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Active ionospheric role in small-scale aurora structuring
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Journal of Atmospheric and Solar-Terrestrial Physics 67 (2005) 687–700 www.elsevier.com/locate/jastp
Active ionospheric role in small-scale aurora structuring L. Zhu, J.J. Sojka, R.W. Schunk Center for Atmospheric and Space Science, Utah State University, Logan, UT 84322-4405, USA Received 19 May 2003; received in revised form 22 November 2004; accepted 14 December 2004 Available online 17 March 2005
Abstract The auroral structures on the spatial scales of 10s–100s km and their associated electrodynamics are key elements in the magnetosphere–ionosphere (M–I) system and are important for ionospheric dynamics. The simulation of these auroras poses a challenge for global magnetohydrodynamic (MHD) M–I models. In this work, an M–I coupling mechanism for the formation of auroral structures on these spatial scales is proposed. In the M–I coupling mechanism, the active role of the ionosphere is taken into account and the auroral structures with spatial scales of 10s–100s km, which do not mirror the features of the magnetospheric drivers, self-consistently develop. The proposed mechanism includes the effects of the ionospheric spatial and temporal scales and the M–I coupling processes. By calculating the reflection of the Alfve´n waves at the ionosphere and the Alfve´n waves launched by the temporal variation of the ionospheric conductivity, the mechanism can provide time-dependent, quantitative information of all electrodynamic parameters associated with the dynamic evolution of structured auroras, including the field-aligned currents, ionospheric horizontal currents, convection field, conductivity, and Joule heating rate. The M–I coupling mechanism has been quantitatively tested and validated by using numerical simulations and model-observation comparisons. Some of the theoretical predictions have been independently confirmed by observations. With its strengths of (a) quantitative capability and (b) emphasize on the active role of the ionosphere, this M–I coupling mechanism complements other mechanisms for the auroral structures as well as the global MHD M–I modeling, thus improving our understanding of the auroral structures and the M–I coupling processes. r 2005 Elsevier Ltd. All rights reserved. Keywords: Auroral structure; Ionospheric electrodynamics; Substorm; Polar cap arcs; Numerical simulation
1. Introduction With the spatial resolution and sensitivity improvements of both ground-based optical measurements and satellite imagers, it has been found that many auroras that looked quite uniform in past observations actually have multiple structures and the brightness of these auroras vary dynamically in both space and time (Samson et al., 1996; Rodriguez et al., 1997; Zhu et Corresponding author.
E-mail address: [email protected] (L. Zhu).
al., 1997). The dynamic features associated with these auroral structures represent the dynamic nature of the physical processes in the magnetosphere and ionosphere as well as the interactions between them. The spatial scales of the auroral structures cover a wide range, which can be 10s–100s m for thin arcs, 10s–100 km for multiple polar cap arcs, and 100s km for the structured aurora brightness associated with substorm onset (Maggs and Davis, 1968; Torbert and Carlson, 1980; Marklund et al., 1983; Valladares and Carlson, 1991). Various mechanisms have been proposed for the formations of the auroras of various spatial scales (e.g.,
1364-6826/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.jastp.2004.12.004
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Goertz et al., 1985; Trakhtengerts and Feldstein, 1991; Calvert, 1987; Smith, 1986; Watanabe and Sato, 1988; Rothwell et al., 1991; Lyatsky et al., 1999; Streltsov and Lotko, 1999, 2004; Zhu et al., 2001; Prakash and Rankin, 2001). A comprehensive summary of these mechanisms as well as the comparisons between them has been done by Borovsky (1993). In this work, we propose an alternative mechanism, M–I coupling mechanism, for the auroral structuring on spatial scales from 10s to 100s km, especially those with multiple structures. The multiple structured auroras on these spatial scales are quite common in the polar cap as well as in the substorm onset regions (Valladares and Carlson, 1991; Samson et al., 1996; Mende et al., 1999). Fig. 1 shows an example of these multiply structured auroras. The unique feature of our proposed mechanism is the inclusion of the active role of the ionosphere in the M–I coupling processes for the formation of the multiple auroral structures and the ionospheric spatial and temporal scales are taken into account. With the inclusion of the Alfve´n waves reflection at the ionosphere and the launching of the Alfve´n waves caused by the temporal change of the ionospheric conductivity, the ionospheric electrodynamics of aurora structuring in the mechanism is fully self-consistent.
The paper is organized as follows. In Section 2, the proposed M–I coupling mechanism for the multiple auroral structure is described. Since the basic mathematical formation of the mechanism has appeared in a previous paper on the topic of polar cap arcs (Zhu et al., 1993), the description will focus on the physics of the mechanism. In addition, the relevant theoretical mechanisms are briefly reviewed and the differences between our mechanism and these mechanisms are identified. In Section 3, we describe how the mechanism was applied to the studies of the structures of substorm aurora and polar cap aurora. We show the quantitative numerical results and discuss the controlling parameters that determine the features of multiple auroral structures. The results of model-observation comparison and the observational confirmations of some of the predictions from this M–I coupling mechanism are presented in Section 4. Finally, a discussion on how to further improve and validate the M–I coupling mechanism is given in Section 5.
2. M–I coupling mechanism for multiple auroral structures In the M–I coupling mechanism for multiple auroral structures (it will be referred to as the M–I coupling
Fig. 1. An image of multiple polar cap arcs taken by the All-Sky Intensified Photometer at Qaanaaq at 0826 UT, November 12, 1990.
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mechanism later on), the electric fields and field-aligned currents associated with propagating Alfve´n waves are calculated from a set of working equations derived from the MHD equations. The enhancement of the ionospheric conductivity is calculated by using a fully timedependent electron continuity equation. The model also calculate the reflection of the Alfve´n waves at the ionosphere as well as the Alfve´n waves launched by the temporal variation of the conductivity in the ionosphere. For the details of the mathematical formulation, it is referred to one of our previous paper (Zhu et al., 1993). The initial driving force comes from the magnetosphere, which can be either relatively uniform large-scale enhanced convection occurred when the IMF turns southward or the small-scale shear convection caused by the various dynamical processes in the magnetosphere, which can take place for both the southward and northward IMF periods. But the dynamic features and characteristics of the resulted structured auroras that we discuss here (with spatial scales of 10s–100s km) are quite different from those of the initial magnetospheric drivers. They are not the simple mapping of these drivers. More importantly, the development of multiple auroral structures will not occur without the ionosphere playing a significant active role in the M–I coupling processes. Note this is a very important augmentation to the M–I coupling mechanism. For the situation where the large-scale magnetospheric convection is enhanced by the southward turning of the IMF, the propagation of the enhanced convection to the ionosphere along magnetic field lines is carried by Alfve´n waves and these Earthward propagating Alfve´n waves carry the field-aligned currents in accordance with the MHD theory. Since the enhanced large-scale convection is relatively uniform, the field-aligned currents associated with it is not very strong and may not directly cause the appearance of aurora. On the other hand, the conductivity in the ionosphere, especially those in the auroral oval is always non-uniform, which can be caused by solar radiation gradient, the ionosphere–thermosphere interaction, or the precipitation due to the loss cone effect that is not directly connected to the magnetospheric convection. These conductivity gradient intrinsic to the ionosphere can a play significant role in the formation of multiple auroral structures. For simplicity, let us assume the enhanced large-scale magnetospheric convection field is uniform. From the MHD theory, the Alfve´n waves associated with a uniform convection field do not carry any field-aligned currents. When this convection field maps to the ionosphere with a non-uniform conductivity, it can force the ionospheric horizontal currents to convert to field-aligned currents. This process can be seen clearly from the diagram in Fig. 2. The newly produced field-aligned currents are actually determined
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Fig. 2. A schematic diagram showing how a uniform magnetospheric convection mapping to the ionosphere can force the horizontal current to convert to the field-aligned currents when a conductivity gradient exists. The positive value of the divergence of horizontal current indicates the downward fieldaligned current.
by the reflection of the Earthward propagating Alfve´n waves at the non-uniform ionosphere in which the spatial scales of the ionospheric conductivity step in. When the reflected Alfve´n waves with the information of the field-aligned currents generated in the ionosphere reach the magnetosphere, it will draw down electrons to the ionosphere, disturb the magnetosphere, and cause new Alfve´n waves propagating toward to the ionosphere. Due to the M–I coupling process via Alfve´n waves, these new Alfve´n waves are significantly different from the initial magnetospheric Alfve´n waves. The convection field associated with these Alfve´n waves is not uniform anymore and structured field-aligned currents are now present. When these new Alfve´n waves reach the ionosphere, the precipitating electrons associated with the magnetospheric upward field-aligned can cause the enhancement of the conductivity. From Fig. 2, it can be seen that the enhanced conductivity caused by the precipitating electrons does not take the shape of the initial conductivity distribution in the ionosphere and they can be spatially dislocated. This leads to further structuring of the convection field associated with the reflected Alfve´n waves and more structures in the fieldaligned current distribution. When the Alfve´n waves propagate back and forth between the magnetosphere and ionosphere and the communication between the two regions (M–I coupling) goes on, the structuring of the aurora could become more and more complicated and eventually multiple structured aurora develop.
