Correlated gravitational wave and neutrino signals from general-relativistic rapidly rotating iron core collapse

We present results from a new set of three-dimensional general-relativistic hydrodynamic simulations of rotating iron core collapse. We assume octant symmetry and focus on axisymmetric collapse, bounce, the early postbounce evolution, and the associated gravitational wave (GW) and neutrino signals. We employ a finite-temperature nuclear equation of state, parametrized electron capture in the collapse phase, and a multispecies neutrino leakage scheme after bounce. The latter captures the important effects of deleptonization, neutrino cooling and heating and enables approximate predictions for the neutrino luminosities in the early evolution after core bounce. We consider $12-M_{\odot }$ and $40-M_{\odot }$ presupernova models and systematically study the effects of (i) rotation, (ii) progenitor structure, and (iii) postbounce neutrino leakage on dynamics, GW, and neutrino signals. We demonstrate that the GW signal of rapidly rotating core collapse is practically independent of progenitor mass and precollapse structure. Moreover, we show that the effects of neutrino leakage on the GW signal are strong only in nonrotating or slowly rotating models in which GW emission is not dominated by inner core dynamics. In rapidly rotating cores, core bounce of the centrifugally deformed inner core excites the fundamental quadrupole pulsation mode of the nascent protoneutron star. The ensuing global oscillations ($f\sim 700–800\mathrm{Hz}$) lead to pronounced oscillations in the GW signal and correlated strong variations in the rising luminosities of antineutrino and heavy-lepton neutrinos. We find these features in cores that collapse to protoneutron stars with spin periods $\lesssim 2.5\mathrm{ms}$ and rotational energies sufficient to drive hyperenergetic core-collapse supernova explosions. Hence, GW or neutrino observations of a core-collapse event could deliver strong evidence for or against rapid core rotation. Joint $\mathrm{GW}+\mathrm{\text{neutrino}}$ observations would allow one to make statements with high confidence. Our estimates suggest that the GW signal should be detectable throughout the Milky Way by advanced laser-interferometer GW observatories, but a water-Cherenkov neutrino detector would have to be of near-megaton size to observe the variations in the early neutrino luminosities from a core collapse event at 1 kpc.

Figure 1

Illustration of the rays along which calculations are performed for the neutrino leakage scheme. Shown here are two layers of rays overlaid on a volumetric visualization of a snapshot of the specific entropy distribution taken in the postbounce phase of model s12WH07j0. Light blue corresponds to low entropy ($0.6k_{\mathrm{B}}{\mathrm{\text{baryon}}}^{-1}$) and red corresponds to high entropy ($15k_{\mathrm{B}}{\mathrm{\text{baryon}}}^{-1}$).

Figure 2

Precollapse structure of the $12-M_{\odot }$ (black graphs) and $40-M_{\odot }$ (red graphs) progenitor models taken from 69. Shown in solid lines is the radial density profile and dashed lines denote the radial entropy distribution as derived from our EOS. Note that, as expected from stellar evolution theory (e.g., 145), the more massive progenitor has, at the onset of collapse, a lower central density, a higher central entropy, and a more extended core than its lower-mass counterpart.

Figure 3

Evolution of the central density (${\rho }_c$, top subpanel), GW signal ($h_{+}D$, rescaled by distance $D$) seen by an equatorial observer (center subpanel), and ${\nu }_e$, ${\overline{\nu }}_e$, ${\nu }_x$ neutrino luminosities $L_{{\nu }_i}$ (bottom subpanel) from shortly before core bounce to 25 ms after bounce in the s12WH07 models ordered according to their precollapse rotation rate (left to right, top to bottom). The $L_{{\nu }_i}$ are scaled to emphasize the very early postbounce phase. Also shown, in dashed lines, are the ${\rho }_c$ evolutions and GW signals of the simulations without neutrino leakage. For the j4 model, we also plot the GW signal as obtained from a simulation with 20% higher resolution (HR). The effects of neutrino leakage on the dynamics and GW emission are strongest in nonrotating or slowly rotating models (j{0–2}). Note the prominent correlated oscillations in ${\rho }_c$, GWs, and neutrino signals starting, at low amplitude, in the j3 model and becoming quite prominent in the j4 and j5 models.

