Analytic models of plausible gravitational lens potentials

Gravitational lenses on galaxy scales are plausibly modelled as having ellipsoidal symmetry and a universal dark matter density profile, with a Sersic profile to describe the distribution of baryonic matter. Predicting all lensing effects requires knowledge of the total lens potential: in this work we give analytic forms for that of the above hybrid model. Emphasising that complex lens potentials can be constructed from simpler components in linear combination, we provide a recipe for attaining elliptical symmetry in either projected mass or lens potential. We also provide analytic formulae for the lens potentials of Sersic profiles for integer and half-integer index. We then present formulae describing the gravitational lensing effects due to smoothly-truncated universal density profiles in cold dark matter model. For our isolated haloes the density profile falls off as radius to the minus fifth or seventh power beyond the tidal radius, functional forms that allow all orders of lens potential derivatives to be calculated analytically, while ensuring a non-divergent total mass. We show how the observables predicted by this profile differ from that of the original infinite-mass NFW profile. Expressions for the gravitational flexion are highlighted. We show how decreasing the tidal radius allows stripped haloes to be modelled, providing a framework for a fuller investigation of dark matter substructure in galaxies and clusters. Finally we remark on the need for finite mass halo profiles when doing cosmological ray-tracing simulations, and the need for readily-calculable higher order derivatives of the lens potential when studying catastrophes in strong lenses.Comment: 24 pages, 10 figures, matches published versio

Massive binary black holes in galactic nuclei and their path to coalescence

Massive binary black holes form at the centre of galaxies that experience a merger episode. They are expected to coalesce into a larger black hole, following the emission of gravitational waves. Coalescing massive binary black holes are among the loudest sources of gravitational waves in the Universe, and the detection of these events is at the frontier of contemporary astrophysics. Understanding the black hole binary formation path and dynamics in galaxy mergers is therefore mandatory. A key question poses: during a merger, will the black holes descend over time on closer orbits, form a Keplerian binary and coalesce shortly after? Here we review progress on the fate of black holes in both major and minor mergers of galaxies, either gas-free or gas-rich, in smooth and clumpy circum-nuclear discs after a galactic merger, and in circum-binary discs present on the smallest scales inside the relic nucleus.Comment: Accepted for publication in Space Science Reviews. To appear in hard cover in the Space Sciences Series of ISSI "The Physics of Accretion onto Black Holes" (Springer Publisher

A research agenda for seed-trait functional ecology

Trait-based approaches have improved our understanding of plant evolution, community assembly and ecosystem functioning. A major challenge for the upcoming decades is to understand the functions and evolution of early life-history traits, across levels of organization and ecological strategies. Although a variety of seed traits are critical for dispersal, persistence, germination timing and seedling establishment, only seed mass has been considered systematically. Here we suggest broadening the range of morphological, physiological and biochemical seed traits to add new understanding on plant niches, population dynamics and community assembly. The diversity of seed traits and functions provides an important challenge that will require international collaboration in three areas of research. First, we present a conceptual framework for a seed ecological spectrum that builds upon current understanding of plant niches. We then lay the foundation for a seed-trait functional network, the establishment of which will underpin and facilitate trait-based inferences. Finally, we anticipate novel insights and challenges associated with incorporating diverse seed traits into predictive evolutionary ecology, community ecology and applied ecology. If the community invests in standardized seed-trait collection and the implementation of rigorous databases, major strides can be made at this exciting frontier of functional ecology.Commonwealth Scientific and Industrial Research Organisation. Grant Number: R‐90470‐0

Supermassive Black Hole Binaries: The Search Continues

Gravitationally bound supermassive black hole binaries (SBHBs) are thought to be a natural product of galactic mergers and growth of the large scale structure in the universe. They however remain observationally elusive, thus raising a question about characteristic observational signatures associated with these systems. In this conference proceeding I discuss current theoretical understanding and latest advances and prospects in observational searches for SBHBs.Comment: 17 pages, 4 figures. To appear in the Proceedings of 2014 Sant Cugat Forum on Astrophysics. Astrophysics and Space Science Proceedings, ed. C.Sopuerta (Berlin: Springer-Verlag

Measurement of the partial widths of the Z into up- and down-type quarks

Using the entire OPAL LEP1 on-peak Z hadronic decay sample, Z -> qbarq gamma decays were selected by tagging hadronic final states with isolated photon candidates in the electromagnetic calorimeter. Combining the measured rates of Z -> qbarq gamma decays with the total rate of hadronic Z decays permits the simultaneous determination of the widths of the Z into up- and down-type quarks. The values obtained, with total errors, were Gamma u = 300 ^{+19}_{-18} MeV and Gamma d = 381 ^{+12}_{-12} MeV. The results are in good agreement with the Standard Model expectation.Comment: 22 pages, 5 figures, Submitted to Phys. Letts.

Search for R-Parity Violating Decays of Scalar Fermions at LEP

A search for pair-produced scalar fermions under the assumption that R-parity is not conserved has been performed using data collected with the OPAL detector at LEP. The data samples analysed correspond to an integrated luminosity of about 610 pb-1 collected at centre-of-mass energies of sqrt(s) 189-209 GeV. An important consequence of R-parity violation is that the lightest supersymmetric particle is expected to be unstable. Searches of R-parity violating decays of charged sleptons, sneutrinos and squarks have been performed under the assumptions that the lightest supersymmetric particle decays promptly and that only one of the R-parity violating couplings is dominant for each of the decay modes considered. Such processes would yield final states consisting of leptons, jets, or both with or without missing energy. No significant single-like excess of events has been observed with respect to the Standard Model expectations. Limits on the production cross- section of scalar fermions in R-parity violating scenarios are obtained. Constraints on the supersymmetric particle masses are also presented in an R-parity violating framework analogous to the Constrained Minimal Supersymmetric Standard Model.Comment: 51 pages, 24 figures, Submitted to Eur. Phys. J.

