What is a flux tube? On the magnetic field topology of buoyant flux structures

We study the topology of field lines threading buoyant magnetic flux structures. The magnetic structures, visually resembling idealized magnetic flux tubes, are generated self-consistently by numerical simulation of the interaction of magnetic buoyancy and a localized velocity shear in a stably stratified atmosphere. Depending on the parameters, the system exhibits varying degrees of symmetry. By integrating along magnetic field lines and constructing return maps, we show that, depending on the type of underlying behaviour, the stages of the evolution, and therefore the degree of symmetry, the resulting magnetic structures can have field lines with one of three distinct topologies. When the x -translational and y -reflectional symmetries remain intact, magnetic field lines lie on surfaces but individual lines do not cover the surface. When the y symmetry is broken, magnetic field lines lie on surfaces and individual lines do cover the surface. When both x and y symmetries are broken, magnetic field lines wander chaotically over a large volume of the magnetically active region. We discuss how these results impact our simple ideas of a magnetic flux tube as an object with an inside and an outside, and introduce the concept of 'leaky' tubes.     

Variable Grid Method: An Intuitive Approach for Simultaneously Quantifying and Visualizing Spatial Data and Uncertainty

Efforts to develop applications and methods that effectively quantify and communicate uncertainty associated with spatial data remains a focus within many scientific communities. However, the inherent complexity of uncertainty makes it difficult to define, characterize, and represent. Frequently, the products of spatial and spatio‐temporal data are presented without a clear explanation of the inherent uncertainty underlying the data. As uses and applications for spatial data and their products continues to increase, so does the importance for utilizing reliable approaches to effectively communicate spatial data along with their inherent uncertainties. To address this need, the Variable Grid Method (VGM) was developed as an intuitive approach that simultaneously communicates both spatial patterns and trends and the uncertainty associated with data or their analyses. This article details the VGM approach and demonstrates the utility of the VGM to provide critical information about the relationship between uncertainty and spatial data, necessary to support the increasing utilization of spatial information for a wide range of research and other needs.     

The High-Resolution Coronal Imager (Hi-C)

The High-Resolution Coronal Imager (Hi-C) was flown on a NASA sounding rocket on 11 July 2012. The goal of the Hi-C mission was to obtain high-resolution (≈?0.3?–?0.4′′), high-cadence (≈?5 seconds) images of a solar active region to investigate the dynamics of solar coronal structures at small spatial scales. The instrument consists of a normal-incidence telescope with the optics coated with multilayers to reflect a narrow wavelength range around 19.3 nm (including the Fe xii 19.5-nm spectral line) and a 4096×4096 camera with a plate scale of 0.1′′?pixel^?1. The target of the Hi-C rocket flight was Active Region 11520. Hi-C obtained 37 full-frame images and 86 partial-frame images during the rocket flight. Analysis of the Hi-C data indicates the corona is structured on scales smaller than currently resolved by existing satellite missions.     

H2 in molecular shocks: observations from 2 to 12 microns

We present spectroscopy of the molecular shock in the supernova remnant IC 443. The H₂ level populations in IC 443 are nearly identical to Orion Peak 1 (Brand et al. 1988; Parmar et al. 1994) and are consistent with a partially dissociative J-shock. The similarity with Orion suggests the shock processes which dominate the emission in both regions are essentially identical.     

Two-body motion in the post-Newtonian approximation

The motion of two massive particles is considered within the framework of the first post-Newtonian approximation. The system Hamiltonian is constructed and normalized through first order using a canonical transformation method of implicit variables. Closed-form solutions for the Delaunay elements in the phase space are obtained. The bridge between the phase space and the state space of the Lagrangian of the motion is provided by a velocity-dependent Legendre transformation. By explicit inversion of this transformation, expressions for the Keplerian elements in the state space are obtained from the Delaunay element solutions.     