Figure 4

Spectrograms of the power spectral densities computed via short-time Fourier transforms of the central density evolution (top panel), GW signal (second panel), $L_{{\nu }_e}$ (third panel), $L_{{\overline{\nu }}_e}$ (fourth panel), and $L_{{\nu }_x}$ (bottom panel). In each panel, the time-domain evolution of the respective quantity is superposed with the scales set by the right ordinates. In the panels showing neutrino luminosity data, we also provide graphs of the time evolution of the corresponding energy- and angle-averaged neutrinosphere radii. All quantities show significant correlated excess power in their power spectral densities (PSDs) around $\sim 700–800\mathrm{Hz}$. The correlation in the ${\nu }_e$ luminosity is weak, since it is primarily sourced by electron capture outside the ${\nu }_e$ neutrinosphere. The spectrograms are obtained by sliding an 8-ms Hann window over the data with a $0.1-\mathrm{ms}$ time step. The scales on which the time series data are shown have been chosen to highlight the correlated multimessenger signal oscillations.

Figure 5

Colormaps of the specific entropy in the meridional plane of the rapidly rotating model s12WH07j4. The contour lines mark isocontours of rest-mass density at $\{{10}^{14},{10}^{13},5\times {10}^{12},{10}^{12}\}\mathrm{g}{\mathrm{cm}}^{-3}$ (in this order from the origin). Velocity vectors are superposed and their length is saturated at $0.01c$. The left panel shows a snapshot at 0.25 ms after bounce while the right panel shows the situation at 0.64 ms. Due to rapid rotation and thus strong centrifugal support at low latitudes, bounce occurs earlier and is stronger (leading to higher specific entropies) near the poles. As shown in the left panel, at 0.25 ms after bounce, the inner core is re-expanding along the polar direction while most of the material near the equatorial plane is still falling in. At the slightly later time shown in the right panel, matter along the rotation axis is receding, while the inner core is expanding on the equator. The flow pattern in the inner core has strong quadrupolar features that excite the fundamental quadrupole oscillation mode.

Figure 6

The time evolution of the radial velocity of the PNS along polar and equatorial directions, bandpassed around the frequency of the leading peak of its oscillation spectrum, for model s12WH07j4. The radial velocity along polar and equatorial directions are out of phase by half a cycle at any given radius in the PNS interior. Such behavior is also exhibited by the ${}^{2}f$ mode of a nonrotating Newtonian star.

Figure 7

Shock position on the equator (along the positive $x$ axis) as a function of time after core bounce for the s12WH07j{0–5} model set. Models without neutrino leakage (“nl,” dashed lines) reach significantly larger shock radii, since they are not, unlike the models that include neutrino leakage (solid lines), affected by neutrino cooling and deleptonization. The rapidly spinning models s12WH07j4 and s12WH07j5 show an initial transient decrease in their equatorial shock radii. This is due to shock formation occurring first at the pole while the equatorial regions of the inner core are still contracting. Note that the discrete shock radius data has been spline-interpolated to produce this plot.

Figure 8

Colormaps of the electron fraction $Y_e$ in the meridional plane at 25 ms after bounce. The contour lines mark isocontours of rest-mass density (in this order from the origin) at $\{{10}^{14},{10}^{13},5\times {10}^{12},{10}^{12},{10}^{11},{10}^{10}\}\mathrm{g}{\mathrm{cm}}^{-3}$. Velocity vectors are superposed and their length is saturated at $0.0125c$ to prevent the high collapse velocities of the outer core outside of the shock from cluttering the plot. The top panels show the nonrotating model s12WH07j0 evolved with postbounce neutrino leakage (left panel) and without (right panel). The bottom panels show the rapidly spinning model s12WH07j4 also with (left panel) and without neutrino leakage (right panel). The simulations with neutrino leakage show the characteristic depletion of $Y_e$ due to electron capture in the region behind the shock. The shock is located at radii of $\sim 110–120\mathrm{km}$ in the simulations with neutrino leakage, at $\sim 125\mathrm{km}$ in the j0 model without leakage, and at $\sim 160\mathrm{km}$ ($\sim 220\mathrm{km}$) at the pole (equator) of the j4 model without leakage. In the PNS core, neutrinos are trapped and $Y_e$ is at essentially its bounce value and only there the simulations with and without leakage yield the same $Y_e$ and structure. The deleptonization and neutrino cooling in the runs with leakage significantly reduce the pressure behind the shock, lead to much smaller shock radii, and allow more material to pile up on the outer PNS core.

