Fast neutrino flavor conversions in a supernova: Emergence, evolution, and effects (2024)

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  Figure 1

  Radial profiles of baryonic density, temperature $T/10$, and $Y_e$ (before and after attenuations) for a snapshot at the postbounce time $t_{\mathrm{pb}}\approx 252\mathrm{ms}$. Orange, blue, and green vertical dashed lines indicate the gain radius, the radii of ${\nu }_e$- and ${\overline{\nu }}_e$-spheres at $r\approx 63$, 40, and 35km, respectively.

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  Figure 2

  Radial profiles of ELN distribution in models II–VII that have different attenuated $Y_e$ profiles. The angular crossings of ELN are indicated by the location of curves with the white color. Model I (without $Y_e$ attenuation) is not shown as it contains no ELN angular crossing.

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  Figure 3

  Deepness ratios of the initial ELN distribution, $\min (|I_{-}|,|I_{+}|)/\max (|I_{-}|,|I_{+}|)$, in models II–V (see text for the definition of $I_{\pm }$).

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  Figure 4

  Growth rates $\mathrm{Im}(\mathrm{\Omega })$ as functions of $K_r$ at $r=41.6\mathrm{km}$ in models II (a)–(c)and V (d)–(f). The values of $\mathrm{Im}(\mathrm{\Omega }{)}_{\max }$ for the cases with $a_1={10}^{-2}$ and $a_1={10}^{-3}$ in (a) and (d) are multiplied by ${10}^2$ and ${10}^3$, respectively, to show the scalability of the dispersion relation discussed in the text.

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  Figure 5

  Growth rates $\mathrm{Im}(\mathrm{\Omega })$ $({\mathrm{km}}^{-1})$ as functions of $K_r$ and $r$ in models II (a)–(c) and V (d)–(f). The cyan dashed curve marks $K_r$ with maximum growth rates.

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  Figure 6

  Maximum growth rates $\mathrm{Im}(\mathrm{\Omega }{)}_{\max }$ as functions of radius $r$ in models II (a) and V (b). For the cases with $a_1={10}^{-2}$ and $a_1={10}^{-3}$, the values of $\mathrm{Im}(\mathrm{\Omega }{)}_{\max }$ are multiplied by ${10}^2$ and ${10}^3$, respectively, for easier comparison. Black and orange dotted curves are obtained using the simple analytical formulas in Refs.[11, 135], respectively.

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  Figure 7

  Maximum growth rates $\mathrm{Im}(\mathrm{\Omega }{)}_{\max }$ as functions of radius $r$ for in models II (a) and V (b). The gray shaded areas indicate the radial regions where ELN angular crossings exist in the initial ELN distribution without oscillations. Blue and red curves represent results with parameters in the cases c0v2 and c1v0, respectively. Dotted and solid curves represent the cases using $a_{\nu \nu }=1$ without and with excluding the spurious noncollective modes, respectively. The dashed curve in (b)is with $a_1={10}^{-3}$ and with all the spurious modes excluded.

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  Figure 8

  Evolution of the dimensionless ratio of off-diagonal mixing $s_{e\mu }$ in $30<r<80\mathrm{km}$ (left) and its associated phase angle ${\varphi }_{e\mu }$ within a smaller radial range $50<r<55\mathrm{km}$ (right) for model II.

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  Figure 9

  Spectrograms with respect to $K_r$ and $r$ for different models at different times (a)–(l). The color bar is for the Fourier transformed magnitude ${\log }_{10}|{\mathcal{F}}_{r,K_r}[{\mathrm{cm}}^{-3}]|$. The cyan dashed curve shows the $K_r$ with maximum growth rates calculated from LSA.

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  Figure 10

  Radial profiles of neutrino number densities between $r=38$ and 40km at $t=64\mathrm{\mu }\mathrm{s}$ in models III and IIIa2.

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  Figure 11

  Radial profiles of neutrino number densities for ${\nu }_e$, ${\overline{\nu }}_e$, and ${\nu }_{\mu }$ in models II–VII (a)–(f).

