Sliding coherence window technique for hierarchical detection of continuous gravitational waves

A novel hierarchical search technique is presented for all-sky surveys for continuous gravitational-wave sources, such as rapidly spinning nonaxisymmetric neutron stars. Analyzing yearlong detector data sets over realistic ranges of parameter space using fully coherent matched-filtering is computationally prohibitive. Thus more efficient, so-called hierarchical techniques are essential. Traditionally, the standard hierarchical approach consists of dividing the data into nonoverlapping segments of which each is coherently analyzed and subsequently the matched-filter outputs from all segments are combined incoherently. The present work proposes to break the data into subsegments shorter than the desired maximum coherence time span (size of the coherence window). Then matched-filter outputs from the different subsegments are efficiently combined by sliding the coherence window in time: Subsegments whose timestamps are closer than coherence window size are combined coherently, otherwise incoherently. Compared to the standard scheme at the same coherence time baseline, data sets longer by about 50-100% would have to be analyzed to achieve the same search sensitivity as with the sliding coherence window approach. Numerical simulations attest to the analytically estimated improvement.Comment: 11 pages, 4 figure

Parameter-space correlations of the optimal statistic for continuous gravitational-wave detection

The phase parameters of matched-filtering searches for continuous gravitational-wave signals are sky position, frequency and frequency time-derivatives. The space of these parameters features strong global correlations in the optimal detection statistic. For observation times smaller than one year, the orbital motion of the Earth leads to a family of global-correlation equations which describes the "global maximum structure" of the detection statistic. The solution to each of these equations is a different hypersurface in parameter space. The expected detection statistic is maximal at the intersection of these hypersurfaces. The global maximum structure of the detection statistic from stationary instrumental-noise artifacts is also described by the global-correlation equations. This permits the construction of a veto method which excludes false candidate events.Comment: 17 pages, 10 figure

Efficient generation and optimization of stochastic template banks by a neighboring cell algorithm

Placing signal templates (grid points) as efficiently as possible to cover a multi-dimensional parameter space is crucial in computing-intensive matched-filtering searches for gravitational waves, but also in similar searches in other fields of astronomy. To generate efficient coverings of arbitrary parameter spaces, stochastic template banks have been advocated, where templates are placed at random while rejecting those too close to others. However, in this simple scheme, for each new random point its distance to every template in the existing bank is computed. This rapidly increasing number of distance computations can render the acceptance of new templates computationally prohibitive, particularly for wide parameter spaces or in large dimensions. This work presents a neighboring cell algorithm that can dramatically improve the efficiency of constructing a stochastic template bank. By dividing the parameter space into sub-volumes (cells), for an arbitrary point an efficient hashing technique is exploited to obtain the index of its enclosing cell along with the parameters of its neighboring templates. Hence only distances to these neighboring templates in the bank are computed, massively lowering the overall computing cost, as demonstrated in simple examples. Furthermore, we propose a novel method based on this technique to increase the fraction of covered parameter space solely by directed template shifts, without adding any templates. As is demonstrated in examples, this method can be highly effective..Comment: PRD accepte

Gamma-ray Timing of Redback PSR J2339-0533: Hints for Gravitational Quadrupole Moment Changes

We present the results of precision gamma-ray timing measurements of the binary millisecond pulsar PSR J2339$-$0533, an irradiating system of "redback" type, using data from the Fermi Large Area Telescope. We describe an optimized analysis method to determine a long-term phase-coherent timing solution spanning more than six years, including a measured eccentricity of the binary orbit and constraints on the proper motion of the system. A major result of this timing analysis is the discovery of an extreme variation of the nominal 4.6-hour orbital period $P_{\rm orb}$ over time, showing alternating epochs of decrease and increase. We inferred a cyclic modulation of $P_{\rm orb}$ with an approximate cycle duration of 4.2 years and a modulation amplitude of $\Delta P_{\rm orb}/ P_{\rm orb} = 2.3 \times 10^{-7}$. Considering different possible physical causes, the observed orbital-period modulation most likely results from a variable gravitational quadrupole moment of the companion star due to cyclic magnetic activity in its convective zone.Comment: 9 pages, 2 figure

