Files contain data related to emission of the pair
annihilation electron anti-neutrinos from pre
-supernova star. </br></br>

s15_nuebar_data.txt : 15 M_sun star </br>
s25_nuebar_data.txt : 25 M_sun star </br>

<b> Description of data: </b> </br>
Column 1 - original stellar evolution code timestep number </br>
Column 2 - time remaining to start of the core-collapse in seconds </br>
Column 3 - total energy ( Q ) emitted in the form of electron anti-neutrinos [erg/s] </br>
Column 4 - number (R) of electron anti-neutrinos emitted from pre-supernova [1/s] </br>
Column 5 - average energy ( Eavg ) of electron anti-neutrinos [MeV] </br>
Column 6 - dispersion ( Sigma ) of the electron anti-neutrino spectrum [MeV] </br>
Column 7 - first parametr ( a ) of the analytical approximation for the spectrum <br>
Column 8 - second parametr ( alpha ) of the analytical approximation for the spectrum <br>
Column 9 - third parametr ( b ) of the analytical approximation for the spectrum </br>
<br>
<br>
Parameters from Cols 7-9 form analytical approximation of the electron anti-neutrino
spectrum emitted by a pre-supernova star with formula:
<br><br>
(1)   dN(t)/dEnu = a*Enu^alpha*exp(-b*Enu) [1/s/MeV] <br>
<br>
Average energy and dispersion for this formula is equal to values provided
by Cols 5 and 6, respectively. Values in Cols 3-6 are exact and may be used
to construct other analytical approximations for the spectrum. Formula (1) however,
works very well under typical pre-supernova  conditions. 
<br>
In the terms of the spectrum moments (R, Q, J - 1st, 2nd and 3rd moment, respectively) 
parameters above are equal to:
<br>
(2)   Eavg=Q/R
<br>
(3)   Sigma = sqrt(R*J-Q*Q)/R
<br>
(4)   alpha = Q*Q/(R*J-Q*Q)-1
<br>
(5)   b =  R*Q/(R*J-Q*Q)
<br>                                  
(6)   a = R*b^(1+alpha)/Gamma(1+alpha)            
<br><br>
Note, that replacing a with a/R gives spectrum
normalized to 1.