The Invisible Majority? Evolution and Detection of Outer Planetary Systems without Gas Giants

We present 230 realizations of a numerical model of planet formation in systems without gas giants. These represent a scenario in which protoplanets grow in a region of a circumstellar disk where water ice condenses (the "ice line''), but fail to accrete massive gas envelopes before the gaseous disk is dispersed. Each simulation consists of a small number of gravitationally interacting oligarchs and a much larger number of small bodies that represent the natal disk of planetesimals. We investigate systems with varying initial number of oligarchs, oligarch spacing, location of the ice line, total mass in the ice line, and oligarch mean density. Systems become chaotic in ~1 Myr but settle into stable configurations in 10-100 Myr. We find: (1) runs consistently produce a 5-9 Earth mass planet at a semimajor axis of 0.25-0.6 times the position of the ice line, (2) the distribution of planets' orbital eccentricities is distinct from, and skewed toward lower values than the observed distribution of (giant) exoplanet orbits, (3) inner systems of two dominant planets (e.g., Earth and Venus) are not stable or do not form because of the gravitational influence of the innermost icy planet. The planets predicted by our model are unlikely to be detected by current Doppler observations. Microlensing is currently sensitive to the most massive planets found in our simulations. A scenario where up to 60% of stars host systems such as those we simulate is consistent with all the available data. We predict that, if this scenario holds, the NASA Kepler spacecraft will detect about 120 planets by two or more transits over the course of its 3.5 yr mission. Future microlensing surveys will detect ~130 analogs over a 5 yr survey. Finally, the Space Interferometry Mission (SIM-Lite) should be capable of detecting 96% of the innermost icy planets over the course of a 5 yr mission.Comment: 17 pages, 16 figure

The Formation of Ice Giants in a Packed Oligarchy: Instability and Aftermath

As many as 5 ice giants--Neptune-mass planets composed of 90% ice and rock and 10% hydrogen--are thought to form at heliocentric distances of 10-25 AU on closely packed orbits spaced ~5 Hill radii apart. Such oligarchies are ultimately unstable. Once the parent disk of planetesimals is sufficiently depleted, oligarchs perturb one another onto crossing orbits. We explore both the onset and the outcome of the instability through numerical integrations, including dynamical friction cooling of planets by a planetesimal disk whose properties are held fixed. To trigger instability and the ejection of the first ice giant in systems having an original surface density in oligarchs of Sigma ~ 1 g/cm^2, the disk surface density s must fall below 0.1 g/cm^2. Ejections are predominantly by Jupiter and occur within 10 Myr. To eject more than 1 oligarch requires s < 0.03 g/cm^2. Systems starting with up to 4 oligarchs in addition to Jupiter and Saturn can readily yield solar-system-like outcomes in which 2 surviving ice giants lie inside 30 AU and have their orbits circularized by dynamical friction. Our numerical simulations support the idea that planetary systems begin in more crowded and compact configurations, like those of shear-dominated oligarchies. In contrast to previous studies, we identify s < 0.1 Sigma as the regime relevant for understanding the evolution of the outer solar system, and we encourage future studies to concentrate on this regime while relaxing our assumption of a fixed planetesimal disk.Comment: Accepted to ApJ Jan 27. Incorporates comments from the referee and community at large. 15 pages, 14 figures, including 7 colo