Arthroscopic subacromial decompression for subacromial shoulder pain (CSAW):a multicentre, pragmatic, parallel group, placebo-controlled, three-group, randomised surgical trial

Background: Arthroscopic sub-acromial decompression (decompressing the sub-acromial space by removing bone spurs and soft tissue arthroscopically) is a common surgery for subacromial shoulder pain, but its effectiveness is uncertain. We did a study to assess its effectiveness and to investigate the mechanism for surgical decompression. Methods: We did a multicentre, randomised, pragmatic, parallel group, placebo-controlled, three-group trial at 32 hospitals in the UK with 51 surgeons. Participants were patients who had subacromial pain for at least 3 months with intact rotator cuff tendons, were eligible for arthroscopic surgery, and had previously completed a non-operative management programme that included exercise therapy and at least one steroid injection. Exclusion criteria included a full-thickness torn rotator cuff. We randomly assigned participants (1:1:1) to arthroscopic subacromial decompression, investigational arthroscopy only, or no treatment (attendance of one reassessment appointment with a specialist shoulder clinician 3 months after study entry, but no intervention). Arthroscopy only was a placebo as the essential surgical element (bone and soft tissue removal) was omitted. We did the randomisation with a computer-generated minimisation system. In the surgical intervention groups, patients were not told which type of surgery they were receiving (to ensure masking). Patients were followed up at 6 months and 1 year after randomisation; surgeons coordinated their waiting lists to schedule surgeries as close as possible to randomisation. The primary outcome was the Oxford Shoulder Score (0 [worst] to 48 [best]) at 6 months, analysed by intention to treat. The sample size calculation was based upon a target difference of 4·5 points (SD 9·0). This trial has been registered at ClinicalTrials.gov, number NCT01623011. Findings: Between Sept 14, 2012, and June 16, 2015, we randomly assigned 313 patients to treatment groups (106 to decompression surgery, 103 to arthroscopy only, and 104 to no treatment). 24 [23%], 43 [42%], and 12 [12%] of the decompression, arthroscopy only, and no treatment groups, respectively, did not receive their assigned treatment by 6 months. At 6 months, data for the Oxford Shoulder Score were available for 90 patients assigned to decompression, 94 to arthroscopy, and 90 to no treatment. Mean Oxford Shoulder Score did not differ between the two surgical groups at 6 months (decompression mean 32·7 points [SD 11·6] vs arthroscopy mean 34·2 points [9·2]; mean difference −1·3 points (95% CI −3·9 to 1·3, p=0·3141). Both surgical groups showed a small benefit over no treatment (mean 29·4 points [SD 11·9], mean difference vs decompression 2·8 points [95% CI 0·5–5·2], p=0·0186; mean difference vs arthroscopy 4·2 [1·8–6·6], p=0·0014) but these differences were not clinically important. There were six study-related complications that were all frozen shoulders (in two patients in each group). Interpretation: Surgical groups had better outcomes for shoulder pain and function compared with no treatment but this difference was not clinically important. Additionally, surgical decompression appeared to offer no extra benefit over arthroscopy only. The difference between the surgical groups and no treatment might be the result of, for instance, a placebo effect or postoperative physiotherapy. The findings question the value of this operation for these indications, and this should be communicated to patients during the shared treatment decision-making process. </p

Measurement of the Strong Coupling alpha s from Four-Jet Observables in e+e- Annihilation

Data from e+e- annihilation into hadrons at centre-of-mass energies between 91 GeV and 209 GeV collected with the OPAL detector at LEP, are used to study the four-jet rate as a function of the Durham algorithm resolution parameter ycut. The four-jet rate is compared to next-to-leading order calculations that include the resummation of large logarithms. The strong coupling measured from the four-jet rate is alphas(Mz0)= 0.1182+-0.0003(stat.)+-0.0015(exp.)+-0.0011(had.)+-0.0012(scale)+-0.0013(mass) in agreement with the world average. Next-to-leading order fits to the D-parameter and thrust minor event-shape observables are also performed for the first time. We find consistent results, but with significantly larger theoretical uncertainties.Comment: 25 pages, 15 figures, Submitted to Euro. Phys. J.

Measurement of the Hadronic Photon Structure Function F_2^gamma at LEP2

The hadronic structure function of the photon F_2^gamma is measured as a function of Bjorken x and of the factorisation scale Q^2 using data taken by the OPAL detector at LEP. Previous OPAL measurements of the x dependence of F_2^gamma are extended to an average Q^2 of 767 GeV^2. The Q^2 evolution of F_2^gamma is studied for average Q^2 between 11.9 and 1051 GeV^2. As predicted by QCD, the data show positive scaling violations in F_2^gamma. Several parameterisations of F_2^gamma are in agreement with the measurements whereas the quark-parton model prediction fails to describe the data.Comment: 4 pages, 2 figures, to appear in the proceedings of Photon 2001, Ascona, Switzerlan

A measurement of the tau mass and the first CPT test with tau leptons

We measure the mass of the tau lepton to be 1775.1+-1.6(stat)+-1.0(syst.) MeV using tau pairs from Z0 decays. To test CPT invariance we compare the masses of the positively and negatively charged tau leptons. The relative mass difference is found to be smaller than 3.0 10^-3 at the 90% confidence level.Comment: 10 pages, 4 figures, Submitted to Phys. Letts.