From Jets to Failed Supernovae: Morphologies and Gravitational-Wave Signatures in Two-Dimensional Magnetorotational Core-Collapse Supernovae

Abstract

Magnetized and rotating core-collapse supernovae (CCSNe) are promising candidates for producing long gamma-ray bursts and hypernovae. In this project, we present 34 two-dimensional magnetized core-collapse supernova simulations with self-consistent neutrino transport, systematically exploring the parameter space of initial magnetic field strengths ($B_0 = 0$--$3.5 \times 10^{12}$~G) and rotation rates ($Ω_0 = 0$--$0.5$~rad~s$^{-1}$) for a 40~$M_\odot$ progenitor. Our simulations reveal four distinct explosion morphologies: failed explosions leading to black hole formation, monopolar jet explosions, bipolar jet explosions, and neutrino-driven explosions. We find that the 40 $M_\odot$ progenitor model failed to explode without magnetic fields in two dimensions, even with rapid rotation. The non-rotating models require strong seed magnetic fields ($B_0 \gtrsim 1.5 \times 10^{12}$~G) to launch magnetically driven explosions, while the introduction of rotation substantially lowers this threshold. The explosion timescale decreases systematically with both increasing magnetic field strength and rotation rate, ranging from $>500$~ms in marginally successful models to $<150$~ms in strongly magnetized, rapidly rotating systems. Diagnostic explosion energies in the most extreme models approach $\sim 10^{51}$~erg within 250~ms and continue growing in time, making them potential hypernovae and long gamma-ray burst progenitors. Finally, we analyze the gravitational wave signatures associated with each morphology and find that the gravitational wave frequencies mainly depend on the rotation rates but are less sensitive to the magnetic field strengths and explosion morphologies. However, the gravitational wave amplitudes strongly depend on the explosion morphologies and magnetic fields, making searches for gravitational waves from magnetorotational core-collapse supernovae more challenging.

Figures (14)

• Figure 1: Time evolution of the averaged shock radius (upper left), central density (upper right), proto-neutron star radius (lower left), and proto-neutron star mass (lower right) for non-rotating models ($\Omega_0=0$). Different colors represent models with different initial magnetic field strengths ranging from $B_0=0$ to $10^{12}$ (see Table \ref{['tab:simulations']}). All non-rotating models with $B_0 \leq 2 \times 10^{11}$ result in failed explosions and black hole formation, while models with $B_0 \geq 4 \times 10^{11}$ exhibit successful neutrino-driven explosions.
• Figure 2: Time evolution of the averaged shock radius for rotating models with different initial magnetic field strengths: $B_0=10^9$ (upper left), $10^{10}$ (upper right), $10^{11}$ (lower left), and $10^{12}$ (lower right). Different transparencies represent models with different initial angular velocities ranging from $\Omega_0=0.1$ to $0.5$ rad s$^{-1}$. The shock evolution demonstrates strong dependence on both magnetic field strength and rotation rate, with higher values generally leading to faster shock expansion and earlier explosions.
• Figure 3: Time evolution of central density for all models that result in black hole formation. Different colors represent models with different magnetic field strengths and rotational speeds (see Table \ref{['tab:simulations']}). The sharp increment in central density marks the moment of black hole formation. All non-rotating models without sufficiently strong magnetic fields ($B_0 < 4 \times 10^{11}$) undergo black hole formation, while some rotating models also fail to explode despite the presence of rotation and magnetic fields.
• Figure 4: Time evolution of magnetic energy for rotating models with $B_0=10^9$, $10^{10}$, and $10^{11}$ (left) and $B_0=10^{12}$ (right). Different transparencies and colors represent models with different initial angular velocities and magnetic field strengths. The magnetic energy shows rapid amplification in successfully exploding models, reaching values several orders of magnitude higher than the initial magnetic energy, indicating efficient magnetic field amplification via MHD instabilities and rotational winding in the post-shock region.
• Figure 5: Time evolution of diagnostic explosion energy for rotating models with $B_0=10^9$, $10^{10}$, and $10^{11}$ (left) and $B_0=10^{12}$ (right). Different transparencies and colors represent models with different initial angular velocities and magnetic field strengths. Models that achieve positive and sustained growth in diagnostic energy are classified as successful explosions, while those showing stagnation or decline lead to failed explosions.