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While I knew that IceCube existed it didn't occur to me until know that I have no idea how they filter out collisions from particles that comes from above or sideways. Is the resulting flash of light not omnidirectional? Is it polarized differently?

One of the amazing things about Cherenkov radiation is that it is not omnidirectional. There are processes (fluorescence, or scintillation, for example) which result in isotropic emission of light from materials. But Cherenkov light is emitted along a conical surface about the axis of the charged particle's direction of travel. As a sister comment said, muons tend to move linearly, so this light stacks up in a particular direction. Electrons, particularly at lower energy, scatter more, and that stacking gets washed out a bit.

That directionality is very useful. The directionality of a muon or electron produced from a neutrino interaction is correlated with the direction of the incident neutrino. That's interesting for the astrophysical kind of questions that IceCube is addressing, and it's also useful in other contexts (background rejection for fundamental physics searches, monitoring of nuclear reactors via neutrinos, ...).

Cherenkov radiation is indeed polarized, but to my knowledge that hasn't ever been made use of.

Tangentially: there's also some really cool work being done on detectors which utilize both Cherenkov and scintillation light at the same time, exploiting the directional (and other) differences to extract the most information possible out of each event.

Right, so without knowing much about physics I'm guessing that momentum is preserved and IceCube works a little bit like a giant cloud chamber but looks for trails of Cherenkov radiation rather than an ionized particle trail.

The cone of Cherenkov radiation produces arcs of "bright pixels" in the detector.

There are very good illustrations of this if you search for "Super-Kamiokande Cherenkov ring." That's a Japanese neutrino telescope with a bunch of huge photomultipliers lining the walls of a giant underground cistern filled with water. Ice Cube has similar light detectors, probably from the same Japanese manufacturer, that were lowered on strings into wells melted into ice.

I believe they reconstruct the paths simply based on the timing of detection events. Muons created by neutrino interactions travel more or less linearly and create a "bow shock" of Cherenkov radiation; it's not a single flash of light, just like a sonic boom is not a single bang. The directions of electron and tau neutrinos are more difficult to reconstruct because the associated particles tend to scatter and bounce around.

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