Coordinate SystemSolar Wind Parameters
The solar wind parameters are from the ACE spacecraft, obtained in real-time,
at a temporal resolution of one-minute.
As such, these values are provisional, and are subject to corrections. The
data used include the position of the ACE spacecraft, the measured
interplanetary (solar wind) magnetic field (IMF), the solar wind ion density,
bulk flow speed, and ion temperature. Linear interpolation is used to
interpolate over small intervals of bad or missing data.
From these values, the solar wind dynamic pressure and the magnetosonic
Mach number are calculated. Small data gaps in the solar wind are seen in
the display as constant values (last known values). An extended period of
time with bad or missing solar wind values will cause the movie to not be
updated, until new solar wind data are taken.
Dynamic Pressure
The dynamic pressure of the solar wind is calculated as the square of
the solar wind bulk speed times the mass density (number density times
its mass) of ions. The ions are assumed to be 96 percent protons and
4 percent He++ by number.
Magnetosonic Mach Number
The solar wind magnetosonic Mach number is calculated from the solar wind
magnetic field intensity and plasma parameters. An electron temperature
of 1.5x105K and a polytropic index of 5/3 is assumed.
Solar Wind Flow Angles
The flow angles of the solar wind are not available in the real-time data sets.
Though the programs used for this web site are equipped to handle varying
flow angles. Instead, an average value of 4 degrees is used, which accounts
for the motion of the Earth around the Sun and the nominal solar wind speed
(aberration).
Convection Time
The convection time of the solar wind is simply estimated as the distance
of the ACE spacecraft from the Earth (or other place) along the (aberrated)
Sun-Earth line, divided by the solar wind speed.
Magnetopause Model
The magnetopause shown in the movie is based upon the empirical model of
Petrinec and Russell [J. Geophys. Res., 101, 137-152, 1996].
This model depends upon the solar wind dynamic pressure and IMF Bz.
Bow Shock Model
The bow shock shown in the movie is based upon the empirical model of
Farris and Russell [J. Geophys. Res., 99, 17681-17689, 1994].
This model depends upon the standoff distance, and 'bluntness' of the
magnetopause, as well as the solar wind magnetosonic Mach number.
Interpolation Scheme
Basically, at each moment in time, many solar wind 'front' positions are
calculated. For simplicity, all 'fronts' are perpendicular planes to
the (aberrated) Sun-Earth line. Then for each 'front', entire 3D
surfaces of the magnetopause and bow shock are calculated, using the
average steady-state empirical models. This means that for a given
time step (e.g., 01:00 UT at Earth), several magnetopause surfaces
and bow shock surfaces are determined. The 3D surfaces are
then cut along a single plane (in the case of the movie, the GSM
equatorial plane). The 'fronts' then determine the locations where each
of the shapes are most appropriate. At present, if one 'front' overtakes
another, then the boundary shapes pertaining to the overtaken 'front'
are dropped from the procedure (this may be changed in the future).
A linear interpolation between each
shape is then performed and displayed. This process is repeated at each
subsequent time step, and the resulting images are merged together. In
this way, variations observed in the solar wind are manifested as 'waves'
along the bow shock and magnetopause.
Programs Used
The primary program used is IDL 5.1. The motion of the dashed green line
was unanticipated, being the result of saving GIF images from computer
memory (the z-buffer, for IDL-philes), rather than from a screen.
The real-time clock is from
http://tycho.usno.navy.mil/howclock.html, and does not work with
Internet Explorer.
Future Work
It is planned that there will be an interactive web page, for which the user
can select the period of time of interest, the view (e.g., meridian or
equatorial planes), add spacecraft trajectories, change the range (in RE)
of the plot, select different empirical models, and many other options.
It is also expected that these efforts will be extremely useful in assessing the accuracy of the empirical models by comparing with actual crossings of boundaries by operating spacecraft, and indicating the directions in which improvements can be made.
Acknowledgments
Many thanks to Mike Rinaldi for help with the cron and perl scripts
that helped make this web site possible.