Searching for continuous gravitational wave signals: the hierarchical Hough transform algorithm

It is well known that matched filtering techniques cannot be applied for searching extensive parameter space volumes for continuous gravitational wave signals. This is the reason why alternative strategies are being pursued. Hierarchical strategies are best at investigating a large parameter space when there exist computational power constraints. Algorithms of this kind are being implemented by all the groups that are developing software for analyzing the data of the gravitational wave detectors that will come online in the next years. In this talk we will report about the hierarchical Hough transform method that the GEO 600 data analysis team at the Albert Einstein Institute is developing. The three step hierarchical algorithm has been described elsewhere. In this talk we will focus on some of the implementational aspects we are currently concerned with.Comment: 9 pages, 1 figure. To appear in the proceedings of the conference ``Gravitational waves: a challenge to theoretical astrophysics'', (June 5-9 2000, Trieste), ICTP Lecture Notes Serie

Mass gap in the 2D O(3) non-linear sigma model with a theta=pi term

By analytic continuation to real theta of data obtained from numerical simulation at imaginary theta we study the Haldane conjecture and show that the O(3) non-linear sigma model with a theta term in 2 dimensions becomes massless at theta=3.10(5). A modified cluster algorithm has been introduced to simulate the model with imaginary theta. Two different definitions of the topological charge on the lattice have been used; one of them needs renormalization to match the continuum operator. Our work also offers a successful test for numerical methods based on analytic continuation.Comment: Latex file, 4 pages. To appear in PRD; it contains the justification of analicity, more details about the fits, more references, et

Behavior near θ=π\theta=\pi of the mass gap in the 2D O(3) non-linear sigma model

The validity of the Haldane's conjecture entails that the mass gap of the 2-dimensional O(3) non-linear sigma model with a $\theta$-term must tend to zero as $\theta$ approaches the value $\pi$ by following a precise law. In the present paper we extract the related critical exponents by simulating the model at imaginary $\theta$.Comment: 24 pages, LaTeX source and 5 eps figure

Data analysis of gravitational-wave signals from spinning neutron stars. V. A narrow-band all-sky search

We present theory and algorithms to perform an all-sky coherent search for periodic signals of gravitational waves in narrow-band data of a detector. Our search is based on a statistic, commonly called the $\mathcal{F}$-statistic, derived from the maximum-likelihood principle in Paper I of this series. We briefly review the response of a ground-based detector to the gravitational-wave signal from a rotating neuron star and the derivation of the $\mathcal{F}$-statistic. We present several algorithms to calculate efficiently this statistic. In particular our algorithms are such that one can take advantage of the speed of fast Fourier transform (FFT) in calculation of the $\mathcal{F}$-statistic. We construct a grid in the parameter space such that the nodes of the grid coincide with the Fourier frequencies. We present interpolation methods that approximately convert the two integrals in the $\mathcal{F}$-statistic into Fourier transforms so that the FFT algorithm can be applied in their evaluation. We have implemented our methods and algorithms into computer codes and we present results of the Monte Carlo simulations performed to test these codes.Comment: REVTeX, 20 pages, 8 figure

Search for Continuous Gravitational Waves from Scorpius X-1 in LIGO O2 Data

We present the results of a search in LIGO O2 public data for continuous gravitational waves from the neutron star in the low-mass X-ray binary Scorpius X-1. We search for signals with $\approx$ constant frequency in the range 40-180 Hz. Thanks to the efficiency of our search pipeline we can use a long coherence time and achieve unprecedented sensitivity, significantly improving on existing results. This is the first search that has been able to probe gravitational wave amplitudes that could balance the accretion torque at the neutron star radius. Our search excludes emission at this level between 67.5 Hz and 131.5 Hz, for an inclination angle $44^\circ \pm 6^\circ$ derived from radio observations (Fomalont et al. 2001), and assuming that the spin axis is perpendicular to the orbital plane. If the torque arm is $\approx$ 26 km -- a conservative estimate of the \alfven\ radius -- our results are more constraining than the indirect limit across the band. This allows us to exclude certain mass-radius combinations and to place upper limits on the strength of the star's magnetic field. We also correct a mistake that appears in the literature in the equation that gives the gravitational wave amplitude at the torque balance (Abbott et al. 2017b, 2019a) and we re-interpret the associated latest LIGO/Virgo results in light of this

Exact Results for Thermodynamics of the Classical Field Theories: Sine- and Sinh-Gordon Models

