A data-driven model of Earth’s magnetosheath is developed by training a Bayesian recurrent neural network to reproduce Magnetospheric MultiScale (MMS) measurements of the magnetosheath plasma and magnetic field using measurements from the Wind spacecraft upstream of Earth at the first Earth-Sun Lagrange point (L1). This model, called PRIME-SH in reference to its progenitor algorithm PRIME (Probabilistic Regressor for Input to the Magnetosphere Estimation), is shown to predict spacecraft observations of magnetosheath conditions accurately in a statistical sense with a continuous rank probability score (CRPS) of $0.227\sigma$ and more accurately than current analytical models of the magnetosheath. Furthermore, PRIME-SH is shown to reproduce physics not explicitly enforced during training, such as field line draping, the dayside plasma depletion layer, the magnetosheath flow stagnation point, and the Rankine-Hugoniot MHD shock jump conditions. PRIME-SH has the additional benefits of being computationally inexpensive relative to global MHD simulations, being capable of reproducing difficult-to-model physics such as temperature anisotropy, and being capable of reliably estimating its own uncertainty to within $3.5\%$.

The interaction of a solar wind discontinuity with the backstreaming particles of the Earth’s ion foreshock can generate hot, tenuous plasma transients such as foreshock bubbles (FB) and hot flow anomalies (HFA). These transients are known to have strong effects on the magnetosphere, distorting the magnetopause (MP), either locally during HFAs or globally during FBs. However, previous studies on the global impact of FBs have not been able to determine whether the response stems directly from the transverse scale size of the phenomenon or its fast motion over the magnetosphere. Here we present the observation of an FB and its impact on the magnetosphere from different spacecraft scattered over the dayside magnetosphere. We are able to constrain the size of the transverse scale of an FB from direct observations to be about 10 $R_\mathrm{E}$. We further suggest that a combination of this scale and the motion of the FB over the MP is responsible for the previously reported global response of the dayside magnetosphere.

A document by Niklas Grimmich. Click on the document to view its contents.

The Earth’s magnetosheath and cusps are the sources of soft X-rays. In the accompanying paper (Part 1) and this paper, we discuss the methods of finding the magnetopause position by analyzing the X-ray images. We use the software developed for the Soft X-ray Imager (SXI) on board the forthcoming Solar wind - Magnetosphere - Ionosphere Link Explorer (SMILE) mission. We show how to find the maximum SXI count rate in noisy count maps. We verify the assumption that the maximum of the X-ray emissivity integrated along the Line-of-Sight (Ix) is tangent to the magnetopause. We consider two cases using two MHD models and apply different methods of magnetospheric masking. Overall, the magnetopause is located close to the maximum Ix gradient or between the maximum Ix gradient and the maximum Ix depending on the method used. But since the angular distance between the maximum Ix gradient and the maximum Ix is relatively small (about 3{degree sign}), the maximum Ix might be used as an indicator of the outer boundary of a wide magnetopause layer usually obtained in MHD simulations.

The magnetopause standoff distance characterizes global magnetospheric compression and deformation in response to changes in the solar wind dynamic pressure and interplanetary magnetic field orientation. We cannot derive this parameter from in-situ spacecraft measurements. However, time-series of the magnetopause standoff distance can be obtained in the near future using observations by soft X-ray imagers. In two companion papers, we describe methods of finding the standoff distance from X-ray images. In Part 1, we present the results of MHD simulations which we use for the calculation of the X-ray emissivity in the magnetosheath and cusps. Some MHD models predict relatively high density in the magnetosphere, larger than observed in the data. Correcting this, we develop magnetospheric masking methods to separate the magnetosphere from the magnetosheath and cusps. We simulate the X-ray emissivity in the magnetosheath for different solar wind conditions and dipole tilts.

We compare the predictions of the GUMICS-4 global magnetohydrodynamic model for the interaction of the solar wind with the Earth’s magnetosphere with Cluster SC3 measurements for over one year, from January 29, 2002, to February 2, 2003. In particular, we compare model predictions with the north/south component of the magnetic field (Bz) seen by the magnetometer, the component of the velocity along the Sun-Earth line (Vx), and the plasma density as determined from a top hat plasma spectrometer and the spacecraft’s potential from the electric field instrument. We select intervals in the solar wind, the magnetosheath, and the magnetosphere where these instruments provided good quality data and the model correctly predicted the region in which the spacecraft is located. We determine the location of the bow shock, the magnetopause and, the neutral sheet from the spacecraft measurements and compare these locations to those predicted by the simulation. The GUMICS-4 model agrees well with the measurements in the solar wind however its accuracy is worse in the magnetosheath. The simulation results are not realistic in the magnetosphere. The bow shock location is predicted well, however, the magnetopause location is less accurate. The neutral sheet positions are located quite accurately thanks to the special solar wind conditions when the By component of the interplanetary magnetic field is small.

