### Localization of the Type III and Type II
Radio Sources Using the Multiple Spacecraft Observations

**G. Thejappa**^{1},
R. J. MacDowall^{2}

^{1}Department of
Astronomy, University of Maryland, College Park MD 20742, USA

^{2}NASA/GSFC, Greenbelt MD 20771, USA

We present a technique to determine the positions of type
III and type II radio burst sources based on the difference in their arrival
times at multiple spacecraft separated from each other by a wide range of angles
and distances. The time of arrival differences at a pair of spacecraft locate
the radio source on a hyperboloid of revolution with foci at the spacecraft. The
time of arrival differences at three spacecraft place the radio source on the
curve of intersection of two such hyperboloids. To fix the position at a point
on this curve of intersection requires additional information. Some examples for
such information are the surface of the sphere with radius corresponding to the
fundamental or second harmonic of the electron plasma frequency (plasma emission
mechanism is assumed), or observations from an another spacecraft providing
additional signal time of arrival differences. The source locations found in
this way at the intersections of hyperboloids and other surfaces can be called
hyperboloic position fixes. The computation of these hyperboloic position fixes
can be reduced to the solution of a quadratic or a quartic equation. However, in
actual situations the low frequency signals experience delays as they propagate
through the solar atmosphere. The refraction of the radio waves in the smoothly
varying background plasma and the scattering by random density fluctuations are
the two main propagation effects. Unless the measured arrival times at
spacecraft are corrected for the propagation effects, the multi-spacecraft data
can not be used to extract the positional information of the radio source. In
this study, we also describe a method to compute the delays in the arrival times
of the radio emissions at spacecraft located at different distances due to
refraction and scattering by random density fluctuations using the Monte Carlo
simulations.