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There are two additional physical processes in this M–I coupling mechanism which would further complicate the aurora structuring. The first is the involvement of the Hall currents in the closure of the field-aligned currents. When the conductivity is non-uniform, The convection field associated with the reflected Alfve´n waves can be rotated, leading to a more complicated configuration of the ionospheric convection. The Hall currents are not divergent-free any more and they can be involved in the dynamic closure of the magnetospheric field-aligned currents in the ionosphere. Fig. 3 shows the numerical results of how the convection field of Alfve´n waves rotates due to the existence of conductance gradient. The convection field associated with the initial earthward propagating Alfve´n waves (or incident waves as indicated in the Fig. 3) only has an x component. When conductivity is uniform, there is no y component in the reflected wave field. When the conductivity gradient increases, it can be seen from Fig. 3 that the y component in the reflected waves start to appear and becomes larger. The appearance of the y component of the reflected waves is because that the Hall currents are closed to the field-aligned currents and the reflected wave field is forced to rotate to satisfy the current continuity. The rotation of the convection field and the closure of the Hall currents to the field-aligned currents will certainly make the aurora more structured and the cause of this complexity is again the conductivity gradient in the ionosphere. The second additional physical process that makes the aurora more structured is the Alfve´n waves launched by the temporal variation of the ionospheric conductivity. When the precipitating electrons brought down by the Alfve´n waves reach the ionosphere, they can cause enhancement of the ionospheric conductivity. The temporal change of the conductivity launches new Alfve´n waves, in addition to the directly reflected Alfve´n waves, toward the magnetosphere. Since these waves are caused by the temporal change of the ionospheric conductivity, they contain the temporal and spatial scales of the ionosphere and represent the active role of the ionosphere in the formation of the auroral structures 20
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and the associated M–I coupling processes. When these ionosphere-originated Alfve´n waves join the incident and reflected Alfve´n waves and interact with the magnetosphere and the ionosphere by bouncing back and forth between the two regions, the structure of the aurora is further complicated. The initial magnetospheric driver for the formation of multiple auroral structures in this mechanism is not necessarily the enhanced large-scale convection and it can also be the small-scale shear convection generated by various physical processes in the magnetosphere. The small-scale shear carries field-aligned currents and the precipitation associated with the upward currents can cause the initial conductivity gradient in the ionosphere, which is needed in our mechanism for the formation of the multiple auroral structures. For the situation when the ionospheric background conductivity is not uniform, this conductivity enhancement caused by the precipitation associated with the small-scale shear magnetospheric convection may cause further complexity of the auroral structures. For the situation when the ionospheric background conductivity is quite uniform, this conductivity enhancement makes the appearance of structured aurora possible. A typical example is the multiple polar cap arcs. In the polar cap, the ionospheric conductivity is quite uniform. Based on the mechanism described in the above, a relatively uniform enhanced large-scale convection will not be able to cause the appearance of aurora when the ionospheric background conductivity is quite uniform. This explains why the enhanced large-scale convection in the polar cap when the IMF turns southward does not help with the appearance of polar cap arcs. There have been several other mechanisms proposed for the aurora on the spatial scales of 10s–100s km we are discussing here. These include the mechanisms of electrostatic mapping (Goertz, 1985), shear in lowlatitude boundary layer (Siscoe et al., 1991), shear in plasma sheet (Birn and Hesse, 1991), ionosphericconductivity feedback instability (Watanabe and Sato, 1988), Earthward ion streams (Lyons, 1991), and electrostatic fluid turbulence (Lotko and Schultz, 1988). Most of these mechanisms treat the ionosphere as a passive load. The magnetospheric drivers are simply mapped to the ionosphere and the features of the resulted auroras just mirror those of the magnetospheric drivers. The only exception is the mechanism of the ionospheric-conductivity feedback instability, in which the ionospheric condition is taken into account for the formation of aurora. Since our mechanism emphasizes the active role of the ionosphere and the M–I coupling effect, in the following, we will specially discuss the differences between the M–I coupling mechanism and the feedback instability mechanism. The ionospheric-conductivity feedback mechanism starts with a uniformly enhanced conductivity patch,
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which causes the appearance of polarization electric field. To depolarize this field, the field-aligned currents develop and they need to be closed at the magnetospheric end. The closure of these depolarization fieldaligned currents at the magnetosphere can bring precipitating electrons to the ionosphere and further enhance the conductivity patch. This is a positive feedback process which eventually leads to the fieldaligned current that are strong enough to cause the appearance of aurora. There are several fundamental differences between the M–I coupling mechanism and the conductivity feedback instability mechanism. (1) In the M–I coupling mechanism, the conductivity gradient plays a major role in the formation of auroral structure and this brings the ionospheric spatial and temporal scales into the M–I coupling process. The feedback mechanism always assume a uniform conductivity and the effect of conductivity gradient is never taken into account. (2) The M–I mechanism can explain how the multiple auroral structures develop, but the feedback mechanism can only be applied to the situation of single arc. (3) In the M–I mechanism, a significant amount of fieldaligned currents can be converted to the Hall currents. This is especially important for the substorm process, since the westward electrojet is mainly the Hall current. The ionospheric current closure in the feedback mechanism is always just between the Pedersen currents and field-aligned currents. (4) The ionospheric electrodynamics in the M–I coupling mechanism is fully selfconsistent which involves the reflection of the Alfve´n waves and the launching of the new Alfve´n waves caused by the temporal variation of the ionospheric conductivity. The feedback mechanism uses electrostatic way to handle the electrodynamics of aurora in the ionosphere. In addition to these fundamental differences between the two mechanisms, the M–I coupling mechanism has been quantitatively tested by the numerical simulations and model-observation comparisons and some of the theoretical predictions have been independently confirmed by observations, which will be presented in the following sections.
3. Numerical simulation results From the above discussion, it can be seen that the proposed M–I coupling mechanism uses the Alfve´n wave treatment instead of simple mapping. It also takes into account the effects of the spatial and temporal variations of the ionospheric conductivity and the M–I coupling, and includes electrodynamic processes of the reflection of Alfve´n waves and the launching of the Alfve´n waves of ionospheric origin. Therefore, the active role of the ionosphere for the formation of the structured auroras is included in the mechanism and
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all the electrodynamic parameters are self-consistent. On one hand, this makes the M–I mechanism physically reasonable, thus being able to explain a wide range of variations of the aurora structures. On the other hand, it leads to mathematical complexity and hence the difficulty of performing analytical analysis. In the following, we describe how the mechanism was applied to the studies of the structures of substorm aurora and polar cap aurora. We will show quantitative numerical results and discuss the controlling parameters that determine the features of multiple aurora structures. 3.1. Structured aurora in the auroral oval during substorms 3.1.1. Brief model description and the initial model inputs In this numerical modeling, the initial magnetospheric driver is the enhanced global magnetospheric convection that is driven by enhanced reconnection at the dayside magnetopause due to a southward turning of the IMF. The ionospheric domain of the substorm modeling covers the magnetic latitudes greater than 501 in the northern hemisphere. Initially, the quiet-time (pre-substorm) ionospheric background conditions for the model were calculated by running the model for a sufficiently long time to reach the asymptotic state. The ionospheric conductance, convection, and precipitation patterns that were obtained in this way are physically self-consistent and are shown in Figs. 4a–c, respectively. It can be seen that the background ionospheric conductivity is not uniform and has a large gradient in the north–south direction. In the simulation, the quiet-time (pre-substorm) period is the period earlier than 1200 UT. The substorm growth phase started at t ¼ 0 min (1200 UT), which is when the Alfve´n waves associated with the enhanced magnetospheric convection that was initiated at the dayside magnetopause reached the ionosphere. A two-cell convection pattern with a polar cap potential drop of about 73 kV (shown in Fig. 4d) was adopted for such an enhanced convection carried by the Alfve´n waves. It needs to be noted that this largescale convection driver does not have the small-scale structures that appear later in the resulting aurora. These global-scale Alfve´n waves were the driving forces for the growth phase dynamics in the ionosphere, which lasted about 24 min. Note that since the ionospheric conductivity is finite and anisotropic, such magnetospheric-enhanced convection cannot be fully loaded on the ionosphere and can also be distorted. The enhanced convection actually loaded on the ionosphere at t ¼ 0 min (1200 UT), which is different from the convection pattern shown in Fig. 4d, is self-consistently determined in the simulation by calculating the reflected Alfve´n waves at the ionosphere. The reflected Alfve´n waves and the new Alfve´n waves launched by the temporal change of the ionospheric conductivity then propagate outward
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Fig. 4. Quiet-time (presubstorm) distributions of the (a) ionospheric Hall conductance, (b) electric potential, and (c) characteristic energy of precipitation. Fig. 4d shows the enhanced magnetospheric convection initiated by the reconnection at the dayside magnetopause.
