Table of Contents
1. Introduction
2. The Predictive Science MHD Code
3. Using the STEREO/MHDWEB interface
4. References
5. Acknowledgements
1. Introduction.
In this
document, we describe the basic features of the STEREO/MHDWEB interface. We
also summarize our modeling approach, in so far as it pertains to these model
results. For simplicity, our initial simulations are all centered on a specific
Carrington rotation. That is, we use a photospheric magnetic field synoptic map
composed of a sequence of observations centered at central meridian and shifted
in longitude by the appropriate amount. This map forms the fundamental boundary
condition at the surface of the Sun. It is supplemented with auxiliary boundary
conditions that approximate the plasma density and temperature.
The web
pages are organized by Mission, instrument, and general tools. The
mission-related pages provide access to spacecraft trajectory data and other
general information related to STEREO. Currently, we are providing explicit
support for the SECCHI and IMPACT instruments (although the tools can be used
for all STEREO instrumentation). In addition to providing an interface to view
images and time series at specific time periods, we provide basic comparisons
between the model results and data as well as visualizations that attempt to
merge data and model results in ways that enhance the interpretation of the
data. In addition, these comparisons provide a simple validation (we hope) of
the model results. At the least, when the comparisons between data and
observations are poor, care should be taken when interpreting observations
using the model results.
The MHDWEB
tools are a suite of general visualization and analysis tools. They are
designed to allow a user to interact with the MHD simulation results
independently of any specific mission. Basic 1-D and 2-D plotting routines
allow the user to produce tailor-made plots. In addition, the Summary Plots
page computes a photo-gallery summarizing the salient parameters of a
particular simulation. We have also pre-computed several post-simulation
parameters, including the coronal hole boundaries, polarized brightness, and an
iso-surface of the heliospheric current sheet. Finally, for the truly brave, we
provide a link to download the data from the simulation. Please consult the
user guide for more information on how to download and analyze the data
offline.
These pages
are our first attempt to provide this level of modeling support for any mission
and are currently a work in progress. If you have any suggestions on how to
improve the experience, please send an email to webmaster@iMHD.net.
2. The
Predictive Science MHD Code
We use a
three-dimensional, time-dependent MHD model, driven by the observed
line-of-sight photospheric magnetic field to model the structure of the inner
heliosphere (1 Solar radii, Rs, to 5 AU). The details of the algorithm have
been discussed by Mikic et al. (1999) and Linker et al. (1999) (and references
therein) and its extension from the solar corona to the inner heliosphere is
discussed by Riley et al. (2001a,b). Briefly speaking, we separate the region
of space from 1 Rs to 5 AU into two distinct regions: the coronal model, which
spans 1 Rs to 30 Rs and the heliospheric model, which spans 30 Rs to 5 AU.
Such an approach is both computationally more efficient and produces a more
realistic heliospheric environment.
The
heliospheric boundary conditions are specified in the following way. First, we
directly input the radial component of the magnetic field as calculated in the
coronal solution. Second, we compute the speed using the coronal magnetic
configuration: At 1 Rs we set the radial speed to be some value, Vslow, at the
boundary between open and closed field lines over a width of ~6 degrees (in a
direction normal to the boundary) and smoothly raise it to Vfast over ~3
degrees. We then map this speed profile outward along the open field lines to
30 Rs. Although this may appear somewhat ad hoc, it is based on the commonly
held view that fast wind emanates from within coronal holes and slow wind is
associated with the boundary between open and closed fields, as would be the
case if closed field lines were sporadically opened, through magnetic
reconnection. Third, we assume momentum flux balance at the inner boundary,
which specifies the plasma density. Fourth, we assume thermal pressure balance,
giving the temperature. Comparisons with in situ observations suggest that this
approach is capable of reproducing the essential features of the large-scale
structure of the inner heliosphere for a variety of solar conditions (Riley et
al., 2001a,b).
Riley et al.
(2001a,b) have discussed the approximations of this model in detail. Here we
make a few brief remarks. First, we neglect the effect of pickup ions, which
are thought to dominate the internal energy of the solar wind beyond 6-10 AU.
Thus we limit our modeling region to ~5 AU. Second, we neglect the effects of
differential rotation, which may play a role in connecting high latitude field
lines near the Sun with lower-latitude interaction regions much further away.
