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Spectral variation across Pulsar Profile due to Coherent Curvature Radiation

The pulsar profile is characterised by two distinct emission components, the core and the cone. The standard model of a pulsar radio emission beam originating from dipolar magnetic fields, places the core at the centre surrounded by concentric layers of inner and outer conal components. The core emission is expected to have steeper spectra compared to the cones. We present a detailed analysis of the relative differences in spectra between the core and conal emission from a large sample of 53 pulsars over a wide frequency range between 100 MHz and 10 GHz. The core was seen to be much steeper than the cones particularly between 100 MHz and 1 GHz with a relative difference between the spectral index $Δα_{core/cone}\sim$ -1.0. In addition we also found the spectra of the outer conal components to be steeper than the inner cone with relative difference in the spectral index $Δα_{in/out}\sim$ +0.5. The flattening of the spectra from the magnetic axis towards the edge of the open field line region with increasing curvature of the field lines is a natural outcome of the coherent curvature radiation from charged soliton bunches, and explains the difference in spectra between the core and the cones. In addition due to the relativistic beaming effect, the radiation is only visible when it is directed towards the observer over a narrow angle $θ\leq 1/γ$, where $γ$ is the Lorentz factor of the outflowing plasma clouds. This restricts the emission particularly from outer cones, that are associated with field lines with larger curvature thereby making the spectra steeper than the inner cones.