Diffusivity in force-free simulations of global magnetospheres

Assuming that the numerical diffusivity triggered by violations of the force-free electrodynamics constraints is a proxy for the physical resistivity, we examine its impact on the overall dynamics of force-free aligned pulsar magnetospheres endowed with an equatorial current sheet (ECS). We assess the constraint violations as a diffusivity source. The effects of modifications on electric fields used to restore force-free conditions are not confined to the ECS, but modify the magnetospheric dynamics on time-scales shorter than the pulsar rotational period. These corrections propagate especially via a channel that was unexplored, namely, changes induced to the electric charge density, rho. We quantify the global consequences of diffusivity by comparing different techniques to model rho. By default, we combine a conservative p-evolution with hyperbolic/parabolic cleaning of inaccuracies in the Maxwell equations. As an alternative, we enforce a constrained evolution, where rho is directly computed as the electric field divergence. The conservative approach reduces the Poynting flux dissipated in the ECS by an order of magnitude, along with an increase of the pulsar luminosity driven by a shift of the Y-point location. The luminosity changes according to L-Y proportional to alpha(0.11), where alpha is the ratio of diffusion to advection time-scales, controlling the amount of (numerical) diffusivity. Our models suggest interpreting the luminosity dependence on the Y-point location as differences in resistivities encountered at the ECS. Alternatively, they could be interpreted in terms of the pair formation multiplicity, kappa, smaller diffusion being consistent with kappa >> 1.