Neutrino emission characteristics and detection opportunities based on three-dimensional supernova simulations

The neutrino emission characteristics of the first full-scale three-dimensional supernova simulations with sophisticated three-flavor neutrino transport for three models with masses 11.2, 20, and $27M_{\odot }$ are evaluated in detail. All the studied progenitors show the expected hydrodynamical instabilities in the form of large-scale convective overturn. In addition, the recently identified lepton-number emission self-sustained asymmetry (LESA) phenomenon is generic for all our cases. Standing accretion-shock instability (SASI) activity appears in the 20 and $27M_{\odot }$ cases, partly in the form of a spiral mode, inducing large but direction- and flavor-dependent modulations of neutrino emission. These modulations can be clearly identified in the existing IceCube and future Hyper-Kamiokande detectors, depending on the distance and detector location relative to the main standing accretion-shock instability sloshing direction.

Figure 1

Luminosity of the ${\nu }_e$, ${\overline{\nu }}_e$, and ${\nu }_x$ species for our $27M_{\odot }$ simulation as measured by a distant observer with angular coordinates close to the plane of the spiral mode in the first SASI period.

Figure 2

Neutrino flux properties of our $27M_{\odot }$ case after integrating over all directions. For ${\nu }_e$, ${\overline{\nu }}_e$, and ${\overline{\nu }}_x$ we show the luminosity, average energy, and shape parameter $\alpha$ from 3D (in black, blue, and red, respectively) and 2D (in grey) simulations for comparison. The single-OM IceCube rate $r$ in the bottom panel is without dead time for a SN distance of 10 kpc. Blue line: Based on ${\overline{\nu }}_e$ flux without flavor oscillations. Red line: Based on ${\overline{\nu }}_x$, i.e., assuming full flavor swap ${\overline{\nu }}_e\leftrightarrow {\overline{\nu }}_e$.

Figure 3

Luminosity of the ${\nu }_e$, ${\overline{\nu }}_e$, and ${\nu }_x$ species for our $20M_{\odot }$ simulation after integrating over all directions.

Figure 4

Luminosity evolution for the $11.2M_{\odot }$ progenitor, separately for ${\nu }_e$, ${\overline{\nu }}_e$, and ${\nu }_x$, as seen by a distant observer, relative to $⟨L⟩$, the time-dependent average over all directions. Blue and magenta curves (i.e., respectively curve on the bottom and curve on the top at 200 ms in the top panel): Observer location on opposite sides along the axis where the flux variations are largest. Black curve: One typical orthogonal direction where the variation is small. The large excursion of the blue and magenta lines represent the LESA phenomenon: The ${\nu }_e$ and ${\overline{\nu }}_e$ emissions show a strong dipole pattern. The small-amplitude fast time variations are caused by large-scale convective overturn. There is no SASI activity in this model.

Figure 5

Evolution of neutrino flux properties for the $11.2M_{\odot }$ progenitor as seen from a distant observer. For ${\nu }_e$, ${\overline{\nu }}_e$, and ${\nu }_x$ we show the luminosity, average energy, and shape parameter $\alpha$. The Magenta and Blue directions are opposite along the LESA axis, corresponding to the magenta and blue curves in Fig. 4, whereas the Black direction is on the LESA equator (black in Fig. 4).

Figure 6

Same as Fig. 5, but for the $27M_{\odot }$ progenitor. The Violet, Black, and Light Blue directions here correspond to the curves of the same color in Fig. 7 that were chosen to show large and small SASI amplitudes, respectively.

Figure 7

Luminosity evolution for the $27M_{\odot }$ progenitor, separately for ${\nu }_e$, ${\overline{\nu }}_e$, and ${\nu }_x$, as seen by a distant observer, relative to $⟨L⟩$, in analogy to Fig. 4. The light-blue and violet curves (i.e., respectively curve in the middle and curve on the top at 100 ms in the middle panel) refer to observer locations in opposite directions approximately within the plane where SASI develops. The black line refers to a location of the observer far from the SASI plane where the modulation of the neutrino signal due to SASI is smaller during the first SASI episode.

Figure 8

Luminosity evolution relative to $⟨L⟩$ for the $27M_{\odot }$ progenitor for the three species, as seen by a distant observer, along the Violet direction, corresponding to the curve of this color in Fig. 7. Between SASI episodes, we see clear evidence for the LESA asymmetry, although the chosen direction does not coincide with the LESA axis.

Figure 9

Sky maps of $L_{{\overline{\nu }}_e}$ relative to the $4\pi$ average for the $27M_{\odot }$ SN progenitor at $t=217$, 225, and 230 ms, corresponding to subsequent SASI maxima and minima.

