NEUTRINOS PROBE SUPERNOVA DYNAMICS

IRENE TAMBORRA GRAPPA Institute, University ofAmsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands

In the delayed explosion scenario of a core-collapse supernova (SN), the accretion phase shows pronounced convective overturns and a low-multipole hydrodynamic instability, the so-called standing accretion shock instability (SASI). Neutrino signal variations from the first full­ scale three-dimensional SN simulations with sophisticated neutrino transport are presented as well as their detection perspectives in IceCube and Hyper-Kamiokande. We also discuss a novel neutrino-hydrodynamical instability emerging from these simulations: "Lepton-number Emission Self-sustained Asymmetry" (LESA). LESA most conspicuous manifestation is the lepton-number flux ve minus emission primarily in one hemisphere. ( De)

1 Introduction Bethe and Wilson's delayed neutrino-driven explosion mechanism remains the standard SN paradigm. At core bounce a shock wave forms, it looses all its energy dissociating atoms within the iron shell and is then revived by neutrino heating after 100 ms During the accretion phase, hydrodynamic� instabilities 1. play an important role. These phenom­ ena include convection in the proto-neutron star, large-scale convective overturn below the stalled shock wave, and the standing accretion shock instability (SASI), involving sloshing motions of the 2 shock front as well as spiral modes (see and references therein). We add a new phenomenon to this list: the "Lepton-number Emission Self-sustained Asymmetry" (LESA). LESA most conspic­ uous manifestation is the lepton-number flux (ve minus De) emission primarily in one hemisphere, but it also involves a dipole deformation of the strength of PNS convection and of the large-scale convective overturn below the stalled shock 3. Our current portfolio of simulated 3D models includes an 11.2 M0 model showing violent large­ scale convection but no signs of SASI activity, a 20 M0 model with a long SASI phase, and a 27 M0 model in which episodes of SASI alternate with phases of dominant large-scale convection 2,3,4. On the other hand, all models exhibit LESA, with different orientations of the emission dipole. The clearest case is the 11.2 M0 model, where LESA is not overlaid with SASI activity. The next galactic SN may reveal these effects in gravitational waves as well as in neutrinos. In fact the SASI activity strongly modulates the neutrino emission, and the detection of such fast time variations of the neutrino signal will offer a unique chance to probe stellar core collapse5'6. IceCube 7 is among the most promising facilities for this task,detecting a large number of Cherenkov photons triggered by neutrinos. Moreover, Super-Kamiokande8, or the next-generation Hyper-Kamiokande (Hyper-K)9 will monitor the neutrino signal without background and provide event-by-event energy information. We here discuss the neutrino signal variations due to hydrodynamical instabilities fromthe first full-scale three-dimensional SN simulations with sophisticated neutrino transport as their detection perspectives. 2 Numerical supernova models The 3D modeling uses the PROMETHEUS-VERTEX hydrodynamics code, including state-of-the-art neutrino interaction rates and relativistic gravity and redshift corrections (see 2•3 for more details and references therein). The adopted description assumes the neutrino momentum distribution to be axisymmetric around the radial direction, implying that the neutrino fluxes are radial. The detectable energy-dependent neutrino emission from the hemisphere facing an observer is therefore determined with a post-processing procedure that includes projection and limb-darkening effects.