Determining stress states using dike swarms: The Lauma Dorsa example

Initial examination of the Magellan coverage of Venus has revealed between 150 and 300 large, radially lineated landforms distributed across the planet's surface. Where the lineaments have been examined in detail, the majority fail to exhibit signatures indicative of relief at or above the resolution of the radar; however, when the sense of topographic relief may be ascertained, the lineaments commonly appear as fissures or flat-floored trenches interpreted as graben. Individual lineaments can display graben, fissure, and zero relief behavior along their length, suggesting either that these differences are a function of the resolution of the radar, or that the morphological distinctions are real but somehow genetically linked. In many instances, radial lineaments exhibiting these characteristics are directly associated with surface volcanism, including flanking and terminal flows, superimposed shield domes and pit chains, and central, calderalike topographic lows. These observable characteristics, as well as theoretical studies and comparison with similar terrestrial features, have led to the working hypothesis that many of the radial fracture systems on Venus are the surface manifestation of subsurface dikes propagating laterally from a central magma source. If this interpretation is correct, studies of terrestrial dikes suggest that the lineament directions, with localized exceptions and barring subsequent deformation, should be perpendicular to the orientation of the least compressive stress at the time of their formation. To test this hypothesis, we briefly examine a radial fracture system (63.7 degrees N, 195 degrees E) located between two deformation belts in Vinmara Planitia, and verify that the lineaments to the east behave in the expected manner. We have also chosen this feature, however, because of its proximity to Lauma Dorsa to the west. On the basis of Venera 15/16 data, both compressional and extensional origins for this deformation belt have been proposed. By examining the stratigraphy and applying our interpretation that the fracture system is linked to the presence of subsurface dikes, we present an independent evaluation of the stress state associated with Lauma Dorsa, and thus contribute to the assessment of its origin

Will Employers Want Aging Boomers?

Explores the status quo of older workers; why baby boomers are likely to work longer; and how changes in needed skills, the characteristics of older workers, and labor force growth will affect demand for older workers. Includes policy recommendations

Empirical Uncertainty Estimators for Astrometry from Digital Databases

In order to understand the positional uncertainties of arbitrary objects in several of the current major databases containing astrometric information, a sample of extragalactic radio sources with precise positions in the International Celestial Reference Frame (ICRF) is compared with the available positions of their optical counterparts. The discrepancies between the radio and various optical positions are used to derive empirical uncertainty estimators for the USNO-A2.0, USNO-A1.0, Guide Star Selection System (GSSS) images, and the first and second Digitized Sky Surveys (DSS-I and DSS-II). In addition, an estimate of the uncertainty when the USNO-A2.0 catalog is transferred to different image data is provided. These optical astrometric frame uncertainties can in some cases be the dominant error term when cross-identifying sources at different wavelengths.Comment: 12 pages including 2 figures and 1 table. Accepted for publication in The Astronomical Journal, October 1999. Values in Table 1 for DSS I corrected 99-07-1

A light-cone gauge for black-hole perturbation theory

The geometrical meaning of the Eddington-Finkelstein coordinates of Schwarzschild spacetime is well understood: (i) the advanced-time coordinate v is constant on incoming light cones that converge toward r=0, (ii) the angles theta and phi are constant on the null generators of each light cone, (iii) the radial coordinate r is an affine-parameter distance along each generator, and (iv) r is an areal radius, in the sense that 4 pi r^2 is the area of each two-surface (v,r) = constant. The light-cone gauge of black-hole perturbation theory, which is formulated in this paper, places conditions on a perturbation of the Schwarzschild metric that ensure that properties (i)--(iii) of the coordinates are preserved in the perturbed spacetime. Property (iv) is lost in general, but it is retained in exceptional situations that are identified in this paper. Unlike other popular choices of gauge, the light-cone gauge produces a perturbed metric that is expressed in a meaningful coordinate system; this is a considerable asset that greatly facilitates the task of extracting physical consequences. We illustrate the use of the light-cone gauge by calculating the metric of a black hole immersed in a uniform magnetic field. We construct a three-parameter family of solutions to the perturbative Einstein-Maxwell equations and argue that it is applicable to a broader range of physical situations than the exact, two-parameter Schwarzschild-Melvin family.Comment: 12 page

