The radio counter-jet of the QSO 3C 48

We present multi- frequency radio observational results of the quasar 3C 48. The observations were carried out with the Very Large Array ( VLA) at five frequencies, 0.33, 1.5, 4.8, 8.4, and 22.5 GHz, and with the Multi- Element Radio Linked Interferometer Network ( MERLIN) at the two frequencies of 1.6 and 5 GHz. The source shows a one- sided jet to the north within 1", which then extends to the northeast and becomes diffuse. Two bright components ( N2 and N3), containing most of the flux density, are present in the northern jet. The spectral index of the two components is alpha(N2) similar to -0.99 +/- 0.12 and alpha(N3) similar to - 0.84 +/- 0.23 ( S proportional to nu(alpha)). Our images show the presence of an extended structure surrounding component N2, suggestive of strong interaction between the jet and the interstellar medium ( ISM) of the host galaxy. A steep- spectrum component, labelled S, located 0.25 " southwest to the flat- spectrum component which could be the core of 3C 48, is detected at a significance of > 15 sigma. Both the location and the steepness of the spectrum of component S suggest the presence of a counter- jet in 3C 48.

Bending of jets in the QSO NRAO 530

We present radio images of NRAO 530 on scales ranging from pc to kpc. The observations include the EVN at 5 GHz, the VLBA at 1.6, 8.6 and 15 GHz, the MERLIN at 1.6 and 5 GHz, and the VLA at 5, 8.4, 15, 22, and 43 GHz. The VLBI images show a core-jet structure with an oscillating trajectory on a scale of about 30 mas north of the strongest compact component (core). Superluminal motions are detected in five of the jet components with apparent velocities in the range of 13.6 to 25.2c. A new component is detected at 15 GHz with the VLBA observations, which appears to be associated with the outburst in 2002. Significant polarized emission is detected around the core with the VLBA observations at 15 GHz. Rapid variations of the polarization intensity and angle are found between the epochs in 2002 and 2004. On the kpc-scale, a distant component (labelled as WL) located 11 aresec west (PA=-86 degrees) of the core is detected beyond the core-jet structure which extended to several hundreds of mas in the north-west direction (-50 degrees). A significant emission between the core-jet structure and the WL is revealed. A clump of diffuse emission (labelled EL, 12 arcsec long) at PA 70 degrees to the core, is also detected in the VLA observations, suggesting the presence of double lobes in the source. The core component shows a flat spectrum, while the distant components WL and EL have steep spectra. The steep spectra of the distant components and the detection of the arched emission suggest that the distant components are lobes or hot-spots powered by the core of NRAO 530. The morphologies from pc- to kpc-scales and the bending of jets are investigated. The observed radio morphology from pc to kcp appears to favor the model in which precession or wobbling of the nuclear disk drives the helical motion of the radio plasma and produces the S-shaped structure on kpc scale.

Free radial oscillation of a sphere in relativistic elasticity theory

The spherically symmetric free radial oscillation in the first post-Newtonian approximation for a homogeneous and isotropic elastic sphere with a constant density is studied. Based on the Xu, Wu, and Soffel formalism, the relation of the oscillation frequency of the sphere with the radius, mass density, and elastic constants of the sphere is derived by using the successive approximation method.