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# The Dipole Tilt Angle Effect on the Cusp Location

As we have seen in Figure 2, the cusp position is quite variable from orbit to orbit. One important factor of this variation is the dipole tilt angle which is defined as the angle between the Earth's north dipole axis and the GSM z-axis. This angle is positive when the dipole tilts toward the Sun, and negative when the dipole tilts away from the Sun. The IMF also plays a significant role in controlling the cusp location. To study the effect of tilt angle, we use data only for northward IMF because the cusp location is weakly dependent on the IMF direction once the IMF is northward. The large variability of the cusp position for southward IMF tends to obscure the tilt effects. Figure 3a, 3b, 3c show the data sets with tilt angle range of (0 °-10° ), (10°-20 °), and >20° respectively. The field lines in these figures are from the Tsyganenko 1989 vacuum model with tilt angle of 5°, 15 °, and 25° . Again, the bars show the median values. For tilt angle of 0 °-10° , the medians are located between field lines of 81 °-82° . For tilts of 10°-20 °, the medians are within field lines of 82 °-83° invariant latitude. For tilts >25° , the medians move a little poleward and are around the field line with an invariant latitude of 83°. Thus, when the dipole tilts more toward the Sun, the cusp moves poleward, to higher invariant latitudes.

Figure 4 shows the invarant latitude of the cusp crossings versus the dipole tilt angle. Here all the data regardless of the IMF condition are shown. The bars are the median values. Again, there is an upward trend in this figure. If we fit these points linearly, we see that the cusp moves 1 ° invariant latitude for 14 ° increase in the tilt angle. We have also examined the possibility of the thickness of the cusp depending on the tilt angle but found no significant dependence.

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