Trends in gravitational wave emission in axisymmetric simulations of rotating core-collapse supernovae

TL;DR

This study investigates how strong rotation and magnetic fields affect gravitational waves from core-collapse supernovae by performing axisymmetric, long-duration MHD simulations of a $17\,M_\odot$ progenitor across a dense grid of initial rotation rates. Using the CoCoNuT-FMT code and Newtonian gravity with a modified potential, the authors find GW frequencies reaching up to ~3 kHz, with both frequencies and amplitudes generally decreasing as rotation increases; p-modes are suppressed in magnetized runs, and no robust resonant amplification is observed. A polar-dominant, high-frequency emission is linked to the compactness and oblateness of the rapidly rotating proto-neutron star, with an analytic estimate $f_{\mathrm{peak}}$ based on $M/R^{2}$ and mean neutrino energy providing good agreement in several cases. Spatially-resolved analysis reveals a two-phase GW emission: an early ringdown near the PNS and later, buoyancy- and accretion-driven modes in the PNS-gain region; a linear eigenmode analysis succeeds for non-rotating cases but breaks down for rapid rotation, underscoring the need for advanced perturbative methods to interpret 2D rotating PNS oscillations. These results inform high-frequency GW template development and motivate further theoretical work on mode coupling and excitation in rapidly rotating, magnetized stellar cores.

Abstract

The quantitative impact of strong rotation on the amplitudes and frequencies of the post-bounce gravitational wave (GW) signal from core-collapse supernovae (CCSNe) is still not fully understood. To study trends in frequencies and amplitudes, and possibly spectacular phenomena like resonant amplification, we perform a series of axisymmetric long-duration magnetohydrodynamic CCSN simulations of a 17 $M_\odot$ progenitor using a finely spaced grid in initial rotation rate from 0.29 rad/s to 3.48 rad/s. We find that these rotating models produce GWs at frequencies of up to 3 kHz, higher than in typical non-rotating models in the literature. The high frequencies arise due to small polar radii of rapidly rotating proto-neutron stars and stabilization by angular momentum gradients at lower latitude. GW frequencies and amplitudes tend to decrease with faster rotation. Different from two complementary simulations without magnetic fields, the magnetohydrodynamic models are characterized by an absence of p-modes above the dominant high-frequency emission band. We find no indication of resonant mode amplification for any rotation rate, although a temporo-spatial and space-frequency analysis reveals some interesting couplings of quadrupolar motions across the proto-neutron star and the gain region. We find that linear mode analysis based on the spherically averaged structure becomes unsuitable in this regime of rapid rotation. More advanced perturbative techniques need to be developed to study the mode structure and mode interaction in the collapse of rapidly rotating massive stars.

Figures (16)

• Figure 1: Initial angular velocities of models in the main set, as listed in Table \ref{['tab:run_summary']}. Models are labeled in the legend by their corresponding angular velocity boost factor over the original progenitor model.
• Figure 2: Shock radius as function of post-bounce time for simulations in the main set. The mean radius is shown as a solid line, and the minimum/maximum range as the shaded area. The minimum and maximum are smoothed within a $10 \, \mathrm{ms}$ window to improve clarity. Lines are labeled by their boost factors in the legend, excluding any prefixes.
• Figure 3: GW amplitudes, $A_{+}\,$, for the 14 models of the main set. For models with large rotation boosts, a quadrupole moment is induced outside the core which produces low frequency ($f \ll 10 \, \mathrm{Hz}$) GWs. This causes $A_{+}\,$ to exhibit a secular offset from zero on the timescale of our simulations. Because we are interested in much higher frequency signals, it is neater to subtract this low frequency signal such that $A_{+}\,$ oscillates approximately around zero and each panel can have the same vertical scale. The low-frequency component is calculated in a post-processing step (since much lower time resolution is required) using the same time-integrated Newtonian quadrupole formula as the un-adjusted signal and restricting to the region $r > 10^{9} \, \mathrm{cm}$. We have confirmed by spectral analysis of both signals that this does not change the spectral properties of GWs in the region of interest.
• Figure 4: Normalized wavelet spectra of $A^{\mathrm{E2}}_{20}$ for $1.5 \, \mathrm{s}$ post-bounce. The color scale is consistent between panels. The black line shows the predicted peak GW signal as computed from Equation \ref{['eqn:fpeak']}. The white and red lines show, respectively, the maximum epicyclic and maximum Brunt-Väisälä frequencies inside a radius of $100 \, \mathrm{km}$.
• Figure 5: Top: Approximate frequency of the dominant GW emission band for the SR1 model (solid line) obtained by finding the maximum frequency in $12 \, \mathrm{ms}$ time windows and performing a moving average on the result to smooth the data. In essence this is a kind of line of best fit to the spectrograms in Figure \ref{['fig:dwt_grid']}. The analytic approximation, $f_\mathrm{peak}$, estimated from electron antineutrino mean energies is shown by the dashed line. Middle: Components of Equation \ref{['eqn:fpeak']} as a function of time. PNS compactness is plotted with a solid line using the left axis while electron antineutrino mean energies are plotted with a dashed line and correspond to the right-hand axis. Bottom: PNS baryonic mass (solid line; left axis) and radius (dashed line; right axis), including the minimum and maximum radius satisfying $\rho > 10^{11} \, \mathrm{g \, cm^{-3}}$ (colored dotted lines).