Matthew Fillingim
GPHYS 523
Final Paper
In the interests of brevity and conciseness, this paper will focus on the nature of the comet-solar wind interactions (mainly through solar wind mass loading) and the resulting manifestations on the dayside of the comets, i.e., on the side of the comet facing the Sun, excluding any discussion of the nightside features such as the cometary dust and ion tails. Nightside comet-solar wind interactions are interesting in their own right, and extensive work has also been done in this area. After a brief discussion of some of the large scale structures observed on the dayside of comets, the concept of mass loading will be introduced. The formation of cometary bow shocks as a direct result of mass loading will be addressed. Finally, the evolution of the plasma distribution function as a function of distance from the comet nucleus as a result of continued mass loading and plasma instabilities will be discussed.
The bow shock is the region where the solar wind flow changes from supersonic to subsonic in the frame of the comet. For a typical comet with a radius of a few kilometers, this occurs at a few 105 to 106 km from the nucleus, depending upon proximity to the Sun and solar wind conditions [Gringauz and Verigin, 1991]. As will be discussed later, the formation of the shock is due to mass loading of the solar wind rather than deflection of the solar wind by a solid object.
Closer to the nucleus, the cometopause (sometimes referred to as cometpause or collisionopause) marks the location of a composition transition region. At this boundary, the plasma composition changes from mostly solar wind in origin to mostly cometary ions. One reason for this composition change is the increased rate of charge transfer collisions between solar wind protons and neutral cometary atoms and molecules due to increased neutral number denisty [Cravens, 1991]. This region occurs at roughly 105 km from the nucleus.
The contact surface is the pressure balance boundary, analogous to the magnetopause at Earth or the ionopause at Venus. To first order, this boundary is formed by the balance between the ram presssure of the solar wind (nmv2) and the ram pressure of the outflowing ions of cometary origin [Luhmann, 1995a]. Inside this boundary, the magnitude of the magnetic field goes to zero. This cavity typically has a radius of a few thousand kilometers.
Far from the comet, millions of kilometers from the nucleus, mass loading is present but does not have a large effect on the solar wind since the mass is being added slowly. As the solar wind approaches the comet, mass loading and its effects begin to play a major role in determining the features of the comet-solar wind interaction. The ion production rate in the cometary atmosphere as a function of distance from the nucleus can be derived following the same steps used to derive Chapman layers in ionospheres [Luhmann, 1995b], except that in the case of the comet, the atmospheric denstiy drops off as 1/r2 instead of exponentially, as is the case for atmospheres in hydrostatic equilibrium.
Here, the ion production rate is the product of the 1/r2 fall off in neutral number density with height and the exponential increase in ionizing solar radiation with height.
As can be seen, the ion production rate rises as 1/r2 at large distances. Closer to the comet, the effect of the attenuation of ionizing radiation becomes more noticable, decreasing the ionization rate as compared to the 1/r2 increase. However, neglected in this simple derivation are the effects of charge exchange which also becomes important near the comet, at the cometopause. Charge transfer collisions would increase the ionization rate near the comet as compared to the simple calculation shown here. It is this rapid increase in the number of cometary ions that can cause a cometary bow shock to form.
The angle between the solar wind velocity vector and the interplanetary magnetic field (the cone angle), greatly influences how cometary ions are picked up. At large cone angles (~90o), there is a motional electric field in the solar wind equal to E = -v x B. When a cometary molecule or atom becomes ionized, it senses this electric field. (Outflowing cometary neutrals have a velocity negligible compared to the solar wind; ~1 km/s compared to ~400 km/s.) The cometary ion is accelerated by this electric field, resulting in a transfer of momentum from the solar wind to the cometary ion through large scale fields. Numerical simulations [Omidi and Winske, 1991] show the efficient slowing of the solar wind in this case forming a sharp shock with the dissipation length scaling with the ion inertial length.
For small cone angles (~0o), the electric field is very small. Once ionized, cometary ions stream through the solar wind at a velocity of -vSW relative to the ambient plasma. Coupling between the solar wind and the cometary ions must take place through microscopic electromagnetic fields generated by plasma instabilites With this geometry, simulations [Omidi and Winske, 1987; Omidi and Winske, 1991] indicate that the shock consists of large amplitude electromagnetic waves generated by the ion beam instability.
At intermediate cone angles, numerical simulations by Omidi and Winske [1991] show that the plasma number density and solar wind magnetic field gradually increase due to mass loading far from the comet. Closer to the comet, there appear to be several large amplitude fluctuations in the number density and magnetic field, but no discontinuity that can be identified as a shock transition. Additionally, these large amplitude fluctuations, which are caused by electromagenic waves generated by the microscopic interactions between the solar wind and the cometary ions, are not stationary with respect to the comet, but convect toward it. Each one of these large amplitude fluctuations slow and thermalize the solar wind plasma and were termed "shocklets." Since these shocklets are slowly convecting toward the comet, plasma downstream of a shocklet is subsonic in the frame of the shocklet, but not necessarily subsonic in the frame of the comet. This suggests that a parcel of solar wind plasma may go through a number of these shocklets before it becomes subsonic in the frame of the comet. Data from comet Giacobini-Zinner [Thomsen et al., 1986] had many similarities with the model output from this intermediate cone angle case, and the observations seemed to be adequately explained using this model.
This ring-beam distribution, however, because of its positive slope, is highly unstable to the growth of low frequency electromagnetic waves. The magnetic fluctuations result in rapid pitch angle scattering of the cometary ions. The initial ring-beam distribution, then, evolves into a shell distribution with a radius in velocity space equal to the local solar wind speed. Picked up cometary ions have energies of 1/2 m vSW2 ~ 15 keV in the solar wind frame. In the spacecraft frame, a picked up ion will have both zero velocity and twice the solar wind velocity during its motion. Therefore, energetic particle detectors measure cometary ions with energies up to 60 keV [Tsurutani, 1991]. The ions also undergo energy diffusion due to scattering by waves moving along the field. The shell distribution thus becomes thicker and more diffuse. The shell also becomes thicker due to the slowing down of the solar wind by the mass loading resulting from the addition of cometary ions [Cravens, 1991].
Once the solar wind crosses the bow shock and undergoes abrupt slowing, cometary ions picked up downstream are much less energetic, with respect to the ambient plasma, than those picked up upstream. A second and lower energy shell begins to form in the ion distribution function [Galeev et al., 1985]. This shell also undergoes thickening due to both wave-particle interactions and the further slowing of the flow.
Both the neutral and plasma number densities become larger as the shocked and mass loaded solar wind approaches the nucleus, and collisional processes start to become important near the cometopause. The charge exchange process is particularly important and removes the hotter ions from the flow, but leaves the distribution as a shell distribution. Very close to the nucleus, however, Coulomb collisions transform the distributuion function into a Maxwellian [Cravens, 1991].
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