A Hitch-hiker’s Guide to Stochastic Differential Equations

In this review, an overview of the recent history of stochastic differential equations (SDEs) in application to particle transport problems in space physics and astrophysics is given. The aim is to present a helpful working guide to the literature and at the same time introduce key principles of the SDE approach via “toy models”. Using these examples, we hope to provide an easy way for newcomers to the field to use such methods in their own research. Aspects covered are the solar modulation of cosmic rays, diffusive shock acceleration, galactic cosmic ray propagation and solar energetic particle transport. We believe that the SDE method, due to its simplicity and computational efficiency on modern computer architectures, will be of significant relevance in energetic particle studies in the years to come.     

Daytime Ionosphere Retrieval Algorithm for the Ionospheric Connection Explorer (ICON)

The NASA Ionospheric Connection Explorer Extreme Ultraviolet spectrograph, ICON EUV, will measure altitude profiles of the daytime extreme-ultraviolet (EUV) OII emission near 83.4 and 61.7 nm that are used to determine density profiles and state parameters of the ionosphere. This paper describes the algorithm concept and approach to inverting these measured OII emission profiles to derive the associated \(\mathrm{O}^{+}\) density profile from 150–450 km as a proxy for the electron content in the F-region of the ionosphere. The algorithm incorporates a bias evaluation and feedback step, developed at the U.S. Naval Research Laboratory using data from the Special Sensor Ultraviolet Limb Imager (SSULI) and the Remote Atmospheric and Ionospheric Detection System (RAIDS) missions, that is able to effectively mitigate the effects of systematic instrument calibration errors and inaccuracies in the original photon source within the forward model. Results are presented from end-to-end simulations that convolved simulated airglow profiles with the expected instrument measurement response to produce profiles that were inverted with the algorithm to return data products for comparison to truth. Simulations of measurements over a representative ICON orbit show the algorithm is able to reproduce hmF2 values to better than 5 km accuracy, and NmF2 to better than 12% accuracy over a 12-second integration, and demonstrate that the ICON EUV instrument and daytime ionosphere algorithm can meet the ICON science objectives which require 20 km vertical resolution in hmF2 and 18% precision in NmF2.     

Extended Pile Driving Model to Predict the Penetration of the Insight/HP<Superscript>3</Superscript> Mole into the Martian Soil

The NASA InSight mission will provide an opportunity for soil investigations using the penetration data of the heat flow probe built by the German Aerospace Center DLR. The Heat flow and Physical Properties Probe (HP³) will penetrate 3 to 5 meter into the Martian subsurface to investigate the planetary heat flow. The measurement of the penetration rate during the insertion of the HP³ will be used to determine the physical properties of the soil at the landing site. For this purpose, numerical simulations of the penetration process were performed to get a better understanding of the soil properties influencing the penetration performance of HP³. A pile driving model has been developed considering all masses of the hammering mechanism of HP³. By cumulative application of individual stroke cycles it is now able to describe the penetration of the Mole into the Martian soil as a function of time, assuming that the soil parameters of the material through which it penetrates are known. We are using calibrated materials similar to those expected to be encountered by the InSight/HP³ Mole when it will be operated on the surface of Mars after the landing of the InSight spacecraft. We consider various possible scenarios, among them a more or less homogeneous material down to a depth of 3–5 m as well as a layered ground, consisting of layers with different soil parameters. Finally we describe some experimental tests performed with the latest prototype of the InSight Mole at DLR Bremen and compare the measured penetration performance in sand with our modeling results. Furthermore, results from a 3D DEM simulation are presented to get a better understanding of the soil response.     

Applications of numerical optimization techniques to design of axial compressor blades

This paper describes the shape optimization of NASA rotor 37 and rotor and stator blades in a single-stage transonic axial compressor.Shape optimization of the blades operating at the design flow condition has been performed using the response surface method and three-dimensional Navier-Stokes analysis.Thin-layer approximation is introduced to the Navier-Stokes equations,and an explicit Runge-Kutta scheme is used to solve the governing equations.The three design variables,blade sweep,lean and skew,are introduced to optimize the three-dimensional stacking line of the blades.The objective function of the shape optimization is an adiabatic efficiency.Throughout the optimization of rotor and stator blades, optimal blade shape can be obtained.It is noted the increase of adiabatic efficiency by optimization of the blade shape with the stacking line in the single-stage transonic axial compressor is more effective in a rotor blade rather than a stator blade because of the large deformation of blade shape in the stator blade.      

