Estimate of Tilt Instability of Mesa-Beam and Gaussian-Beam Modes for Advanced LIGO

Sidles and Sigg have shown that advanced LIGO interferometers will encounter a serious tilt instability, in which symmetric tilts of the mirrors of an arm cavity cause the cavity's light beam to slide sideways, so its radiation pressure exerts a torque that increases the tilt. Sidles and Sigg showed that the strength T of this torque is 26.2 times greater for advanced LIGO's baseline cavities -- nearly flat spherical mirrors which support Gaussian beams (``FG'' cavities), than for nearly concentric spherical mirrors which support Gaussian beams with the same diffraction losses as the baseline case -- ``CG'' cavities: T^{FG}/T^{CG} = 26.2. This has motivated a proposal to change the baseline design to nearly concentric, spherical mirrors. In order to reduce thermoelastic noise in advanced LIGO, O'Shaughnessy and Thorne have proposed replacing the spherical mirrors and their Gaussian beams by ``Mexican-Hat'' (MH) shaped mirrors which support flat-topped, ``mesa'' shaped beams. In this paper we compute the tilt-instability torque for advanced-LIGO cavities with nearly flat MH mirrors and mesa beams (``FM'' cavities) and nearly concentric MH mirrors and mesa beams (``CM'' cavities), with the same diffraction losses as in the baseline FG case. We find that the relative sizes of the restoring torques are T^{CM}/T^{CG} = 0.91, T^{FM}/T^{CG} = 96, T^{FM}/T^{FG} = 3.67. Thus, the nearly concentric MH mirrors have a weaker tilt instability than any other configuration. Their thermoelastic noise is the same as for nearly flat MH mirrors, and is much lower than for spherical mirrors.Comment: 10 pages, 3 figures, 4 table

Fractal-dimensional properties of subordinators

This work looks at the box-counting dimension of sets related to subordinators (non-decreasing Lévy processes). It was recently shown in Savov (Electron Commun Probab 19:1–10, 2014) that almost surely limδ→0U(δ)N(t,δ)=t , where N(t,δ) is the minimal number of boxes of size at most δ needed to cover a subordinator’s range up to time t, and U(δ) is the subordinator’s renewal function. Our main result is a central limit theorem (CLT) for N(t,δ) , complementing and refining work in Savov (2014). Box-counting dimension is defined in terms of N(t,δ) , but for subordinators we prove that it can also be defined using a new process obtained by shortening the original subordinator’s jumps of size greater than δ . This new process can be manipulated with remarkable ease in comparison with N(t,δ) , and allows better understanding of the box-counting dimension of a subordinator’s range in terms of its Lévy measure, improving upon Savov (2014, Corollary 1). Further, we shall prove corresponding CLT and almost sure convergence results for the new process

Extinction threshold in the spatial stochastic logistic model: space homogeneous case

We consider the extinction regime in the spatial stochastic logistic model in R^d (a.k.a. Bolker–Pacala–Dieckmann–Law model of spatial populations) using the first-order perturbation beyond the mean-field equation. In space homogeneous case (i.e. when the density is non-spatial and the covariance is translation invariant), we show that the perturbation converges as time tends to infinity; that yields the first-order approximation for the stationary density. Next, we study the critical mortality – the smallest constant death rate which ensures the extinction of the population – as a function of the mean-field scaling parameter ε>0. We find the leading term of the asymptotic expansion (as ε→0) of the critical mortality which is apparently different for the cases d≥3, d = 2, and d = 1

