Misestimation of temperature when applying Maxwellian distributions to space plasmas described by kappa distributions

This paper presents the misestimation of temperature when observations from a kappa distributed plasma are analyzed as a Maxwellian. One common method to calculate the space plasma parameters is by fitting the observed distributions using known analytical forms. More often, the distribution function is included in a forward model of the instrument’s response, which is used to reproduce the observed energy spectrograms for a given set of plasma parameters. In both cases, the modeled plasma distribution fits the measurements to estimate the plasma parameters. The distribution function is often considered to be Maxwellian even though in many cases the plasma is better described by a kappa distribution. In this work we show that if the plasma is described by a kappa distribution, the derived temperature assuming Maxwell distribution can be significantly off. More specifically, we derive the plasma temperature by fitting a Maxwell distribution to pseudo-data produced by a kappa distribution, and then examine the difference of the derived temperature as a function of the kappa index. We further consider the concept of using a forward model of a typical plasma instrument to fit its observations. We find that the relative error of the derived temperature is highly depended on the kappa index and occasionally on the instrument’s field of view and response

Modeling the Plasma Flow in the Inner Heliosheath with a Spatially Varying Compression Ratio

We examine a semi-analytical non-magnetic model of the termination shock location previously developed by Exarhos & Moussas. In their study, the plasma flow beyond the shock is considered incompressible and irrotational, thus the flow potential is analytically derived from the Laplace equation. Here we examine the characteristics of the downstream flow in the heliosheath in order to resolve several inconsistencies existing in the Exarhos & Moussas model. In particular, the model is modified in order to be consistent with the Rankine– Hugoniot jump conditions and the geometry of the termination shock. It is shown that a shock compression ratio varying along the latitude can lead to physically correct results. We describe the new model and present several simplified examples for a nearly spherical, strong termination shock. Under those simplifications, the upstream plasma is nearly adiabatic for large (∼100 AU) heliosheath thickness

Long-term Correlations of Polytropic Indices with Kappa Distributions in Solar Wind Plasma near 1 au

The polytropic behavior of space plasmas defines a power law between the plasma moments during the transition of the plasma from one state to another under constant specific heat. Knowledge of the polytropic index—the power-law exponent—is essential for understanding the dynamics of plasma particles, while a full kinetic description can be established by the study of the velocity distribution of plasma particles. The particle velocities of collisionless space plasmas, such as the solar wind, follow the kappa distribution function. The kappa index, the parameter that labels and governs these distributions, is an independent variable that describes the state of plasmas and is required for a complete description of the plasma properties. Previous studies showed and demonstrated how the kappa and polytropic indices are related to each other in the presence of potential energy, and their relationship also depends on the potential degrees of freedom. This paper extends these analyses and derives the kappa and polytropic indices of the solar wind proton plasmas using Wind observations during the last two solar cycles. We examine and show the systematic long-term correlation between these indices, the magnetic field strength, and the solar activity

General Allee Effect in Two-Species Population Biology

The main objective of this work is to present a general framework for the notion of the strong Allee effect in population models, including competition, mutualistic, and predator–prey models. The study is restricted to the strong Allee effect caused by an inter-specific interaction. The main feature of the strong Allee effect is that the extinction equilibrium is an attractor. We show how a ‘phase space core’ of three or four equilibria is sufficient to describe the essential dynamics of the interaction between two species that are prone to the Allee effect. We will introduce the notion of semistability in planar systems. Finally, we show how the presence of semistable equilibria increases the number of possible Allee effect cores

The oblique firehose instability in a bi-kappa magnetized plasma

In this work, we derive a dispersion equation that describes the excitation of the oblique (or Alfv\'en) firehose instability in a plasma that contains both electron and ion species modelled by bi-kappa velocity distribution functions. The equation is obtained with the assumptions of low-frequency waves and moderate to large values of the parallel (respective to the ambient magnetic field) plasma beta parameter, but it is valid for any direction of propagation and for any value of the particle gyroradius (or Larmor radius). Considering values for the physical parameters typical to those found in the solar wind, some solutions of the dispersion equation, corresponding to the unstable mode, are presented. In order to implement the dispersion solver, several new mathematical properties of the special functions occurring in a kappa plasma are derived and included. The results presented here suggest that the superthermal characteristic of the distribution functions leads to reductions to both the maximum growth rate of the instability and of the spectral range of its occurrence

