Polynomial Fit to the Data

A 3rd order polynomial (cubic) expressing $\log\,$Flux versus $\log\,$Frequency was fitted to the data in the first two columns of the Table to produce the values in the third column. All values were given equal weight. The fitting procedure does not cope particularly well with the complex spectral shape of 1934-638, and deviates by as much as $\sim$1% from a smooth curve drawn by hand (eg all the 4.8GHz data points fall slightly below the fit). Proceeding to a 4th order polynomial did not greatly improve the fit however and given the convenience of the polynomial form, no attempt has been made to investigate other methods of interpolation or fitting. It should be noted that at frequencies other than those tabulated here (eg 6.7GHz) the polynomial fit may not interpolate accurately the true spectral shape of 1934-638 and errors somewhat larger than 1-2% are possible. The derived 3rd order polynomial is given by;

$\log S = -30.7667 + 26.4908\log F - 7.0977(\log F)^{2} + 0.605334(\log F)^{3}$,

where $S$ is the flux density of 1934-638 in Jy, and $F$ is the frequency in MHz. The fit is drawn in Figure 1, with the measurements tabulated in column 2 of the Table shown as crosses.

Figure F.1: Flux density measurements of 1934-638, with 3rd order polynomial fit.