3 Detection perspectives of the hydrodynamical instabilites In the largest operating detectors, IceCube and Super-K, neutrinos are mainly detected by inverse beta decay, De + p --+ n + e+. We represent the neutrino energy spectra in the form of Gamma distributions lO,ll and estimate the neutrino signal as described in 4, assumingan overall background 3 rate of Rbkgd = 1.48 10 ms-1 (comparable to the signal rate for a SN at 10 kpc). IceCube will registerx 0(106) events above background for a SN at 10 kpc. While the future Hyper-K, with a fiducial mass of 740 kton, will provide a background-free signal of roughly 1/3 the IceCube rate. Moreover Hyper-K will give us event-by-event energy information (which we do not use). To get a first impression of the neutrino signal modulation \Ve consider the 27 ... model 2. Figure 1 shows the expected rate in IceCube and Hyper-K. This model shows clear SASI71.,f0 activity at 120-260 ms. At �220 ms a SASI spiral mode sets in and remains confined to an almost stable plane not aligned with the polar grid of the simulation. The first SASI episode ends abruptly with the accretion of the Si/SiO interface, followed by large-scale convection with much smaller and less periodic signal modulations. After about 410 ms, SASI activity begins again until the end of our simulation. In the top panel, we select an observer located in the SASI plane in a favorable direction and show the expected IceCube signal. While the second panel of Fig. 1 is for a direction orthogonal to the plane of the first SASI episode (i.e., the signal modulation is smaller than before). Neutrinos cliange their flavor as they propagate fromthe SN core to the detector. Other than the Mikheev-Smirnov-Wolfenstein (MSW) neutrino flavor conversions, neutrino-neutrino interac­ tions occur while neutrinos propagate through the SN envelope. However, since we still miss a detailed picture of the impact of neutrino-neutrino interactions on the SN neutrino signal due to the non-linear nature of the problem, we choose to show the two extreme scenarios in Fig. 1. One case assumes the signal caused by unoscillated De (i.e., ignoring flavor conversions), while the other one assumes complete flavor conversion so that the signal is caused by Dx (with Dx a combination of Dµ and Dr . Note as both cases reveal large signal modulations with a clear periodicity and, therefore, assuming) that the observed signal will be anything in between these two extreme cases, SASI modulations will be clearly detectable. In the third panel of Fig. 1 we show the IceCube De signal in 5 ms bins, including a random shot noise realization since the main limitation to observing signal modulations are random fluctuations in the detected neutrino time sequence. The SASI modulation of the neutrino signal will be clearly visible for a SN up to 20kpc (roughly the edge of the expected galactic SN distance distribution 12). In the bottom panel of Fig. 1, we show the expected signal in Hyper-K. For SN distances beyond some 10 kpc, the future Hyper-K detector would be superior to IceCube. In fact in spite of its smaller signal rate (about 1/3 of lceCube), its lack of background implies a better signal-to-noise ratio because of reduced shot noise for those distances where IceCube is dominated by background fluctuations. To exploit the full Hyper-K potential, its event-by-event energy determination should be used as well. The observed signal is strictly dependent on the location of the observer and, for fixed location of the observer, the detected rate oscillates with time. Due to the modulation of the emitted Figure 1 - Detection rate for the 27 M0 SN progenitor, upper panels for IceCube, bottom one for Hyper­ K. The observer direction is chosen for strong signal modulation, except for the second panel minimal modu­ lation . Upper two panels:( IceCube rate at) 10 kpc for no flavor con­ version and for Vxv, complete( flavor conversion) . The lower( two panels in­ clude a random) shot-noise realization, 5 ms bins, for the indicated SN dis­ tances. For IceCube also the back­ ground fluctuations without a SN sig­ nal are shown .

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Figure 2 - Relative amplitude of the Ve rate modulation see Eq. 1 on a sky-plot of observer directions during the first SAS! episode 120-250ms of the 27 M0 model on the( left and) during the SAS! episode 140-300ms of the 20 M0 model on the( right . ) ( ) ( ) ( ) neutrino signal, locations with the highest detection rate became afterwords the ones with lowest rate and viceversa. In order to quantify the chances to detect SASI, in Fig. 2 (left panel) we show the relative amplitude of the IceCube detection rate during the first SASI episode. In a given direction we define the relative time-dependent rate and consider its root mean square deviation for the first SASI episode ([t1, t2] [120, 250] ms), observing that the signal rate, averaged over all directions is not modulated: = /2 dt (1) CT= . The time integrated analysis still reveals(1:2 a dominant [ R (r) sloshing ry direction, which is responsible for two signal "hot spots" in two opposite directions, Rsurrounded by directions with much smaller modulations. Almost the 50% of the locations an observer will detect SASI. Figure 3 shows the IceCube rate forthe other two analyzed progenitors (11.2 and 20 M0) in op­ timal observing directions. For the heavier case, a strong SASI phase appears for t [140, 300] ms. For this progenitor, the signal large-amplitude modulations are more pronouncedE than for the 27 M0 progenitor, only one SASI phase occurs. Moreover, the SASI plane is different fromthe one of the 27 M0 SN progenitor and this is clearly shown in Fig. 2 (compare the left with the right 1000 lceCube 800

" 600 Figure 3 - IceCube rate for optimal � observing directions for the 11.2 and 20 M0 models at 10 kpc, as in the top � panel of Fig. 1.

