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If neutrino detectors keep improving so that a fair number of neutrinos can be observed, would they be as informative for astronomy as photons are?

They are of course a very valuable complement to photons, but I'm thinking about neutrinos in and of themselves. Photons have wavelength, spectral lines, redshift, diffraction, polarization which reveal their origin and interactions on the way to us. Do neutrinos say more than just what direction they come from?

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This is a very broad question and though a comprehensive answer lies outside the scope of this simple Q&A format, I give you a couple of examples where "neutrino telescopes" would revolutionary.

  1. There is a predicted cosmic neutrino background, analogous to the cosmic microwave background. Neutrinos decoupled at 1 second after the big bang, filling the universe with neutrinos that should have now cooled to a temperature of about 1.9 K. Confirming this would be a(nother) spectacular validation of the big bang model. However, there is a wrinkle; now that we know neutrinos have mass, it turns out that these neutrinos are non-relativistic at the present epoch. That means they are capable of being diverted and concentrated by gravitational structures - potentially making them fantastic probes of such structure and perhaps more sensitive than photons. So neutrino telescopes would make a fantastic contribution to our understanding of cosmology.

  2. Neutrinos arise from energetic processes in the cores of stars. These processes are otherwise invisible, we certainly can't see them directly with light and can only probe them indirectly using techniques such as asteroseismology or looking at the mixing of chemical elements from the core to the surface. Neutrinos potentially tell us much more; for instance giving a direct estimate of the number of nuclear reactions taking place per second. Neutrino emission is also the predominant way that cooling takes place in supernovae, and in hot neutron stars and white dwarfs. A neutrino telescope could therefore be fundamental for a deep (literally) understanding of stellar evolution and particularly the late stages of stellar evolution.

In terms of what can be measured; you can measure the flux of neutrinos and the neutrino energy spectrum. There is also of course the timing information that you might get from transient events like supernovae. There is also the question of flavour oscillations and the mix of neutrino types that are observed. I don't understand enough about this to make any predictions about how astronomically useful this property is - but I bet it will be.

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