Meter-Scale Slopes of Candidate InSight Landing Sites from Point Photoclinometry

Photoclinometry was used to analyze the small-scale roughness of areas within the proposed Mars InSight landing ellipse. The landing ellipse presented in this study is in Elysium Planitia.This study was able to constrain surface slopes on length scales comparable to the HiRISE image resolution (0.25 meters/pixel and coarser). The InSight mission has various engineering constraints that each candidate landing ellipse must satisfy. These constraints indicate that the statistical value of the slopes at one, two, and five meter baselines are an important criterion. This technique estimates surface slopes across large swaths of each image, and builds up slope statistics for the images in the landing ellipse. The slopes I derived for the InSight landing site ellipse in this study are within the small-scale roughness constraints put forth by the InSight project. These results have provided input into the landing hazard assessment process.     

Thermosphere-Ionosphere-Electrodynamics General Circulation Model for the Ionospheric Connection Explorer: TIEGCM-ICON

The NASA Ionospheric Connection explorer (ICON) will study the coupling between the thermosphere and ionosphere at low- and mid-latitudes by measuring the key parameters. The ICON mission will also employ numerical modeling to support the interpretation of the observations, and examine the importance of different vertical coupling mechanisms by conducting numerical experiments. One of these models is the Thermosphere-Ionosphere-Electrodynamics General Circulation Model-ICON (TIEGCM-ICON) which will be driven by tidal perturbations derived from ICON observations using the Hough Mode Extension method (HME) and at high latitude by ion convection and auroral particle precipitation patterns from the Assimilative Mapping of Ionospheric Electrodynamics (AMIE). The TIEGCM-ICON will simulate the thermosphere-ionosphere (TI) system during the period of the ICON mission. In this report the TIEGCM-ICON is introduced, and the focus is on examining the effect of the lower boundary on the TI-system to provide some guidance for interpreting future ICON model results.     

Old-Aged Primary Distance Indicators

Old-aged stellar distance indicators are present in all Galactic structures (halo, bulge, disk) and in galaxies of all Hubble types and, thus, are immensely powerful tools for understanding our Universe. Here we present a comprehensive review for three primary standard candles from Population II: (i) RR Lyrae type variables (RRL), (ii) type II Cepheid variables (T2C), and (iii) the tip of the red giant branch (TRGB). The discovery and use of these distance indicators is placed in historical context before describing their theoretical foundations and demonstrating their observational applications across multiple wavelengths. The methods used to establish the absolute scale for each standard candle is described with a discussion of the observational systematics. We conclude by looking forward to the suite of new observational facilities anticipated over the next decade; these have both a broader wavelength coverage and larger apertures than current facilities. We anticipate future advancements in our theoretical understanding and observational application of these stellar populations as they apply to the Galactic and extragalactic distance scale.     

X-Ray Spectroscopy of Galaxy Clusters: Beyond the CIE Modeling

X-ray spectra of galaxy clusters are dominated by the thermal emission from the hot intracluster medium. In some cases, besides the thermal component, spectral models require additional components associated, e.g., with resonant scattering and charge exchange. The latter produces mostly underluminous fine spectral features. Detection of the extra components therefore requires high spectral resolution. The upcoming X-ray missions will provide such high resolution, and will allow spectroscopic diagnostics of clusters beyond the current simple thermal modeling. A representative science case is resonant scattering, which produces spectral distortions of the emission lines from the dominant thermal component. Accounting for the resonant scattering is essential for accurate abundance and gas motion measurements of the ICM. The high resolution spectroscopy might also reveal/corroborate a number of new spectral components, including the excitation by non-thermal electrons, the deviation from ionization equilibrium, and charge exchange from surface of cold gas clouds in clusters. Apart from detecting new features, future high resolution spectroscopy will also enable a much better measurement of the thermal component. Accurate atomic database and appropriate modeling of the thermal spectrum are therefore needed for interpreting the data.     

