Beyond the Thin Lens Approximation

We obtain analytic formulae for the null geodesics of Friedmann-Lema\^{\i}tre-Robertson-Walker spacetimes with scalar perturbations in the longitudinal gauge. From these we provide a rigorous derivation of the cosmological lens equation, and obtain an expression for the magnification of a bundle of light rays without restriction to static or thin lens scenarios. We show how the usual magnification matrix naturally emerges in the appropriate limits.Comment: 37 pages plus 3 appended figures, plain TeX. Submitted to Ap

Using the Sunyaev-Zel'dovich Effect to Probe the Gas in Clusters

The thermal Sunyaev-Zel'dovich effect is an important probe of clusters of galaxies, and has the attractive property of being proportional to the thermal energy content of the intracluster medium. With the assistance of X-ray data, the effect can be used to measure the number of hot electrons in clusters, and thus measure cluster baryon contents. Cluster absolute distances and other structural parameters can also be measured by combining thermal Sunyaev-Zel'dovich, X-ray, and other data. This review presents an introduction to the effect, shows some representative results, and sketches imminent developments.Comment: Review for Carnegie Observatories Centennial Symposium 3. 16 pages of LaTeX with 5 embedded Postscript figures figure

Cluster-Induced Fluctuations in the Microwave Background Radiation

The research proposed was to detect, map and interpret the Sunyaev-Zel dovich (SZ) effects in two samples of distant clusters of galaxies with the OVRO 40-m telescope: an optically selected sample of 26 clusters at the North Ecliptic Pole, and an X-ray selected sample of clusters based on the Einstein Medium Sensitivity Survey, to make small maps of the strongest cluster SZ effects using the OVRO 40-m telescope, to combine the SZ and X-ray data for well-detected clusters to determine the value of the Hubble constant and set limits to the value of the deceleration parameter, and to study the properties of cluster atmospheres using the SZ effect

Entrepreneurship In Multinational Corporations: The Initiative Process In Foreign Subsidiaries

This is an empirical study of initiatives in the subsidiaries of multinational corporations. An initiative is the subsidiary-driven creation of a value-adding activity. While previous research has focused on the world product mandates earned as a result of initiatives, or the corporate systems that facilitate subsidiary initiatives, this study is concerned with the internal processes that actively drive subsidiary initiatives. This issue is of vital importance to subsidiary managers who are looking for ways to enhance their value-added role in the corporation: it also has substantial implications for corporate strategy and for theoretical models of multinational management and entrepreneurship.;Two research questions drove this research: What forms do subsidiary initiatives take? and What is the initiative process? The research was undertaken using an inductive approach, building knowledge from an iterative combination of empirical evidence and theory. A total of 39 initiatives from six Canadian subsidiaries of U.S. multinational corporations formed the final sample. Data was gathered through over 100 personal interviews, but also from two questionnaires and archival and secondary sources.;There were two key findings. First, four distinct types of subsidiary initiatives were identified, labelled reconfiguration , local market , competitive bid and mandate extension . These four types were empirically validated, and conceptualized in terms of the market opportunities they tapped into. Second, the initiative process was analyzed in depth, and found to consist of four phases representing the increasing viability of the initiative. The process was found to be strongly influenced by the organizational context of the subsidiary, as predicted by Burgelman\u27s model of corporate venturing. The key contribution, however, is the observation that the internally-defined subsidiary context is a more critical driver of initiative than the externally-defined corporate context.;The implication for the management of multinational subsidiaries is that the assignment of subsidiary roles has limitations, because it assumes the opportunity set of the subsidiary can be prejudged and better understood from the centre than the periphery. Subsidiaries should have sufficient slack that opportunities can be identified and developed; and they should attempt to build an internal management context to foster the entrepreneurial spirit. Theoretical and managerial implications are developed around these core insights

Galaxy gas ejection in radio galaxies: the case of 3C 35

We report results from XMM-Newton and Chandra observations of the nearby (z = 0.067) giant radio galaxy 3C 35. We find evidence for an X-ray emitting gas belt, orthogonal to and lying between the lobes of 3C 35, which we interpret as fossil-group gas driven outwards by the expanding radio lobes. We also detect weak emission from a second, more extended group-type environment, as well as inverse-Compton X-ray emission from the radio lobes. The morphological structure of the radio lobes and gas belt point to co-evolution. Furthermore, the radio source is powerful enough to eject galaxy-scale gas out to distances of 100kpc, and the ages of the two features are comparable (tsynch~140Myr, tbelt~80 Myr). The destruction of 3C 35's atmosphere may offer clues as to how fossil systems are regulated: radio galaxies need to be of power comparable to 3C 35 to displace and regulate fossil-group gas. We discuss the implications of the gas belt in 3C 35 in terms of AGN fuelling and feedback.Comment: 18 pages, accepted to MNRA

Null Geodesics in Perturbed Spacetimes

We present a generalization and refinement of the Sachs-Wolfe technique which unifies many of the approaches taken to date and clarifies both the physical and the mathematical character of the method. We illustrate the formalism with a calculation of the behavior of light passing a moving lens on a Minkowski background.Comment: 24 page

