Why under ice?
The Cherenkov Effect and More
As we've discovered, since neutrinos only weakly intereact with other particles, it makes them incredibly difficult to detect. However, charged particles have a property that allows them to emit a cone of bluish light when they are travelling at ultra-relativistic speeds. This is called the Cherenkov effect, and while it's not 'seeing' a neutrino directly, it's more like observing the effects of it. This is not the easiest concept to understand, but we'll try to break it down here.
First of all, this Cherenkov effect only applies to charged particles, and neutrinos are neutral! The first step in all of this is the neutrino interacting with a nucleon in some medium, producing other particles. If the neutrino is a muon neutrino, it naturally produces a muon. The muon is a charged particle and can now produce cherenkov light
When a jet breaks the sound barrier in air, not only is there a sonic boom, but there is a visible cone of condensation from a dramatic change in pressure. This occurs when something moves faster than the speed of sound. When something moves faster than the speed of light, there is the cherenkov effect!
Jets breaking the sound barrier
Muons breaking the 'light barrier'
Faster than the speed of light? Most of the time that's impossible, but keep in mind that the 3*10^8 value that you learn in physics class is the speed of light in a vacuum. When light is traveling through some medium such as water or ice or glass, it slows down according to the refractive index of the medium. So when we have a muon that is traveling at ultra-relativistic speeds, we can set up the following diagram and set of equations
Let segment AB be the path of the light emitted (remember it is emitted as a cone) and AC be the path of the particle radiating the light. In some time t, they will each cover a certain distance and by using the distance traveled by each, we can find out at what angle this light is being emitted.
The first thing is to set up the speeds of each of the paths. We know that the velocity of the particle (v) will be faster than light in the medium (c/n). We can put both term in units of light with gives us the next expression. Finally we can express the qantity v/c as beta.
Now we set up a simple trig ratio for the angle of the light. We can use our already simplified side lengths, and simply further to one rational exppression. Finally, if our particle is travelling at ultra-relavivistic speeds, the ratio v/c or beta as we call it, will be basically 1. This causes the expression to simplify further. Now to find theta, we just take the inverse cosine of 1/(refractive index of medium). In water, this angle will be about 43 degrees, and in ice about 41.
So why do we need to build these detectors underwater or underice? First of all, the environment needs to be dark. The light emitted by these interactions (in the 300-600 nm range) is incredibly dim, and there is no chance of spotting it in daylight or with any source of ambient light. By going kilometers under the ice or underwater, teams can be assured of minimal interference. Also, these provide a transparent medium for the muons and the light to travel trough. This effect can take place in say rock, but there would be no way to detect it. Ice and water allows the light to travel with minimal absorbtion and scattering. Finally, water and ice are relatively inexpensive compared with some of the alternatives. You could hollow out a cave and place a detector undeground to be guaranteed a dark envoronment, but for something like IceCube which is a kilometer scale detector, the cost and dangers of drilling and hollowing that much dirt and rock would astronomical. Water and ice provide inexpensive, natural detectors.
There is some debate as to which medium is better, water or ice. And the answer is: it depends. Each of the mediums have qualities that make them more suitable depending on the situation. What you really need to look at is the attenuation of the medium. Attenuation is a property based on the absorbtion and the scattering of the meduim. In water, light is absorbed much quicker than in ice, but it has the advantage of much smaller scattering. This means light will not travel as far, but the muons will travel undeflected so the reconstructed tracks are more accurate. In ice, the absorbtion length is much longer, but the scattering is higher. This means that you can see events from farther away, but there is less certainty that the light actually came from any particular direction. The scattering of light, together with the timing recision of the OMs, determine a neutrino telescope angular resolution.