  Some of the radio galaxies show distortion in their jets, forming tailed or
winged sources. X-shaped radio galaxies are a subclass of winged sources
formation mechanism of which is still unclear. The focus of this work is to
understand hydro-dynamical back-flows and their role in dynamics and
non-thermal emission signatures (in presence of radiative losses and diffusive
shock acceleration) during the initial phase of these galaxies. We have
performed relativistic MHD simulations of an under-dense jet travelling in a
tri-axial ambient using a hybrid Eulerian-Lagrangian framework to incorporate
effects of micro-physical processes. We have demonstrated the dominant role
played by pressure gradient in shaping XRGs in thermally dominated cases. We
show that the prominence of the formed structure decreases as the jet deviates
from the major axis of the ambient. The wing evolution is mainly governed by
re-energized particles due to shocks that keep the structure active during the
evolution time. The synthetic intensity maps of the radio galaxy show
similarities with morphologies that are typically found in observed XRGs. This
includes the cases with wider wings than the active lobes. The characteristic
emission signatures in terms of its synchrotron spectra and implication of
equipartition condition in age estimation are also discussed here.
Additionally, we show that discrepancy of age can be attributed to mixing of
different aged particle populations. Further, the effect of viewing angle on
the difference of spectral index of the active lobes and the wings $(\Delta
\alpha)$ shows a large variation and degenerate behaviour. We have demonstrated
the role of diffusive shocks in the obtained variation and have concluded that
the spread of $(\Delta \alpha)$ is not a dependable characteristic in
determining the formation model of XRGs.
