Interpretation of the Shakeshaft-Scheuer Data in Terms of the 4-Parameter Evolutionary Models

Abstract

We are grateful to Dr Shakeshaft and to Dr Scheuer for pointing out our error of interpretation of the Cambridge counts. As our interest was in N/N₀ rather than N , and for $$S\gt2\times10^{-26}$$ watts m ⁻² (c/s) ⁻¹ the observations were already plotted in that form by Ryle and Clarke, it appeared to us logical and expedient to use their graph for $$S\gt2\times10^{-26}$$ and to plot N/N₀ for $$S\gt2\times10^{-26}$$ from the Ryle and Neville paper, using the value for our $$\bar n_0\bar P_0^{3/2}$$ which we find quoted as $$\rho_0P_0^{3/2}$$ at tne foot of p.352 of the Ryle Clarke paper. On this page of their paper Ryle and Clarke define $$\rho_0P_0^{3/2}$$ as the “constant of proportionality” in the luminosity function “for the region containing the more intense sources”. Again, lower on the same page they state that “at distances corresponding to small red shift the expected number of sources N per unit solid angle which have flux density greater than S is given by $$N=\frac13\rho_0P_0^{3/2}S^{-3/2}$$ ”. It therefore seemed to us natural and compelling to interpret the value given for $$\rho_0P_0^{3/2}$$ as the required value for our $$\bar n_0\bar P_0^{3/2}$$ . In the light of the comments by Shakeshaft and Scheuer it now appears that this interpretation was in error and that what we attributed to statistical fluctuations in the limited Ryle and Neville observations may not be so attributed.