On the origin of the Trojan asteroids: Effects of Jupiter's mass accretion and radial migration

We present analytic and numerical results which illustrate the effects of Jupiter's accretion of nebular gas and the planet's radial migration on its Trojan companions. Initially, we approximate the system by the planar circular restricted three-body problem and assume small Trojan libration amplitudes. Employing an adiabatic invariant calculation, we show that Jupiter's thirty-fold growth from a $10 M_\oplus$ core to its present mass causes the libration amplitudes of Trojan asteroids to shrink by a factor of about 2.5 to $\sim 40$ of their original size. The calculation also shows that Jupiter's radial migration has comparatively little effect on the Trojans; inward migration from 6.2 to 5.2 AU causes an increase in Trojan libration amplitudes of $\sim4$. In each case, the area enclosed by small tadpole orbits, if made dimensionless by using Jupiter's semimajor axis, is approximately conserved. Similar adiabatic invariant calculations for inclined and eccentric Trojans show that Jupiter's mass growth leaves the asteroid's eccentricities and inclinations essentially unchanged, while one AU of inward migration causes an increase in both of these quantities by $\sim 4$. Numerical integrations confirm and extend these analytic results. We demonstrate that our predictions remain valid for Trojans with small libration amplitudes even when the asteroids have low, butComment: Submitted to Icarus - 13 Fig

The river model of black holes

This paper presents an under-appreciated way to conceptualize stationary black holes, which we call the river model. The river model is mathematically sound, yet simple enough that the basic picture can be understood by non-experts. %that can by understood by non-experts. In the river model, space itself flows like a river through a flat background, while objects move through the river according to the rules of special relativity. In a spherical black hole, the river of space falls into the black hole at the Newtonian escape velocity, hitting the speed of light at the horizon. Inside the horizon, the river flows inward faster than light, carrying everything with it. We show that the river model works also for rotating (Kerr-Newman) black holes, though with a surprising twist. As in the spherical case, the river of space can be regarded as moving through a flat background. However, the river does not spiral inward, as one might have anticipated, but rather falls inward with no azimuthal swirl at all. Instead, the river has at each point not only a velocity but also a rotation, or twist. That is, the river has a Lorentz structure, characterized by six numbers (velocity and rotation), not just three (velocity). As an object moves through the river, it changes its velocity and rotation in response to tidal changes in the velocity and twist of the river along its path. An explicit expression is given for the river field, a six-component bivector field that encodes the velocity and twist of the river at each point, and that encapsulates all the properties of a stationary rotating black hole.Comment: 16 pages, 4 figures. The introduction now refers to the paper of Unruh (1981) and the extensive work on analog black holes that it spawned. Thanks to many readers for feedback that called attention to our omissions. Submitted to the American Journal of Physic

Diffusion algorithms and data reduction routine for onsite launch predictions for the transport of Titan 3 C exhaust effluents

The NASA/MSFC multilayer diffusion algorithms have been specialized for the prediction of the surface impact for the dispersive transport of the exhaust effluents from the launch of a Titan 3 vehicle. This specialization permits these transport predictions to be made at the launch range in real time so that the effluent monitoring teams can optimize their monitoring grids. Basically, the data reduction routine requires just the meteorology profiles for the thermodynamics and kinematics of the atmosphere as an input. These profiles are graphed along with the resulting exhaust cloud rise history, the center line concentrations and dosages, and the hydrogen chloride isopleths

Public knowledge about polar regions increases while concerns remain unchanged

The authors of this brief conduct the first comparative analysis of the polar questions that were part of the National Opinion Research Center\u27s 2006 and 2010 General Social Survey. Developed by scientists at the National Science Foundation\u27s Office of Polar Programs, these questions covered topics such as climate change, melting ice and rising sea levels, and species extinction. The authors report that the public\u27s knowledge about the north and south polar regions significantly improved between 2006 and 2010--before and after the International Polar Year. In addition, respondents who know more about science in general, and polar facts specifically, tend to be more concerned about polar changes. More knowledgeable respondents also tend to favor reserving the Antarctic for science, rather than opening it for commercial development