Search for gravitational waves from binary inspirals in S3 and S4 LIGO data

We report on a search for gravitational waves from the coalescence of compact binaries during the third and fourth LIGO science runs. The search focused on gravitational waves generated during the inspiral phase of the binary evolution. In our analysis, we considered three categories of compact binary systems, ordered by mass: (i) primordial black hole binaries with masses in the range 0.35 M(sun) < m1, m2 < 1.0 M(sun), (ii) binary neutron stars with masses in the range 1.0 M(sun) < m1, m2 < 3.0 M(sun), and (iii) binary black holes with masses in the range 3.0 M(sun)< m1, m2 < m_(max) with the additional constraint m1+ m2 < m_(max), where m_(max) was set to 40.0 M(sun) and 80.0 M(sun) in the third and fourth science runs, respectively. Although the detectors could probe to distances as far as tens of Mpc, no gravitational-wave signals were identified in the 1364 hours of data we analyzed. Assuming a binary population with a Gaussian distribution around 0.75-0.75 M(sun), 1.4-1.4 M(sun), and 5.0-5.0 M(sun), we derived 90%-confidence upper limit rates of 4.9 yr^(-1) L10^(-1) for primordial black hole binaries, 1.2 yr^(-1) L10^(-1) for binary neutron stars, and 0.5 yr^(-1) L10^(-1) for stellar mass binary black holes, where L10 is 10^(10) times the blue light luminosity of the Sun.Comment: 12 pages, 11 figure

All-sky search for periodic gravitational waves in LIGO S4 data

We report on an all-sky search with the LIGO detectors for periodic gravitational waves in the frequency range 50-1000 Hz and with the frequency's time derivative in the range -1.0E-8 Hz/s to zero. Data from the fourth LIGO science run (S4) have been used in this search. Three different semi-coherent methods of transforming and summing strain power from Short Fourier Transforms (SFTs) of the calibrated data have been used. The first, known as "StackSlide", averages normalized power from each SFT. A "weighted Hough" scheme is also developed and used, and which also allows for a multi-interferometer search. The third method, known as "PowerFlux", is a variant of the StackSlide method in which the power is weighted before summing. In both the weighted Hough and PowerFlux methods, the weights are chosen according to the noise and detector antenna-pattern to maximize the signal-to-noise ratio. The respective advantages and disadvantages of these methods are discussed. Observing no evidence of periodic gravitational radiation, we report upper limits; we interpret these as limits on this radiation from isolated rotating neutron stars. The best population-based upper limit with 95% confidence on the gravitational-wave strain amplitude, found for simulated sources distributed isotropically across the sky and with isotropically distributed spin-axes, is 4.28E-24 (near 140 Hz). Strict upper limits are also obtained for small patches on the sky for best-case and worst-case inclinations of the spin axes.Comment: 39 pages, 41 figures An error was found in the computation of the C parameter defined in equation 44 which led to its overestimate by 2^(1/4). The correct values for the multi-interferometer, H1 and L1 analyses are 9.2, 9.7, and 9.3, respectively. Figure 32 has been updated accordingly. None of the upper limits presented in the paper were affecte

Astrophysically Triggered Searches for Gravitational Waves: Status and Prospects

In gravitational-wave detection, special emphasis is put onto searches that focus on cosmic events detected by other types of astrophysical observatories. The astrophysical triggers, e.g. from gamma-ray and X-ray satellites, optical telescopes and neutrino observatories, provide a trigger time for analyzing gravitational wave data coincident with the event. In certain cases the expected frequency range, source energetics, directional and progenitor information is also available. Beyond allowing the recognition of gravitational waveforms with amplitudes closer to the noise floor of the detector, these triggered searches should also lead to rich science results even before the onset of Advanced LIGO. In this paper we provide a broad review of LIGO's astrophysically triggered searches and the sources they target

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

A Joint Search for Gravitational Wave Bursts with AURIGA and LIGO

The first simultaneous operation of the AURIGA detector and the LIGO observatory was an opportunity to explore real data, joint analysis methods between two very different types of gravitational wave detectors: resonant bars and interferometers. This paper describes a coincident gravitational wave burst search, where data from the LIGO interferometers are cross-correlated at the time of AURIGA candidate events to identify coherent transients. The analysis pipeline is tuned with two thresholds, on the signal-to-noise ratio of AURIGA candidate events and on the significance of the cross-correlation test in LIGO. The false alarm rate is estimated by introducing time shifts between data sets and the network detection efficiency is measured with simulated signals with power in the narrower AURIGA band. In the absence of a detection, we discuss how to set an upper limit on the rate of gravitational waves and to interpret it according to different source models. Due to the short amount of analyzed data and to the high rate of non-Gaussian transients in the detectors noise at the time, the relevance of this study is methodological: this was the first joint search for gravitational wave bursts among detectors with such different spectral sensitivity and the first opportunity for the resonant and interferometric communities to unify languages and techniques in the pursuit of their common goal.Comment: 18 pages, IOP, 12 EPS figure