3C 273 and the power-law myth

There is no doubt that power-law representations fit the continuum observations of quasars very well over limited (about one decade) frequency ranges, notably the radio and X-ray. Over the entire observed frequency range (spanning 14 decades), however, the subjective goodness of fit can be distorted by the method used to plot the data. The continuous fall in the log of the flux density when this is plotted against increasing log-frequency can give the impression of a reasonable fit to a power law, whereas the physically more meaningful plot of the log (ν x flux density), which peaks at frequencies where most of the energy is emitted, tends to reveal more structure in the energy distributions and to show up the limitations of power-law fits. It is found that a log normal (Gaussian) distribution in photon energy is a significantly better fit to the data than a power law and, in addition, has the advantage of much reducing the number of allowed free parameters. (author)