Local re-acceleration and a modified thick target model of solar flare electrons

The collisional thick target model (CTTM) of solar hard X-ray (HXR) bursts has become an almost 'Standard Model' of flare impulsive phase energy transport and radiation. However, it faces various problems in the light of recent data, particularly the high electron beam density and anisotropy it involves.} {We consider how photon yield per electron can be increased, and hence fast electron beam intensity requirements reduced, by local re-acceleration of fast electrons throughout the HXR source itself, after injection.} {We show parametrically that, if net re-acceleration rates due to e.g. waves or local current sheet electric (${\cal E}$) fields are a significant fraction of collisional loss rates, electron lifetimes, and hence the net radiative HXR output per electron can be substantially increased over the CTTM values. In this local re-acceleration thick target model (LRTTM) fast electron number requirements and anisotropy are thus reduced. One specific possible scenario involving such re-acceleration is discussed, viz, a current sheet cascade (CSC) in a randomly stressed magnetic loop.} {Combined MHD and test particle simulations show that local ${\cal E}$ fields in CSCs can efficiently accelerate electrons in the corona and and re-accelerate them after injection into the chromosphere. In this HXR source scenario, rapid synchronisation and variability of impulsive footpoint emissions can still occur since primary electron acceleration is in the high Alfv\'{e}n speed corona with fast re-acceleration in chromospheric CSCs. It is also consistent with the energy-dependent time-of-flight delays in HXR features.Comment: 8 pages, 2 figure

Planetary astronomy

The authors profile the field of astronomy, identify some of the key scientific questions that can be addressed during the decade of the 1990's, and recommend several facilities that are critically important for answering these questions. Scientific opportunities for the 1990' are discussed. Areas discussed include protoplanetary disks, an inventory of the solar system, primitive material in the solar system, the dynamics of planetary atmospheres, planetary rings and ring dynamics, the composition and structure of the atmospheres of giant planets, the volcanoes of IO, and the mineralogy of the Martian surface. Critical technology developments, proposed projects and facilities, and recommendations for research and facilities are discussed

Penrose Diagram for a Transient Black Hole

A Penrose diagram is constructed for a spatially coherent black hole that smoothly begins an accretion, then excretes symmetrically as measured by a distant observer, with the initial and final states described by a metric of Minkowski form. Coordinate curves on the diagram are computationally derived. Causal relationships between space-time regions are briefly discussed. The life cycle of the black hole demonstrably leaves asymptotic observers in an unaltered Minkowski space-time of uniform conformal scale.Comment: 14 pages, 9 figures, spelling correction

Long-Term Stability of Horseshoe Orbits

Unlike Trojans, horseshoe coorbitals are not generally considered to be long-term stable (Dermott and Murray, 1981; Murray and Dermott, 1999). As the lifetime of Earth's and Venus's horseshoe coorbitals is expected to be about a Gyr, we investigated the possible contribution of late-escaping inner planet coorbitals to the lunar Late Heavy Bombardment. Contrary to analytical estimates, we do not find many horseshoe objects escaping after first 100 Myr. In order to understand this behaviour, we ran a second set of simulations featuring idealized planets on circular orbits with a range of masses. We find that horseshoe coorbitals are generally long lived (and potentially stable) for systems with primary-to-secondary mass ratios larger than about 1200. This is consistent with results of Laughlin and Chambers (2002) for equal-mass pairs or coorbital planets and the instability of Jupiter's horseshoe companions (Stacey and Connors, 2008). Horseshoe orbits at smaller mass ratios are unstable because they must approach within 5 Hill radii of the secondary. In contrast, tadpole orbits are more robust and can remain stable even when approaching within 4 Hill radii of the secondary.Comment: Accepted for MNRA

The spectral difference between solar flare HXR coronal and footpoint sources due to wave-particle interactions

Investigate the spatial and spectral evolution of hard X-ray (HXR) emission from flare accelerated electron beams subject to collisional transport and wave-particle interactions in the solar atmosphere. We numerically follow the propagation of a power-law of accelerated electrons in 1D space and time with the response of the background plasma in the form of Langmuir waves using the quasilinear approximation.}{We find that the addition of wave-particle interactions to collisional transport for a transient initially injected electron beam flattens the spectrum of the footpoint source. The coronal source is unchanged and so the difference in the spectral indices between the coronal and footpoint sources is \Delta \gamma > 2, which is larger than expected from purely collisional transport. A steady-state beam shows little difference between the two cases, as has been previously found, as a transiently injected electron beam is required to produce significant wave growth, especially at higher velocities. With this transiently injected beam the wave-particle interactions dominate in the corona whereas the collisional losses dominate in the chromosphere. The shape of the spectrum is different with increasing electron beam density in the wave-particle interaction case whereas with purely collisional transport only the normalisation is changed. We also find that the starting height of the source electron beam above the photosphere affects the spectral index of the footpoint when Langmuir wave growth is included. This may account for the differing spectral indices found between double footpoints if asymmetrical injection has occurred in the flaring loop.Comment: 10 pages, 10 FIgures, accepted for publication in A&

