Basic Results of MHD Tomography Analysis Method for IPS
Observation
Keiji Hayashi∗ , Ken’ichi Fujiki∗ , Masayoshi Kojima∗ and Munetoshi Tokumaru∗
∗ Solar-Terrestrial
Environment Laboratory, Nagoya University, Toyokawa,442-8507,Japan
Abstract. We present the tomography analysis method using MHD simulation code to derive three-dimensional solar wind
structures from IPS observations. By incorporating MHD simulation, this new tomography method, hereafter called MHD
tomography, can treat the nonlinear MHD process in solar wind and will improve the result of the reconstruction of global
solar wind structure from IPS measurement data. The practical calculation is done as iteration procedure. At the first step of
iteration, MHD simulation is carried out with given provisional boundary conditions, and the numerical three-dimensional
solar wind is made. At the next step, the IPS observations are simulated in this three-dimensional solar wind. The discrepancy
between the actual IPS measurement and the numerically reproduced ones are traced back along streamlines onto the inflow
boundary surface. Then, the velocity distribution on the boundary surface is modified so that the differences may be reduced.
The modified boundary distribution is used in the next iteration, and the iteration is continued until the three-dimensional solar
wind structure matching the LOS-integrated IPS observational data is obtained. The basic result of this analysis is shown, and
the possible applications of this MHD-based and observation-based solar wind are demonstrated.
INTRODUCTION
The observation of the interplanetary scintillation (IPS)
is, at present, a unique ground-based observation technique for the solar wind. Solar-Terrestrial Environment
Laboratory (STEL) at Nagoya University, Japan has the
multi-site observational facilities for IPS that can observe
the velocity and density at r = 0.2 ∼ 1 AU and makes
more than 400 observations during one month. The solar wind quantities derived from the IPS observation is,
however, line-of-sight (LOS) integrated properties and
do not directly represent the quantities at the particular
positions.
Jackson et al. [1] and Kojima et al. [2] developed the
inversion algorithm called the computer assisted tomography (CAT) and succeeded in reconstructing the spatial
distribution of the solar wind from the LOS-integrated
IPS observational data. However, the nonlinear process
of the hydrodynamics (HD) nor magnetohydrodynamics
(MHD) had not been treated exactly in the CAT analysis.
Recently, we have developed the MHD tomography
analysis method, in which the MHD simulation code
is embedded [3] (hereafter Paper I). The MHD code in
this analysis method enables the CAT analysis to treat
the MHD process of the solar wind and reconstruct
the MHD-based three-dimensional structure of the solar wind from the IPS observational velocity data. At the
same time, the CAT analysis allows the MHD code to
deal with the situation detected by IPS observation. We
anticipate that this mutual relation between the observa-
tion analysis and the numerical simulation will enhance
the study of the solar wind. In this paper, the basic result
of MHD tomography is briefly shown, and the simulation of disturbance propagation and the extrapolation of
the solar wind at r > 1 AU are demonstrated as the examples of the applications of the MHD-based and IPSobservation-based solar wind.
METHOD
Figure 1 is the flowchart of MHD tomography analysis
to find the solution of the three-dimensional solar wind
structure best matching IPS observational velocity data,
with the thick arrows showing the recursion part. The
algorithm is based on the analysis by Kojima et al. [2],
but the additional procedures are introduced in order to
carry out the MHD simulation. The details are described
in Paper I.
In this presented analysis, the inner boundary of the
MHD simulation is the 50 solar radii sphere. This choice
is determined from the two factors. The one is the domain
of sensitivity of IPS observation (0.2AU < r < 1AU for
STELab IPS observation at 327 Mhz), and the other is the
requirement from the MHD simulation method used in
this analysis that the solar wind must be super-Alfvénic
on the inner boundary and in the domain of computation.
We address here that we can choose the inner boundary
more close to the Sun, for example, 10 or 20 Rs sphere,
CP679, Solar Wind Ten: Proceedings of the Tenth International Solar Wind Conference,
edited by M. Velli, R. Bruno, and F. Malara
© 2003 American Institute of Physics 0-7354-0148-9/03/$20.00
144
Heliographic latitude
Reconstructed Velocity Distribution
Carrington longitude
FIGURE 1.
