Augmented Superfield Approach to Nilpotent Symmetries in the Modified Version of 2D Proca Theory

We derive the complete set of off-shell nilpotent and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST), anti-BRST and (anti-)co-BRST symmetry transformations for all the fields of the modified version of two (1+1)-dimensional (2D) Proca theory by exploiting the "augmented" superfield formalism where the (dual-)horizontality conditions and (dual-)gauge-invariant restrictions are exploited together. We capture the (anti-)BRST and (anti-)co-BRST invariance of the Lagrangian density in the language of superfield formalism. We also express the nilpotency and absolute anticommutativity of the (anti-)BRST and (anti-)co-BRST charges within the framework of augmented superfield formalism. This exercise leads to some novel observations which have, hitherto, not been pointed out in the literature within the framework of superfield approach to BRST formalism. For the sake of completeness, we also mention, very briefly, a unique bosonic symmetry, the ghost-scale symmetry and discrete symmetries of the theory and show that the algebra of conserved charges captures the cohomological aspects of differential geometry. Thus, our present modified 2D Proca theory is a model for the Hodge Theory.Comment: LaTeX file, 32 pages, journal reference give

The Origin of X-shaped Radio Galaxies: Clues from the Z-symmetric Secondary Lobes

Existing radio images of a few X-shaped radio galaxies reveal Z-symmetric morphologies in their weaker secondary lobes which cannot be naturally explained by either the galactic merger or radio-lobe backflow scenarios, the two dominant models for these X-shaped radio sources. We show that the merger picture can explain these morphologies provided one takes into account that, prior to the coalescence of their supermassive black holes, the smaller galaxy releases significant amounts of gas into the ISM of the dominant active galaxy. This rotating gas, whose angular momentum axis will typically not be aligned with the original jets, is likely to provide sufficient ram pressure at a distance ~10 kpc from the nucleus to bend the extant jets emerging from the central engine, thus producing a Z-symmetry in the pair of radio lobes. Once the two black holes have coalesced some 10^7 yr later, a rapid reorientation of the jets along a direction close to that of the orbital angular momentum of the swallowed galaxy relative to the primary galaxy would create the younger primary lobes of the X-shaped radio galaxy. This picture naturally explains why such sources typically have powers close to the FR I/II break. We suggest that purely Z-symmetric radio sources are often en route to coalescence and the concomitant emission of substantial gravitational radiation, while X-shaped ones have already merged and radiated.Comment: 12 pages, 1 compressed figure; accepted for publication in ApJ Letter