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

The so-called Spectral Curvature Parameter(SCP), when plotted versus the high-frequency spectral index ($alpha_{high}$) 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-$alpha$ diagram is the enhanced reliability of extracting multiple injection spectra, $alpha_{inj}$. Different from the colour-colour diagram, tracks of different $alpha_{inj}$s, especially when the synchrotron particles are young, exhibit less overlap and less smearing in the SCP-$alpha$ diagram. Three giant radio galaxies(GRGs) and a sample of Compact steep spectrum(CSS) souces are presented. GRGs exhibit asymmetries of their injection spectral indices $alpha_{inj}$ in the SCP-$alpha_{high}$ diagram. The obtained $alpha_{inj}$s and the trends in the sources are cross-checked with the literature and show remarkable confidence. Besides the spectral steepening, spectral flattening is prominent in the radio lobes. The spectral flattening is a clue to efficient re-acceleration processes in the lobes. It implies 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 $B_{sync}$ field with $B_{sync} > B_{CMB}$. In the CSS sources, our result confirms the CI model and $B_{sync} >> B_{CMB}$. The synchrotron self-absorption is significant in the CSS sample.