Flowchart of MHD tomography analysis.
in case that solar wind r < 50Rs are to be reconstructed.
The MHD code embedded in this analysis method derives three-dimensional global solar wind variables at
r > 50Rs using the distribution of solar wind variables
at 50Rs as the initial values. Since the boundary velocity at 50Rs is modified by referring the observational IPS
velocity data, the IPS data contribute as the constraints
of the conditions in the MHD simulation. To begin the
MHD simulation, the other variables, density, temperature and magnetic field at 50Rs must be prepared. We
derived the empirical functions n(V ) and T (V ) from the
Helios data to determine the density and temperature on
the inner boundary at 50Rs . We used the observational
photospheric magnetic field data and calculated the magnetic field at 50Rs by means of the potential field model.
Therefore, all variables at 50Rs are determined from the
observational data.
Writing the time-dependent MHD equations in the
matrix-vector form,
~
~
~
~
∂W
∂W
1 ∂W
1 ∂W
− Mφ
+ ~S, (1)
= −Mr
− Mθ
∂t
∂r
r ∂θ
r sin θ ∂ φ
the equations the MHD code are to solve can be written
as
Ã
!
~
~
~
∂W
1 ∂W
1 ∂W
−1
~
= Mr
−Mθ
− Mφ
+S
(2)
∂r
r ∂θ
r sin θ ∂ φ
because the solar wind to be simulated (> 50Rs ) is always super-Alfvenic and the solar wind quantities can be
calculated using the solar wind parameters at the upwind.
We used the two-step centered-differencing method to
increment the radius and derive the solar wind variables
at r > 50Rs . The practical calculation is done using conservative variables.
145
FIGURE 2. The boundary velocity map of the quiet solar
wind reconstructed by the MHD tomography analysis. The
darker gray represents the slower wind, and the brighter does
the faster. The range of derived velocity is approximately from
200 to 800 km/s.
BASIC RESULT AND APPLICATIONS
The gray scale of Figure 2 shows the solar wind velocity at 50Rs derived by the MHD tomography analysis
for the period of Carrington rotation number 1939, as
an example. That is, the MHD-based three-dimensional
solar wind with this boundary distribution is best matching the LOS integrated IPS observation data made during
this period. The other variables, density, temperature and
magnetic field are also calculated together with plasma
flow speed from 50 Rs to 1 AU for the CAT analysis.
As shown later, the MHD code can expand the steady
solar wind from 1 AU to several AUs. In Paper I, we
showed good positive correlations of density, temperature, flow speed and magnetic field between the derived
three-dimensional solar wind and the direct measurement
by spacecrafts, Ulysses, IMP8, ACE, WIND and ISEE3.
Simulation of interplanetary disturbance
propagation for space weather prediction
The MHD simulation of interplanetary disturbance
propagation is one of the most suitable applications
where the IPS-MHD tomography analysis shows its ability. Because the time-evolution of the interplanetary disturbance depends on not only the properties of the trigger event like flare and coronal mass ejection (CME) but
also the structure of the background quiet solar wind, to
know the structure of the quiet solar wind in advance will
be greatly helpful for the space weather prediction.
The time-dependent MHD simulation of the disturbance propagation can be initiated by giving the mimic
CME-associated material injection at the inner numerical
boundary surface into the quiet solar wind and by solving the response of the system. In our case, the IPS-based
FIGURE 3. Cross sections view of the density enhancements
propagating in the interplanetary space. The numerical perturbation was given on the inner boundary sphere at 50Rs .
FIGURE 4. Line of interplanetary magnetic field or streamlines viewed in the rotating frame at 50Rs < r < 6 AU. The
thickness of lines represents the local flow speed.
and MHD-based steady solar wind can be used. Figure 3
shows the cross-section view of the solar wind plasma
density enhancement of the interplanetary disturbance
simulated in this way. The shape of disturbance shock
front depends on the ambient background solar wind,
which is now obtained from the IPS observational data
through the tomography analysis. In the demonstrated
case, the artificial mass injection was symmetry, and the
bent shape of the shock, in other word, the dependence
of shock upon directions were obtained.