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  Figure 12

  Radial profiles of neutrino mean energies for ${\nu }_e$, ${\overline{\nu }}_e$, ${\nu }_{\mu }$, and ${\overline{\nu }}_{\mu }$ in models II–VII (a)–(f).

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  Figure 13

  Evolution of the angular distributions of the ELN, $G(v_r)$ (upper row) and that of each neutrino species at $r\approx 36\mathrm{km}$ (lower row) in models III (a),(b) and IV (c),(d).

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  Figure 14

  Evolution of the angular distributions of the ELN, $G(v_r)$ (upper row), and that of each neutrino species at $r\approx 50\mathrm{km}$ (lower row) in models II (a),(b), III (c),(d), and IV (e),(f). Note that $⟨{\varrho }_{\nu }{⟩}_E$ are shown in $-0.2\le v_r\le 1$ because most of neutrinos propagate outward.

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  Figure 15

  Radial profiles of neutrino number densities (a) and mean energies (b)in model Vc0.

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  Figure 16

  Comparison of the radial profiles of neutrino number density ratios $n_{\nu }(t)/n_{\nu }(t=0)$ between two-flavor (dashed) and three-flavor (solid) schemes for model II at $320\mathrm{\mu }\mathrm{s}$ (a), model IV at $32\mathrm{\mu }\mathrm{s}$ (b), and at $320\mathrm{\mu }\mathrm{s}$ (c). Note that the scales for heavy-lepton neutrinos are labeled on the right axes.

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  Figure 17

  Comparison of the radial profiles of neutrino number density ratios $n_{\nu }(t)/n_{\nu }(t=0)$ (blue) in models II (a), III (b), and IV (c)at $64\mathrm{\mu }\mathrm{s}$ with different attenuation factors $a_1={10}^{-3}$ (blue), $2\times {10}^{-3}$ (green), $4\times {10}^{-3}$ (red), and $1\times {10}^{-2}$ (black in model II). Note that the scales for the ratio of ${\nu }_{\mu }$ are labeled on the right axes.

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  Figure 18

  Comparison of the radial profiles of neutrino number density ratios $n_{\nu }(t)/n_{\nu }(t=0)$ between models IV and IVv2 at $64\mathrm{\mu }\mathrm{s}$. The scale for the ratio of ${\nu }_{\mu }$ is labeled on the right axis.

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  Figure 19

  Comparison of the specific heating-cooling rate after the prompt FFCs at $t=32\mathrm{\mu }\mathrm{s}$ (a) and in the asymptotic state at $t=160\mathrm{\mu }\mathrm{s}$ (b)for models II (blue), III (green), IV (cyan), and V (red). The original heating rates without flavor conversions are shown by the black curves and are indistinguishable for all models. The cyan dashed curve in (a)is for model IV at $t=3.2\mathrm{\mu }\mathrm{s}$. The magenta curve in (c)is for model Vc0 at $t=32\mathrm{\mu }\mathrm{s}$, compared to model V (red).

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  Figure 20

  Comparison of the equilibrium electron fraction $Y_e^{\nu ,\mathrm{eq}}$ after the prompt FFCs (a) and at a later time $t=160\mathrm{\mu }\mathrm{s}$ (b)for models II (blue), III (green), IV (cyan), and V (red). The dashed curves show the corresponding profiles without flavor conversions for comparisons.

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  Figure 21

  Free-streaming neutrino energy spectra at $t=320\mathrm{\mu }\mathrm{s}$ in models II (a), III (b), IV (c), V (d), VI (e), IIf3 (g), IIIf3 (h), and IVf3 (i). Note that the (f)shows the spectrum after the prompt FFC at $t=64\mathrm{\mu }\mathrm{s}$ in model IV for illustration. The dashed curves show the corresponding spectra without flavor conversions for comparisons.

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  Figure 22

  Radial profiles of neutrino number density (a) and mean energy (b)based on boltztran (black), cose$\nu$ without NES (green), and cose$\nu$ with NES (red) in model I.

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