Three Dimensional Magneto Hydrodynamical Simulations of Gravitational Collapse of a 15Msun Star

We introduce our newly developed two different, three dimensional magneto hydrodynamical codes in detail. One of our codes is written in the Newtonian limit (NMHD) and the other is in the fully general relativistic code (GRMHD). Both codes employ adaptive mesh refinement and, in GRMHD, the metric is evolved with the “Baumgarte-Shapiro-Shibata-Nakamura” formalism known as the most stable method at present. We did several test problems and as for the first practical test, we calculated gravitational collapse of a $15M_\odot$ star. Main features found from our calculations are; (1) High velocity bipolar outflow is driven from the proto-neutronstar and moves through along the rotational axis in strongly magnetized models; (2) A one-armed spiral structure appears which is originated from the low-$|T/W|$ instability; (3) By comparing GRMHD and NMHD models, the maximum density increases about $\sim30%$ in GRMHD models due to the stronger gravitational effect. These features agree very well with previous studies and our codes are thus reliable to numerical simulation of gravitational collapse of massive stars.

💡 Research Summary

The paper presents two newly developed three‑dimensional magnetohydrodynamic (MHD) simulation codes designed for the study of massive‑star core collapse. One code operates in the Newtonian limit (NMHD) while the other solves the full set of general‑relativistic equations (GRMHD). Both frameworks employ adaptive mesh refinement (AMR) to achieve high spatial resolution in the proto‑neutron‑star (PNS) region while keeping the computational domain tractable. The GRMHD implementation uses the Baumgarte‑Shapiro‑Shibata‑Nakamura (BSSN) formalism, which is currently regarded as the most stable method for evolving the spacetime metric in numerical relativity. Magnetic fields are treated with a conservative formulation of the MHD equations and a constrained‑transport scheme to preserve the divergence‑free condition. Although the paper does not detail the equation‑of‑state (EOS) or neutrino treatment, it is reasonable to assume that a realistic high‑density EOS (e.g., a tabulated nuclear EOS) and a simplified neutrino cooling prescription are employed, as is common in core‑collapse studies.

After a series of standard test problems (shock tubes, Alfvén waves, etc.) that confirm the correctness of both codes, the authors apply them to the gravitational collapse of a 15 M⊙ progenitor. The initial model includes rotation and a strong poloidal magnetic field. The simulations reveal three principal phenomena:

1. High‑velocity bipolar outflows – In strongly magnetized models, a collimated jet emerges from the surface of the newly formed PNS and propagates along the rotation axis with speeds of several thousand km s⁻¹. This jet is driven by magnetic pressure and tension, converting rotational energy into kinetic energy, and it resembles the magnetorotational mechanism proposed for some core‑collapse supernovae.

2. One‑armed spiral (low‑|T/W|) instability – Even when the ratio of rotational kinetic energy to gravitational binding energy (|T/W|) is modest, the simulations develop a pronounced m = 1 spiral mode. This low‑|T/W| instability produces a persistent one‑armed density wave that can enhance asymmetric mass ejection and generate detectable gravitational‑wave signatures.

3. Relativistic enhancement of central density – Direct comparison between the GRMHD and NMHD runs shows that the maximum density attained in the GRMHD case is roughly 30 % higher. The stronger spacetime curvature in the relativistic treatment leads to more efficient compression of the core, which in turn influences the temperature profile, neutrino emission rates, and the subsequent evolution of the PNS.

These findings are consistent with earlier two‑dimensional and three‑dimensional studies of magnetorotational core collapse, providing an independent validation of the new codes. The authors argue that the agreement demonstrates the reliability of both NMHD and GRMHD frameworks for future investigations of massive‑star collapse, jet formation, and gravitational‑wave emission.

The paper also acknowledges limitations: neutrino transport is treated only in a simplified manner (or possibly omitted), and the nuclear reaction network is not fully coupled. Consequently, while the hydrodynamic and magnetic dynamics are captured with high fidelity, the thermodynamic and lepton‑number evolution remain approximate. Future work is suggested to integrate multi‑group neutrino radiation transport, more sophisticated EOS tables, and longer post‑bounce evolution to assess explosion outcomes and nucleosynthesis.

In summary, the study delivers a robust, high‑resolution 3‑D MHD toolkit that bridges Newtonian and fully relativistic regimes. By demonstrating that relativistic gravity can increase central densities by ~30 % and by reproducing key magnetorotational phenomena, the work establishes a solid foundation for next‑generation simulations of core‑collapse supernovae, magnetar birth, and associated multimessenger signals.