50 100 150 200 250 300 Time [ms] panel). The 11.2 M0 model exhibits neutrino-driven convection without any clear signs of large­ amplitude coherent SASI motions (see Fig. 3). The detection rate for this progenitor is smaller than for the other two progenitors because of a lower luminosity. The power spectrum of the IceCube event rate for our three SN models shows a clear peak at �so Hz for the 27 and 20 M0 progenitors where strong SASI appears. Note that for both the two heavier progenitors the SASI frequenciesare similar because of similar neutron star radii (the same equation of state is used) and mean shock radii in the first 250ms.

4 Lepton-number Emission Self-sustained Asymmetry To provide an impression of this new and intriguing phenomenon, Fig. 4 shows the distribution of lepton-number emission (ve minus De) forthe 11.2 M0 model over the stellar surface at post-bounce times of 148, 169, 210, and 240ms. In each panel, the lepton-number flux is normalized to the instantaneous average. The positive dipole direction is indicated with a black dot, the negative direction with a cross. We also show the track of the positive dipole direction a dark-gray line. While at 148 ms the dipole pattern is not yet strong, the subsequent snapshotsas reveal a strong dipole pattern with large amplitude: In the negative-dipole direction, the lepton-number flux is around zero, and even negative in some small regions, whereas in the positive direction it is roughly twice the average and even larger in some small regions. Once the dipole is strongly developed, its direction remains essentially stable and shows no correlation with cartesian axes of the numerical grid. To quantifythe time evolution of our new effect we consider the lowest-order multipole compo-

Figure 4 - Lepton-number flux ( minus De) for our 11.2 M0 model as a function of direction forthe indicated times post bounce. The flux in each panelve is normalized to its average, i.e., the quantity (Fve - Foe )/(Fve - Foe ) is color coded. The lepton-number emission asymmetry has clear dipole character at later times. The black dots indicate the positive dipole direction of the flux distribution, the black crosses mark the negative dipole direction. The dipole track is shown as a dark-gray line.

1 oc 11 Msun 20 Msun 27 Msun

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100 200 300 400 500 Time After Bounce [ms)