Estimations of the Seismic Pressure Noise on Mars Determined from Large Eddy Simulations and Demonstration of Pressure Decorrelation Techniques for the Insight Mission

The atmospheric pressure fluctuations on Mars induce an elastic response in the ground that creates a ground tilt, detectable as a seismic signal on the InSight seismometer SEIS. The seismic pressure noise is modeled using Large Eddy Simulations (LES) of the wind and surface pressure at the InSight landing site and a Green’s function ground deformation approach that is subsequently validated via a detailed comparison with two other methods: a spectral approach, and an approach based on Sorrells’ theory (Sorrells, Geophys. J. Int. 26:71–82, 1971; Sorrells et al., Nat. Phys. Sci. 229:14–16, 1971). The horizontal accelerations as a result of the ground tilt due to the LES turbulence-induced pressure fluctuations are found to be typically \(\sim 2 \mbox{--} 40~\mbox{nm}/\mbox{s}^{2}\) in amplitude, whereas the direct horizontal acceleration is two orders of magnitude smaller and is thus negligible in comparison. The vertical accelerations are found to be \(\sim 0.1\mbox{--}6~\mbox{nm}/\mbox{s}^{2}\) in amplitude. These are expected to be worst-case estimates for the seismic noise as we use a half-space approximation; the presence at some (shallow) depth of a harder layer would significantly reduce quasi-static displacement and tilt effects.We show that under calm conditions, a single-pressure measurement is representative of the large-scale pressure field (to a distance of several kilometers), particularly in the prevailing wind direction. However, during windy conditions, small-scale turbulence results in a reduced correlation between the pressure signals, and the single-pressure measurement becomes less representative of the pressure field. The correlation between the seismic signal and the pressure signal is found to be higher for the windiest period because the seismic pressure noise reflects the atmospheric structure close to the seismometer.In the same way that we reduce the atmospheric seismic signal by making use of a pressure sensor that is part of the InSight Auxiliary Payload Sensor Suite, we also the use the synthetic noise data obtained from the LES pressure field to demonstrate a decorrelation strategy. We show that our decorrelation approach is efficient, resulting in a reduction by a factor of \(\sim 5\) in the observed horizontal tilt noise (in the wind direction) and the vertical noise. This technique can, therefore, be used to remove the pressure signal from the seismic data obtained on Mars during the InSight mission.     

Heliosheath Processes and the Structure of the Heliopause: Modeling Energetic Particles,Cosmic Rays,and Magnetic Fields

This paper summarizes the results obtained by the team “Heliosheath Processes and the Structure of the Heliopause: Modeling Energetic Particles, Cosmic Rays, and Magnetic Fields” supported by the International Space Science Institute (ISSI) in Bern, Switzerland. We focus on the physical processes occurring in the outer heliosphere, especially at its boundary called the heliopause, and in the local interstellar medium. The importance of magnetic field, charge exchange between neutral atoms and ions, and solar cycle on the heliopause topology and observed heliocentric distances to different heliospheric discontinuities are discussed. It is shown that time-dependent, data-driven boundary conditions are necessary to describe the heliospheric asymmetries detected by the Voyager spacecraft. We also discuss the structure of the heliopause, especially due to its instability and magnetic reconnection. It is demonstrated that the Rayleigh–Taylor instability of the nose of the heliopause creates consecutive layers of the interstellar and heliospheric plasma which are magnetically connected to different sources. This may be a possible explanation of abrupt changes in the galactic and anomalous cosmic ray fluxes observed by Voyager 1 when it was crossing the heliopause structure for a period of about one month in the summer of 2012. This paper also discusses the plausibility of fitting simulation results to a number of observational data sets obtained by in situ and remote measurements. The distribution of magnetic field in the vicinity of the heliopause is discussed in the context of Voyager measurements. It is argued that a classical heliospheric current sheet formed due to the Sun’s rotation is not observed by in situ measurements and should not be expected to exist in numerical simulations extending to the boundary of the heliosphere. Furthermore, we discuss the transport of energetic particles in the inner and outer heliosheath, concentrating on the anisotropic spatial diffusion diffusion tensor and the pitch-angle dependence of perpendicular diffusion and demonstrate that the latter can explain the observed pitch-angle anisotropies of both the anomalous and galactic cosmic rays in the outer heliosheath.