and interact with the magnetosphere. To simplify the simulation, we assume the magnetospheric source region is a perfect current source, thus allowing us to use a reflection coefficient to represent the Alfve´n wave interaction with the magnetosphere. While the Alfve´n waves propagate back and forth between the magnetosphere and ionosphere, the numerical simulation continued until t ¼ 35 min (1235 UT), which is when the substorm reached the expansion maximum. In the simulation, various electrodynamical parameters were calculated, including convection, precipitation (energy flux and characteristic energy), field-aligned and horizontal currents, Hall and Pedersen conductances, and Joule heating rates. All these physical parameters are time-varying, with a resolution of 5 s, and are physically self-consistent. 3.1.2. Resulted aurora structures Fig. 5 shows snapshots of the global distributions of the energy flux of precipitating electrons, the magnitude
of the electric field, and the Hall conductance at various times. The growth phase of the substorm started at t ¼ 0 min (1200 UT) and the expansion phase started at around t ¼ 24 min (1224 UT). The expansion maximum was achieved at around t ¼ 35 min (1235 UT). It can be seen clearly from Fig. 5 that energy flux, electric field, and Hall conductance are all highly structured around the onset region and these structures do not exist in either the background ionosphere or the initial magnetospheric convection driver. Fig. 6 shows the temporal variations of the energy flux in the substorm onset region (1800–0200 MLT, 55–851 magnetic latitude). The snapshots start at 1200 UT (the beginning of the growth phase) and end at 1235 UT (the expansion maximum) with a 5 min interval. Before the substorm starts, there is a well-defined precipitation band stretching in the east–west direction with the center at about 671. This quiet-time precipitation is the diffuse aurora precipitation and corresponds to the quiet-time auroral oval. When the substorm starts, the auroral oval
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Fig. 5. Snapshots of distributions of the energy flux (left column), the magnitude of electric field (middle column), and the Hall conductance (right column).
gradually expands poleward during the growth phase. After the substorm onset (around 1224 UT), structured precipitation quickly develops in the localized region around 751 and 21 MLT, where the substorm aurora breaks up and the bulge-like aurora forms. The developed substorm aurora is highly structured, which corresponds to the channeled precipitation. In the
aurora break-up region, the energy flux increases from the quiet-time level of less than 0.3 to about 1 erg/cm2/s at the end of the growth phase, then quickly reaches 7 erg/cm2/s at the expansion maximum. Correspondingly, the maximum values of the characteristic energy in this region changes from 0.5 keV (1200 UT) to 1.8 keV (1224 UT), and then to 7 keV (1235 UT).
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Fig. 6. Temporal variation of the energy flux in the substorm onset region.
These results strongly support the proposed M–I coupling mechanism for auroral structures from the numerical simulation aspect and clearly indicate that the ionosphere can play an important role in the formation of the auroral structures. 3.2. Structured aurora in the polar cap To further test the proposed mechanism for the auroral structures, we have also applied the theory to the studies of the multiple polar cap arcs. 3.2.1. Brief model description and initial model inputs As discussed in the above, the conductivity in the polar cap is quite uniform and the enhanced large-scale convection caused by the southward turning of the IMF is unlikely to cause the appearance of polar cap arcs. For this reason, we adopted a magnetospheric shear convection as the initial magnetospheric driver for the numerical simulation. The ionospheric simulation domain is 3000 km long in X (midnight–noon) direction, and 1000 km wide in Y (dawn–dusk) direction. The grid size is 30 km in X direction, and 10 km in Y direction. The third dimension along the magnetic field lines is a pseudo-dimension which merely serves to provide the Alfve´n wave traveling time scale. Since the magnetic field lines in the polar cap are mainly connected to the open-field line region, we can then simplify the magnetospheric source region as a constant voltage source, thus again we can use a reflection coefficient to simplify the Alfve´n waves interaction with the magnetosphere. Fig. 7 shows the ionospheric background conditions and the initial perturbation of the magnetosphereoriginated shear flow carried by downward propagating Alfve´n waves. The top panel of Fig. 7 shows the Hall conductance distribution in the noon–midnight crosssection. In the dawn–dusk direction, we assume the Hall
conductance to be uniform. This background ionospheric conductance is merely due to the solar contribution, and for simplicity, we assume it decreases linearly towards the nightside. The actual noon–midnight spatial gradient of the background conductivity varies widely with the variations of the season and F10.7 conditions. The initial magnetospheric shear flow carried by the propagating Alfve´n waves in our modeling is represented by a potential in Gaussian distribution as shown by the solid line in the bottom panel of Fig. 7. The shear flow is uniform in the noon–midnight direction. The corresponding electric field distribution, which is convergent in the center and divergent on the edges of the shear flow, is shown by the dashed line in the bottom panel of Fig. 7. 3.2.2. Resulted multiple polar cap arcs 3.2.2.1. Development of multiple polar cap arcs:. The initial shear flow carried by Alfve´n waves arrives in ionosphere at t ¼ 0 min; which leads to the bouncing of Alfve´n waves between the magnetosphere and ionosphere and the development of polar cap arcs. As long as the external environment of the coupled M–I system remains unchanged, the bouncing Alfve´n waves eventually will be damped by the finite ionospheric conductance and the development of polar cap arcs will approach an asymptotic steady state. In this case, such a steady state of polar cap arcs is achieved in about 8–10 min. Fig. 8 shows the field-aligned current distribution at the asymptotic stage, in which dashed lines denote upward field-aligned currents and solid lines denote downward field-aligned currents. Note that only a portion of the simulation domain is shown in this figure, in order to display the detailed structures associated with polar cap arcs. It can be seen from Fig. 8 that in the self-consistent development of a polar cap arc, a single peak precipitation associated with the
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initial magnetospheric shear flow has been split into multiple peaks, leading to multiple structures of the polar cap arcs. The individual arcs are about 30–40 km wide and are separated by a narrow downward current region. This results clearly shows an important point that the observed multiple polar cap arcs do not have to be the results of the multiple structures in the magnetospheric source region, instead, such a multiple feature is generated in the M–I coupling processes in which the ionosphere plays an active role. Such a point can be seen more clearly from the comparison of the field-aligned profiles shown in the mid- and bottom panels in Fig. 8, where the field-aligned current associated with the initial magnetospheric shear convection (middle panel) and that associated with the developed arcs (bottom panel) are presented. 3.2.2.2. How the ionosphere and M–I coupling determine the aurora structures:. To improve our understanding
of the M–I coupling mechanism, in the polar cap arc study, we used the numerical simulation to study how the ionospheric conditions and M–I coupling processes affect the features of the structured aurora. First of all, we found that the magnitude of the ionospheric background convection field can significantly affect the multiplicity of the structured polar cap arcs. The results in Fig. 9 show that when the magnitude of the ionospheric background convection increases, more and more structures of the polar cap arcs developed. Second, we found that the intensity of the ionospheric conductivity also has significant effect on the features of polar cap arc structures (results not shown here). When the background conductance is too low, the polar cap arcs hardly develop in the polar cap. This is because the ionosphere has a very large resistivity and the magnetospheric currents cannot be dynamically closed in the ionosphere. When the
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conductance is too high, there is no structured arc and only a bright single sun-aligned arc exists. This can be explained by the fact that the high ionospheric conductance allows the magnetospheric currents to be freely closed in the ionosphere, which acts to smooth localized discrete structures. Only when the conductance is in the middle range (0.5–1.5 mho for our specific model runs, which are for winter and solar maximum conditions), can the multiple polar cap arcs develop.
