Seismic gravity-gradient noise in interferometric gravitational-wave detectors

When ambient seismic waves pass near and under an interferometric gravitational-wave detector, they induce density perturbations in the Earth, which in turn produce fluctuating gravitational forces on the interferometer’s test masses. These forces mimic a stochastic background of gravitational waves and thus constitute a noise source. This seismic gravity-gradient noise has been estimated and discussed previously by Saulson using a simple model of the Earth’s ambient seismic motions. In this paper, we develop a more sophisticated model of these motions, based on the theory of multimode Rayleigh and Love waves propagating in a multilayer medium that approximates the geological strata at the LIGO sites, and we use this model to reexamine seismic gravity gradients. We characterize the seismic gravity-gradient noise by a transfer function, T(f )≡x̃(f )/W̃(f ), from the spectrum of rms seismic displacements averaged over vertical and horizontal directions, W̃(f ), to the spectrum of interferometric test-mass motions, x̃(f )≡Lh̃(f ); here L is the interferometer arm length, h̃(f ) is the gravitational-wave noise spectrum, and f is frequency. Our model predicts a transfer function with essentially the same functional form as that derived by Saulson, T≃4πGρ(2πf )-2β(f ), where ρ is the density of Earth near the test masses, G is Newton’s constant, and β(f )≡γ(f )Γ(f )β′(f ) is a dimensionless reduced transfer function whose components γ≃1 and Γ≃1 account for a weak correlation between the interferometer’s two corner test masses and a slight reduction of the noise due to the height of the test masses above the Earth’s surface. This paper’s primary foci are (i) a study of how β′(f )≃β(f ) depends on the various Rayleigh and Love modes that are present in the seismic spectrum, (ii) an attempt to estimate which modes are actually present at the two LIGO sites at quiet times and at noisy times, and (iii) a corresponding estimate of the magnitude of β′(f ) at quiet and noisy times. We conclude that at quiet times β′≃0.35–0.6 at the LIGO sites, and at noisy times β′≃0.15–1.4. (For comparison, Saulson’s simple model gave β=β′=1/sqrt[3]=0.58.) By folding our resulting transfer function into the “standard LIGO seismic spectrum,” which approximates W̃(f ) at typical times, we obtain the gravity-gradient noise spectra. At quiet times this noise is below the benchmark noise level of “advanced LIGO interferometers” at all frequencies (though not by much at ∼10 Hz); at noisy times it may significantly exceed the advanced noise level near 10 Hz. The lower edge of our quiet-time noise constitutes a limit, beyond which there would be little gain from further improvements in vibration isolation and thermal noise, unless one can also reduce the seismic gravity gradient noise. Two methods of such reduction are briefly discussed: monitoring the Earth’s density perturbations near each test mass, computing the gravitational forces they produce, and correcting the data for those forces; and constructing narrow moats around the interferometers’ corner and end stations to shield out the fundamental-mode Rayleigh waves, which we suspect dominate at quiet times

Technology Adoption Factors in the Digitization of Popular Culture: Analyzing the Online Gambling Market

This study explores the psychological factors that influence market diffusion of popular culture digital services. Digital service websites have been diffusing through global markets with relative ease, but the factors influencing this are not well understood. The transition from the brick and mortar services to a digital outlet represents a form of market disruption but the way that this impacts the consumer experience and the way firms engage in innovation are not fully understood, nor are the various cognitive factors driving the adoption rates. There is a need to understand cognitions that influence intent to engage, as well as the perceptions of the social environment in which the service offering occurs. Therefore, we offer an examination of different social contexts (US and UK) to explore the impact of certain attitudes and norms toward online gambling consumption. The results of study demonstrate how variations between online and offline environments impact consumer adoption and market diffusion. Additionally, the results further support the need for more studies to focus on the soft factors that influence their innovation capabilities

Strong-field tidal distortions of rotating black holes: Formalism and results for circular, equatorial orbits

Tidal coupling between members of a compact binary system can have an interesting and important influence on that binary's dynamical inspiral. Tidal coupling also distorts the binary's members, changing them (at lowest order) from spheres to ellipsoids. At least in the limit of fluid bodies and Newtonian gravity, there are simple connections between the geometry of the distorted ellipsoid and the impact of tides on the orbit's evolution. In this paper, we develop tools for investigating tidal distortions of rapidly rotating black holes using techniques that are good for strong-field, fast-motion binary orbits. We use black hole perturbation theory, so our results assume extreme mass ratios. We develop tools to compute the distortion to a black hole's curvature for any spin parameter, and for tidal fields arising from any bound orbit, in the frequency domain. We also develop tools to visualize the horizon's distortion for black hole spin $a/M \le \sqrt{3}/2$ (leaving the more complicated $a/M > \sqrt{3}/2$ case to a future analysis). We then study how a Kerr black hole's event horizon is distorted by a small body in a circular, equatorial orbit. We find that the connection between the geometry of tidal distortion and the orbit's evolution is not as simple as in the Newtonian limit.Comment: 37 pages, 8 figures. Accepted for publication to Physical Review D. This version corrects a number of typographical errors found when reviewing the page proof

