The spectral-curvature parameter: an alternative tool for the analysis of synchrotron spectra

A new intuitive tool for the analysis of synchrotron spectra is presented. The so–called Spectral Curvature Parameter (SCP), when plotted versus the high–frequency spectral index (αhigh) of synchrotron sources, provides crucial parameters on the continuum spectrum of synchrotron radiation without the more complex modeling of spectral ageing scenarios. An important merit of the SCP-α diagram, in respect to the conventional colour-colour diagram (i.e. α-α diagram), is the enhanced reliability of extracting multiple injection spectra, αinj. Different from the colour-colour diagram, tracks of different αinjs, especially when the synchrotron particles are young, exhibit less overlap and less smearing in the SCP-α diagram. Three giant radio galaxies (GRGs) and a sample of Compact steep spectrum (CSS) souces, which are particularly suitable for this kind of analysis, are presented. GRGs exhibit asymmetries of their injection spectral indices αinj in the SCP αhigh diagram. The obtained αinjs and the trends in the sources are cross-checked with the literature and show remarkable confidence. Besides the spectral steepening which is well understood in the framework of synchrotron ageing models, spectral flattening is prominent in the radio lobes. The spectral flattening is a clue to efficient re-acceleration processes in the lobes. This implies that interaction with the surrounding intergalactic or intra-cluster medium is an important characteristic of GRGs. In the SW lobe of DA240, there is a clear sign of CI and KP/JP bifurcation at the source extremity. This indicates a highly relativistic energy transportation from the core or in situ acceleration in this typical FR I lobe. Our analysis proves, if exists, KP spectra imply the existence of strong Bsync field with Bsync > BCMB. In the CSS sources, our result confirms the CI model and Bsync BCMB. The synchrotron self-absorption is significant in the CSS sample.