine year-olds’ work. Further evidence of gender differences was also revealed. Evidence for the suggestion that drawing from a model may enhance drawing performance (Gardner, 1980) was also obtained. In part two, subjective judgements of drawings revealed further evidence that a model may enhance drawing ability since drawings made in a model continuously-present vs. a model-absent condition were correctly discriminated by all age groups, four year-olds through adults, at a consistent level