Submillimetre observations of a sample of broad absorption line quasars

The broad absorption line (BAL) features seen in a small fraction of quasar optical/UV spectra are attributed to bulk outflows away from the quasar core. Observational evidence suggests that dust plays a key role in these systems, although whether the inferred dust properties are a signature of orientation effects or whether they are indicative of an evolutionary sequence remains an outstanding issue. Submillimetre (submm) detections of BAL quasars (BALQSOs), which would clearly help to resolve this issue, have so far been sparse. This paper reports on new submm observations of seven BALQSOs. The strongest influence on the observed flux is found to be the redshift, with the two highest redshift sources appearing intrinsically more submm-luminous than the lower redshift ones. Since this trend is also seen in other high redshift AGN, including non-BAL quasars it implies that the dust emission properties of these systems are no different from those of the general AGN population, which is difficult to reconcile with the evolutionary interpretation of the BAL phenomenon.Comment: 5 Pages, to appear in ApJ Letter

Gravitational-wave confusion background from cosmological compact binaries: Implications for future terrestrial detectors

Increasing the sensitivity of a gravitational-wave (GW) detector improves our ability to measure the characteristics of detected sources. It also increases the number of weak signals that contribute to the data. Because GW detectors have nearly all-sky sensitivity, they can be subject to a confusion limit: Many sources which cannot be distinguished may be measured simultaneously, defining a stochastic noise floor to the sensitivity. For GW detectors operating at present and for their planned upgrades, the projected event rate is sufficiently low that we are far from the confusion-limited regime. However, some detectors currently under discussion may have large enough reach to binary inspiral that they enter the confusion-limited regime. In this paper, we examine the binary inspiral confusion limit for terrestrial detectors. We consider a broad range of inspiral rates in the literature, several planned advanced gravitational-wave detectors, and the highly advanced "Einstein Telescope" design. Though most advanced detectors will not be impacted by this limit, the Einstein Telescope with a very low frequency "seismic wall" may be subject to confusion noise. At a minimum, careful data analysis will be require to separate signals which will appear confused. This result should be borne in mind when designing highly advanced future instruments.Comment: 19 pages, 6 figures and 3 tables; accepted for publication in Phys. Rev.

Approximating the inspiral of test bodies into Kerr black holes

We present a new approximate method for constructing gravitational radiation driven inspirals of test-bodies orbiting Kerr black holes. Such orbits can be fully described by a semi-latus rectum $p$, an eccentricity $e$, and an inclination angle $\iota$; or, by an energy $E$, an angular momentum component $L_z$, and a third constant $Q$. Our scheme uses expressions that are exact (within an adiabatic approximation) for the rates of change ($\dot{p}$, $\dot{e}$, $\dot{\iota}$) as linear combinations of the fluxes ($\dot{E}$, $\dot{L_z}$, $\dot{Q}$), but uses quadrupole-order formulae for these fluxes. This scheme thus encodes the exact orbital dynamics, augmenting it with approximate radiation reaction. Comparing inspiral trajectories, we find that this approximation agrees well with numerical results for the special cases of eccentric equatorial and circular inclined orbits, far more accurate than corresponding weak-field formulae for ($\dot{p}$, $\dot{e}$, $\dot{\iota}$). We use this technique to study the inspiral of a test-body in inclined, eccentric Kerr orbits. Our results should be useful tools for constructing approximate waveforms that can be used to study data analysis problems for the future LISA gravitational-wave observatory, in lieu of waveforms from more rigorous techniques that are currently under development.Comment: 15 pages, 5 figures, submitted to PR

Confirmation of the effectiveness of sub-mm source redshift estimation based on rest-frame radio to FIR photometry

We present a comparison between the published optical, IR and CO spectroscopic redshifts of 15 (sub-)mm galaxies and their photometric redshifts as derived from long-wavelength (radio-mm-FIR) photometric data. The redshift accuracy measured for 12 sub-mm galaxies with at least one robustly-determined colour in the radio-mm-FIR regime is dz=0.30 (r.m.s.). Despite the wide range of spectral energy distributions in the local galaxies that are used in an un-biased manner as templates, this analysis demonstrates that photometric redshifts can be efficiently derived for sub-mm galaxies with a precision of dz < 0.5 using only the rest-frame FIR to radio wavelength data.Comment: submitted to MNRAS (1 object removed from analysis, shortening of paper

