*C. T. Russell, ^{1} T. Mulligan,^{1} M. Delva,^{2} T. L. Zhang^{2}
and K. Schwingenschuh^{2}
*

^{1} Institute of Geophysics and Planetary Physics, University of
California Los Angeles, Los Angeles, CA 90024-
1567, U.S.A.

^{2} Space Research Institute, Graz, Austria

Israelevich (1996) raises a valid concern that when performing a cross correlation between
two variables of cyclic measure the resulting correlation coefficient can depend on the starting
and stopping points over which the 360^{o} range is chosen. To illustrate his point he replots
one of the figures that we used in showing that the direction of the magnetic field in the Mars
magnetotail follows the direction of the interplanetary magnetic field (IMF) perpendicular to
the flow (Russell et al. 1995.) While the data points in our original figure 4b appeared to be
well spread over the range -180^{o} to +180^{o}, Israelevich noted that the data were more clustered
when plotted over the range 0 to 360^{0} and thus the correlation coefficient was smaller over
this range. Thus he questions how well the IMF and Martian magnetotail fields are
correlated. In order to answer that question, we have used all of the data in our original
Figures 4a and 4b showing the comparison angles 2.25 hours earlier and later. These two
data sets are nearly statistically independent since all the IMF data were obtained at well
separated times as were many of the tail data. In Table 1 we show the results of our cross-
correlation analysis on these data over eight different choices of range, each covering 360^{o}
but each starting at a different (by 45^{o}) point on the unit circle. The mean slope is close to
unity as one would expect if they were indeed correlated and the mean correlation coefficient
is 0.85, very close to what we initially reported. Such a high correlation coefficient leaves
little room for another source for the Mars magnetotail field. Thus, we reiterate the
conclusion of our initial paper, "Any magnetic field intrinsic to the planet plays at most a
minor role in the dynamics of the solar wind interaction with Mars."

Angular Range | Slope | Correlation Coefficient |

0 to 360^{o} | 0.77 | |

-45 to 315^{o} | 0.91 | |

-90 to 270^{o} | 1.13 | |

-135 to 225^{o} | 1.34 | |

-180 to 180^{o} | 1.31 | |

-225 to 135^{o} | 0.97 | |

-270 to 90^{o} | 0.86 | |

-315 to 45^{o} | 0.63 | |

Mean | 0.99 | |

Median | 0.94 |

This work was supported by the National Aeronautics and Space Administration under research grant NAGW-2573.

**C. T. Russell, Mulligan, T., Delva, M., Zhang, T. L. and Schwingenschuh, K.** "A simple
test of the induced nature of the Martian tail," *Planet. Space Sci.*, **43**,
875-879, 1995.

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