Third, we found that the spacing of the polar cap arcs structures is closely related to the hardness of the precipitation, which is determined by the M–I coupling processes. A quantitative relationship between the spacing of the multiple polar cap arcs and the Hall–Pedersen conductance ratio, which reflect the hardness of the precipitation, is obtained from our numerical modeling and is shown in Fig. 10. It indicates that polar cap arcs with wider spacing are associated with harder precipitation.
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Fig. 9. Field-aligned currents associated with the polar cap arcs for six different ionospheric background convection field strengths.
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To test and validate the M–I coupling mechanism, we performed some preliminary model-observation comparison studies. The observational data we used for the model-observation comparison study were the image data from the All-Sky Intensified Photometer at Qaanaaq during the months of November and December of 1990. We used the ionospheric conditions that are in overall agreement to those when the multiple arcs were observed to start the numerical runs and then compared the dynamic developments of the observed polar cap arcs and the simulated ones. Fig. 11 shows one example from these runs. The observed polar cap arcs occurred on December 11, 1990 in the evening sector of the dark polar cap. It started from a single arc, then gradually developed into a multiple arcs. The time period we are interested in is from 2112 to 2118 UT. The IMF turned northward at about 1800 UT and remained northward until 0030 UT
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Fig. 11. The comparison between the observed multiple polar cap arcs and the simulated arcs.
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Fig. 12. Statistical relationship between the average energy of the precipitation and the spacing of multiple polar cap arcs from the Akebono satellite precipitation data (Obara et al., 1996).
of the next day. During the period we are interested in, the Bz was 5 nT and By was 1:5 nT; and Kp was 1. The simulation for this case started at 2108 UT, which is the time when the assumed downward propagating Alfve´n wave hit the ionosphere. Fig. 11 shows snapshots of the evolution of the field-aligned current distribution from the modeling (right column) and the sequence of polar cap arc images (left column). The images starts at 2112 UT with a 2-min interval. The arc pattern consists of two arcs with an edge-to-edge spacing of about 90 km. By comparing the dynamic development of the observed arcs and the simulated arcs, the features are similar in some degree. This indicates that the physical processes proposed in the M–I coupling mechanism may be largely reasonable. In addition to the positive results from our modelobservation comparison studies, several theoretical predictions from the M–I coupling mechanism have been independently confirmed by observations. One is the predicted relationship between the spacing of the multiple polar cap arcs and the hardness of the precipitation shown in Fig. 10. Fig. 12 shows the statistical relationship between the average energy of the precipitation and the spacing of multiple polar cap arcs from the Akebono satellite precipitation data (Obara et al., 1996). Clearly, the variation trend shown in Fig. 12 is qualitatively consistent with the predicted relationship shown in Fig. 10.
5. Discussion and further improvements An alternative mechanism for the auroral structures on the order of 10s–100s km is proposed. In this mechanism, the active role of the ionosphere is stressed and the ionospheric spatial and temporal scales and the
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M–I coupling effect are put into account for the formation of the auroral structures. With the inclusion of the Alfve´n waves reflection at the ionosphere and the launching of the new Alfve´n waves caused by the temporal change of the ionospheric conductivity, the ionospheric electrodynamics of aurora structuring in the mechanism is fully self-consistent. The mechanism has been put into quantitative tests by using the means of the numerical simulations and model-observation comparisons and some of the theoretical predictions have been independently confirmed by observations. From its quantitative capability, the M–I coupling mechanism has made several interesting quantitative prediction on the features of auroral structures which have been and can be tested by observations. One example is the conjugate effect on the auroral structures. The mechanism predicts that if the conductance is too low, there will be no aurora, and when the conductance is too high, aurora is unlikely structured. Only when the ionospheric conductance is in a suitable range, the structured aurora could appear. By applying the M–I coupling mechanism to a simple model, this prediction can be further quantified with realistic ionospheric conditions in two hemispheres and the outcomes can be directly compared with conjugate observations. There are still several important improvements down the road for the M–I coupling mechanism. The first is the inclusion of the interaction between the Alfve´n waves and the field-aligned potential drop structures. This is especially important for the aurora structure development in the substorm onset regions, where the potential drop can reach the level of more than 10 kv. The interaction between the Alfve´n waves and the fieldaligned potential drop structure can bring in new spatial and temporal scales into the mechanism and will enable the mechanism to explain more complicated aurora structures associated with the substorms. The second is the inclusion of a dynamic interaction between the outward propagating Alfve´n waves and the magnetosphere. In the present mechanism, such an interaction is simplified by assuming the magnetospheric source regions are either a constant current source or a constant voltage source. The removal of this assumption in future will allow a more self-consistent M–I coupling and the assumed unlimited capability of the magnetospheric supply for accommodating the ionospheric request can be removed. In conclusion, the aurora structures on the scales of 10s–100s km and the associated electrodynamic processes are important for the ionospheric dynamics and to simulate them poses a challenge for the global MHD simulation (Watanabe and Sato, 1990; Walker et al., 1993; Raeder, 1994; Raeder et al., 2001). With its strengths of quantitative capability and emphasizing the active role of the ionosphere, the proposed M–I coupling mechanism will complement the other mechanisms for
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the auroral structures in a unique way and will greatly improve our understanding of the physical processes associated with auroral structures as well as the magnetosphere–ionosphere coupling.
Acknowledgements This research was supported by NASA Grant NAG511880, NSF Grants ATM9901927, ATM0000171, and DMS0413653 to Utah State University.
References Birn, J., Hesse, M., 1991. The substorm current wedge and field-aligned currents in MHD simulations of magnetotail reconnection. Journal of Geophysical Research 96, 1611–1618. Borovsky, J.E., 1993. Auroral arc thicknesses as predicted by various theories. Journal of Geophysical Research 98, 6101–6138. Calvert, W., 1987. Auroral precipitation caused by auroral kilometer radiation. Journal of Geophysical Research 92, 8792–8794. Goertz, C.K., 1985. Auroral arc formation: kinetic and MHD effects. Space Science Review 42, 499–513. Lotko, W., Schultz, C.G., 1988. Internal shear layers in auroral dynamics. In: Moore, T.E., Waite, J.H. (Eds.), Modeling Magnetospheric Plasma. American Geophysical Union. Lyatsky, W., Elphinstone, R.D., Pao, Q., Cogger, L.L., 1999. Field line resonance interference model for multiple arc generation. Journal of Geophysical Research 104, 263–268. Lyons, L.R., 1991. Discrete auroras and Magnetotail Processes. In: Meng, C.-I., Rycroft, M.J., Frank, L.A. (Eds.), Auroral Physics. Cambridge University Press, New York. Maggs, J.E., Davis, T.N., 1968. Measurements of the thicknesses of auroral structures. Planetary Space Science 16, 205. Marklund, G., Baumjohann, W., Sandahl, I., 1983. Rocket and ground-based study of an auroral breakup event. Planetary Space Science 31, 207–220. Mende, S.B., Frey, H.U., Geller, S.P., Doolittle, J.H., 1999. Multi-station observations of auroras: polar cap substorms. Journal of Geophysical Research 104, 2333–2342. Obara, T., et al., 1996. Multiple polar cap arcs: Akebono (EXOS D) observations. Radio Science 31, 645–654. Prakash, M., Rankin, R., 2001. Role of ionospheric effects and plasma sheet dynamics in the formation of auroral arcs. Space Science Reviews 95, 513. Raeder, J., 1994. Global MHD simulations of the dynamics of the magnetosphere: Weak and strong solar wind forcing. In: Kan, J.R., Craven, J.D., Akasofu, S.-I. (Eds.), Proceedings of the Second International Conference on Substorms. University of Alaska Press, Fairbanks.
