Coronal mass ejections (CMEs) are formed in the solar corona by the ejection of material from closed field regions that were not previously participating in the solar wind expansion. CMEs commonly exhibit a signature consisting of a counterstreaming flux of suprathermal electrons with energies above about 80 eV, indicating closed field structures that are either rooted at both ends in the sun or entirely disconnected from it. About 30 percent of all CME events at 1 AU exhibit large, coherent internal field rotations typical of magnetic flux ropes. It is suggested that interplanetary magnetic flux ropes form as a result of reconnection within rising, previously sheared coronal magnetic loops.

Coronal Mass Ejections and Magnetic Flux Ropes in Interplanetary Space

A kinematic method of representing the three-dimensional solar wind flow is devised by taking into account qualitatively the stream-stream interaction which leads to the formation of a shock pair. Solar wind particles move radially away from the Sun, satisfying the frozen-magnetic field condition. The uniqueness of the present approach is that one can incorporate both theoretical and observational results by adjusting the parameters involved and that a self-consistent data set can be simulated. One can then infer the three-dimensional structure of the solar wind which is vital in understanding the interaction between the solar wind and the magnetosphere, and it is for this reason that the present kinematic method is devised. In the first part of this paper, the present kinematic method is described in detail by demonstrating that the following solar wind features can be simulated: (i) Variations of the solar wind quantities (such as the solar wind speed, the density and the IMF vector), associated with the solar rotation, at the Earth; (ii) the solar wind flow pattern in the meridian planes; (iii) the three-dimensional structure of the corotating interaction region (CIR); and (iv) the three-dimensional structure of the warped solar current sheet. In Section 2, the three-dimensional structure of solar wind disturbances are studied by introducing a flare-generated high speed stream into the two-stream model of the solar wind developed in Section 1. The treatment of the stream-stream interaction is generalized to deal with a flare-generated high speed stream, yielding a shock pair. The shock pair causes three-dimensional distortion of the solar current sheet as it propagates outward from the Sun. It is shown that a set of characteristic time variations of the solar wind speed, density, the interplanetary magnetic field magnitude B and angles Θ (theta) and gf (phi) result at the time of the passage at the location of the Earth for a given set of flare conditions. These quantities allow us to compute the solar wind-magnetosphere energy coupling function ɛ. Time variations of the two geomagnetic indices AE and Dst are then estimated from ɛ. The simulated geomagnetic storms are compared with observed ones. In the third part, it is shown that recurrent geomagnetic storms can reasonably be reproduced, if fluctuating components of the interplanetary magnetic field (IMF) are superposed on the kinematic model of the solar wind developed in the first part. As an example, we simulate the fluctuating components by linearly polarized Alfven waves and by random variations of the IMF angle Θ (theta). Characteristics of the simulated and observed geomagnetic storms are discussed in terms of the simulated and observed AE and Dst indices. If the fluctuating components of the IMF can generally be identified as hydromagnetic waves, they may be an important cause for individual magnetospheric substorms, while the IMF magnitude B and the solar wind speed V modulate partially the intensity of magnetospheric substorms and storms.

Simulation of three-dimensional solar wind disturbances and resulting geomagnetic storms

We utilize a 21/2-D MHD time-dependent model to perform a parametric study of interplanetary shock propagation to 1 AU. The input conditions are represented by the following variables:(1) initial shock velocity, (2) duration of the driving pulse, and (3) width of the pulse at the near-Sun position (18 solar radii). The total net energy added to the solar wind was calculated for each pulse. The forward shock's travel time to, and the peak dynamic pressure at, 1 AU as a function of location along the shock front have been studied over a range of total input pulse energies from 1029 to 1032 ergs. For input pulses with modest angular width and temporal duration, we find that the propagation of the resulting interplanetary fast forward shock waves depends primarily upon the net input energy. The dependence of the transit time upon energy is a power law with a -1/3 index which corresponds to the classical, piston driven case. Reverse shocks are also formed behind all but the lowest energy shocks. Their properties, although also a function of input energy, depend upon the specific values of the input pulse shock velocity, width and duration. We also briefly discuss the propagation of the shocks out to 1 AU, and the conditions for which the interplanetary shocks depart from being symmetric about the input pulse central meridian due to magnetic and dynamic effects.

