**A Study of Plasma Phenomena Using the Tomographic 3-Dimensional
Reconstruction Techniques Developed for the**

**Solar Mass Ejection Imager (SMEI)**

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B.V. Jackson, P.P. Hick

Center for Astrophysics and Space Sciences

University of California San Diego

**ABSTRACT**

We are developing tomographic techniques for analyzing remote sensing
observations of heliospheric density and velocity structure as observed
in Thomson scattering (e.g. using the HELIOS photometer data) for
eventual use with Solar Mass Ejection Imager (SMEI) observations.

We have refined the tomography program to enable us to analyze
time-dependent phenomena, such as the evolution of corotating
heliospheric structures and more discrete events such as coronal mass
ejections. Both types of phenomena are discerned in our data, and are
reconstructed in three dimensions. We use our tomography technique to
study the interaction of these phenomena as they move outward from the
Sun for an event sequence in late November 1977 that has been studied by
multiple spacecraft in-situ observations \[Burlaga et al., 1980\]. The
tomographic analysis from the HELIOS photometers shows a brightness
increase associated with the density enhancement behind a shock. We
generalize these shock observations using observations of density
enhancements behind shocks from other HELIOS photometer remote-sensing
observations.

This work was supported by NASA grants NAG5-8504 and NAG5-9423.

# **Introduction**

The heliosphere is such a large region that it is not cost effective to
place spacecraft at the necessary locations within it to provide
information about its overall physical parameters. The challenge is
therefore to accurately provide as many of the detailed physical
parameters by remotely sensed heliospheric observations as possible. In
addition, the techniques that provide the best overall three-dimensional
depiction also provide a way to map these features in real time in order
to show heliospheric structures prior to their arrival at Earth.

Heliospheric remote sensing observations, such as interplanetary
scintillation (IPS) and Thomson scattering observations, provide global
information about the 3D structure of the heliospheric velocity and
density. Each observation represents the integrated effect of
contributions from the solar wind everywhere along a line of sight
(Figure 1).

Heliospheric tomography combines information from many different lines
of sight, sampling the solar wind from many different perspectives, for
an unbiased reconstruction of the solar wind density and velocity
distribution. For heliospheric observations different perspectives are
obtained, not only from solar rotation, but also due to the large range
of elongations covered from solar wind outflow.

# **Time-Dependent Tomography**

In order that the tomographic reconstruction map CMEs and other
time-varying heliospheric features, the iterative least-squares
algorithm used to determine a 3D model from a single point in space must
use radial solar wind outflow almost exclusively to provide perspective
views. The iterative procedure minimizes the differences between the
actual remote sensing observations and the values obtained by
integrating through a model that varies with time -- "time-dependent"
tomography.

We relate all lines of sight within the volume accessed to a single
source surface below the lowest line of sight. Where the lines of sight
cross on the source surface from the three-dimensional space above it,
we can reconstruct the solar wind model (Figure 2a and 2b example). The
model time steps and spatial resolution (that must be commensurate with
the quantity and quality of data used) have so far been limited to
intervals as short as 8 hours and resolution elements as small as 5°×5°.
We currently require that at least more than one line of sight crosses
near the source surface resolution element (usually set digitally at
20°×20° for the Nagoya, Japan IPS data and 10°×10° for the HELIOS
photometer data) in order to reconstruct the solar wind structure at
that heliographic latitude and longitude.

# 

# **Solar Wind Model**

In our reconstructions to date we have assumed strictly radial outward
solar wind flow. The kinematic models we reconstruct assume that solar
wind mass is conserved and that the interactions between high and low
speed wind also conserve momentum. The solar wind model relates all
lines of sight within the volume accessed to a single source surface
below the lowest line of sight and accords each line of sight segment a
weighted influence on this surface. Where several lines of sight cross
on the source surface from the three-dimensional space above it, the
solar wind model can be reconstructed iteratively using tomographic
inversion techniques.

The source surface at the lower boundary of the kinematic model thus
forms a boundary condition for the model. Although the model digital
resolution is currently set at 10°×10° heliographic latitude and
longitude and time steps of one day for the HELIOS photometer data, a
set of Gaussian filters relate different resolution elements to one
another in space and time, and thus the size structures reconstructed
are dependent on these filters.

The kinematic model is only one possible solar wind model that we could
have used in our reconstruction, and in fact we currently work to
provide an interface that can accommodate 3D-MHD physics into our
tomographic representation.

