As previously mentioned, polarization measurements of auroral roar emissions Shepherd et al.,  indicate that direct X mode mechanisms cannot produce auroral roar emissions and suggest that an indirect mechanism involving, for example, electrostatic upper hybrid Z mode waves, is more likely. Such a mechanism requires a conversion to escaping O mode waves in order to explain the ground-based observations. Theoretical support for Z mode generation is given by Kaufmann , who calculates that positive slopes in measured energetic electron distribution functions during rocket flights over bright aurora are large enough to drive electrostatic instabilities that peak when = 2. The role of UH waves is also supported by rocket data which show that UH waves are particularly intense when the condition 2 is met [Cartwright and Kellogg, 1974; Carlson et al., 1977]. For example, Gough and Urban,  observed strong modulations in the auroral electrons at the local upper hybrid frequency when 2.65 MHz 2. Recently, a more general electromagnetic treatment of the magnetoionic growth rate calculations confirms that the 2 and 3 modes are largest when the upper hybrid matching condition is satisfied [Yoon et al., 1998]. Here Z2 and Z3 represent Z mode waves at 2 and 3 respectively.
This Z mode generation theory requires that the upper hybrid matching condition be satisfied somewhere in the ionosphere at all the altitudes where the observed emission frequency matches the local gyroharmonic (2 or 3). The ISR data can be used to test this mechanism as follows: first, the International Geomagnetic Reference Field (IGRF) model for the Earth's magnetic field [International Association of Geomagnetism and Aeronomy Division I Working Group 1, 1985] is used to determine the altitude profile of , 2, and 3. Second, the profile is combined with measured by the ISR to obtain a profile of the upper hybrid frequency ( = + ) over the plane scanned by the radar. The upper hybrid matching condition ( = 2 or 3) is then determined over this plane. Finally, the observed auroral roar frequencies are used to compute an altitude range over which the matching condition must be satistfied. In Plates 1-6, a solid black contour on each color plot indicates where the computed upper hybrid matching condition = 2 or 3 occurs based on the radar estimate of , and a dotted and dashed contour indicate the larger region in which this condition may hold when the density-dependent uncertainty in the radar electron density measurement is taken into account. Horizontal dashed lines in each ISR scan mark the altitude range corresponding to the emission observed during the displayed scan. Likewise, the horizontal dotted lines represent the altitude range of the entire auroral roar event, including portions occurring before and after the radar scan shown. In order for the upper hybrid matching condition theory to explain the observed auroral roar emissions, a solid, dotted, or dashed contour must span the entire altitude range defined by the horizontal dashed lines.
Plate 1 shows that during the first roar event on August 3, 1995, the upper hybrid matching condition is not obtained in the F region during the observation of either 2 or 3 auroral emissions. For the time during which roar is observed at 3 in segment B, a small region which satisfies the matching condition is seen around 300 km altitude, but none exists at higher altitudes to explain the lower frequencies of the observed emissions. Possible weak 3 roar is observed in segment C with even less evidence of the matching condition. The time during which 2 is most strongly observed in segment E shows essentially no upper hybrid matching in the required altitude range, except at the very lower edge (~200 km).
On the other hand, Plate 2 shows that on August 15, 1995, during the times of the strongest 2 observation in segment D there is a region roughly 150 km geographically southeast of the radar where the matching condition is satisfied through the entire frequency range of the observed auroral emission. The matching condition also holds through the entire frequency ranges of less intense observed roar during segments B-E. Unfortunately there is limited radar data available for the time from 0301:08 to 0305:43 UT (panel F) during which an intense auroral roar is observed. However, even with the limited data it can be seen that matching exists nearly through the entire range of roar frequencies observed.
Plate 3 shows that often several spatially separated regions exist in the ionosphere for which the matching condition is satisfied over the observed frequency range of the emission. On November 1, 1995, starting at 1923:52 UT (segment A), regions approximately 100 km south, 100 km southwest, and 250 km northwest of the radar all show large areas where matching exists at all observed frequencies. In segments A-C, an area ~250 km long, 100-200 km southeast of the radar, in which the matching condition is satisfied through the entire observed emission frequency range, persists for nearly 20 min. Even during times of weak or intermittent roar emissions, such as segments D, E, and F, the matching condition occurs throughout nearly the observed auroral roar frequency range. As noted above, auroral roar may occur at these times in the ionosphere but is screened from the ground station by enhanced electron density at low altitudes.
Plate 4 shows auroral emissions on March 12, 1996, when the ISR performed a series of elevation scans. Strong emissions in segment A coincide with areas ~200 km southeast and ~300 km northwest of the radar where the matching condition is satisfied throughout the entire frequency range of the emission. In the subsequent radar scans B-D the matching condition exists at all observed roar frequencies, although the emission is weak or absent. The strong emission during segment E is most likely associated with a matching condition region nearly directly overhead.
Plate 5 shows a 2 roar event on March 29, 1996 (segment C). Unfortunately, the fits to ISR autocorrelation functions exhibited large uncertainties above 300 km due to poor signal-to-noise ratio. Within these uncertainties, the matching condition appears to explain the full range of observed auroral roar frequencies. Similar regions where the matching condition is met occur in the other scans. In particular, the ISR briefly obtains data from >300 km in scan B which indicate that the matching condition exists at altitudes >300 km and probably throughout the full range of observed frequencies for this event.
Plate 6 shows that during the onset of the 2 roar emission in segments A and B on April 9, 1997, the matching condition occurs through the entire frequency range of the observed auroral roar emission. During radar scan C, it appears probable that the matching condition is obtained over the entire range of auroral roar source altitudes, although this cannot be established with certainty due to large uncertainty in the radar measurements at critical locations. In scans D, E, and F the matching condition is obtained 400 km south of the radar for a large part of the observed frequency range of weak intermittent roar emissions.
Table 1 summarizes the presence or absence of the hybrid matching condition = 2 or 3 during the six days of auroral roar observations analyzed in this paper. The matching condition was satisfied at some location for nearly the entire frequency range of the observed auroral roar emissions in 16 out of 18 ISR scans. The matching condition was satisfied at least at some of the observed auroral roar frequency ranges for the remaining two cases. In particular, in all three elevation scans, in which the radar measures electron densities directly above the station, the upper hybrid matching condition is satisfied for the entire frequency range of the observed auroral roar emissions. These data strongly suggest that the upper hybrid matching condition plays a role in the generation of auroral roar. The few scans that have no matching between observed auroral roar frequency ranges could be attributed to the limited spatial/temporal resolution and spatial coverage of the ISR as configured for these runs. As previously stated, radio data from other stations suggest that auroral roar most likely originate from nearly overhead, and add greater weight to the three elevation scans which all show matching regions (see Plate 4). At the very least, the ISR data do not rule out the theories of auroral roar generation which are based on excitation of upper hybrid waves when = 2 or 3.