Current three-dimensional, data-based models for the terrestrial exosphere have been derived from measurements of optically thin Lyman-alpha (Ly-α) emissions scattered by neutral hydrogen atoms. Such models are only valid for the middle exospheric region (3-8 Earth radii geocentric distances) since the orbital paths of the space-based platforms used to acquire Ly-α radiance were located within the exosphere, thus precluding the proper detection of the faint outer exospheric emission. Notwithstanding, accurate specifications of density distributions beyond 8 RE are needed to support comprehensive studies of the solar-terrestrial interactions. Two upcoming missions, the Solar wind Magnetosphere-Ionosphere Link Explorer (SMILE) and the Lunar Environment Heliospheric X-ray Imager (LEXI), will image the Earth’s magnetosheath in soft X-rays, and neutral densities are crucial to extract ion distributions through inversion of the acquired images. This work develops a technique to estimate the Earth’s outer exospheric density distributions using far-ultraviolet wide-field data acquired by the Lyman-Alpha Imaging Camera (LAICA) onboard the Proximate Object Close Flyby with Optical Navigation mission. Our approach formulates an inverse problem based on the linearity between measurements of scattered Ly-α flux and the local atomic hydrogen density, which is solved using the Bayesian approach known as Maximum a posteriori estimation. We use the LAICA image to derive global, 3-D hydrogen density distributions at 6-35 RE geocentric distances. We find that the spatial structure of the outer exosphere agrees well with the predictions of radiation pressure theory. Further, we find that the mean hydrogen density at 10 RE subsolar point is 26.51 atoms/cm3.

Global magnetohydrodynamic models predict that plasma velocities vary almost linearly from 0 km s-1 along the stagnation streamline leading from the nose of the stationary magnetopause to 0.25 VSW at the nose of the bow shock, where VSW is the solar wind velocity. This paper presents a proof-of-concept study showing how two-point measurements of the plasma velocity in the subsolar magnetosheath can be used to determine gradients in the plasma velocity and consequently the steady-state or slowly-moving locations of both the nose of the magnetopause and the nose of the bow shock. The results may be of use to those binning magnetosheath observations to develop empirical models, those testing models for magnetopause erosion or deposition in response to magnetic reconnection, and those determining the stand-off distance of the bow shock as a function of solar wind conditions.

A new model for the shape of the magnetopause is presented using a closed-form analytic function known as a tractrix. This shape is derived from several physics-based underpinnings, eliminating the need for fitting ad-hoc functional forms that, while convenient, are not physically motivated. One feature of the magnetopause predicted by this model is that the magnetotail flares outward until it reaches a constant width, a feature that has significant observational evidence but is seldom represented in functional forms of the magnetopause shape. To optimize the parameters of this model, a dataset of over 13,000 magnetopause crossings from THEMIS/ARTEMIS, Cluster, Geotail, Interball, and several other spacecraft is utilized. Using a Bayesian approach combined with a Markov Chain Monte Carlo (MCMC) method to estimate the posterior probability distribution in parameter space, the maximum likelihood parameters for the model that optimize its performance on this dataset are determined. The modelâ\euro™s performance is compared to that of other popular models of the magnetopause with a focus on their relative performance, and is shown to outperform models that assume the tail flares outward to infinity at far distances. The optimized model more accurately predicts magnetopause position along the tail than other popular static analytic magnetopause models, while still being easy to implement for a variety of applications.

Forecasting relativistic electron fluxes at geostationary Earth orbit (GEO) has been a long term goal of the scientific community, and significant advances have been made in the past, but the relation to the interior of the radiation belts, that is, to lower $L-$shells is still not clear. In this work we have identified 60 relativistic electron enhancement events at GEO to study the radial response of outer belt fluxes and the correlation between the fluxes at GEO and those at lower $L-$shells. The enhancement events occurred between 1 October 2012 and 31 December 2017 and were identified using GOES 15 $>$2 MeV fluxes at GEO, which we have used to characterize the radial response of the radiation belt, by comparing to fluxes measured by the Van Allen probes ECT-REPT between $2.55.0$, and generally similar for $L>4.5$. Post enhancement maximum fluxes show a remarkable correlation for all $L > 4.0$ although the magnitude of the pre-existing fluxes on the outer belt plays a significant role and makes the ratio of pre-to-post enhancement fluxes less predictable in the region $4.0

We present a study analyzing relativistic and ultra relativistic electron energization and the evolution of pitch angle distributions using data from the Van Allen Probes. We study the connection between energization and isotropization to determine if there is a coherence across storms and across energies. Pitch angle distributions are fit with a Jsinθ function, and the variable ‘n’ is characterized as the pitch angle index and tracked over time. Our results show that, consistently across all storms with ultra relativistic electron energization, electrons become most anisotropic within around a day of Dst and relax down to prestorm isotropization levels in the following week. In addition, each consecutively higher energy channel is associated with higher anisotropy after storm main phase. Changes in the pitch angle index are reflected in each energy channel; when 1.8 MeV electrons increase (or decrease) in pitch angle index, so do all the other energy channels. In a superposed epoch study, we show that the peak anisotropies differ between CME- and CIR- driven storms and measure the relaxation rate as the anisotropy falls after the storm. The relaxation rate in pitch angle index for CME-driven storms is -0.14+/-0.023 at 1.8 MeV, -0.28+/-0.01 at 3.4 MeV, and -0.36±0.02 at 5.2 MeV. For CIR-driven storms, the relaxation rates are -0.09±0.01 for 1.8 MeV, -0.12±0.02 for 3.4 MeV, and -0.11±0.02 for 5.2 MeV. This study shows that there is a global coherence across energies and that storm type may play a role in the evolution of electron pitch angle distributions.