Quasi-constant time gap in multiple rings of elves

TL;DR

Using the Pierre Auger Observatory's fluorescence detectors with 100 ns timing, the study analyzes double and triple elves across four storms to test whether their inter-ring delays arise from ground-reflected EMPs or from lightning waveform properties. The authors extract peak times from per-pixel elf traces via Gaussian fits, define inter-peak delays $ΔT_d$ and $ΔT_t$, and correlate these with arc distance $D_{arc}$ and lightning waveform features, notably the base time $t_{b2}$ of the second waveform component. They find that $ΔT$ is largely independent of $D_{arc}$, challenging EMP ground-reflection models, and reveal a strong association between larger delays and the duration of the lightning current pulse, suggesting waveform-driven elf generation. The results imply that current mechanisms for multi-elves are incomplete and highlight the need to prioritize lightning waveform characteristics in future models and measurements.

Abstract

We present evidence that the time delay between the multiple rings of elves is not caused by the ground reflection of the electromagnetic pulse produced by intracloud lightning. To investigate temporal differences of multi-elves, we analyzed data from four storms occurring at various times and distances from the Pierre Auger Observatory in Malargüe, Argentina. The Auger fluorescence detector's high temporal resolution of 100 ns enabled the frequent observation of multi-elves, accounting for approximately 23% of the events. By examining the traces of 70 double and 24 triple elves, we demonstrate that the time delay between the rings remains relatively constant regardless of the arc distance to the lightning. These results deviate from the trend expected from the electromagnetic pulse (EMP) ground reflection model, which predicts a decreasing time delay with increasing arc distance from an intracloud lightning at a given height. The first emission ring is due to a direct path of the EMP to the ionosphere, with the reflected EMP creating the second ring. Simulations conducted with this model demonstrate that short energetic in-cloud pulses can generate four-peak elves, and a temporal resolution of at least 25 $μ$s is required to separate them. Therefore, temporal resolution is crucial in the study of multi-elves. Our observations in the Córdoba province, central Argentina, indicate that the current understanding of the mechanism generating these phenomena may be incomplete, and further studies are needed to assess whether multi-elves are more likely related to the waveform shape of the lightning than to its altitude.

Figures (9)

• Figure 1: Left panel: pixels of two FD cameras triggered by a typical single elve. This event was detected on April 28, 2020, at 04:08:13 UTC. The colours show the time evolution of the light as seen in the FD cameras, which usually lasts around 300 $\mu$s. Right panel: time evolution of the event as projected at the base of the ionosphere fixed at an altitude of 92 km. After correcting for the transit time from the emission layer to the FD, we observe the concentric spread of light from the source lightning at 36.57$^\circ$ S and 64.54$^\circ$ W (Auger bolt location). The Earth Networks (ENTLN) lightning location correlated with this event, 36.64$^\circ$ S and 64.53$^\circ$ W, aligns with our determined location. The red stars indicate the locations of the four FD buildings.
• Figure 2: Top panel: time evolution of the first peak of a double elve event detected by an FD telescope on April 28, 2020, at 03:09:17 UTC (left), and a triple elve event at 02:07:17 UTC (right). The highlighted pixel in each camera was selected to illustrate typical double-peak and triple-peak signals. Middle panel: examples of prominent peaks $t_1$ and $t_2$ for the double elve in row 16 pixels, and $t_1$, $t_2$, $t_3$ for the triple elve in row 8 pixels. Row numbers increase with pixel elevation, and column numbers decrease with azimuth, as shown in the top panel. The distinct parabolic patterns of the elves emission are visible in both cases ($t_1$ fit, $t_2$ fit and $t_3$ fit). Bottom panel: examples of Gaussian fitting for the double elve signal in row 16, column 11, and the triple elve signal in row 8, column 7.
• Figure 3: a) Schematic of the arc distance ($\mathrm{D_{arc}}$) between the lightning source ($\mathrm{Lat_s}$, $\mathrm{Lon_s}$) and the emission point at the ionosphere P. We determine the position of point P ($\mathrm{Lat_{pix}}$, $\mathrm{Lon_{pix}}$) by projecting a camera pixel's position onto the ionosphere, using the associated site coordinates ($\mathrm{Lat_{site}}$, $\mathrm{Lon_{site}}$). Additionally, we calculate the lightning location ($\mathrm{Lat_s}$, $\mathrm{Lon_s}$) based on the observed light-time distributions of recorded elves. b) Time delay between two peaks of an elve, given by the equations \ref{['eq:distances']} and \ref{['eq:dt']}, with the ionosphere height fixed at 92 km and various values of lightning height ($h_\mathrm{s}$). c) Varying the ionosphere height does not significantly change the functionality of the curves of $\Delta T$ with distance $\mathrm{D_{arc}}$.
• Figure 4: a) All traces of the double elve event from Figure \ref{['fig:peakfinder']} in Coihueco (CO), with the first peak aligned to the lightning source time ($t=0$). b) Time difference of the event at CO and Los Leones (LL), with a mean value of $(87\pm1) \,\mu$s. The bouncing mechanism model curves for 5, 10, and 20 km lightning heights are also displayed. c) Traces of the triple elve event from Figure \ref{['fig:peakfinder']} in CO, with the first peak aligned to the lightning source time ($t=0$). d) The result of $(t_2-t_1)$ and $(t_3-t_1)$ from LL and CO, with mean values of $(19 \pm 2)\mu$s and $(98 \pm 8) \,\mu$s respectively. e) Traces from an event showing multiple pulses that are significantly wider (halo) compared to typical elve pulses, occurring between 20 and 150 km of $\mathrm{D_{arc}}$. $t=0$ is the time of the lightning bolt occurring on April 28, 2020, at 03:10:01.795992 UTC. Beyond 150 km, traces of a double elve are observed (see zoomed-in plot). f) Time difference ($t_2 - t_1$) for the double elve, with a mean value of $(10 \pm 1)\, \mu$s. Other values represent the time difference between the double elve and halo traces ($t_H - t_E$). This event was detected at two FD buildings, CO and LL.
• Figure 5: Distribution of the average time difference of the multi-elves of four storms detected by the FD. Each storm has a different distribution, with the April storm having the most events. The FD high temporal resolution allows reporting events with $\overline{\Delta T}< 10 \,\mu$s. The fifth histogram shows that most events fall within the 10 to 40 $\mu$s range and between 60 and 100 $\mu$s. Additionally, some events exhibit $\overline{\Delta T}$ values exceeding 200 $\mu$s, and in rare cases, around 450 $\mu$s, associated with combined elves and halo events.