Raeder, J., et al., 2001. Global simulation of the Geospace Environment Modeling substorm challenge event. Journal of Geophysical Research 106, 381–396. Rodriguez, J.V., Valladares, C.E., Fukui, K., Gallagher Jr., H.A., 1997. Antisunward decay of polar cap arcs, 102, 27227–27248. Rothwell, P.L., Silevitch, M.B., Block, L.P., Falthammar, C.G., 1991. Prebreakup arcs: a comparison between theory and experiment. Journal of Geophysical Research 96, 13967–13975. Samson, J.C., Cogger, L.L., Pao, Q., 1996. Observations of field line resonances, auroral arcs, and auroral vortex structures. Journal of Geophysical Research 101, 17373–17384. Siscoe, G.L., Lotko, W., Sonnerup, B.U., 1991. A high-latitude, low-latitude boundary layer model of the convection current system. Journal of Geophysical Research 96, 3487–3495. Smith, R.A., 1986. Effects of anomalous transport on the potentials of discrete auroral arcs. Geophysical Research Letters 5, 889–892. Streltsov, A.V., Lotko, W., 1999. Small-scale, ‘‘electrostatic’’ auroral structure and Alfve´n waves. Journal of Geophysical Research 104, 4411–4426. Streltsov, A.V., Lotko, W., 2004. Multiscale electrodynamics of the ionosphere–magnetosphere system, 109, A09214. Torbert, R.B., Carlson, C.W., 1980. Evidence for parallel electric field particle acceleration in the dayside auroral oval. Journal of Geophysical Research 85, 2909–2914. Trakhtengerts, V.Y., Feldstein, A.Y., 1991. Turbulent Alfve´n boundary layer in the polar ionosphere 1. Excitation conditions and energetics. Journal of Geophysical Research 96, 19363–19374. Valladares, C.E., Carlson, H.C., 1991. The electrodynamic, thermal, and energetic character of intense sun-aligned arcs in the polar cap. Journal of Geophysical Research 96, 1379–1400. Walker, R.J., Ogino, T., Raeder, J., Ashour-Abdalla, M., 1993. A global magnetohydrodynamic simulation of the magnetosphere when the interplanetary magnetic field is southward: the onset of magnetotail reconnection. Journal of Geophysical Research 98, 17235–17249. Watanabe, K., Sato, T., 1988. Self-excitation of auroral arcs in a three-dimensionally coupled magnetosphere–ionosphere system. Geophysical Research Letters 15, 717–720. Watanabe, K., Sato, T., 1990. Global simulation of the solar wind-magnetosphere interaction: the importance of its numerical validity. Journal of Geophysical Research 95, 75–88. Zhu, L., Sojka, J.J., Schunk, R.W., Crain, D.J., 1993. A timedependent model of polar cap arcs. Journal of Geophysical Research 98, 6139–6150. Zhu, L., Schunk, R.W., Sojka, J.J., 1997. Polar cap arcs: a review. Journal Atmospheric and Solar-Terrestrial Physics 59, 1087–1126. Zhu, H., Otto, A., Lummerzheim, D., Rees, M.H., Lanchester, B.S., 2001. Ionosphere–magnetosphere simulation of smallscale structure and dynamics. Journal of Geophysical Research 106, 1795–1806.
Journal of Atmospheric and Solar-Terrestrial Physics 67 (2005) 687–700 www.elsevier.com/locate/jastp
Active ionospheric role in small-scale aurora structuring L. Zhu, J.J. Sojka, R.W. Schunk Center for Atmospheric and Space Science, Utah State University, Logan, UT 84322-4405, USA Received 19 May 2003; received in revised form 22 November 2004; accepted 14 December 2004 Available online 17 March 2005
Abstract The auroral structures on the spatial scales of 10s–100s km and their associated electrodynamics are key elements in the magnetosphere–ionosphere (M–I) system and are important for ionospheric dynamics. The simulation of these auroras poses a challenge for global magnetohydrodynamic (MHD) M–I models. In this work, an M–I coupling mechanism for the formation of auroral structures on these spatial scales is proposed. In the M–I coupling mechanism, the active role of the ionosphere is taken into account and the auroral structures with spatial scales of 10s–100s km, which do not mirror the features of the magnetospheric drivers, self-consistently develop. The proposed mechanism includes the effects of the ionospheric spatial and temporal scales and the M–I coupling processes. By calculating the reflection of the Alfve´n waves at the ionosphere and the Alfve´n waves launched by the temporal variation of the ionospheric conductivity, the mechanism can provide time-dependent, quantitative information of all electrodynamic parameters associated with the dynamic evolution of structured auroras, including the field-aligned currents, ionospheric horizontal currents, convection field, conductivity, and Joule heating rate. The M–I coupling mechanism has been quantitatively tested and validated by using numerical simulations and model-observation comparisons. Some of the theoretical predictions have been independently confirmed by observations. With its strengths of (a) quantitative capability and (b) emphasize on the active role of the ionosphere, this M–I coupling mechanism complements other mechanisms for the auroral structures as well as the global MHD M–I modeling, thus improving our understanding of the auroral structures and the M–I coupling processes. r 2005 Elsevier Ltd. All rights reserved. Keywords: Auroral structure; Ionospheric electrodynamics; Substorm; Polar cap arcs; Numerical simulation
1. Introduction With the spatial resolution and sensitivity improvements of both ground-based optical measurements and satellite imagers, it has been found that many auroras that looked quite uniform in past observations actually have multiple structures and the brightness of these auroras vary dynamically in both space and time (Samson et al., 1996; Rodriguez et al., 1997; Zhu et Corresponding author.
E-mail address: [email protected] (L. Zhu).
al., 1997). The dynamic features associated with these auroral structures represent the dynamic nature of the physical processes in the magnetosphere and ionosphere as well as the interactions between them. The spatial scales of the auroral structures cover a wide range, which can be 10s–100s m for thin arcs, 10s–100 km for multiple polar cap arcs, and 100s km for the structured aurora brightness associated with substorm onset (Maggs and Davis, 1968; Torbert and Carlson, 1980; Marklund et al., 1983; Valladares and Carlson, 1991). Various mechanisms have been proposed for the formations of the auroras of various spatial scales (e.g.,
1364-6826/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.jastp.2004.12.004
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Goertz et al., 1985; Trakhtengerts and Feldstein, 1991; Calvert, 1987; Smith, 1986; Watanabe and Sato, 1988; Rothwell et al., 1991; Lyatsky et al., 1999; Streltsov and Lotko, 1999, 2004; Zhu et al., 2001; Prakash and Rankin, 2001). A comprehensive summary of these mechanisms as well as the comparisons between them has been done by Borovsky (1993). In this work, we propose an alternative mechanism, M–I coupling mechanism, for the auroral structuring on spatial scales from 10s to 100s km, especially those with multiple structures. The multiple structured auroras on these spatial scales are quite common in the polar cap as well as in the substorm onset regions (Valladares and Carlson, 1991; Samson et al., 1996; Mende et al., 1999). Fig. 1 shows an example of these multiply structured auroras. The unique feature of our proposed mechanism is the inclusion of the active role of the ionosphere in the M–I coupling processes for the formation of the multiple auroral structures and the ionospheric spatial and temporal scales are taken into account. With the inclusion of the Alfve´n waves reflection at the ionosphere and the launching of the Alfve´n waves caused by the temporal change of the ionospheric conductivity, the ionospheric electrodynamics of aurora structuring in the mechanism is fully self-consistent.
The paper is organized as follows. In Section 2, the proposed M–I coupling mechanism for the multiple auroral structure is described. Since the basic mathematical formation of the mechanism has appeared in a previous paper on the topic of polar cap arcs (Zhu et al., 1993), the description will focus on the physics of the mechanism. In addition, the relevant theoretical mechanisms are briefly reviewed and the differences between our mechanism and these mechanisms are identified. In Section 3, we describe how the mechanism was applied to the studies of the structures of substorm aurora and polar cap aurora. We show the quantitative numerical results and discuss the controlling parameters that determine the features of multiple auroral structures. The results of model-observation comparison and the observational confirmations of some of the predictions from this M–I coupling mechanism are presented in Section 4. Finally, a discussion on how to further improve and validate the M–I coupling mechanism is given in Section 5.
2. M–I coupling mechanism for multiple auroral structures In the M–I coupling mechanism for multiple auroral structures (it will be referred to as the M–I coupling
Fig. 1. An image of multiple polar cap arcs taken by the All-Sky Intensified Photometer at Qaanaaq at 0826 UT, November 12, 1990.