Third, although our MHD model is time-dependent, we assume that the flow at the
inner boundary is time-stationary. Thus the flow at the inner boundary rotates
rigidly with a period of 25.38 days and spatial variations are responsible for
the generation of dynamic phenomena in the solution. Consequently, our results
do not include transient phenomena such as coronal mass ejections. Finally, the
grid resolution necessary to model a region of space spanning 5 AU in radius
precludes us from accurately modeling shock waves. However, since we would not
expect shock waves to overtake, and hence alter the shape of the HCS within
8-10 AU, this limitation has no obvious impact on our results.
Since the model,
as implemented here, is driven by synoptic maps of the line-of-sight
photospheric magnetic field observed at the Kitt Peak observatory, each
solution describes an "average" picture for that Carrington rotation. And,
while the solution does not contain any transient phenomena such as coronal
mass ejecta, it can be interpreted as the "underlying" solution, assuming that
the magnetic configuration responsible for the transient event returned to its
initial state after eruption. However, as shown by Riley et al. (2002), even
under solar maximum conditions, such an approach can produce results that
compare favorably with in situ observations.
3. Using
the STEREO/MHDWEB interface
Introduction
We hope that
the design of the web page makes a detailed description of each option
unnecessary. However, there are a few "nuances" that you need to be aware of,
both in the way the data is displayed and in how to interpret the results from
the simulations. We present them as a series of topics.
1. How
to tell if the model results are accurate, good, or useless.
There
are several ways to assess the quality of the simulation results. We are
currently testing a "traffic signal" labeling system that should provide a
basic assessment of a particular solution, however, because solutions may be
accurate for some applications does not mean they are accurate for all. Thus it
cannot replace user verifying the quality of the solution for himself/herself.
One of the first places to look is the "Summary Plots" gallery page. By scanning
through these plots, you can quickly identify potential numerical artifacts.
The most useful of these are the "histories" plots at the bottom of the page.
They summarize the time history of a number of parameters, including the time
step (dt). Evidence of problems can be seen in wildly fluctuating values, or
values that don't (but should) asymptote to a constant. Other indications of
problems can be seen in lat-lon plots of some of the parameters, including the
phi component of the current density (jp) and the radial component of the
magnetic field (Br). Specifically, the appearance of "ringing", where
alternating cells display high and low values suggest a possible numerical
instability.
2. Retrieving
the data and plotting/analyzing it yourself.
The
"backend" of this website consists of a library of IDL routines. We plan to
develop a SOLARSOFT package for these simulation results, and, with the
approval of the SOLARSOFT maintainer, distribute the source code in the future.
3. The
limitations of the models
a. No CMEs.
The
model results available here do not contain any CMEs! Current research does not
allow us to routinely model specific CME events. In the future, it may be
possible to incorporate simple CME generators into the web interface for specific
campaign events.
b. A Polytropic Solution.
The
model currently implemented here is our "polytropic" model. In this model, we
use a polytropic expression to relate density and pressure, where gamma, is
1.05. This crudely mimics the near isothermal nature of the corona but evades
any meaningful treatment of energy flow in the solar corona. The results is
that the density and temperature variations should be treated with skepticism.
In addition, under such a simple approximation, it is not possible to produce
high-speed coronal flow of 750 km/s. We have partially circumvented this in the
heliospheric solution by implementing a novel mapping technique. However, it is
also an ad hoc technique. Moreover, it means that the speeds computed from the
coronal solution and those computed in the heliospheric solution do not match
at the boundary between the two codes. We have already developed a full
thermodynamic model that addresses many of these limitations. It is currently
under final testing and these results will be added to the polytopic solutions
currently available.
c. Understanding
4. References
Pete Riley
et al., "A Comparison between Global Solar Magnetohydrodynamic and Potential
Field Source Surface Model Results", Ap. J., 653, 1510, 2006.
Pete Riley,
Z. Mikic, and J. A. Linker, "Dynamical evolution of the inner heliosphere
approaching solar activity maximum: Interpreting Ulysses observations using a
global MHD model", in press, Annales Geophysicae, 2003.
Pete Riley,
J. A. Linker, and Z. Mikic, "Modeling the heliospheric current sheet:
Solar-cycle variations ",
J. Geophys. Res., DOI 10.1029/2001JA000299, 107, 2002.
Pete Riley,
Jon Linker, and Zoran Mikic, "An empirically-driven global MHD model of the
corona and inner heliosphere ", J. Geophys. Res., 106, 15,889, 2001.
5. Acknowledgements
We are
grateful for the continued support from NASA (Heliophysics Theory, SR&T,
and GI Programs) and NSF (CISM and SHINE
programs).