1. Institute of Geophysics and Planetary Physics, University of California, Los Angeles, CA 90024, U.S.A.
2. Naval Research Laboratory, Washington, D. C. 20375, U.S.A.
Three dimensional MHD simulations have been performed for four different sets of solar wind conditions and cometary outgassing rates appropriate to the Halley encounters. Even though the simulations are single fluid calculations, it is possible to separate the solar wind and cometary ions using the divergenceless nature of the solar wind ions. We then integrate the cometary ion density along the line-of-sight from the observer through the comet to determine how the comet would look to a distant observer under these different conditions. In general comet tails appear longer when the interplanetary magnetic field lies in the plane of the sky rather than along the line-of- sight. Also the tail shrinks as the speed of the solar wind increases and/or the mass loading rate decreases.
In-situ observations are now available from two comets; Halley and Giacobini-Zinner, but while these data are extremely valuable they are also limited. For example, although Halley was visited by several spacecraft over a period of a week, the solar wind conditions and cometary outgassing rate varied little over this period compared with the range of conditions encountered as comets approach and recede from the sun. Furthermore, the sampling has been limited in terms of spatial coverage. Thus there still is an important role for MHD simulations.
While MHD codes do not simulate all of the physical and chemical processes occurring in a comet, they do reproduce the deceleration of the solar wind, the pile up of the magnetic field and the subsequent acceleration of the cometary plasma. It is the purpose of this paper to examine one such MHD simulation as a function of varying cometary and solar wind parameters to determine what parameters control the visual appearance of a comet. The simulation results used will be from a time-dependent model but at a time by which it had achieved steady-state conditions. Nevertheless, these simulations should provide clues as to the possible causes of apparently dynamic phenomena which are actually transitions from one steady-state to another. These simulations should be an aid to cometary researchers in determining what parameters to examine in studying the observed behavior of comets Halley and Giacobini-Zinner.
The 3-D MHD simulation was developed at the Naval Research Laboratory /l/. The comet is taken to be a spherically symmetric outgassing body, releasing gas of atomic weight 20 amu. which expands at 1 km/sec. The ionization rate is taken to be 10-6 s-1 and is due solely to photoionization. The equations of continuity, momentum, and pressure and Faraday's, Ampere's, and Ohm's laws are solved with a partial donor cell method on a mash of dimension 33 x 29 x 29 extending 2.4 x 106 km upstream, 7.6 x 106 km downstream and 1.2 x 106 km in each of the other four directions from the nucleus. The interplanetary magnetic field is taken to be perpendicular to the solar wind.
In order to determine how the comet should appear visually, we must first separate the solar wind ions from the cometary ions and then integrate the number of cometary ions along the line-of-sight. To separate the solar wind ions we note that the solar wind mass flux is divergenceless, i.e.,
This can be determined from the MHD solution by taking the numerical divergence appropriate for the Partial Donor Cell method used in the computations:
where S is the area of the face of a cube in the computational grid and a denotes the direction of each component or operator in the Cartesian grid. This equation is used to determine the downstream value of the mass flux from the previous upstream value, thus allowing the determination of the mass flux added by the comet (which is not divergenceless).
The favorable comparison between the calculated magnetic field profile and that observed by the VEGA spacecraft /2,3/ gives us confidence in the model's applicability. The observed magnetic field profile differs significantly from the predicted profile only close to the nucleus where the distance to the nucleus approaches the grid spacing of the simulation. The simulation also predicts convection times similar to those observed /3/.
Below we examine four simulation runs: normal, slow and fast solar wind under GIOTTO encounter mass-loading conditions and for normal solar wind under VEGA encounters mass- loading conditions. The parameters used are shown in Table 1.
|Fig. 1. Magnetic field lines in the plane containing the nucleus for slow solar wind (top panel), normal solar wind (upper middle panel), fast solar wind (lower middle panel) all for a mass- loading rate of 0.6 x 1030 molecules s-1 and normal solar wind for a mass-loading rate of 1.3 x 1030 molecules s-1 (bottom panel).|
Figure 1 shows the magnetic field lines in the plane containing the solar wind flow, the upstream magnetic field, and the cometary nucleus for our four runs. The spacing of field lines is proportional to the square root of the magnetic field strength along the sun-comet line. Hence the field lines are not isochrons. We see that the draping is stronger for the faster flowing solar wind. The higher mass loading rate makes a wider tail containing more magnetic flux.
