# The delay between neutrinos and gammas in a supernova, and the absolute mass scale of neutrinos

In a supernova explosion (of some type), there is a huge amount of neutrinos and gamma rays produced by a runaway nuclear reaction at the stellar core. In a recent comment, dmckee noted that the neutrinos actually make it out of the supernova earlier than the gamma rays because the latter do scatter in trying to get out, and that the precise details of this delay, if measured, could shed light on just how small the (nonzero) neutrino mass is.

Is there some simple way of explaining the different models at stake, or what the essential physics is behind this? Is there some accessible reference about this?

• How about this: Raffelt, G. G. (2010). Physics opportunities with supernova neutrinos. Progr. in Particle and Nuclear Phys., 64(2), 393-399. online Dec 1 '13 at 14:31

The time delay between neutrinos and photons does not tell us directly about the absolute mass of the neutrinos. The time delay between a neutrino of mass $m$ and a massless neutrino does: $$\Delta t = \frac{d}{v} - \frac{d}{c} \approx 0.5 \left(\frac{mc^2}{E}\right)^2 d,$$ where $\Delta t$ is the time delay in seconds, $v \approx c[1-\frac{1}{2}\left(\frac{mc^2}{E}\right)^2]$ from relativistic calculation, $d$ the distance to the supernova in 10 kpc (a "typical" value for Galactic supernova), neutrino rest mass $m$ in eV and neutrino energy in MeV. So it is a propagation-speed problem.
2. Yet it is not hot enough to influence two of the three neutrinos, $\nu_{\mu}$ and $\nu_{\tau}$, almost at all, and only slightly for another ($\nu_{e}$); they just fly out of the core. (weak interaction)
Take SN1987A for example, the neutrinos arrived 2-3 hours before the photons. On the other hand, $\Delta t$ calculated above, if detected, would be $\leq 1$ sec. With these two values and a bit more thinking, you might conclude that this "time of flight" method could not constrain very well the neutrinos with smaller-than-eV masses; and you would be right. There are better ways to do that. Here is a reference: http://arxiv.org/pdf/astro-ph/0701677v2.pdf.