Density-Dependence as a Size-Independent Regulatory Mechanism

The growth function of populations is central in biomathematics. The main dogma is the existence of density dependence mechanisms, which can be modelled with distinct functional forms that depend on the size of the population. One important class of regulatory functions is the $\theta$-logistic, which generalises the logistic equation. Using this model as a motivation, this paper introduces a simple dynamical reformulation that generalises many growth functions. The reformulation consists of two equations, one for population size, and one for the growth rate. Furthermore, the model shows that although population is density-dependent, the dynamics of the growth rate does not depend either on population size, nor on the carrying capacity. Actually, the growth equation is uncoupled from the population size equation, and the model has only two parameters, a Malthusian parameter $\rho$ and a competition coefficient $\theta$. Distinct sign combinations of these parameters reproduce not only the family of $\theta$-logistics, but also the van Bertalanffy, Gompertz and Potential Growth equations, among other possibilities. It is also shown that, except for two critical points, there is a general size-scaling relation that includes those appearing in the most important allometric theories, including the recently proposed Metabolic Theory of Ecology. With this model, several issues of general interest are discussed such as the growth of animal population, extinctions, cell growth and allometry, and the effect of environment over a population.Comment: 41 Pages, 5 figures Submitted to JT

Effect of binary collisions on electron acceleration in magnetic reconnection

Context. The presence of energetic X-ray sources in the solar corona indicates there are additional transport effects in the acceleration region. A prime method of investigation is to add collisions into models of particle behaviour at the reconnection region.<p></p> Aims. We investigate electron test particle acceleration in a simple model of an X-type reconnection region. In particular, we explore the possibility that collisions will cause electrons to re-enter the acceleration more frequently, in turn causing particles to be accelerated to high energies.<p></p> Methods. The deterministic (Lorentz) description of particle gyration and acceleration has been coupled to a model for the effects of collisions. The resulting equations are solved numerically using Honeycutt’s extension of the RK4 method to stochastic differential equations. This approach ensures a correct description of collisional energy loss and pitch-angle scattering combined with a sufficiently precise description of gyro-motion and acceleration.<p></p> Results. Even with initially mono-energetic electrons, the competition between collisions and acceleration results in a distribution of electron energies. When realistic model parameters are used, electrons achieve X-ray energies. A possible model for coronal hard X-ray sources is indicated. Conclusions. Even in competition with energy losses, pitch-angle scattering results in a small proportion of electrons reaching higher energies than they would in a collisionless situation.<p></p&gt

The macro-economic effects of health co-benefits associated with climate change mitigation strategies

The UK government has specific targets for greenhouse gas (GHG) emission reduction to lower the risk of dangerous climate change. Strategies to reduce GHG emissions are sometimes perceived as expensive and difficult to implement but previous work has demonstrated significant potential health co-benefits from ‘Active Travel and low carbon driving’, ‘Housing Insulation/Ventilation’, and ‘Healthy Diet’ scenarios which may be attractive to policymakers. Here a Computable General Equilibrium model is used to assess the financial effects of such health co-benefits on the wider economy including changes in labour force, social security payments and healthcare costs averted. Results suggest that for all scenarios the financial impacts of the health co-benefits will be positive and increased active travel in particular is likely to make a substantial contribution, largely due to health care costs averted. Strategies to reduce GHG emissions and improve health are likely to result in substantial and increasing positive contributions to the economy which may offset some potential economic costs and thereby be seen more favourably in times of economic austerity

Turbulent cross-field transport of non-thermal electrons in coronal loops: theory and observations

<p><b>Context:</b> A fundamental problem in astrophysics is the interaction between magnetic turbulence and charged particles. It is now possible to use Ramaty High Energy Solar Spectroscopic Imager (RHESSI) observations of hard X-rays (HXR) emitted by electrons to identify the presence of turbulence and to estimate the magnitude of the magnetic field line diffusion coefficient at least in dense coronal flaring loops.</p> <p><b>Aims:</b> We discuss the various possible regimes of cross-field transport of non-thermal electrons resulting from broadband magnetic turbulence in coronal loops. The importance of the Kubo number K as a governing parameter is emphasized and results applicable in both the large and small Kubo number limits are collected.</p> <p><b>Methods:</b> Generic models, based on concepts and insights developed in the statistical theory of transport, are applied to the coronal loops and to the interpretation of hard X-ray imaging data in solar flares. The role of trapping effects, which become important in the non-linear regime of transport, is taken into account in the interpretation of the data.</p> <p><b>Results:</b> For this flaring solar loop, we constrain the ranges of parallel and perpendicular correlation lengths of turbulent magnetic fields and possible Kubo numbers. We show that a substantial amount of magnetic fluctuations with energy ~1% (or more) of the background field can be inferred from the measurements of the magnetic diffusion coefficient inside thick-target coronal loops.</p&gt

Simulations of partially coherent focal plane imaging arrays: Fisher matrix approach to performance evaluation

Focal plane arrays of bolometers are increasingly employed in astronomy at far--infrared to millimetre wavelengths. The focal plane fields and the detectors are both partially coherent in these systems, but no account has previously been taken of the effect of partial coherence on array performance. In this paper, we use our recently developed coupled--mode theory of detection together with Fisher information matrix techniques from signal processing to characterize the behaviour of partially coherent imaging arrays. We investigate the effects of the size and coherence length of both the source and the detectors, and the packing density of the array, on the amount of information that can be extracted from observations with such arrays.Comment: 14 pages, 7 figures, submitted to MNRAS 7th March 200