A Continuous-Time Mathematical Model and Discrete Approximations for the Aggregation of \u3cem\u3eβ\u3c/em\u3e-Amyloid

Alzheimer\u27s disease is a degenerative disorder characterized by the loss of synapses and neurons from the brain, as well as the accumulation of amyloid-based neuritic plaques. While it remains a matter of contention whether β-amyloid causes the neurodegeneration, β-amyloid aggregation is associated with the disease progression. Therefore, gaining a clearer understanding of this aggregation may help to better understand the disease. We develop a continuous-time model for β-amyloid aggregation using concepts from chemical kinetics and population dynamics. We show the model conserves mass and establish conditions for the existence and stability of equilibria. We also develop two discrete-time approximations to the model that are dynamically consistent. We show numerically that the continuous-time model produces sigmoidal growth, while the discrete-time approximations may exhibit oscillatory dynamics. Finally, sensitivity analysis reveals that aggregate concentration is most sensitive to parameters involved in monomer production and nucleation, suggesting the need for good estimates of such parameters

Determining the Kappa Distributions of Space Plasmas from Observations in a Limited Energy Range

Spacecraft observations allow us to reconstruct the velocity distributions of space plasmas, which fully describe the kinetic state of the plasma. Space plasmas often exist in stationary states out of equilibrium, which are typically described by kappa distributions. Thus, the kappa index and temperature that govern these distributions are parameters that need to be determined for a full and accurate description of these plasmas. In this study, we demonstrate a novel and reliable way to determine the kappa index and temperature of plasma distribution functions constructed from counts observed in a narrow energy range by typical electrostatic sensors. Our method applies to cases in which the high-energy tail of the plasma is observed with significant uncertainty, or not observed at all. For the validation of our method, we produce pseudo-observations for typical input plasma parameters, specifically considering the design of the ion plasma instrument SWA-PAS on board the Solar Orbiter mission. Our method reliably estimates the relevant plasma parameters by fitting the angular spread of the distribution in a narrow energy range around the core bulk energy. We compare the output of our technique with the input parameters used to generate artificial data for a selected range of the kappa index and the temperature, and for a bulk energy typical for the solar wind. In addition, we study the effects of Poisson errors on the instrument's counting statistics, test our method against Helios 2 measurements, and discuss its potential applications and limitations

Nonextensive statistical mechanics, superstatistics and beyond: theory and applications in astrophysical and other complex systems

A brief illustration is presented about the scientific motivation and contributions of this Special Issue

New Horizons Solar Wind Around Pluto (SWAP) Observations of the Solar Wind From 11-33 AU

The Solar Wind Around Pluto (SWAP) instrument on NASA's New Horizon Pluto mission has collected solar wind observations en route from Earth to Pluto, and these observations continue beyond Pluto. Few missions have explored the solar wind in the outer heliosphere making this dataset a critical addition to the field. We created a forward model of SWAP count rates, which includes a comprehensive instrument response function based on laboratory and flight calibrations. By fitting the count rates with this model, the proton density (n), speed (V), and temperature (T) parameters are determined. Comparisons between SWAP parameters and both propagated 1 AU observations and prior Voyager 2 observations indicate consistency in both the range and mean wind values. These comparisons as well as our additional findings confirm that small and midsized solar wind structures are worn down with increasing distance due to dynamic interaction of parcels of wind with different speed. For instance, the T-V relationship steepens, as the range in V is limited more than the range in T with distance. At times the T-V correlation clearly breaks down beyond 20 AU, which may indicate wind currently expanding and cooling may have an elevated T reflecting prior heating and compression in the inner heliosphere. The power of wind parameters at shorter periodicities decreases with distance as the longer periodicities strengthen. The solar rotation periodicity is present in temperature beyond 20 AU indicating the observed parcel temperature may reflect not only current heating or cooling, but also heating occurring closer to the Sun.Comment: 55 pages, 29 Figures, accepted for publication in The Astrophysical Journal Supplements (ApJS