AN ESTIMATE OF THE LOCATION OF THE MODULATION BOUNDARY FOR E-GREATER-THAN-70 MEV GALACTIC COSMIC-RAYS USING VOYAGER AND PIONEER SPACECRAFT DATA

We have estimated the location of the modulation boundary for >70 MeV per nucleon Galactic cosmic rays using observations of their intensity and radial gradients between Voyager 2 (V2) and Pioneer 10 (P10) in the outer heliosphere along with new estimates of the >70 MeV interstellar cosmic-ray intensity. In the first case, we have used the method described by Cummings et al. (1994) in which the local current sheet tilt is correlated with the radial gradient between the two spacecraft when the tilt is <30 degrees to extrapolate the intensity to the boundary. By this method we obtain a boundary at an average distance of 79 +/- 3 AU between 1986.5 and 1987.5. In the second instance, we have also used the summation procedure of Cummings et al. (1994), the only difference being that we did not correlate the local radial gradient with the tilt of the neutral sheet but simply used the observed radial gradient between V2 and P10 in the summation. Using this method we find that for 7 years from 1983 to 1990 this modulation boundary remained constant at 83 +/- 5 AU. We infer from these studies that a modulation boundary can be estimated only by extrapolating the observed radial gradients as we have done when the solar magnetic polarity is such that the cosmic-ray particles are drifting in the heliosphere inward toward Earth along the neutral sheet. These boundary distances are larger than estimates of the solar wind termination shock distance of 67 +/- 5 made using the same method for the anomalous cosmic rays (Cummings et al. 1993), but well inside the heliopause distance of 112-177 AU recently determined by Gurnett et al. (1993). The fact that this modulation boundary is not much farther out than the termination shock suggests that modulation effects within the heliosheath region between the termination shock and the heliopause are probably not a major contributor to the overall solar modulation at this time and at these energies.