Optimized Blind Gamma-ray Pulsar Searches at Fixed Computing Budget

The sensitivity of blind gamma-ray pulsar searches in multiple years worth of photon data, as from the Fermi LAT, is primarily limited by the finite computational resources available. Addressing this "needle in a haystack" problem, we here present methods for optimizing blind searches to achieve the highest sensitivity at fixed computing cost. For both coherent and semicoherent methods, we consider their statistical properties and study their search sensitivity under computational constraints. The results validate a multistage strategy, where the first stage scans the entire parameter space using an efficient semicoherent method and promising candidates are then refined through a fully coherent analysis. We also find that for the first stage of a blind search incoherent harmonic summing of powers is not worthwhile at fixed computing cost for typical gamma-ray pulsars. Further enhancing sensitivity, we present efficiency-improved interpolation techniques for the semicoherent search stage. Via realistic simulations we demonstrate that overall these optimizations can significantly lower the minimum detectable pulsed fraction by almost 50% at the same computational expense.Comment: 22 pages, 13 figures; includes ApJ proof correction

Parameter-space metric of semicoherent searches for continuous gravitational waves

Continuous gravitational-wave (CW) signals such as emitted by spinning neutron stars are an important target class for current detectors. However, the enormous computational demand prohibits fully coherent broadband all-sky searches for prior unknown CW sources over wide ranges of parameter space and for yearlong observation times. More efficient hierarchical "semicoherent" search strategies divide the data into segments much shorter than one year, which are analyzed coherently; then detection statistics from different segments are combined incoherently. To optimally perform the incoherent combination, understanding of the underlying parameter-space structure is requisite. This problem is addressed here by using new coordinates on the parameter space, which yield the first analytical parameter-space metric for the incoherent combination step. This semicoherent metric applies to broadband all-sky surveys (also embedding directed searches at fixed sky position) for isolated CW sources. Furthermore, the additional metric resolution attained through the combination of segments is studied. From the search parameters (sky position, frequency, and frequency derivatives), solely the metric resolution in the frequency derivatives is found to significantly increase with the number of segments.Comment: 14 pages, 5 figures (matching Phys.Rev.D version

Exploiting Large-Scale Correlations to Detect Continuous Gravitational Waves

Fully coherent searches (over realistic ranges of parameter space and year-long observation times) for unknown sources of continuous gravitational waves are computationally prohibitive. Less expensive hierarchical searches divide the data into shorter segments which are analyzed coherently, then detection statistics from different segments are combined incoherently. The novel method presented here solves the long-standing problem of how best to do the incoherent combination. The optimal solution exploits large-scale parameter-space correlations in the coherent detection statistic. Application to simulated data shows dramatic sensitivity improvements compared with previously available (ad hoc) methods, increasing the spatial volume probed by more than 2 orders of magnitude at lower computational cost.Comment: 4 pages, 2 figure

Quantum state preparation and macroscopic entanglement in gravitational-wave detectors

Long-baseline laser-interferometer gravitational-wave detectors are operating at a factor of 10 (in amplitude) above the standard quantum limit (SQL) within a broad frequency band. Such a low classical noise budget has already allowed the creation of a controlled 2.7 kg macroscopic oscillator with an effective eigenfrequency of 150 Hz and an occupation number of 200. This result, along with the prospect for further improvements, heralds the new possibility of experimentally probing macroscopic quantum mechanics (MQM) - quantum mechanical behavior of objects in the realm of everyday experience - using gravitational-wave detectors. In this paper, we provide the mathematical foundation for the first step of a MQM experiment: the preparation of a macroscopic test mass into a nearly minimum-Heisenberg-limited Gaussian quantum state, which is possible if the interferometer's classical noise beats the SQL in a broad frequency band. Our formalism, based on Wiener filtering, allows a straightforward conversion from the classical noise budget of a laser interferometer, in terms of noise spectra, into the strategy for quantum state preparation, and the quality of the prepared state. Using this formalism, we consider how Gaussian entanglement can be built among two macroscopic test masses, and the performance of the planned Advanced LIGO interferometers in quantum-state preparation

Searching for a Stochastic Background of Gravitational Waves with LIGO

The Laser Interferometer Gravitational-wave Observatory (LIGO) has performed the fourth science run, S4, with significantly improved interferometer sensitivities with respect to previous runs. Using data acquired during this science run, we place a limit on the amplitude of a stochastic background of gravitational waves. For a frequency independent spectrum, the new limit is $\Omega_{\rm GW} < 6.5 \times 10^{-5}$. This is currently the most sensitive result in the frequency range 51-150 Hz, with a factor of 13 improvement over the previous LIGO result. We discuss complementarity of the new result with other constraints on a stochastic background of gravitational waves, and we investigate implications of the new result for different models of this background.Comment: 37 pages, 16 figure