Friday, September 10, 2010

Neutrinos and Supernovae

Over at the astronomers' forum Galaxy Zoo, member Graham D discusses implications of the unequal $\nu$ and $\overline{\nu}$ Koide masses for cosmology and astrophysics.

In particular, he notes that the very small masses indicate appearance threshold temperatures of relatively recent cosmic epochs. The smallest mass (for the electron neutrino) is $0.0038$ eV and this corresponds to a temperature of $4.41$ K at a cosmological redshift of $z = 0.60$. Graham argues that such recent universal phase changes ought to have observable effects on stellar processes at these special epochs. For instance, supernovas emitting significant energy in massive neutrinos would appear to be dimmed in the optical. It is noted that the supernovae data (see plot below) are beginning to reach a point where kinks at certain redshifts may be detected. Similarly for other stellar processes.

This example merely scratches the surface of ramifications of this Koide sector for astrophysics. Graham rightly chastises me for not elaborating on the possible significance of the $24$th root of unity, namely the phase $\pi /12$. Like Brannen, he appears to be fond of a $12$ neutrino description of mass generation, but personally I see no reason to describe quantum gravitational degrees of freedom with the old language when the terminology of M theory black hole physics is available.

That there is an arithmetic significance to the information dimension $24$ is obvious to mathematicians. For example, the modular discriminant is the $24$th power of the Dedekind eta function on the upper half plane. The Leech lattice in dimension $24$ exists basically because $1^2 + 2^2 + \cdots + 24^2 = 70^2$, and $24$ is the only integer $> 1$ with this square property. The Leech lattice may be given as three copies of the E8 lattice in dimension $8$. Ultimately, this is why I am happy to think about the eighth roots (namely the $\pi /4$ of the basic $R_2$ matrix), because they are also fundamental.

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