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mechanism later on), the electric fields and field-aligned currents associated with propagating Alfve´n waves are calculated from a set of working equations derived from the MHD equations. The enhancement of the ionospheric conductivity is calculated by using a fully timedependent electron continuity equation. The model also calculate the reflection of the Alfve´n waves at the ionosphere as well as the Alfve´n waves launched by the temporal variation of the conductivity in the ionosphere. For the details of the mathematical formulation, it is referred to one of our previous paper (Zhu et al., 1993). The initial driving force comes from the magnetosphere, which can be either relatively uniform large-scale enhanced convection occurred when the IMF turns southward or the small-scale shear convection caused by the various dynamical processes in the magnetosphere, which can take place for both the southward and northward IMF periods. But the dynamic features and characteristics of the resulted structured auroras that we discuss here (with spatial scales of 10s–100s km) are quite different from those of the initial magnetospheric drivers. They are not the simple mapping of these drivers. More importantly, the development of multiple auroral structures will not occur without the ionosphere playing a significant active role in the M–I coupling processes. Note this is a very important augmentation to the M–I coupling mechanism. For the situation where the large-scale magnetospheric convection is enhanced by the southward turning of the IMF, the propagation of the enhanced convection to the ionosphere along magnetic field lines is carried by Alfve´n waves and these Earthward propagating Alfve´n waves carry the field-aligned currents in accordance with the MHD theory. Since the enhanced large-scale convection is relatively uniform, the field-aligned currents associated with it is not very strong and may not directly cause the appearance of aurora. On the other hand, the conductivity in the ionosphere, especially those in the auroral oval is always non-uniform, which can be caused by solar radiation gradient, the ionosphere–thermosphere interaction, or the precipitation due to the loss cone effect that is not directly connected to the magnetospheric convection. These conductivity gradient intrinsic to the ionosphere can a play significant role in the formation of multiple auroral structures. For simplicity, let us assume the enhanced large-scale magnetospheric convection field is uniform. From the MHD theory, the Alfve´n waves associated with a uniform convection field do not carry any field-aligned currents. When this convection field maps to the ionosphere with a non-uniform conductivity, it can force the ionospheric horizontal currents to convert to field-aligned currents. This process can be seen clearly from the diagram in Fig. 2. The newly produced field-aligned currents are actually determined
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Fig. 2. A schematic diagram showing how a uniform magnetospheric convection mapping to the ionosphere can force the horizontal current to convert to the field-aligned currents when a conductivity gradient exists. The positive value of the divergence of horizontal current indicates the downward fieldaligned current.
by the reflection of the Earthward propagating Alfve´n waves at the non-uniform ionosphere in which the spatial scales of the ionospheric conductivity step in. When the reflected Alfve´n waves with the information of the field-aligned currents generated in the ionosphere reach the magnetosphere, it will draw down electrons to the ionosphere, disturb the magnetosphere, and cause new Alfve´n waves propagating toward to the ionosphere. Due to the M–I coupling process via Alfve´n waves, these new Alfve´n waves are significantly different from the initial magnetospheric Alfve´n waves. The convection field associated with these Alfve´n waves is not uniform anymore and structured field-aligned currents are now present. When these new Alfve´n waves reach the ionosphere, the precipitating electrons associated with the magnetospheric upward field-aligned can cause the enhancement of the conductivity. From Fig. 2, it can be seen that the enhanced conductivity caused by the precipitating electrons does not take the shape of the initial conductivity distribution in the ionosphere and they can be spatially dislocated. This leads to further structuring of the convection field associated with the reflected Alfve´n waves and more structures in the fieldaligned current distribution. When the Alfve´n waves propagate back and forth between the magnetosphere and ionosphere and the communication between the two regions (M–I coupling) goes on, the structuring of the aurora could become more and more complicated and eventually multiple structured aurora develop.
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There are two additional physical processes in this M–I coupling mechanism which would further complicate the aurora structuring. The first is the involvement of the Hall currents in the closure of the field-aligned currents. When the conductivity is non-uniform, The convection field associated with the reflected Alfve´n waves can be rotated, leading to a more complicated configuration of the ionospheric convection. The Hall currents are not divergent-free any more and they can be involved in the dynamic closure of the magnetospheric field-aligned currents in the ionosphere. Fig. 3 shows the numerical results of how the convection field of Alfve´n waves rotates due to the existence of conductance gradient. The convection field associated with the initial earthward propagating Alfve´n waves (or incident waves as indicated in the Fig. 3) only has an x component. When conductivity is uniform, there is no y component in the reflected wave field. When the conductivity gradient increases, it can be seen from Fig. 3 that the y component in the reflected waves start to appear and becomes larger. The appearance of the y component of the reflected waves is because that the Hall currents are closed to the field-aligned currents and the reflected wave field is forced to rotate to satisfy the current continuity. The rotation of the convection field and the closure of the Hall currents to the field-aligned currents will certainly make the aurora more structured and the cause of this complexity is again the conductivity gradient in the ionosphere. The second additional physical process that makes the aurora more structured is the Alfve´n waves launched by the temporal variation of the ionospheric conductivity. When the precipitating electrons brought down by the Alfve´n waves reach the ionosphere, they can cause enhancement of the ionospheric conductivity. The temporal change of the conductivity launches new Alfve´n waves, in addition to the directly reflected Alfve´n waves, toward the magnetosphere. Since these waves are caused by the temporal change of the ionospheric conductivity, they contain the temporal and spatial scales of the ionosphere and represent the active role of the ionosphere in the formation of the auroral structures 20
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and the associated M–I coupling processes. When these ionosphere-originated Alfve´n waves join the incident and reflected Alfve´n waves and interact with the magnetosphere and the ionosphere by bouncing back and forth between the two regions, the structure of the aurora is further complicated. The initial magnetospheric driver for the formation of multiple auroral structures in this mechanism is not necessarily the enhanced large-scale convection and it can also be the small-scale shear convection generated by various physical processes in the magnetosphere. The small-scale shear carries field-aligned currents and the precipitation associated with the upward currents can cause the initial conductivity gradient in the ionosphere, which is needed in our mechanism for the formation of the multiple auroral structures. For the situation when the ionospheric background conductivity is not uniform, this conductivity enhancement caused by the precipitation associated with the small-scale shear magnetospheric convection may cause further complexity of the auroral structures. For the situation when the ionospheric background conductivity is quite uniform, this conductivity enhancement makes the appearance of structured aurora possible. A typical example is the multiple polar cap arcs. In the polar cap, the ionospheric conductivity is quite uniform. Based on the mechanism described in the above, a relatively uniform enhanced large-scale convection will not be able to cause the appearance of aurora when the ionospheric background conductivity is quite uniform. This explains why the enhanced large-scale convection in the polar cap when the IMF turns southward does not help with the appearance of polar cap arcs. There have been several other mechanisms proposed for the aurora on the spatial scales of 10s–100s km we are discussing here. These include the mechanisms of electrostatic mapping (Goertz, 1985), shear in lowlatitude boundary layer (Siscoe et al., 1991), shear in plasma sheet (Birn and Hesse, 1991), ionosphericconductivity feedback instability (Watanabe and Sato, 1988), Earthward ion streams (Lyons, 1991), and electrostatic fluid turbulence (Lotko and Schultz, 1988). Most of these mechanisms treat the ionosphere as a passive load. The magnetospheric drivers are simply mapped to the ionosphere and the features of the resulted auroras just mirror those of the magnetospheric drivers. The only exception is the mechanism of the ionospheric-conductivity feedback instability, in which the ionospheric condition is taken into account for the formation of aurora. Since our mechanism emphasizes the active role of the ionosphere and the M–I coupling effect, in the following, we will specially discuss the differences between the M–I coupling mechanism and the feedback instability mechanism. The ionospheric-conductivity feedback mechanism starts with a uniformly enhanced conductivity patch,
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which causes the appearance of polarization electric field. To depolarize this field, the field-aligned currents develop and they need to be closed at the magnetospheric end. The closure of these depolarization fieldaligned currents at the magnetosphere can bring precipitating electrons to the ionosphere and further enhance the conductivity patch. This is a positive feedback process which eventually leads to the fieldaligned current that are strong enough to cause the appearance of aurora. There are several fundamental differences between the M–I coupling mechanism and the conductivity feedback instability mechanism. (1) In the M–I coupling mechanism, the conductivity gradient plays a major role in the formation of auroral structure and this brings the ionospheric spatial and temporal scales into the M–I coupling process. The feedback mechanism always assume a uniform conductivity and the effect of conductivity gradient is never taken into account. (2) The M–I mechanism can explain how the multiple auroral structures develop, but the feedback mechanism can only be applied to the situation of single arc. (3) In the M–I mechanism, a significant amount of fieldaligned currents can be converted to the Hall currents. This is especially important for the substorm process, since the westward electrojet is mainly the Hall current. The ionospheric current closure in the feedback mechanism is always just between the Pedersen currents and field-aligned currents. (4) The ionospheric electrodynamics in the M–I coupling mechanism is fully selfconsistent which involves the reflection of the Alfve´n waves and the launching of the new Alfve´n waves caused by the temporal variation of the ionospheric conductivity. The feedback mechanism uses electrostatic way to handle the electrodynamics of aurora in the ionosphere. In addition to these fundamental differences between the two mechanisms, the M–I coupling mechanism has been quantitatively tested by the numerical simulations and model-observation comparisons and some of the theoretical predictions have been independently confirmed by observations, which will be presented in the following sections.
