The graph below shows some of the shocks detected by Voyager 2 during the year 1992. The solar cycle causes changes in the ion activity at 30 keV - 10 MeV energies which may be classified as quiet, recurrently active (Corotating Interaction Regions or CIR's seen during 1992 are typical) or active (CIR's and solar flare or Coronal Mass Ejection (CME) events).

This plot is data collected by the LECP and is primarily protons at about 1 MeV energy. The circular plot is a pie plot containing the count rates in 8 different look directions called sectors. Each sector is 45 degrees which corresponds to the acceptance angle of the detector. The detector actually accepts particles within a cone 22.5 degrees from the perpendicular bisector of the detector (in the case of low energy ions) so that the sector (pie) plot is really a 2 dimensional cut through the plane of the detector. The 3 dimensional nature of the particle flux accepted into the detector is not considered in our Voyager work. The radial length of each slice of the pie corresponds to the count rate in that direction normalized to the averaged rate in the most active sector during the averaging period.

The LECP detector on the Voyager 1 and 2 spacecraft contains a large number of energy and mass discriminated channels. Many of these channels contain 7 look directions since the entire detector rotates in a plane stopping at 45 degree intervals to acquire data. Although the Plasma detectors (PLS) on the Voyager 1 and 2 spacecraft are generally used to determine solar wind velocities, the Voyager 1 PLS detector has been partially inoperable and thus solar wind data after the Saturn encounter in 1980-1981 is not available. Therefore, the angular rate information available from the LECP channels in some cases may be used if the spectrum of the ambient solar wind particles above 30 keV is known.

Assuming that the distribution of particles in the flow frame of the solar wind is an isotropic distribution of protons (and electrons which are not used), particles entering a detector not in the solar wind frame at various incident angles relative to the solar wind vector will appear to result from a population of the form

where v is the particle velocity, V is the solar wind bulk flow velocity, and gamma is the spectral index of the distribution. The predominant form of the distribution in the solar wind above 30 keV is power law in transient shocks and may be approximated as a power law for CIR shocks in a limited range of energies at about 1 MeV.

In order to obtain the bulk flow velocity, we first obtained the angular averaged spectrum of CIR events during a particular year, using 5 day averaged fluxes. The CIR spectra were found to be well described by

where j is the particle flux and E the incident particle energy in the detector frame of reference. The spectra during 1992 of various CIR's were all quite similar, and the average spectrum was used to determine the spectral index to be used as the power law spectral index of the rest frame population. The flux f can then be used after converting to count rates using the detector characteristics to do a best fit to the sectored data in the best channel currently available, Channel 1. The result of the fit will be a best value for the bulk flow velocity V determined from the existing count rate anisotropy in one channel, the angular averaged spectral index from the CIR spectrum at peak activity, and the assumption of rest frame power law isotropy. The quadratic form yielded a slowly varying slope near 1 MeV so that our adaptation of the spectral index from the quadratic form to use in the convected power law form of f yielded good results.

There are several methods by which we may use the LECP data to obtain solar wind velocities. They vary according to the level of count rate activity and include the methods described above. In summary, for active periods near solar maximum and early in the mission, we can fit power law and quadratic spectra to multiple low energy channels from 30 keV to 10 MeV using all sectors and obtain a best fit convection velocity to the entire array at 1 day resolution. For less active periods, we obtain a spectral index from angular averaged data from ion channels and fit the angular response of Channel 1 to obtain V. For more quiet periods, we may use the spectral index from periods of CIR peak activity during that year to derive a spectral index and then fit the angular response of Channel 1 to get V. For the most quiet periods, we can use the known solar wind speed from Voyager 2 to derive a spectral index at Voyager 2, assume the same spectrum exists at Voyager 1, then fit Channel 1 to derive V at Voyager 1. This obviously has the drawback that the Voyagers are not at the same place but hopefully sample similar particle populations. The history of the mission shows this is usually but not always the case, where spectra at large transients and CIR's have in cases been remarkably similar. As we move to more quiet times, the time averaging required grows longer from 1 day to 26 days or longer.

We have thus far completed a large portion of the Voyager 1 mission using a variety of techniques and averaging. While this plot is not to be considered the final word and is not yet ready for publication, it illustrates the general nature of the Voyager 1 velocity of the solar wind.

We would refer the interested reader to the papers linked in the parent directory and invite any response. We hope to have a paper ready for publication in the coming months (fall-winter 2001).