Figure 10

Variation of the luminosity for ${\nu }_e$, ${\overline{\nu }}_e$, and ${\nu }_x$ relative to the one computed as average over all directions for the $20M_{\odot }$ SN progenitor at 10 kpc in analogy to Fig. 4. The green and orange curves (i.e., respectively curve on the bottom and curve on the top at 150 ms in the top panel) refer to locations of the observer close to the plane where SASI develops and on opposite sides of the emitting sphere. The black line refers to a location of the observer far from the SASI plane where the modulation of the neutrino signal due to SASI is smaller.

Figure 11

Luminosity evolution relative to $⟨L⟩$ for the $20M_{\odot }$ progenitor for the three species, as seen by a distant observer along the “Orange” direction, corresponding to the curve of this color in Fig. 10. See Fig. 8 for comparison.

Figure 12

Sky maps of $L_{{\overline{\nu }}_e}$ relative to the $4\pi$ average for the $20M_{\odot }$ SN progenitor at $t=186$, 193, and 200 ms, corresponding to subsequent SASI maxima and minima in analogy to Fig. 9.

Figure 13

SASI vs LESA dipole as a function of time for the $27M_{\odot }$ (left) and the $20M_{\odot }$ (right) simulations. We describe the SASI dipole (top panels) in terms of the neutrino energy flux of all six neutrino species. For the $27M_{\odot }$ model (left), it reaches a maximum of 0.16 relative to its monopole at 200 ms, while for the $20M_{\odot }$ model (right) the maximum is reached at 180 ms with the same relative strength. The LESA dipole (bottom panels) is described in terms of the lepton-number flux (${\nu }_e$ minus ${\overline{\nu }}_e$) and reaches a relative maximum of 2 times the monopole at 500 ms for the $27M_{\odot }$ case (left) and of 1.4 times the monopole at 280 ms for $20M_{\odot }$.

Figure 14

Sky maps showing the evolution of the LESA direction (i.e., direction of the dipole of the lepton-number flux) in gray color scale and of the SASI direction (i.e., direction of the dipole of the neutrino energy flux of all six neutrino species) in blue color scale for the $27M_{\odot }$ SN progenitor (left) and the $20M_{\odot }$ SN progenitor (right) during the periods of strongest SASI activity. The color hues become lighter as time progresses. The size of the dots scales with the length of the plotted dipole vector. While for the $27M_{\odot }$ SN progenitor the LESA dipole is close to the SASI plane, for the $20M_{\odot }$ case they are nearly perpendicular to each other and no clear correlation exists between the LESA dipole direction and the SASI one.

Figure 15

IceCube and Hyper-Kamiokande detection rates $R$ for our 27, 20, and $11.2M_{\odot }$ SN progenitors at a distance of 10 kpc. The rates are shown for ${\overline{\nu }}_e$ and for ${\overline{\nu }}_x$ (i.e., assuming full swap by flavor conversion). For the 27 and $20M_{\odot }$ progenitors, the observer direction is close to the SASI plane where the signal modulation is strong.

Figure 16

Sky map of $\sigma /{\sigma }_{\max }$ with ${\sigma }^2$ defined in Eq. (6). Top panel: $27M_{\odot }$ progenitor during the first SASI phase (120–250 ms). Bottom panel: $20M_{\odot }$ progenitor during 150–330 ms.

Figure 17

Sketch of the quantities appearing in the calculation of the SN neutrino flux measured by a distant observer. The neutrino intensity is defined in terms of the location $\mathbf{R}$ of the emitting surface element $dA$ and the angle $\omega =(\theta ,\varphi )$ of emission relative to the direction $\mathbf{R}$. The observer is located at a distance $D\gg R$ in an arbitrary direction $\mathrm{\Omega }=(\mathrm{\Theta },\mathrm{\Phi })$, and $\gamma$ is the angle between the location of the radiating surface element and the direction of the observer.

Figure 18

Normalized energy distribution of ${\overline{\nu }}_e$, assuming a Gamma distribution (solid black line) with $A_{\nu }=13\mathrm{MeV}$ and ${\alpha }_{\nu }=3$. Corresponding normalized positron distribution (solid blue line) after folding with an inverse-beta decay cross section. Approximation with a Gamma distribution (dashed red line) with same $⟨{\epsilon }_e⟩$ and $⟨{\epsilon }_e^2⟩$. Assuming an inverse-beta cross section scaling with ${\epsilon }_{\nu }^2$ and no recoils gives the dashed black spectrum.