3. Numerical simulation results From the above discussion, it can be seen that the proposed M–I coupling mechanism uses the Alfve´n wave treatment instead of simple mapping. It also takes into account the effects of the spatial and temporal variations of the ionospheric conductivity and the M–I coupling, and includes electrodynamic processes of the reflection of Alfve´n waves and the launching of the Alfve´n waves of ionospheric origin. Therefore, the active role of the ionosphere for the formation of the structured auroras is included in the mechanism and
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all the electrodynamic parameters are self-consistent. On one hand, this makes the M–I mechanism physically reasonable, thus being able to explain a wide range of variations of the aurora structures. On the other hand, it leads to mathematical complexity and hence the difficulty of performing analytical analysis. In the following, we describe how the mechanism was applied to the studies of the structures of substorm aurora and polar cap aurora. We will show quantitative numerical results and discuss the controlling parameters that determine the features of multiple aurora structures. 3.1. Structured aurora in the auroral oval during substorms 3.1.1. Brief model description and the initial model inputs In this numerical modeling, the initial magnetospheric driver is the enhanced global magnetospheric convection that is driven by enhanced reconnection at the dayside magnetopause due to a southward turning of the IMF. The ionospheric domain of the substorm modeling covers the magnetic latitudes greater than 501 in the northern hemisphere. Initially, the quiet-time (pre-substorm) ionospheric background conditions for the model were calculated by running the model for a sufficiently long time to reach the asymptotic state. The ionospheric conductance, convection, and precipitation patterns that were obtained in this way are physically self-consistent and are shown in Figs. 4a–c, respectively. It can be seen that the background ionospheric conductivity is not uniform and has a large gradient in the north–south direction. In the simulation, the quiet-time (pre-substorm) period is the period earlier than 1200 UT. The substorm growth phase started at t ¼ 0 min (1200 UT), which is when the Alfve´n waves associated with the enhanced magnetospheric convection that was initiated at the dayside magnetopause reached the ionosphere. A two-cell convection pattern with a polar cap potential drop of about 73 kV (shown in Fig. 4d) was adopted for such an enhanced convection carried by the Alfve´n waves. It needs to be noted that this largescale convection driver does not have the small-scale structures that appear later in the resulting aurora. These global-scale Alfve´n waves were the driving forces for the growth phase dynamics in the ionosphere, which lasted about 24 min. Note that since the ionospheric conductivity is finite and anisotropic, such magnetospheric-enhanced convection cannot be fully loaded on the ionosphere and can also be distorted. The enhanced convection actually loaded on the ionosphere at t ¼ 0 min (1200 UT), which is different from the convection pattern shown in Fig. 4d, is self-consistently determined in the simulation by calculating the reflected Alfve´n waves at the ionosphere. The reflected Alfve´n waves and the new Alfve´n waves launched by the temporal change of the ionospheric conductivity then propagate outward
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Fig. 4. Quiet-time (presubstorm) distributions of the (a) ionospheric Hall conductance, (b) electric potential, and (c) characteristic energy of precipitation. Fig. 4d shows the enhanced magnetospheric convection initiated by the reconnection at the dayside magnetopause.
and interact with the magnetosphere. To simplify the simulation, we assume the magnetospheric source region is a perfect current source, thus allowing us to use a reflection coefficient to represent the Alfve´n wave interaction with the magnetosphere. While the Alfve´n waves propagate back and forth between the magnetosphere and ionosphere, the numerical simulation continued until t ¼ 35 min (1235 UT), which is when the substorm reached the expansion maximum. In the simulation, various electrodynamical parameters were calculated, including convection, precipitation (energy flux and characteristic energy), field-aligned and horizontal currents, Hall and Pedersen conductances, and Joule heating rates. All these physical parameters are time-varying, with a resolution of 5 s, and are physically self-consistent. 3.1.2. Resulted aurora structures Fig. 5 shows snapshots of the global distributions of the energy flux of precipitating electrons, the magnitude
of the electric field, and the Hall conductance at various times. The growth phase of the substorm started at t ¼ 0 min (1200 UT) and the expansion phase started at around t ¼ 24 min (1224 UT). The expansion maximum was achieved at around t ¼ 35 min (1235 UT). It can be seen clearly from Fig. 5 that energy flux, electric field, and Hall conductance are all highly structured around the onset region and these structures do not exist in either the background ionosphere or the initial magnetospheric convection driver. Fig. 6 shows the temporal variations of the energy flux in the substorm onset region (1800–0200 MLT, 55–851 magnetic latitude). The snapshots start at 1200 UT (the beginning of the growth phase) and end at 1235 UT (the expansion maximum) with a 5 min interval. Before the substorm starts, there is a well-defined precipitation band stretching in the east–west direction with the center at about 671. This quiet-time precipitation is the diffuse aurora precipitation and corresponds to the quiet-time auroral oval. When the substorm starts, the auroral oval
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Fig. 5. Snapshots of distributions of the energy flux (left column), the magnitude of electric field (middle column), and the Hall conductance (right column).
gradually expands poleward during the growth phase. After the substorm onset (around 1224 UT), structured precipitation quickly develops in the localized region around 751 and 21 MLT, where the substorm aurora breaks up and the bulge-like aurora forms. The developed substorm aurora is highly structured, which corresponds to the channeled precipitation. In the
aurora break-up region, the energy flux increases from the quiet-time level of less than 0.3 to about 1 erg/cm2/s at the end of the growth phase, then quickly reaches 7 erg/cm2/s at the expansion maximum. Correspondingly, the maximum values of the characteristic energy in this region changes from 0.5 keV (1200 UT) to 1.8 keV (1224 UT), and then to 7 keV (1235 UT).
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Fig. 6. Temporal variation of the energy flux in the substorm onset region.
These results strongly support the proposed M–I coupling mechanism for auroral structures from the numerical simulation aspect and clearly indicate that the ionosphere can play an important role in the formation of the auroral structures. 3.2. Structured aurora in the polar cap To further test the proposed mechanism for the auroral structures, we have also applied the theory to the studies of the multiple polar cap arcs. 3.2.1. Brief model description and initial model inputs As discussed in the above, the conductivity in the polar cap is quite uniform and the enhanced large-scale convection caused by the southward turning of the IMF is unlikely to cause the appearance of polar cap arcs. For this reason, we adopted a magnetospheric shear convection as the initial magnetospheric driver for the numerical simulation. The ionospheric simulation domain is 3000 km long in X (midnight–noon) direction, and 1000 km wide in Y (dawn–dusk) direction. The grid size is 30 km in X direction, and 10 km in Y direction. The third dimension along the magnetic field lines is a pseudo-dimension which merely serves to provide the Alfve´n wave traveling time scale. Since the magnetic field lines in the polar cap are mainly connected to the open-field line region, we can then simplify the magnetospheric source region as a constant voltage source, thus again we can use a reflection coefficient to simplify the Alfve´n waves interaction with the magnetosphere. Fig. 7 shows the ionospheric background conditions and the initial perturbation of the magnetosphereoriginated shear flow carried by downward propagating Alfve´n waves. The top panel of Fig. 7 shows the Hall conductance distribution in the noon–midnight crosssection. In the dawn–dusk direction, we assume the Hall
conductance to be uniform. This background ionospheric conductance is merely due to the solar contribution, and for simplicity, we assume it decreases linearly towards the nightside. The actual noon–midnight spatial gradient of the background conductivity varies widely with the variations of the season and F10.7 conditions. The initial magnetospheric shear flow carried by the propagating Alfve´n waves in our modeling is represented by a potential in Gaussian distribution as shown by the solid line in the bottom panel of Fig. 7. The shear flow is uniform in the noon–midnight direction. The corresponding electric field distribution, which is convergent in the center and divergent on the edges of the shear flow, is shown by the dashed line in the bottom panel of Fig. 7. 3.2.2. Resulted multiple polar cap arcs 3.2.2.1. Development of multiple polar cap arcs:. The initial shear flow carried by Alfve´n waves arrives in ionosphere at t ¼ 0 min; which leads to the bouncing of Alfve´n waves between the magnetosphere and ionosphere and the development of polar cap arcs. As long as the external environment of the coupled M–I system remains unchanged, the bouncing Alfve´n waves eventually will be damped by the finite ionospheric conductance and the development of polar cap arcs will approach an asymptotic steady state. In this case, such a steady state of polar cap arcs is achieved in about 8–10 min. Fig. 8 shows the field-aligned current distribution at the asymptotic stage, in which dashed lines denote upward field-aligned currents and solid lines denote downward field-aligned currents. Note that only a portion of the simulation domain is shown in this figure, in order to display the detailed structures associated with polar cap arcs. It can be seen from Fig. 8 that in the self-consistent development of a polar cap arc, a single peak precipitation associated with the
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Fig. 7. Polar cap ionospheric background conductance (top) and the initial magnetospheric shear flow (bottom).
