SIMBAD references

The very steep spectrum radio sources (VSSRSs) found in clusters of galaxies are believed to be relic radio galaxies whose nuclei have ceased their activity. The unusually steep spectra of the sources (α≤-2.0) are explained by the synchrotron losses of energy of relativistic electrons after the cessation of the injection of fresh particles into the radio lobes. Such strongly evolved spectra provide a good opportunity to choose between the two principal models of spectral ageing - that of Kardashev and Pacholczyk (which assumes an anisotropic pitch angle distribution of the relativistic electrons) and that of Jaffe and Perola (which assumes an isotropic distribution of them). However, when the integrated spectra of the relic radio sources are considered, an additional factor, a finite time of the injection of the relativistic particles, could be important. We modify the two models to take this factor into account. We also study the role of the energy loss due to inverse Compton scattering of 3K background photons and found that this prevents the formation of the power law region with spectral index (4/3)α₀-1 in the KP-model unless the magnetic fields are stronger than 10^–4 G. The position of the high-frequency cutoff caused by the losses depends only on the time since activity ceased (and on redshift) and as a result the shape of our version of the KP-spectrum could be used to estimate the magnetic fields strength in the VSSRSs and correspondingly to test the equipartition hypothesis. We compared the predicted spectra with the observed ones of six VSSRSs - Mol0100-221, Cul0038-096, 4C63.10, 4C38.39, 3C318.1, and 3C464. The goodness of fits of our models and estimations of their free parameters were determined by using the minimum χ² technique. Remarkably good fits are provided by our version of the KP-model with the injection spectral index α₀=-0.5, and the exponential cutoff at high frequencies caused by the inverse Compton losses. In the context of the model we found typical magnetic fields in the VSSRSs of order 10^–5G, several times higher than the equipartition values, and the typical time of their decay, τ ≃10⁸yr. Our version of the JP-model provides worse fits. However, significant improvement can be achieved if one takes into account possible strong variations of magnetic field strength (H_max/H_min > 3) in these sources. By considering the active stages of these VSSRSs we found that their progenitors were high luminosity (≥10⁴³ erg/s) radio galaxies rarely found in clusters of galaxies. Most other relic sources probably escape from flux limited samples due to a drop of their luminosity.