3-D Simulations of Protostellar Jets in Stratified Ambient Media

We present fully three-dimensional hydrodynamical simulations of radiative cooling jets propagating into stratified isothermal ambient media with power-law density and pressure distributions. The parameters used are mainly suitable for protostellar jets but results applicable to extragalactic jets are also presented. Comparisons are made with previous simulations of jets through homogeneous media. We find that for radiative cooling jets propagating into regions where the ambient medium has an increasing density (and pressure) gradient, the ambient gas tends to compress the cold, low-pressure cocoon of shocked material that surrounds the beam and destroy the bow shock-like structure at the head. The compressing medium collimates the jet and promotes the development of Kelvin-Helmholtz instabilities which cause beam focusing, wiggling and the formation of internal traveling shocks, $close$ $to$ $the$ $head$, via pinching along the beam. This remarkably resembles the structure of some observed systems (e.g. Haro 6-5B northern and HH 24G jets). These effects are larger for jets with smaller density ratio between jet and environment $\eta$ (tested for $\eta$=1, 3, and 10) and larger Mach number $M_a=v_j/c_a$ (tested for $M_a=$12 and 24, where $v_j$ is the jet velocity and $c_a$ the ambient sound speed). In an ambient medium of decreasing density (and pressure), the beam is poorly collimated and relaxes, becoming faint. This could explain ''invisible'' jet sections, like the gap between the parent source and collimated beam (e.g., in HH30 jet). Although, on average, jets propagating into an increasing (decreasing) density environment are decelerated (accelerated) by the increasing (decreasing) ram pressure of the ambient medium, we find that their propagation velocities have an oscillating pattern.Comment: 33 pp, LaTeX file, 13 figures upon request. To appear in the Astrophys. J., vol 471, nov. 10t

The gas distribution in the high-redshift cluster MS 1054-0321

We investigate the gas mass distribution in the high redshift cluster MS 1054-0321 using Chandra X-ray and OCRA SZ effect data. We use a superposition of offset $\beta$-type models to describe the composite structure of MS 1054-0321. We find gas mass fractions f_{gas}^\rm{X\mbox{-}ray} = 0.087_{-0.001}^{+0.005} and f_{gas}^\rm{SZ} = 0.094_{-0.001}^{+0.003} for the (main) eastern component of MS 1054-0321 using X-ray or SZ data, but f_{gas}^\rm{X\mbox{-}ray} = 0.030 _{-0.014}^{+0.010} for the western component. The gas mass fraction for the eastern component is in agreement with some results reported in the literature, but inconsistent with the cosmic baryon fraction. The low gas mass fraction for the western component is likely to be a consequence of gas stripping during the ongoing merger. The gas mass fraction of the integrated system is $0.060_{-0.009}^{+0.004}$: we suggest that the missing baryons from the western component are present as hot diffuse gas which is poorly represented in existing X-ray images. The missing gas could appear in sensitive SZ maps.Comment: 12 pages, 4 figures, and 5 table

Determining Tangential Peculiar Velocities of Clusters of Galaxies using Gravitational Lensing

We propose two new methods for measuring tangential peculiar velocities of rich clusters of galaxies. Our first method is based on weak gravitational lensing and takes advantage of the differing images of background galaxies caused by moving and stationary gravitational potentials. Our second method is based on measuring relative frequency shifts between multiple images of a single strongly lensed background galaxy. We illustrate this method using the example of galaxy cluster CL 0024+1654.Comment: LateX, 4 pages, 2 figures, accepted for publication in Part 1 of The Astrophysical Journa

Interaction between the intergalactic medium and central radio source in the NGC 4261 group of galaxies

Using observations from the Chandra and XMM-Newton X-ray observatories, we examine the interaction between the intra-group medium and central radio source in the nearby NGC 4261 galaxy group. We confirm the presence of cavities associated with the radio lobes and estimate their enthalpy to be ~2.4x10^58 erg. The mechanical power output of the jets is >=10^43 erg/s, at least a factor of 60 greater than the cooling luminosity in the region the lobes inhabit. We identify rims of compressed gas enclosing the lobes, but find no statistically significant temperature difference between them and their surroundings, suggesting that the lobe expansion velocity is approximately sonic (Mach<=1.05). The apparent pressure of the radio lobes, based on the synchrotron minimum energy density argument, is a factor of 5 lower than that of the intra-group medium. Pressure balance could be achieved if entrainment of thermal gas provided additional non-radiating particles in the lobe plasma, but the energy required to heat these particles would be ~20 per cent. of the mechanical energy output of the radio source. NGC 4261 has a relatively compact cool core, which should probably be categorised as a galactic corona. The corona is capable of fuelling the active nucleus for considerably longer than the inferred source lifetime, but can be only inefficiently heated by the AGN or conduction. The expansion of the radio lobes has affected the structure of the gas in the galaxy, compressing and moving the material of the corona without causing significant shock heating, and expelling gas from the immediate neighbourhood of the jets. We discuss the possible implications of this environment for the duration of the AGN outburst, and consider mechanisms which might lead to the cessation of nuclear activity.Comment: Accepted for publication in MNRAS, 17 pages, 6 figure