Empirically extending the range of validity of parameter-space metrics for all-sky searches for gravitational-wave pulsars

All-sky searches for gravitational-wave pulsars are generally limited in sensitivity by the finite availability of computing resources. Semicoherent searches are a common method of maximizing search sensitivity given a fixed computing budget. The work of Wette and Prix [Phys. Rev. D 88, 123005 (2013)] and Wette [Phys. Rev. D 92, 082003 (2015)] developed a semicoherent search method which uses metrics to construct the banks of pulsar signal templates needed to search the parameter space of interest. In this work we extend the range of validity of the parameter-space metrics using an empirically-derived relationship between the resolution (or mismatch) of the template banks and the mismatch of the overall search. This work has important consequences for the optimization of metric-based semicoherent searches at fixed computing cost.Comment: 14 pages, 5 figures, 4 table

Lattice template placement for coherent all-sky searches for gravitational-wave pulsars

All-sky, broadband, coherent searches for gravitational-wave pulsars are restricted by limited computational resources. Minimizing the number of templates required to cover the search parameter space, of sky position and frequency evolution, is one important way to reduce the computational cost of a search. We demonstrate a practical algorithm which, for the first time, achieves template placement with a minimal number of templates for an all-sky search, using the reduced supersky parameter-space metric of Wette and Prix [Phys. Rev. D 88, 123005 (2013)]. The metric prescribes a constant template density in the signal parameters, which permits that templates be placed at the vertices of a lattice. We demonstrate how to ensure complete coverage of the parameter space, including in particular at its boundaries. The number of templates generated by the algorithm is compared to theoretical estimates, and to previous predictions by Brady et al. [Phys. Rev. D 57, 2101 (1998)]. The algorithm may be applied to any search parameter space with a constant template density, which includes semicoherent searches and searches targeting known low-mass X-ray binaries.Comment: 16 pages, 14 figure

Parameter-space metric for all-sky semicoherent searches for gravitational-wave pulsars

The sensitivity of all-sky searches for gravitational-wave pulsars is primarily limited by the finite availability of computing resources. Semicoherent searches are a widely-used method of maximizing sensitivity to gravitational-wave pulsars at fixed computing cost: the data from a gravitational-wave detector are partitioned into a number of segments, each segment is coherently analyzed, and the analysis results from each segment are summed together. The generation of template banks for the coherent analysis of each segment, and for the summation, requires knowledge of the metrics associated with the coherent and semicoherent parameter spaces respectively. We present a useful approximation to the semicoherent parameter-space metric, analogous to that presented in Wette and Prix [Phys. Rev. D 88, 123005 (2013)] for the coherent metric. The new semicoherent metric is compared to previous work in Pletsch [Phys. Rev. D 82, 042002 (2010)], and Brady and Creighton [Phys. Rev. D 61, 082001 (2000)]. We find that semicoherent all-sky searches require orders of magnitude more templates than previously predicted.Comment: 21 pages, 13 figures, 2 table

Flat parameter-space metric for all-sky searches for gravitational-wave pulsars

All-sky, broadband, coherent searches for gravitational-wave pulsars are computationally limited. It is therefore important to make efficient use of available computational resources, notably by minimizing the number of templates used to cover the signal parameter space of sky position and frequency evolution. For searches over the sky, however, the required template density (determined by the parameter-space metric) is different at each sky position, which makes it difficult in practice to achieve an efficient covering. Previous work on this problem has found various choices of sky and frequency coordinates that render the parameter-space metric approximately constant, but which are limited to coherent integration times of either less than a few days, or greater than several months. These limitations restrict the sensitivity achievable by hierarchical all-sky searches, and hinder the development of follow-up pipelines for interesting gravitational-wave pulsar candidates. We present a new flat parameter-space metric approximation, and associated sky and frequency coordinates, that do not suffer from these limitations. Furthermore, the new metric is numerically well-conditioned, which facilitates its practical use.Comment: 19 pages, 20 figure

Implementation and characterization of BinaryWeave: A new search pipeline for continuous gravitational waves from Scorpius X-1

Scorpius X-1 (Sco X-1) has long been considered one of the most promising targets for detecting continuous gravitational waves with ground-based detectors. Observational searches for Sco X-1 have achieved substantial sensitivity improvements in recent years, to the point of starting to rule out emission at the torque-balance limit in the low-frequency range \sim 40--180 Hz. In order to further enhance the detection probability, however, there is still much ground to cover for the full range of plausible signal frequencies \sim 20--1500 Hz, as well as a wider range of uncertainties in binary orbital parameters. Motivated by this challenge, we have developed BinaryWeave, a new search pipeline for continuous waves from a neutron star in a known binary system such as Sco X-1. This pipeline employs a semi-coherent StackSlide F-statistic using efficient lattice-based metric template banks, which can cover wide ranges in frequency and unknown orbital parameters. We present a detailed timing model and extensive injection-and-recovery simulations that illustrate that the pipeline can achieve high detection sensitivities over a significant portion of the parameter space when assuming sufficiently large (but realistic) computing budgets. Our studies further underline the need for stricter constraints on the Sco X-1 orbital parameters from electromagnetic observations, in order to be able to push sensitivity below the torque-balance limit over the entire range of possible source parameters.Comment: 19 pages, 7 figures, 3 table

Deep searches for X-ray pulsations from Scorpius X-1 and Cygnus X-2 in support of continuous gravitational wave searches

Neutron stars in low mass X-ray binaries are hypothesised to emit continuous gravitational waves that may be detectable by ground-based observatories. The torque balance model predicts that a higher accretion rate produces larger-amplitude gravitational waves, hence low mass X-ray binaries with high X-ray flux are promising targets for gravitational wave searches. The detection of X-ray pulsations would identify the spin frequency of these neutron stars, and thereby improve the sensitivity of continuous gravitational-wave searches by reducing the volume of the search parameter space. We perform a semi-coherent search for pulsations in the two low mass X-ray binaries Scorpius X-1 and Cygnus X-2 using X-ray data from the \textit{ Rossi X-ray Timing Explorer} Proportional Counter Array. We find no clear evidence for pulsations, and obtain upper limits (at $90\%$ confidence) on the fractional pulse amplitude, with the most stringent being $0.034\%$ for Scorpius X-1 and $0.23\%$ for Cygnus X-2. These upper limits improve upon those of Vaughan et al. (1994) by factors of $\sim 8.2$ and $\sim 1.6$ respectively.Comment: 10 pages, 11 figure