Quantifying temporal and spatial variations in sediment, nitrogen and phosphorus transport in stream inflows to a large eutrophic lake

High-frequency sampling of two major stream inflows to a large eutrophic lake (Lake Rotorua, New Zealand) was conducted to measure inputs of total suspended sediment (TSS), and fractions of nitrogen and phosphorus (P). A total of 17 rain events were sampled, including three during which both streams were simultaneously monitored to quantify how concentration–discharge (Q) relationships varied between catchments during similar hydrological conditions. Dissolved inorganic nitrogen (DIN) concentrations declined slightly during events, reflecting dilution of groundwater inputs by rainfall, whereas dissolved inorganic P (PO₄–P) concentrations were variable and unrelated to Q, suggesting dynamic sorptive behaviour. Event loads of total nitrogen (TN) were predominantly DIN, which is available for immediate uptake by primary producers, whereas total phosphorus (TP) loads predominantly comprised particulate P (less labile). Positive correlations between Q and concentrations of TP (and to a lesser extent TN) reflected increased particulate nutrient concentrations at high flows. Consequently, load estimates based on hourly Q during storm events and concentrations of routine monthly samples (mostly base flow) under-estimated TN and TP loads by an average of 19% and 40% respectively. Hysteresis with Q was commonly observed and inclusion of hydrological variables that reflect Q history in regression models improved predictions of TN and TP concentrations. Lorenz curves describing the proportions of cumulative load versus cumulative time quantified temporal inequality in loading. In the two study streams, 50% of estimated two-year loads of TN, TP and TSS were transported in 202–207, 76–126 and 1–8 days respectively. This study quantifies how hydrological and landscape factors can interact to influence pollutant flux at the catchment scale and highlights the importance of including storm transfers in lake loading estimates

Low-dose alum application trialled as a management tool for internal nutrient loads in Lake Okaro, New Zealand

Aluminium sulfate (alum) was applied to Lake Okaro, a eutrophic New Zealand lake with recurrent cyanobacterial blooms, to evaluate its suitability for reducing trophic status and bloom frequency. The dose yielded 0.6 g aluminium m–3 in the epilimnion. Before dosing, pH exceeded 8 in epilimnetic waters but was optimal for flocculation (6–8) below 4 m depth. After dosing, there was no significant change in water clarity, hypolimnetic pH decreased to 5.5, and soluble aluminium exceeded recommended guidelines for protection of freshwater organisms. Epilimnetic phosphate concentrations decreased from 40 to 5 mg m–3 and total nitrogen (TN):total phosphorus (TP) mass ratios increased from 7:1 to 37:1. The dominant phytoplankton species changed from Anabaena spp. before dosing, to Ceratium hirudinella , then Staurastrum sp. after dosing. Detection of effectiveness of dosing may have been limited by sampling duration and design, as well as the low alum dose. The decrease in hypolimnetic pH and epilimnetic TP, and increase in Al3+ and chlorophyll a, are attributed to the low alkalinity lake water and coincidence of alum dosing with a cyanobacterial bloom and high pH

A high resolution UV absorption spectrum of supernova ejecta in SN1006

We report a high resolution, far-ultraviolet, STIS E140M spectrum of the strong, broad Si II, III, and IV features produced by the ejecta of SN1006 seen in absorption against the background Schweizer-Middleditch star. The spectrum confirms the extreme sharpness of the red edge of the redshifted Si II 1260 A feature, supporting the idea that this edge represents the location of the reverse shock moving into the freely expanding ejecta. The expansion velocity of ejecta at the reverse shock is measured to be 7026 +-3(relative) +-10(absolute) km/s. If the shock model is correct, then the expansion velocity should be decreasing at the observable rate of 2.7 +-0.1 km/s per year. The pre-shock velocity, post-shock velocity, and post-shock velocity dispersion are all measured from the Si II 1260 A feature, and consistency of these velocities with the shock jump conditions implies that there is little or no electron heating in this fast (2680 km/s) Si-rich shock.Comment: 9 pages, 5 embedded postscript fig