**Solar Wind Model Displays**

We show solar wind model reconstruction in two dimensions in the form of
Carrington rotation 1661-62 maps at a given solar distance and time in
the examples of Figure 3a-d. We have chosen to display these day by day
transient structure changes in the heliosphere at the solar surface in
the form of density variations from one day to the next. The solar wind
model we use relates brightness changes to model density according to
the equations relating solar brightness to electron brightness found in
Billings \[1966\]. We use spacecraft average *in situ* observations of
density at HELIOS during the rotation in question to provide a
calibration of the solar wind total density at the time of the
observation.

We can also display these same models used for Figure 3a-b and 3c-d as
three-dimensional projections observed from a distance in Figure 4a-b.
In the views chosen, the Sun is centered with the Earth a blue dot shown
from the perspective view of an observer situated at 3 AU, 30° above the
ecliptic plane in the direction approximately 45 degrees west of the
Sun-Earth line. The view includes the oval Earth orbit for reference.

**Global Comparisons**

Perhaps the best global comparisons of the tomography can be found by
fitting to other's ideas of the heliosphere studied by classical
techniques. Figure 5 is a map of the heliosphere as presented by Burlaga
\[1980\] and is the same time interval reconstructed by time-dependent
tomographic techniques using the HELIOS photometer data shown in Figure
3a-b and Figure 4a. The tomography accurately reconstructs most aspects
of the gross heliospheric structure including:

1)  The corotating structure

2)  The CME to the solar southwest

3)  The fuzzy density enhancement interpreted as the shock that passed
    the HELIOS spacecraft on approximately 24 November.

**How well to we do?**

Other than the reconstruction of well-studied intervals such as depicted
in Figures 3, 4 and 5 there is no easy way to determine how well the
tomography works over the total extent of the heliosphere since
spacecraft sample only relatively minor portions of the three
dimensional solar wind values we reconstruct.

However, the overall consistency between observed and model brightness
is shown in Figure 6 that gives a typical comparison for the HELIOS 2
photometer data from November 14 -- December 25, 1977. The observed
brightness has been edited to remove a zodiacal light model, de-glitched
to remove proton flux spikes, and presented with a running mean 8-day
base removed. The observed data are noisy relative to the time-dependent
model that smoothly approximates it.

We are able to determine the solar wind model values at the position of
HELIOS and Earth, and these can be compared with *in situ* measurements
at HELIOS and Earth. These comparisons show a correlation in density
change that can be as good as 0.8 -- 0.9 over month-long periods when
*in situ* measurements are degraded to the temporal resolution of the
tomographic model. Work in kinematic model definition (filtering and
density fall-off with heliocentric distance) play an important part in
these current analysis schemes.

**The Density Enhancements Behind Shocks**

The HELIOS photometers observed the density enhancements behind shocks.
Figure 7a shows an example on April 23, 1979 of the *in situ*
enhancement behind a shock from a list of these events \[R. Schwenn
(private communication, 1986\]. This enhancement of density is observed
as a brightness increase (Figure 7b) in two different sectors of the
HELIOS photometer in different colors of light. To check the extent of
these density enhancements relative to the Sun-spacecraft line, the
enhancement columnar density is plotted in Figure 8 in different color
light. Every density enhancement on the ordinate (parallel to the
y*-*axis) measured *in situ* as it passes the spacecraft is observed to
be at least as extensive measured remotely 90° from the Sun-spacecraft
line and plotted in the abscissa direction. This implies that the
structures that pass the spacecraft behind shocks are somewhat more
extensive perpendicular to the Sun-spacecraft line than along it. There
is no evidence within the errors in measurement that shocks are anything
other than the color of Thomson scattered sunlight from electrons. This
implies that no fine dust is charged and swept up by the shock front.

**Conclusions**

The HELIOS photometers observed many of the large heliospheric
structures that have been analyzed to date using *in situ* observations.
These features are readily observed in their entirety in terms of
density in the time-dependent tomographic modeling that has been
developed for the Solar Mass Ejection Imager (SMEI) spacecraft scheduled
for launch later this year. SMEI will provide 1000 times more data than
available from the HELIOS spacecraft with far more photometric precision
along each line of sight, and this translates to a heliospheric
resolution of at least a factor of ten better in all four dimensions
than depicted in the analyses shown.

The STEREO heliospheric imagers view only a portion of the heliosphere.
These same structures should also be observed in the STEREO heliospheric
images. From their vantage points, and provided the images from this
instrument retain a calibrated photometric precision, they can be used
in a similar way. These images can be used both in collaboration with
the SMEI analyses and to provide views of the same structures
simultaneously in order to remove the ambiguities in three-dimensional
heliospheric modeling techniques.

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**References:**

Billings, D.E., A Guide to the Solar Corona, p. 150, Academic, New York
(1966).

Burlaga et al., *J. Geophys. Res.*, 85, 2227, 1980