Estimating background and threshold nitrate concentrations using probability graphs

Because of the ubiquitous nature of anthropogenic nitrate (NO3(-)) in many parts of the world, determining background concentrations of NO3(-) in shallow ground water from natural sources is probably impossible in most environments. Present-day background must now include diffuse sources of NO3(-) such as disruption of soils and oxidation of organic matter, and atmospheric inputs from products of combustion and evaporation of ammonia from fertilizer and livestock waste. Anomalies can be defined as NO3(-) derived from nitrogen (N) inputs to the environment from anthropogenic activities, including synthetic fertilizers, livestock waste, and septic effluent. Cumulative probability graphs were used to identify threshold concentrations separating background and anomalous NO(3)-N concentrations and to assist in the determination of sources of N contamination for 232 spring water samples and 200 well water samples from karst aquifers. Thresholds were 0.4, 2.5, and 6.7 mg/L for spring water samples, and 0.1, 2.1, and 17 mg/L for well water samples. The 0.4 and 0.1 mg/L values are assumed to represent thresholds for present-day precipitation. Thresholds at 2.5 and 2.1 mg/L are interpreted to represent present-day background concentrations of NO(3)-N. The population of spring water samples with concentrations between 2.5 and 6.7 mg/L represents an amalgam of all sources of NO3(-) in the ground water basins that feed each spring; concentrations > 6.7 mg/L were typically samples collected soon after springtime application of synthetic fertilizer. The 17 mg/L threshold (adjusted to 15 mg/L) for well water samples is interpreted as the level above which livestock wastes dominate the N sources.     

Consistent Two-Equation Closure Modelling for Atmospheric Research: Buoyancy and Vegetation Implementations

A self-consistent two-equation closure treating buoyancy and plant drag effects has been developed, through consideration of the behaviour of the supplementary equation for the length-scale-determining variable in homogeneous turbulent flow. Being consistent with the canonical flow regimes of grid turbulence and wall-bounded flow, the closure is also valid for homogeneous shear flows commonly observed inside tall vegetative canopies and in non-neutral atmospheric conditions. Here we examine the most often used two-equation models, namely and E − ω (where is the dissipation rate of turbulent kinetic energy, E, and is the specific dissipation), comparing the suggested buoyancy-modified closure against Monin–Obukhov similarity theory. Assessment of the closure implementing both buoyancy and plant drag together has been done, comparing the results of the two models against each other. It has been found that the E − ω model gives a better reproduction of complex atmospheric boundary-layer flows, including less sensitivity to numerical artefacts, than does the model. Re-derivation of the equation from the ω equation, however, leads to the model implementation that produces results identical to the E − ω model. Overall, numerical results show that the closure performs well, opening new possibilities for application of such models to tasks related to the atmospheric boundary layer—where it is important to adequately account for the influences of both vegetation and atmospheric stability.     

Long-Term Mean Wind Profiles Based on Similarity Theory

We provide general forms for long-term mean wind profiles from similarity-based wind profiles, beginning with a probabilistic adaptation of Monin–Obukhov similarity theory. We develop an analytical formulation for the stability distributions prevailing in the atmospheric surface layer, which in turn facilitates the derivation of a long-term mean wind profile based on Monin–Obukhov similarity theory. The modelled stability distributions exhibit good agreement with measurements from sites having different local conditions. The long-term wind profile formulation is further extended to include the influence of the depth of the atmospheric boundary layer (h), which becomes relevant for heights above h/3, and the resultant long-term ‘tall’ profile form also matches observations.     

Numerical simulations of hot halo gas in galaxy mergers

Galaxy merger simulations have explored the behaviour of gas within the galactic disc, yet the dynamics of hot gas within the galaxy halo have been neglected. We report on the results of high-resolution hydrodynamic simulations of colliding galaxies with metal-free hot halo gas. To isolate the effect of the halo gas, we simulate only the dark matter halo and the hot halo gas over a range of mass ratios, gas fractions and orbital configurations to constrain the shocks and gas dynamics within the progenitor haloes. We find that (i) a strong shock is produced in the galaxy haloes before the first passage, increasing the temperature of the gas by almost an order of magnitude to   T ∼ 10^6.3 K  . (ii) The X-ray luminosity of the shock is strongly dependent on the gas fraction; it is  ≳10³⁹ erg s⁻¹  for halo gas fractions larger than 10 per cent. (iii) The hot diffuse gas in the simulation produces X-ray luminosities as large as  10⁴² erg s⁻¹  . This contributes to the total X-ray background in the Universe. (iv) We find an analytic fit to the maximum X-ray luminosity of the shock as a function of merger parameters. This fit can be used in semi-analytic recipes of galaxy formation to estimate the total X-ray emission from shocks in merging galaxies. (v) ∼10–20 per cent of the initial gas mass is unbound from the galaxies for equal-mass mergers, while 3–5 per cent of the gas mass is released for the 3:1 and 10:1 mergers. This unbound gas ends up far from the galaxy and can be a feasible mechanism to enrich the intergalactic medium with metals.