Figure 5 - Time evolution of the lepton-number emission (ve minus Ve) forthe 11.2, 20 and 27 M0 models labelled. For each model, the overall lepton number flux (monopole of the angular distribution; red curve) is shownas and its dipole component (blue curve). nents of the lepton-number flux asa function of emission direction. Figure 5 shows the evolution of the monopole and the dipole of the lepton number for our three progenitors. The total lepton­ number emission is at firstoff -scale, corresponding to the usual prompt Ve burst, and then decreases monotonically with small modulations caused by large-scale convection. The monopole evolution strongly depends on the accretion rate and varies between the models, whereas the maximum dipole amplitude is similar in all cases and shows a similar initial growth phase. In all models, the dipole component becomes discernible at about 50 ms, grows for 100-150 ms, and later decreases, more or less in parallel with the overall decline of the lepton-number emission. In this later phase, the dipole amplitude sometimes exceeds the monopole, meaning that in the negative dipole direction, the lepton-number flux is somewhat negative (excess of De over Ve emission). The overall dipole strength is similar in all three progenitor models, at the peak reaching a value of 3-4 x 1056 s-1. The dipole persists (and can even grow) during the indicated phases of pronounced SASI activity. The dipole directions are different in all cases, bear no correlation to the numerical grid, and they drift only slowly even during SASI phases (marked in Fig. 5 by horizontal bars). Moreover, the LESA dipole direction is not even correlated with the main direction of SASI sloshing. When a stable dipolar pattern emerges, it reaches maximum amplitudes of around 103 for Ve and 153 for De at roughly 180ms after bounce. A positive amplitude for Ve is correlated with a negative one for De and vice versa, and local maxima (minima) of the Ve emission generally coincide in time with minima (maxima) of the De emission. The dipole asymmetry is large in the Ve and De fluxes, whereas heavy-lepton neutrinos, Vx, exhibit at most a few-percent effect. The Vx emission is slightly enhanced in the direction of small lepton-number (high De) flux. Both luminosity and number fluxesclearly show the emission dipole (anti-)aligned with the lepton-number dipole axis. In contrast to the individual luminosities and number fluxes, the sums L.,e + Lve and N.,e + Nve> vary only on the few-percent level. The observations suggest that the LESA phenomenon must physically depend on a complicated interplay of different effects. The initial growth over 100-150 ms parallels the growth of large­ scale convection in the gain region, suggesting gain-region convection as the primary engine. On the other hand, the persistence throughout SASI episodes and the near-universal dipole strength suggest that LESA must also be anchored to deeper regions. It indeed originates in the PNS convection region. In fact the global accretion asymmetry is maintained by anisotropic neutrino heating in the gain layer behind the stalled SN shock, because De leave the neutrinospherc with higher mean energy than Ve· Therefore, neutrino heating is stronger on the side of lower lepton­ number flux, despite the nearly isotropic energy flux of Ve plus De. Stronger neutrino heating enhances convective overturn in the postshock layer, pushes the shock to a larger stagnation radius and thus produces a dipolar deformation of the shock surface. This shock deformation in turn deflects the accretion flow falling through the shock and, in the time-averaged sense, amplifies the accretion flux to the hemisphere of the PNS facing away from the greater shock

10'7 radius. Anisotropic neutrino heating therefore establishes a feedback mechanism between the neutrino-emission asymmetry on one side and shock deformation and accretion asymmetry on the other. It thus mediates a complex, mutual dependence between lepton-number transport by neutrino fluxesand convection inside the PNS on the one hand and anisotropic convective overturn in the gain layer on the other. The feedback, which involves neutrinos as crucial players, allows the global dipolar asymme­ try to become a self-sustained phenomenon, which exists in quasi-stationary conditions despite the presence of vigorous convective overturns and even through phases of violent SASI activity. Stochastic fluctuations of this convective overturn or of the convection in the PNS mantle are probably responsible for initiating the development of the hemispheric asymmetry. The convective SN core seems to be generically unstable against such a dipolar mode of asymmetry. LESA could have important implications for a variety of physical processes in the SN core, most importantly nucleosynthesis in the neutrino-heated ejecta, and potentially NS kicks and neutrino-flavor conversion.

5 Conclusions The first 3D SN simulations with sophisticated neutrino transport are available for 11, 20 and 27 M8 SN progenitors. They show pronounced spiral SASI activity for the two more massive progenitors, while the lighter one is dominated by large-scale convective overturn activity. detectable instabilities appear to be dependent on the progenitor properties. If detected by IceCubeSuch and the future Hyper-K, the neutrino signal of the next galactic SN will offera unique opportunity to diagnose different types of hydrodynamical instabilities and to test the supernova explosion mechanism. Besides the traditional hydrodynamical instabilities, for all the three progenitors, we find a new phenomenon: "Lepton-number Emission Self-sustained Asymmetry" (LESA). LESA manifests ve De), itself most conspicuously in the lepton-number flux( minus whose dipole amplitude can reach 1003 of its 4rr directional average, i.e., in one direction the lepton-number flux can exceed twice the average. LESA could have important implications for avariety of physical processes in the SN core, as nucleosynthesis in the neutrino-heated ejecta, and potentially NS kicks and neutrino-flavor conversion.

6 Acknowledgments The results presented here were mainly obtained in Refs. 4•3•13. The author is grateful to the Rencontres de Moriond EW 2014 organizers forkind hospitality.

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