initial magnetospheric shear flow has been split into multiple peaks, leading to multiple structures of the polar cap arcs. The individual arcs are about 30–40 km wide and are separated by a narrow downward current region. This results clearly shows an important point that the observed multiple polar cap arcs do not have to be the results of the multiple structures in the magnetospheric source region, instead, such a multiple feature is generated in the M–I coupling processes in which the ionosphere plays an active role. Such a point can be seen more clearly from the comparison of the field-aligned profiles shown in the mid- and bottom panels in Fig. 8, where the field-aligned current associated with the initial magnetospheric shear convection (middle panel) and that associated with the developed arcs (bottom panel) are presented. 3.2.2.2. How the ionosphere and M–I coupling determine the aurora structures:. To improve our understanding
of the M–I coupling mechanism, in the polar cap arc study, we used the numerical simulation to study how the ionospheric conditions and M–I coupling processes affect the features of the structured aurora. First of all, we found that the magnitude of the ionospheric background convection field can significantly affect the multiplicity of the structured polar cap arcs. The results in Fig. 9 show that when the magnitude of the ionospheric background convection increases, more and more structures of the polar cap arcs developed. Second, we found that the intensity of the ionospheric conductivity also has significant effect on the features of polar cap arc structures (results not shown here). When the background conductance is too low, the polar cap arcs hardly develop in the polar cap. This is because the ionosphere has a very large resistivity and the magnetospheric currents cannot be dynamically closed in the ionosphere. When the
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Fig. 8. Field-aligned current distribution associated with a well developed polar cap arcs (top), cross-section profile of the field-aligned currents associated with the initial magnetospheric driver (middle), and cross-section profile of the field-aligned currents associated with the developed polar cap arcs (bottom).
conductance is too high, there is no structured arc and only a bright single sun-aligned arc exists. This can be explained by the fact that the high ionospheric conductance allows the magnetospheric currents to be freely closed in the ionosphere, which acts to smooth localized discrete structures. Only when the conductance is in the middle range (0.5–1.5 mho for our specific model runs, which are for winter and solar maximum conditions), can the multiple polar cap arcs develop.
Third, we found that the spacing of the polar cap arcs structures is closely related to the hardness of the precipitation, which is determined by the M–I coupling processes. A quantitative relationship between the spacing of the multiple polar cap arcs and the Hall–Pedersen conductance ratio, which reflect the hardness of the precipitation, is obtained from our numerical modeling and is shown in Fig. 10. It indicates that polar cap arcs with wider spacing are associated with harder precipitation.
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Fig. 9. Field-aligned currents associated with the polar cap arcs for six different ionospheric background convection field strengths.
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Fig. 10. Predicted relationship between the spacing of multiple polar cap arcs and the conductance ratio. Curve A is for the edge-to-edge spacing and curve B is for the peak-to-peak spacing.
To test and validate the M–I coupling mechanism, we performed some preliminary model-observation comparison studies. The observational data we used for the model-observation comparison study were the image data from the All-Sky Intensified Photometer at Qaanaaq during the months of November and December of 1990. We used the ionospheric conditions that are in overall agreement to those when the multiple arcs were observed to start the numerical runs and then compared the dynamic developments of the observed polar cap arcs and the simulated ones. Fig. 11 shows one example from these runs. The observed polar cap arcs occurred on December 11, 1990 in the evening sector of the dark polar cap. It started from a single arc, then gradually developed into a multiple arcs. The time period we are interested in is from 2112 to 2118 UT. The IMF turned northward at about 1800 UT and remained northward until 0030 UT
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Fig. 11. The comparison between the observed multiple polar cap arcs and the simulated arcs.
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Fig. 12. Statistical relationship between the average energy of the precipitation and the spacing of multiple polar cap arcs from the Akebono satellite precipitation data (Obara et al., 1996).
of the next day. During the period we are interested in, the Bz was 5 nT and By was 1:5 nT; and Kp was 1. The simulation for this case started at 2108 UT, which is the time when the assumed downward propagating Alfve´n wave hit the ionosphere. Fig. 11 shows snapshots of the evolution of the field-aligned current distribution from the modeling (right column) and the sequence of polar cap arc images (left column). The images starts at 2112 UT with a 2-min interval. The arc pattern consists of two arcs with an edge-to-edge spacing of about 90 km. By comparing the dynamic development of the observed arcs and the simulated arcs, the features are similar in some degree. This indicates that the physical processes proposed in the M–I coupling mechanism may be largely reasonable. In addition to the positive results from our modelobservation comparison studies, several theoretical predictions from the M–I coupling mechanism have been independently confirmed by observations. One is the predicted relationship between the spacing of the multiple polar cap arcs and the hardness of the precipitation shown in Fig. 10. Fig. 12 shows the statistical relationship between the average energy of the precipitation and the spacing of multiple polar cap arcs from the Akebono satellite precipitation data (Obara et al., 1996). Clearly, the variation trend shown in Fig. 12 is qualitatively consistent with the predicted relationship shown in Fig. 10.
5. Discussion and further improvements An alternative mechanism for the auroral structures on the order of 10s–100s km is proposed. In this mechanism, the active role of the ionosphere is stressed and the ionospheric spatial and temporal scales and the
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M–I coupling effect are put into account for the formation of the auroral structures. With the inclusion of the Alfve´n waves reflection at the ionosphere and the launching of the new Alfve´n waves caused by the temporal change of the ionospheric conductivity, the ionospheric electrodynamics of aurora structuring in the mechanism is fully self-consistent. The mechanism has been put into quantitative tests by using the means of the numerical simulations and model-observation comparisons and some of the theoretical predictions have been independently confirmed by observations. From its quantitative capability, the M–I coupling mechanism has made several interesting quantitative prediction on the features of auroral structures which have been and can be tested by observations. One example is the conjugate effect on the auroral structures. The mechanism predicts that if the conductance is too low, there will be no aurora, and when the conductance is too high, aurora is unlikely structured. Only when the ionospheric conductance is in a suitable range, the structured aurora could appear. By applying the M–I coupling mechanism to a simple model, this prediction can be further quantified with realistic ionospheric conditions in two hemispheres and the outcomes can be directly compared with conjugate observations. There are still several important improvements down the road for the M–I coupling mechanism. The first is the inclusion of the interaction between the Alfve´n waves and the field-aligned potential drop structures. This is especially important for the aurora structure development in the substorm onset regions, where the potential drop can reach the level of more than 10 kv. The interaction between the Alfve´n waves and the fieldaligned potential drop structure can bring in new spatial and temporal scales into the mechanism and will enable the mechanism to explain more complicated aurora structures associated with the substorms. The second is the inclusion of a dynamic interaction between the outward propagating Alfve´n waves and the magnetosphere. In the present mechanism, such an interaction is simplified by assuming the magnetospheric source regions are either a constant current source or a constant voltage source. The removal of this assumption in future will allow a more self-consistent M–I coupling and the assumed unlimited capability of the magnetospheric supply for accommodating the ionospheric request can be removed. In conclusion, the aurora structures on the scales of 10s–100s km and the associated electrodynamic processes are important for the ionospheric dynamics and to simulate them poses a challenge for the global MHD simulation (Watanabe and Sato, 1990; Walker et al., 1993; Raeder, 1994; Raeder et al., 2001). With its strengths of quantitative capability and emphasizing the active role of the ionosphere, the proposed M–I coupling mechanism will complement the other mechanisms for
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the auroral structures in a unique way and will greatly improve our understanding of the physical processes associated with auroral structures as well as the magnetosphere–ionosphere coupling.
Acknowledgements This research was supported by NASA Grant NAG511880, NSF Grants ATM9901927, ATM0000171, and DMS0413653 to Utah State University.
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