Evolution of circular, non-equatorial orbits of Kerr black holes due to gravitational-wave emission: II. Inspiral trajectories and gravitational waveforms

The inspiral of a ``small'' ($\mu \sim 1-100 M_\odot$) compact body into a ``large'' ($M \sim 10^{5-7} M_\odot$) black hole is a key source of gravitational radiation for the space-based gravitational-wave observatory LISA. The waves from such inspirals will probe the extreme strong-field nature of the Kerr metric. In this paper, I investigate the properties of a restricted family of such inspirals (the inspiral of circular, inclined orbits) with an eye toward understanding observable properties of the gravitational waves that they generate. Using results previously presented to calculate the effects of radiation reaction, I assemble the inspiral trajectories (assuming that radiation reacts adiabatically, so that over short timescales the trajectory is approximately geodesic) and calculate the wave generated as the compact body spirals in. I do this analysis for several black hole spins, sampling a range that should be indicative of what spins we will encounter in nature. The spin has a very strong impact on the waveform. In particular, when the hole rotates very rapidly, tidal coupling between the inspiraling body and the event horizon has a very strong influence on the inspiral time scale, which in turn has a big impact on the gravitational wave phasing. The gravitational waves themselves are very usefully described as ``multi-voice chirps'': the wave is a sum of ``voices'', each corresponding to a different harmonic of the fundamental orbital frequencies. Each voice has a rather simple phase evolution. Searching for extreme mass ratio inspirals voice-by-voice may be more effective than searching for the summed waveform all at once.Comment: 15 pages, 11 figures, accepted for publication in PRD. This version incorporates referee's comments, and is much less verbos

The SCUBA 8-mJy survey - I: Sub-millimetre maps, sources and number counts

We present maps, source lists, and number counts from the largest, unbiassed, extragalactic sub-mm survey so far undertaken with the SCUBA camera on the JCMT. Our maps cover 260 sq. arcmin, to a noise level S(850)=2.5 mJy/beam. We have reduced the data using both SURF, and our own pipeline which produces zero-footprint maps and noise images. The uncorrelated noise maps produced by the latter approach have allowed application of a maximum-likelihood method to measure the statistical significance of each peak, leading to properly quantified flux-density errors for all potential sources. We detect 19 sources with S/N > 4, 38 with S/N > 3.5, and 72 with S/N > 3. To assess completeness and the impact of source confusion we have applied our source extraction algorithm to a series of simulated images. The result is a new estimate of the sub-mm source counts in the flux-density range S(850)=5-15mJy, which we compare with other estimates, and with model predictions. Our estimate of the cumulative source count at S(850) > 8 mJy is 320 (+80,-100) per square degree. Assuming that the majority of sources have z > 1.5, the co-moving number density of high-z galaxies forming stars at a rate >1000 solar masses per year is 10^-5 per Mpc^3, with only a weak dependence on the precise redshift distribution. This number density corresponds to that of massive ellipticals with L > 3-4 L* at low redshift and is also the same as the co-moving number density of comparably massive, passively-evolving objects in the redshift band 1<z<2 inferred from recent surveys of extremely red objects. Thus the bright sub-mm sources can plausibly account for the formation of all present-day massive ellipticals. Improved z constraints, and a proper measurement of sub-mm clustering can refine or refute this picture.Comment: Minor revisions. 27 pages, 13 figures. Higher resolution versions of Figs 5,6,7 and 8 are available from the autho

Nearly horizon skimming orbits of Kerr black holes

An unusual set of orbits about extreme Kerr black holes resides at the Boyer-Lindquist radius $r = M$, the coordinate of the hole's event horizon. These ``horizon skimming'' orbits have the property that their angular momentum $L_z$ {\it increases} with inclination angle, opposite to the familiar behavior one encounters at larger radius. In this paper, I show that this behavior is characteristic of a larger family of orbits, the ``nearly horizon skimming'' (NHS) orbits. NHS orbits exist in the very strong field of any black hole with spin a\agt 0.952412M. Their unusual behavior is due to the locking of particle motion near the event horizon to the hole's spin, and is therefore a signature of the Kerr metric's extreme strong field. An observational hallmark of NHS orbits is that a small body spiraling into a Kerr black hole due to gravitational-wave emission will be driven into orbits of progressively smaller inclination angle, toward the equator. This is in contrast to the ``normal'' behavior. For circular orbits, the change in inclination is very small, and unlikely to be of observational importance. I argue that the change in inclination may be considerably larger when one considers the evolution of inclined eccentric orbits. If this proves correct, then the gravitational waves produced by evolution through the NHS regime may constitute a very interesting and important probe of the strong-field nature of rotating black holes.Comment: 9 pages, 5 figures, accepted for publication in PR