The integrated density of cometary ions has been calculated along the line-of-sight for two orientations of the interplanetary magnetic field and the observer at infinity perpendicular to the solar wind flow. In the top panel of each display the magnetic field is perpendicular to the line-of-sight, and in the bottom panel along it. Thus in the top panel the observer is looking along the thickest part of the ion tail and in the lower panel across the thinnest part of the sheet. Figure 2 shows contour plots for the normal solar wind case. As one would expect the tail visually extends further from the comet when the magnetic field is perpendicular to the line-of-sight than when it is along it. Thus simple rotations of the IMF about the solar wind flow vector can cause the cometary ion tail to appear to lengthen or shorten without any real change in the comet.
|Fig. 2. Line-of-sight integration of the cometary ion density for normal solar wind conditions and a mass-loading rate of 0.6 x 1030 molecules -s-1. The top panel shows the integrated density projected onto the plane containing the interplanetary magnetic field. The bottom panel shows the projection onto the orthogonal plane.|
|Fig. 3. Line-of-sight integrated densities for fast solar wind and mass-loading rate of 0.6 x 1030 molecules s-1. Integrated densities are given in units of 1010 ions cm-2.|
Figure 3 shows the analogous displays for the fast solar wind. Here the difference between the two orthogonal views is less because the ion sheet is not so ribbon-like. The ion tail, perhaps counter- intuitively is shorter. This occurs because the fast solar wind carries cometary ions away faster so that the density does not build up to as high a value. Figure 4 shows the integrated cometary ion density for the slow solar wind. As expected from the comparison of the normal and fast solar wind cases, the slow solar wind causes a much longer visible tail because the ion density builds up to higher values when the flow is slower. Since the ion sheet here is thin and ribbon-like the difference in the orthogonal views is quite marked. Figure 5 shows the integrated cometary ion density for the higher mass-loading rate appropriate to the VEGA encounters. The difference in the two views is again quite marked even more so than at lower mass-loading rates. In comparison with the slow solar wind case, the tail is longer when viewed orthogonal to the magnetic field and shorter when viewed along it. Closer to the nucleus we find that the cometary ion density is greater at all orientations of the field for this higher mass-loading rate and extends further upstream.
|Fig. 4. Line-of-sight integrated densities for slow solar wind conditions and a mass- loading rate of 0.6 x 1030 molecules s-1.|
|Fig. 5. Line-of-sight integrated densities for normal solar wind conditions and a mass- loading rate of 1.3 x 1030 molecules s-1.|
The cometary magnetic tail and its ion tail are not coincident. The greatest ion density lies at the sharp kink in the magnetic field and extends in a ribbon whose thinnest dimension is in the vertical direction in Figure 1 and whose width is in the direction into the page. Thus, the integrated density along the line-of-sight will vary depending on whether the observer is sighting along the thickest or thinnest dimension of the ion tail.
Computer simulations complement in situ observations even if they do not duplicate all the physical processes occurring at comets because they allow the entire volume around a comet to be probed and because they permit parametric studies to be undertaken. Our studies with the NRL 3-D MHD model show that comets are very sensitive to solar wind conditions and mass- loading rates. Long tails occur when the solar wind is slow or when the outgassing rate is high. Thus, the simulations help us to see how the comets appearance is affected by both solar wind variability and changes in outgassing rate. Moreover because comets are not cylindrically symmetric their visual appearance changes as one's point of view rotates from along the magnetic field component perpendicular to the flow to along it. When one sights along the magnetic field the integrated cometary ion density is a minimum and the tail appears shortest. So the models show us that, in combination, varying solar wind conditions, interplanetary field orientation, and outgassing rates can produce many changes in a comet's appearance without the need for exotic processes and instabilities.
This research was supported by the National Aeronautics and Space Administration under research contract NAGW-717.
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