Secondary CZA from Sun Pillar

* For ease of reading, in the following texts: CZA = circumzenithal arc, CNA = circumnadir arc.

The Siziwang Qi display (http://www.thehalovault.blogspot.com/2020/02/intense-kern-arc-from-china.html) on Feb 14 2020 has almost certainly secured itself a spot in the halo history book, featuring record-high 44° parhelia, full circle Kern arc and off-the-chart overall intensity.

The story doesn't just end there.

In a discussion with Marko Riikonen, he pointed us to a similar Finnish moonlight display in 2013 (https://www.taivaanvahti.fi/observations/show/19422), during which a novel arc was discovered below the moon CZA. Seven years have passed and a repeat event is long overdue. Now the wait is officially over.

As more Siziwang Qi material emerged, one of them caught our attention. In the following iPhone photo by LI Tingfang, there seems to be hint of a long, sun-vex arc below the dazzling CZA.

© LI Tingfang, shown with permission

With some minor processing, the arc stands out and appears surprisingly well defined. It looks exactly like the novel arc in the 2013 Finnish display.

© LI Tingfang, shown with permission

© LI Tingfang, shown with permission

Back then, Nicolas Lefaudeux managed to replicate the Finnish display scene with simulation and identified the novel arc to be a multi-scattered secondary CZA created by the moon pillar. In the Siziwang Qi display, strong sun pillar appeared in most material and multi-scattering has been proven intense, so it's very likely Nicolas' theory applies here too. After some experiments, we managed to reproduce the secondary CZA in simulation by introducing a large amount of pillar-making wobbly plates.

Simulation by ZHANG Jiajie

At first the appearance of the secondary CZA in both displays baffled us. It's hard to imagine how the long and diffuse pillars create such a sharp-looking arc. With the help of ZHANG Jiajie's simulation program we were able to dissect the arc and fully grasp the underlying mechanism.

First let's review the CZA mechanism:

• Light source altitude 0° ~ 33°: CZA ray path 1-3 works. When light source drops to 0°, CZA reaches minimum altitude of around 57°. 
• Light source altitude -33° ~ 0°: CZA ray path 1-3 no longer works. Instead, the 'flipped' CNA ray path 2-1-3 kicks in and produces a flipped CNA overhead. This flipped CNA doesn't get lower than 57° either. 

Simulation by ZHANG Jiajie, sun altitude ranges from -35° to 35° at 2.5° increment.

When the pillar is treated as the light source in multi-scattering scenarios, it can effectively be viewed as an infinite number of light sources with altitude covering the 33° to -33° range. The 0° to 33° portion creates an infinite number of CZAs, while the -33° to 0° portion creates an infinite number of flipped CNAs. These two light clusters turn out in simulation as two broad, sun-vex, zenith-hugging arcs, both capping sharply at 57° altitude.

Simulation by ZHANG Jiajie, sun altitude 20.8°

These two secondary arcs together get us the sharp-looking novel arc in the Finnish and Siziwang Qi displays. As long as the pillar covers the horizon, the arc's overall appearance hardly changes as light source rises. The intensity of the arc peaks when light source sits low, which makes sense since pillar also peaks under the same condition.

Simulation by ZHANG Jiajie, sun altitude ranges from 0° to 25° at 5° increment.

When light source altitude drops below 15°, the arc's close proximity to the original CZA could severely hinder detection. According to the animation below, altitude 15° to 25° may be the most ideal observing window.

Simulation by ZHANG Jiajie, sun altitude ranges from 0° to 25° at 5° increment.

There's one thing in the actual display that doesn't go well with simulations. The azimuthal extent of the arc is very long in the actual photo, as if it'll go full circle. The simulated arc, however, hardly goes beyond the 46° halo. To make it longer in simulation, very thick triangular plates need to be employed, which doesn't sound very realistic. There're probably other light sources responsible for the arc's azimuthal extension and we'll need your help to figure it out : )

Jia Hao