Figure 9

Comparison of select models of the s12WH07 model set (using the $12-M_{\odot }$ progenitor) with their s40WH07 counterparts (using the 40-$M_{\odot }$ progenitor). Shown are the evolution of the GW signal seen by an equatorial observer (left ordinate) and of the central rest-mass density (right ordinate). The GW signal $h_{+}$ is rescaled by source distance $D$ and plotted in units of centimeters, the central rest-mass density ${\rho }_c$ is given in units of ${10}^{14}\mathrm{g}{\mathrm{cm}}^{-3}$, and the time is measured in milliseconds relative to the time of core bounce in each model. The central density evolutions in all s12WH07 and s40WH07 models are extremely close to one another. The GW signals of the nonrotating models (top left panel) differ significantly. However, with increasing rotation (from left to right, top to bottom), the dominant parts of the GW signal grow very similar.

Figure 10

Comparison of the spectral GW energy densities [($d{E}_{\mathrm{GW}}/df$; Eq. (14)] of select models using the $12-M_{\odot }$ and the $40-M_{\odot }$ progenitor at the same precollapse rotation rate. Top panel: Nonrotating case (j0); the spectra vary greatly. Center panel: Moderate rotation (j2); the spectra exhibit many similar features. Bottom panel: Rapid rotation (j5); the spectra are nearly identical.

Figure 11

Comparison of the approximate ${\nu }_e$ (top panel), ${\overline{\nu }}_e$ (center panel), and ${\nu }_x$ (bottom) luminosities in models s12WH07j0, s12WH07j4, s12WH07j5 (all solid lines) with their s40WH07j0, s40WH07j4, s40WH07j5 counterparts (all dashed lines). The vertical scales have been chosen to emphasize the oscillations observed primarily in $L_{{\overline{\nu }}_e}$ and $L_{{\nu }_x}$ of the rapidly spinning j4 and j5 models. While quantitative aspects should be regarded as approximate, one notes that the s40WH07 models have systematically larger early postbounce luminosities than their s12WH07 counterparts.

Figure 12

Rotation rate $T/|W|$ as a function of time after bounce for the rotating models of the s12WH07 (black lines) and s40WH07 (red lines) model sets. Results for simulations with (solid lines) and without (dashed lines) neutrino leakage are shown. s12WH07 and s40WH07 models show qualitatively and quantitatively very similar $T/|W|$ evolutions. s40WH07 models, which are endowed with slightly less angular momentum than their s12WH07 counterparts, have slightly lower $T/|W|$ (see Tables ). In rapidly rotating models, neutrino leakage leads to a more rapid contraction and spin-up after bounce than predicted by models without leakage. Nonaxisymmetric instability at low $T/|W|$ is likely to occur in models with j3, j4, and j5 rotation. The j5 models may even reach the threshold of 27% for the high-$T/|W|$ dynamical instability within a few hundred milliseconds of bounce.

Figure 13

Comparison of projected Advanced LIGO broadband [zero-detuning, high-power (aLIGO ZD-HP)] [103], KAGRA/LCGT [126], and potential Advanced Virgo wideband (AdV WB) [127] sensitivity with the characteristic GW amplitudes $h_{\mathrm{char}}(f)f^{-1/2}$ of the s12WH07j{0–5} model set at a source location of 10 kpc.

Figure 14

Predicted neutrino signals and associated statistical error in Super-Kamiokande (SK, blue error bars), Hyper-Kamiokande (HK, green error bars), and IceCube (IC, red error bars) from model s12WH07j5 at 1 kpc. The solid black line is the ${\overline{\nu }}_e$ luminosity from our simulation. In the inset we show only the HK and IC predicted signals and errors, zoomed in between 8 and 11 ms. The error of the IC signal is small, but the imposed bin width of 1.6384 ms averages out variations on time scales smaller than this. If binned in 1.6384-ms bins, the Hyper-Kamiokande SNR would be approximately half of the SNR in IceCube.