Sun. The grayscale represents the flow speed, and the
streamlines drawn start with the uniform interval in longitude at r = 50Rs . It is observed that the longitudinal
intervals between streamlines vary with distances. This
variation of the streamline intervals represents the nonlinear evolution of the solar wind with distances.
The solar wind properties can be extracted from this
three-dimensional numerical solar wind. For the extrapolation at several AUs, considering the travel time of the
solar wind from 1 AU, the numerical quiet solar wind
derived from the IPS data made during the previous Carrington rotation is used.
Figure 5 demonstrates the comparison of the analyzed
data with near-Earth data (at 1 AU) and Ulysses data (at
about 4.5 AU) during period of CR 1848 as an example.
The positive correlations at these two different heliocentric distances show that both reconstruction of the solar
wind at r < 1AU and extrapolation for r > 1AU work
with reliable accuracy.
Extrapolation of solar wind properties at
r > 1 AU
The MHD simulation code embedded in the MHD
tomography analysis can expand the solar wind outward using the results of our MHD tomography analysis for r < 1 AU and make extrapolations of the solar
wind quantities at r > 1 AU. This extrapolation will be
greatly helpful for the study of the distant solar wind
from the Sun, for example, the interactions with planets
and interstellar medium. Because the solar wind evolution along distance depends both its longitudinal and latitudinal variations, our method that can reconstruct the
global solar wind structure is a unique method to make
observation-based extrapolation of the global solar wind
at the regions distant from the Sun.
Figure 4 shows the streamlines within 6 AUs where
the streamlines are defined in the frame rotating with the
146
SUMMARY
In this paper, we briefly described the algorithm of the
MHD tomography and demonstrated the velocity map of
the solar wind reconstructed with the MHD tomography
from the IPS observational data. Then, as an example of
the application of the analysis result, the time-dependent
MHD simulation of the disturbance propagation that may
be applicable to the space weather prediction study is
shown. Additionally, the extended global solar wind at
r > 1 AU are shown, together with the comparisons with
Ulysses and near-Earth data.
The presented MHD tomography assumes that the solar wind is steady and super-Alfvénic in the domain of
analysis. However, transient events such as interplanetary disturbances exist in reality, and even the global
structure varies in time. In addition, to combine the
trans-Alfvénic regions (1Rs < r < 10Rs ) with the superAlfvénic regions may be useful for the study of the SunEarth connection of space weather and the solar wind
heating/acceleration mechanism. To handle these, we are
studying "time-dependent" MHD tomography.
Radial Component of Velocity in km/s
Earth
Cor= 0.80
200.00
874.50
Ulysses
200.00
Cor= 0.77
635.03
Number Density in cm^(-3)
Earth
Cor= 0.69
Ulysses
Cor= 0.38
ACKNOWLEDGMENTS
This work is supported by the IPS project of the SolarTerrestrial Environment Laboratory, Nagoya University.
REFERENCES
0.00
37.18
0.00
1.90
1. Jackson,V.B., Hick,P.L., Kojima,M. and Yokobe,A., J.
Geophys. Res.103, 12049–12067, 1998.
2. Kojima,M., Tokumaru,M., Watanabe,H. and Yokobe,A., J.
Geophys. Res.103, 1981–1989, 1998.
3. Hayashi,K, Kojima,M., Tokumaru,M, and Fujiki,K.,
submitted J. Geophys. Res., 2002.
Temperature in 1000 K
Earth
0.00
Cor= 0.56
814.34
Ulysses
0.00
Cor= 0.49
102.01
Azimuthal Comp. of Magnetic Field in nT
Earth
-12.70
Cor= 0.64
9.30
Ulysses
-3.87
Cor= 0.64
1.59
FIGURE 5. Correlation maps of analyzed (ordinate) and
measured (abscissa) solar wind variables at Earth (1 AU ;
left) and Ulysses spacecraft (4.5 AU ; right) during CR 1848.
From the top, daily averaged values of the radial component
of plasma velocity, plasma number density, plasma temperature and azimuthal component of azimuthal magnetic field are
plotted, together with the square-fitting lines. Correlation coefficients are written on the top of each box. The range of values
along x- and y-axis are identical and denoted at the bottom.
147