A Wittgenstein Workbook by Christopher Coope, Peter Geach, Timothy Potts, Roger White

By Christopher Coope, Peter Geach, Timothy Potts, Roger White

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One feature is that the spectrum of direct neutrinos emitted by the fluid, at the decoupling temperature of Tν = 100 GeV, peaks at a lower energy than the spectrum of neutrinos that would be emitted directly as Hawking radiation. The peaks are located approximately at √ Tν TH for the fluid and at 5TH for the Hawking neutrinos. 15: The instantaneous direct neutrino spectra emerging from the fluid with neutrino-sphere located at Tν = 100 GeV compared to the direct Hawking radiation. Also shown are neutrinos arising from pion, direct muon and indirect muon decays at a decoupling temperature of Tf = 100 MeV.

36 We assume that dmax < λγγ for simplicity, although that assumption can be relaxed if necessary. Let Adet denote the effective area of the detector that can measure gamma rays with energies equal to or greater than Emin . The average number of gamma rays detected from a single explosion a distance dmax away is Adet Nγ (E > Emin ) = 4πd2max ∞ Emin dNγ Adet m2P Tf dE = . 41) Obviously we should have Emin as small as possible to get the largest number, but it cannot be so small that the simple E −4 behavior of the emission spectrum is invalid.

All curves are for one flavor of neutrino or anti-neutrino. viscous flow degrades the average energy of particles composing the fluid, but the number of particles is greater as a consequence of energy conservation. In the viscous fluid picture of the black hole explosion direct neutrinos are emitted as Hawking radiation without any rescattering when TH < Tν , whereas when TH > Tν they are assumed to rescatter and then be emitted from the neutrino-sphere located at Tν . It is incorrect to add the two curves shown in these figures.

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