Probing the morphology of the Gum Nebula through pulsar observables and a novel distance estimation method
Various existing models of the Gum Nebula differ significantly in their parameters and suggested origins, which can be independently tested for consistency with data on some key observables of pulsars in the direction of the nebula. Our analysis of such data on the Vela pulsar, assuming a dominant scattering region in its foreground, suggests that the fractional distance of the scatterer is $0.89 \pm 0.01$, and for the given distance of the Vela pulsar, it translates to $254 \pm 16$ pc. Using independent distances of ten pulsars, we suggest a refined description of the Gum Nebula electron density model with its basic morphology similar to that used in the YMW16 model, which now provides better estimates of pulsar distances in these directions. In our new Gum Nebula model, as expected, the Vela pulsar would be behind the frontal edge of the Gum shell, which was intriguingly located in front of the nebula in the YMW16 model. We also present a new technique to better constrain the pulsar distances using their dispersion measure and temporal broadening simultaneously, and find that it is less affected by the uncertainties in the Galactic electron density distribution models. Notably, the new approach shows that the expected temporal broadening as a function of trial distance does not follow a monotonic increasing trend, but instead exhibits oscillations at regions of enhanced electron density. This behaviour is expected, as the method employs the integral form of temporal broadening with the appropriate weighting kernel, leading to more reliable estimates.