MHD study of temporal and spatial evolution of simulated interplanetary shocks in the ecliptic plane within 1 AU

The solar flare-initiated shock can be considered to be an initially driven shock that converts into a blast wave as it propagates through the interplanetary medium In our simplified shock modeling, to estimate the time of the shock arrival at a specified position in space we assume that the shock is initially driven from the flare position at the velocity indicated by the type II solar radio burst We assume the shock is driven until the initiating solar flare energy is somewhat expended After this initially driven phase, the shock front then propagates with the characteristic speed expected of the shock front of a blast wave In the interplanetary medium with its 1/r² density dependence, the blast wave shock front speed should be proportional to r−05 We find that this r−05 speed dependence is a general characteristic of the shock front speed when the speeds are determined in the solar wind reference frame The blast wave “rides over” the preexisting solar wind so that the disturbance speed of the shock front at any instant of time is the speed of the shock front added vectorially to the solar wind speed Application of these principles enables a consistent “timing” of solar flare-initiated shock waves that is event independent We show that this concept is consistent with the time position profile derived from the analysis of kilometric type II events that are associated with interplanetary shocks

A simplified model for timing the arrival of solar flare‐initiated shocks

[1] Space weather research requires investigation of a complex chain of coupled dynamic phenomena occurring simultaneously on various spatial and temporal scales between the Sun and Earth. Specialized physically based numerical models have been developed to address particular aspects of the entire system. However, an integrated modeling approach is necessary to provide a complete picture suitable for interpretation of various remote and in situ observations and for development of forecasting capabilities. In this paper we demonstrate merging of coronal and heliospheric MHD models for a two-dimensional hypothetical case involving a magnetic cloud, shock, streamer belt, and current sheet. The disruption of a sheared helmet streamer launches a coronal mass ejection (CME) (simulated by the coronal model), which evolves during its propagation through interplanetary space (simulated by the heliospheric model). These models employ different physical approximations and numerical grids to simulate physical phenomena over their respective spatial and temporal domains. The merging of the models enables accurate tracking of a CME from its origin in the solar atmosphere to its arrival at Earth.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2002JA009334

Merging of coronal and heliospheric numerical two‐dimensional MHD models

The dynamic behavior of flare-associated disturbances has been investigated using a time-dependent two-dimensional MHD numerical model for a one-fluid solar wind with adiabatic expansion. Simulations of the development and propagation of perturbations have been performed between 18 R/sub S/ and 226 R/sub S/ (where R/sub S/ = solar radius) in an angular sector of the equatorial plane of the sun 90/sup 0/ wide. Several test computations have been carried out with different initial pulse characteristics. These pulses are set arbitrarily at the inner boundary assuming that a shock wave is already formed. The parameters are the velocity of the shock front, the angular width of the perturbation, and its time duration at 18 R/sub S/. It is shown that in every case the time delay between 18 R/sub S/ and 226 R/sub S/ depends on the total amount of energy released by the prototype flare (hence in the pulse). This dependence is stronger with the initial velocity than with the angular width. Also it appears that the shock wave propagates according to a power law of time: R = at/sup b/. After a relatively short time the expansion of the wave is dominated by the internal energy so that themore » longitudinal extent of the perturbation at 1 AU seems to be only a function of the time elapsed after the arrival of the front shock at this distance. The existence of a reverse shock which is formed after a few hours is shown to last a time long enough to reach 1 AU. Its longitudinal extension is limited to the area around the flare central meridian where the pressure gradient induced by the initial condition is strong enough.« less

S. M. Han

Papers

Spatial structure of flare‐associated perturbations in the solar wind simulated by a two‐dimensional numerical MHD model