An improved algorithm for crossing curved light surfaces: rapidly rotating pulsar magnetospheres in curved space–time

Abstract

The structure of force-free, steady and axisymmetric magnetosphere of a neutron star (NS) is governed by the Grad-Shafranov (GS) equation, which is a second-order differential equation but degrades to first-order on the light surface (LS). The key to numerically solving the GS equation is to enable magnetic field lines smoothly cross the LS, and crossing a straight LS in flat spacetime has been a well-studied problem. But the numerical algorithm implementation becomes complicate in the presence of a bent LS, e.g. in curved spacetime, since there is no suitable computation grid adapted to it. We propose to circumvent this grid-LS mismatch problem by introducing a new coordinate frame designed such that the LS in it is a straight line. As an application, we investigate the general relativistic (GR) effect in magnetosphere structure of rapidly rotating pulsars in detail, where the LS is bent towards the central NS. We split the GR effect into two parts, curvature and frame-dragging; measure each of them and examine their dependence on the NS mass and the angular velocity for pulsars embedded in aligned dipole and multipole magnetic fields. Qualitatively speaking, we find that the curvature effect compactifies the magnetic field lines near the NS, therefore reduces the open magnetic flux and the Poynting luminosity, while the frame-dragging effect contributes a minor part in shaping the magnetosphere structure but plays a role in enhancing the spacelike current generation.

Toward a Full MHD Jet Model of Spinning Black Holes. I. Framework and a Split Monopole Example

“…The numerical techniques are similar to those in previous work (e.g. Contopoulos et al 2013;Nathanail & Contopoulos 2014;Mahlmann et al 2018;Pan et al 2017;Huang et al 2016Huang et al , 2018Huang et al , 2019. On can obtain converged {Ψ (l) , Ω (l) , L (l) } with field lines smoothly crossing the inner/outer Alfvén surface after sufficient evolution.…”

“…Step 1 The MHD GS equation is a second-order differential equation which degrades to first order on the Alfvén surfaces where A(r, θ) = 0. Numerical techniques for dealing this problem have been well developed in previous force-free studies (Contopoulos et al 2013;Nathanail & Contopoulos 2014;Huang et al 2016Huang et al , 2018Pan et al 2017;Mahlmann et al 2018), and we briefly recap them here.…”