Using the recently obtained exact results for the expectation values of operators in the sine- and sinh-Gordon models [A. B. Zamolodchikov and S. Lukyanov, Nucl. Phys. B{\bf 493}, 571 (1997), V. Fateev, S. Lukyanov, A. B. Zamolodchikov and Al. B. Zamolodchikov, Phys. Lett. B{\bf 406}, 83 (1997)] we calculate the specific heat of the corresponding two dimensional Euclidean (classical) models. We show that the temperature dependence of the specific heat of the sine-Gordon model, in the commensurate phase, has a maximum well below the Kosterlitz-Thouless transition and that the sinh-Gordon model is thermodynamically unstable in the strong coupling regime. We give also the temperature dependence of the specific heat in the incommensurate phase of the sine-Gordon model.Comment: 14 pages, including 6 figures; updated version; submitted to Phys. Rev.

Finite-size scaling and the deconfinement transition in gauge theories

We introduce a new method for determining the critical indices of the deconfinement transition in gauge theories. The method is based on the finite size scaling behavior of the expectation value of simple lattice operators, such as the plaquette. We test the method for the case of SU(3) pure gauge theory in (2+1) dimensions and obtain a precise determination of the critical index $\nu$, in agreement with the prediction of the Svetitsky-Yaffe conjecture.Comment: 6 pages. Several comments and one reference added, results unchange

Constraints on r-modes and mountains on millisecond neutron stars in binary systems

Continuous gravitational waves are nearly monochromatic signals emitted by asymmetries in rotating neutron stars. These signals have not yet been detected. Deep all-sky searches for continuous gravitational waves from isolated neutron stars require significant computational expense. Deep searches for neutron stars in binary systems are even more expensive, but potentially these targets are more promising emitters, especially in the hundreds-Hz region, where ground-based gravitational wave detectors are most sensitive. We present here an all-sky search for continuous signals with frequency between 300 and 500 Hz, from neutron stars in binary systems with orbital period between 15 and 60 days, and projected semi-major axis between 10 and 40 light-seconds. This is the only binary search on Advanced-LIGO data that probes this frequency range. Compared to previous results, our search is over an order of magnitude more sensitive. We do not detect any signals, but our results exclude plausible and unexplored neutron star configurations, for example, neutron stars with relative deformations greater than 3e-6 within 1 kpc from Earth and r-mode emission at the level of alpha ~ few 1e-4 within the same distance.Comment: Accepted for publication in The Astrophysical Journal Letter

Topology in CP(N-1) models: a critical comparison of different cooling techniques

Various cooling methods, including a recently introduced one which smoothes out only quantum fluctuations larger than a given threshold, are applied to the study of topology in 2d CP(N-1) models. A critical comparison of their properties is performed.Comment: Poster at LATTICE99(Topology and confinement), 3 pages, 5 eps figures, uses espcrc2.st

Deep Einstein@Home all-sky search for continuous gravitational waves in LIGO O3 public data

We present the results of an all-sky search for continuous gravitational waves in the public LIGO O3 data. The search covers signal frequencies $20$ Hz $\leq f \leq 800$ Hz and a spin-down range down to $-2.6\times 10^{-9}$ Hz s$^{-1}$1, motivated by detectability studies on synthetic populations of Galactic neutron stars. This search is the most sensitive all-sky search to date in this frequency/spin-down region. The initial search was performed using the first half of the public LIGO O3 data (O3a), utilizing Graphical Processing Units provided in equal parts by the volunteers of the Einstein@Home computing project and by the ATLAS cluster. After a hierarchical follow-up in seven stages, 12 candidates remain. Six are discarded at the eighth stage, by using the remaining O3 LIGO data (O3b). The surviving six can be ascribed to continuous-wave fake signals present in the LIGO data for validation purposes. We recover these fake signals with very high accuracy with our last stage search, which coherently combines all O3 data. Based on our results, we set upper limits on the gravitational wave amplitude $h_0$, and translate these in upper limits on the neutron star ellipticity and on the $r$-mode amplitude. The most stringent upper limits are at $203$ Hz, with $h_0=8.1 \times 10^{-26}$ at the 90% confidence level. Our results exclude neutron stars rotating faster than $5$ ms with ellipticities greater than $5\times 10^{-8} \left[{d\over{100~\textrm{pc}}}\right]$ within a distance $d$ from Earth and $r$-mode amplitudes $\alpha \geq 10^{-5} \left[{d\over{100~\textrm{pc}}}\right]$ for neutron stars spinning faster than $150$ Hz.Comment: Accepted for publication in The Astrophysical Journal on 31 May 2023. 13 pages, 10 figures, 3 table