Reply to "Comment on 'A Simple Test of the Induced Nature of the Martian Tail' by C. T. Russell et al.," by P. L. Israelevich

C. T. Russell,¹ T. Mulligan,¹ M. Delva,² T. L. Zhang² and K. Schwingenschuh²

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

Originally published in:
Planet. Space. Sci., 45, 749, 1997.

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 360⁰ 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."

Table 1. Correlation of IMF and Mars Magnetotail Clock Angles over Varying Angular Ranges

Angular Range	Slope	Correlation Coefficient
0 to 360^o	0.77	0.79
-45 to 315^o	0.91	0.81
-90 to 270^o	1.13	0.89
-135 to 225^o	1.34	0.95
-180 to 180^o	1.31	0.93
-225 to 135^o	0.97	0.83
-270 to 90^o	0.86	0.80
-315 to 45^o	0.63	0.78
Mean	0.99	0.85
Median	0.94	0.82

Acknowledgments

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

References

Israelevich, P. L. Comment on "A simple test of the induced nature of the Martian tail" by C. T. Russell et al., Planet. Space Sci., 44, 795-796, 1996.

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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