Computer Simulation of Cytoskeleton-Induced Blebbing in Lipid Membranes

Blebs are balloon-shaped membrane protrusions that form during many physiological processes. Using computer simulation of a particle-based model for self-assembled lipid bilayers coupled to an elastic meshwork, we investigated the phase behavior and kinetics of blebbing. We found that blebs form for large values of the ratio between the areas of the bilayer and the cytoskeleton. We also found that blebbing can be induced when the cytoskeleton is subject to a localized ablation or a uniform compression. The results obtained are qualitatively in agreement with the experimental evidence and the model opens up the possibility to study the kinetics of bleb formation in detail.Comment: To appear in Physical Review

Stress-Energy Tensor for the Massless Spin 1/2 Field in Static Black Hole Spacetimes

The stress-energy tensor for the massless spin 1/2 field is numerically computed outside and on the event horizons of both charged and uncharged static non-rotating black holes, corresponding to the Schwarzschild, Reissner-Nordstrom and extreme Reissner-Nordstr\"om solutions of Einstein's equations. The field is assumed to be in a thermal state at the black hole temperature. Comparison is made between the numerical results and previous analytic approximations for the stress-energy tensor in these spacetimes. For the Schwarzschild (charge zero) solution, it is shown that the stress-energy differs even in sign from the analytic approximation. For the Reissner-Nordstrom and extreme Reissner-Nordstrom solutions, divergences predicted by the analytic approximations are shown not to exist.Comment: 5 pages, 4 figures, additional discussio

Capital Planning, Selection, and Investment (Integrating Sustainability in Decision-making)

Inspired by Pope Francis’s call for a new journey that instills the importance of conservation and care for the environment, we propose a practical model that mathematically incorporates sustainability issues into capital planning, selection, and investment. Evidence suggests that managers apply net present value (NPV) methodologies in a way that disadvantages environmentally sustainable investments. If an NPV model does not consider the costs and risks of non-sustainable projects, then the potential benefits of alternative sustainable investments will appear much less valuable than present costs. Sustainable investments also often require larger initial investments with long-term benefits and distant cash flow time horizons that are discounted at exponentially higher rates. Moreover, identified environmental costs and benefits are generally limited to savings associated with energy costs, while hidden reductions in externalities are ignored. Thus, as commonly used, NPV models bias against sustainable alternatives in investment selection. This article integrates accounting, finance, and engineering literatures to develop a model that incorporates sustainability and environmental impacts into capital selection through a life-cycle impact assessment (LCIA) appraisal. We operationalize LCIA so that hidden environmental costs and benefits can be identified, analyzed, and priced, thus resulting in a better prediction of cash flows. The model also integrates environmental risks into the cost of capital by developing a sustainability risk-adjusted discount rate and sustainability-cost NPV that effectively captures the sustainability exposures of capital projects, thus resulting in a risk-adjusted sustainable framework for decision-making

Capital Planning, Selection, and Investment (Integrating Sustainability in Decision-making)

Inspired by Pope Francis’s call for a new journey that instills the importance of conservation and care for the environment, we propose a practical model that mathematically incorporates sustainability issues into capital planning, selection, and investment.Evidence suggests that managers apply net present value (NPV) methodologies in a way that disadvantages environmentally sustainable investments. If an NPV model does not consider the costs and risks of non-sustainable projects, then the potential benefits of alternative sustainable investments will appear much less valuable than present costs. Sustainable investments also often require larger initial investments with long-term benefits and distant cash flow time horizons that are discounted at exponentially higher rates. Moreover, identified environmental costs and benefits are generally limited to savings associated with energy costs, while hidden reductions in externalities are ignored. Thus, as commonly used, NPV models bias against sustainable alternatives in investment selection.This article integrates accounting, finance, and engineering literatures to develop a model that incorporates sustainability and environmental impacts into capital selection through a life-cycle impact assessment (LCIA) appraisal. We operationalize LCIA so that hidden environmental costs and benefits can be identified, analyzed, and priced, thus resulting in a better prediction of cash flows. The model also integrates environmental risks into the cost of capital by developing a sustainability risk-adjusted discount rate and sustainability-cost NPV that effectively captures the sustainability exposures of capital projects, thus resulting in a risk-adjusted sustainable framework for decision-making