Impact of rotation on the multimessenger signatures of a hadron-quark phase transition in core-collapse supernovae

We study the impact of rotation on the multimessenger signals of core-collapse supernovae (CCSNe) with the occurrence of a first-order hadron-quark phase transition (HQPT). We simulate CCSNe with the flash code starting from a $20M_{\odot }$ progenitor with different rotation rates, and using the RDF equation of state from Bastian 2021 that prescribes the HQPT. Rotation is found to delay the onset of the HQPT and the resulting dynamical collapse of the protocompact star (PCS) due to the centrifugal support. All models with the HQPT experience a second bounce shock which leads to a successful explosion. The oblate PCS as deformed by rotation gives rise to strong gravitational-wave (GW) emission around the second bounce with a peak amplitude larger by a factor of $\sim 10$ than that around the first bounce. The breakout of the second bounce shock at the neutrinosphere produces a ${\overline{\nu }}_e$-rich neutrino burst with a luminosity of serveral ${10}^{53}\mathrm{erg}{\mathrm{s}}^{-1}$. In rapidly rotating models the PCS pulsation following the second bounce generates oscillations in the neutrino signal after the burst. In the fastest rotating model with the HQPT, a clear correlation is found between the oscillations in the GW and neutrino signals immediately after the second bounce. In addition, the HQPT-induced collapse leads to a jump in the ratio of rotational kinetic energy to gravitational energy ($\beta$) of the PCS, for which persistent GW emission may arise due to secular nonaxisymmetric instabilities.

Figure 1

Hadron-quark phase diagram in the RDF 1.9 EOS. Blue lines are the boundaries of the hadronic and mixed phases and red lines are the boundaries of the mixed and quark phases. Dashed, solid and dotted lines correspond to the electron fraction $Y_e$ of 0.1, 0.25 and 0.5. The turning behavior for $Y_e=0.5$ and $k_{\mathrm{B}}T=15–25\mathrm{MeV}$ is likely an artifact due to the tabulated EOS.

Figure 2

Time evolution of the central density (upper panel), mean shock radius (thick lines in the lower panel) and diagnostic explosion energy (thin lines in the lower panel) after the first bounce. $\mathrm{rot}i$ refers to the model with ${\mathrm{\Omega }}_0=i\mathrm{rad}{\mathrm{s}}^{-1}$ in Eq. (1). The gray shaded horizontal bands mark the transition densities from the hadron phase to the mixed phase (${\rho }_{\mathrm{tran}1}$) and from the mixed phase to the quark phase (${\rho }_{\mathrm{tran}2}$), taking their dependence on temperature and $Y_e$ into account.

Figure 3

Time evolution of the central density (upper panel) and central quark volume fraction (lower panel) from 300 ms before to 20 ms after the second bounce $t_{2\mathrm{b}}$. Note the scales are different in the epochs before and after $t_{2\mathrm{b}}$, which is marked by the black vertical line. The gray shaded horizontal bands are the same as those in Fig. 2. The spurious sudden increase of ${\rho }_{\mathrm{c}}$ as well as $X_{\mathrm{quark},\mathrm{c}}$ at $t_{2\mathrm{b}}-0.13\mathrm{s}$ and $t_{2\mathrm{b}}-0.05\mathrm{ms}$ in the model rot2 is confined the central few km and has negligible dynamical effect on the protocompact star, cf. Fig. 5.

Figure 4

Snapshots illustrate the PCS dynamics and the development of the second bounce shock at $t=t_{2\mathrm{b}}$ (left panel), $t=t_{2\mathrm{b}}+0.3\mathrm{ms}$ (middle panel) and $t=t_{2\mathrm{b}}+0.6\mathrm{ms}$ (right panel). $t=t_{2\mathrm{b}}$ and $t=t_{2\mathrm{b}}+0.6\mathrm{ms}$ correspond to the times of the maximum ${\rho }_{\mathrm{c}}$ and the following dip for model rot2 in Fig. 3. The color maps encode the magnitude of entropy, the black curves mark the isodensity surfaces with densities of ${10}^{14}$, ${10}^{13}$, ${10}^{12}$, ${10}^{11}\mathrm{g}{\mathrm{cm}}^{-3}$ from the inside out, and the arrows depict velocities. The white curves mark the locus of the second shock.

Figure 5

Black lines show the time evolution of the radius at fixed enclosed masses $r(M)$, where $M$ ranges from $0.1M_{\odot }$ to $2.1M_{\odot }$ with a step of $0.1M_{\odot }$. The color map shows the time evolution of the angular-averaged density profile. The time of the second bounce is marked by the vertical white line.

Figure 6

Coefficients with $l=0$, 1, 2 of the Legendre decomposition of the radial velocities at 10 km. An angular resolution of 4° is used for the Legendre decomposition.

Figure 7

Time evolution of the mass (upper panel) and radius (lower panel) of the protocompact star after the first bounce. The open stars in the upper panel mark the critical $M_{\mathrm{PCS}}$ immediately before the second collapse. The inset in the lower panel exemplifies the evolution of $R_{\mathrm{PCS}}$ around the second bounce.

Figure 8

Time evolution of the parameter $\beta$ (upper panel) and the total angular momentum (lower panel) of the protocompact star after the first bounce.

Figure 9

Time evolution of the GW strain from 0.02 s before to 0.3 s after the first bounce in the models $\mathrm{rot}0\dots \mathrm{rot}2$. The inset exemplifies the episode between $t_{1\mathrm{b}}-0.01\mathrm{s}$ and $t_{1\mathrm{b}}+0.02\mathrm{s}$ and includes the models rot3 and rot4.

Figure 10

Same as Fig. 9, but for the time evolution of the GW from 0.05 s before to 0.05 s after the second bounce in the models $\mathrm{rot}0\dots \mathrm{rot}2$.

Figure 11

Time evolution of the GW strain from 2 ms before to 10 ms after the second bounce in the models $\mathrm{rot}0\dots \mathrm{rot}2$. This figure focuses on the episode in Fig. 10 with saturated magnitudes. Note the different $y$-axis scale compared to that in Fig. 10.

Figure 12

Characteristic GW strain $h_{\mathrm{char}}$ for the models $\mathrm{rot}0\dots \mathrm{rot}2$ in the 100-ms Hann window centered at $t_{2\mathrm{b}}$ (cf. Fig. 10). The black solid line is the amplitude spectral density of the detector noise multiplied by the square root of frequency for Advanced LIGO at its design sensitivity. The $h_{\mathrm{char}}$ spectra assume a source distance of 10 kpc except the thick red line whose distance is 1 Mpc.

Figure 13

Time evolution of the angular-averaged luminosity (upper panel) and mean energy (lower panel) of electron antineutrinos around the second collapse and bounce.

Figure 14

Time evolution of the angular dependent luminosity of electron antineutrinos (top panel), the coefficients $a_l$ of its Legendre decomposition (middle panel) and $a_l/a_0$ (bottom panel). An angular bin of 20° is used in the upper panel to reduce numerical noises. An angular resolution of 4° is used for the Legendre decomposition.

Figure 15

Time evolution of the central density (panel a), PCS radius (panel b), GW strain (panel c) and angular-averaged luminosity of electron anti-neutrinos (panel d) in the model rot2 with different spatial resolutions. The setup of hr1 is used in the main text. See text for the detailed description of each simulation.