spontaneous symmetry breaking in supernova neutrinos · author's personal copy figure 3:...

Author's personal copy

Spontaneous Symmetry Breaking in Supernova Neutrinos

Georg G. Raffelt

Max-Planck-Institut fur Physik (Werner-Heisenberg-Institut), Fohringer Ring 6, 80805 Munchen, Germany

Abstract

Some recent developments in supernova neutrino physics are introduced where spontaneous symmetry breaking isa common theme. The physics of self-induced flavor conversion has acquired a new complication in that a new classof instabilities breaks axial symmetry of a neutrino stream, the multi-azimuth angle (MAA) instability. A completelydifferent new phenomenon, discovered in the first realistic three-dimensional (3D) simulations, is the Lepton-EmissionSelf-sustained Asymmetry (LESA) during the accretion phase. Here, a neutrino-hydrodynamical instability breaksglobal spherical symmetry in that the lepton-number flux (νe minus νe) develops a stable dipole pattern such that thelepton flux is almost exclusively emitted in one hemisphere.

Keywords: Supernova, Neutrinos, Flavor Oscillations, Neutrino detectors

1. Introduction

Since 2010 when I last reported about supernova (SN)neutrinos at a NOW conference [1], several importantdevelopments have shaped this topic and its relevancefor neutrino physics. One seminal development hasbeen the measurement of the mixing angle θ13 at the re-actor experiments Double Chooz, Daya Bay and RENO.The sizeable value sin2 2θ13 = 0.093 ± 0.008 [2] hascleared the path towards an eventual measurement ofthe neutrino mass ordering and leptonic CP violation.

As a consequence, the interest in SN neutrinos asa possible source of hierarchy information has waned.Had θ13 been very small, self-induced flavor conversioncaused by neutrino-neutrino refraction in SNe wouldhave been perhaps the only physical environment where1–3 oscillations would have been relevant [3, 4, 5, 6, 7].Of course, self-induced flavor conversion is probablysuppressed during the early SN phase [8, 9, 10, 11, 12,13, 14]. The usual MSW effect for 1–3 oscillations inthe SN envelope has a strong and predictable impact onthe flavor-dependent fluxes [15]. While diagnosing themodified spectra by the Earth matter effect [16, 17] maybe rather difficult [18], the signal rise time in IceCuberemains a fairly robust diagnostic [19, 20].

The eventual observation of a high-statistics SN neu-trino signal requires the long-term operation of large-scale detectors [21]. The prospect of measuring theneutrino mass ordering and leptonic CP violation inthe laboratory has brought us much closer to the re-alization of a new large-scale liquid scintillator de-tector (JUNO [22]), a liquid-argon TPC (LBNO/E/F[23, 24, 25]), and a megaton water Cherenkov detec-tor (Hyper-Kamiokande [26]). Moreover, the discoveryof very high energy astrophysical neutrinos in IceCubeas well as the PINGU idea will almost certainly lead toan increase of the deployed number of optical modulesand thus to a yet larger SN neutrino sensitivity [27].

The only possible problem with such large detectorsis the enormous counting rate if the SN is relativelyclose and then makes high demands on the data acquisi-tion system. For the 20 kt JUNO project, the maximumexpected counting rate as a function of SN distance isshown in Fig. 1.

It is basically guaranteed that the missing neutrinomixing parameters, notably the mass ordering, will bemeasured in laboratory experiments. The focus of inter-est therefore has shifted to SN neutrinos as astrophys-ical messengers, notably to learn about the physics of

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Nuclear and Particle Physics Proceedings 265–266 (2015) 81–86

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http://dx.doi.org/10.1016/j.nuclphysbps.2015.06.022


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Figure 1: Maximum SN neutrino capture rate at the projected 20 ktliquid scintillator detector JUNO as a function of distance. In the up-per panel, the shaded range was obtained from a variety of SN models.The insert refers to Betelgeuse (distance 0.197±0.45 kpc), the closestpossible SN progenitor. The lower panel shows the SN probabilityin our galaxy according to three different estimates. (Figure from theJUNO Yellow Book, in preparation.)

core collapse and SN explosions. One exciting signa-ture would be fast time variations of the neutrino signal(frequency some 80 Hz) caused by the standing accre-tion shock instability (SASI) mode. This point had beenmade a few years ago based on two-dimensional (2D)hydrodynamical simulations [28].

As another seminal development, the first full-scale3D simulations with sophisticated neutrino transporthave become available, thus far only by the Garch-ing group [29]. Previous 3D studies with simplifiedneutrino transport had suggested SASI activity with

a strongly reduced amplitude at best. However, theGarching simulation of a 27 M� progenitor shows vio-lent SASI activity and produces a strong time variationof the neutrino signal [30]. Similar findings have beenreported for a 20 M� progenitor, whereas a 11.2 M� pro-genitor shows only large-scale convective overturn andno discernible fast signal variation (see Fig. 2).

Large-scale convection as well as SASI sloshingbreak spherical symmetry and lead to the neutrino sig-nal depending on the observer direction [31, 32]. Thestrong signal variations shown in Fig. 2 are optimistic,i.e., in a direction where the SASI activity is large. Inthe orthogonal direction the signature would be muchsmaller, although the SASI plane need not remain fixedso that some imprint would be expected in any direction.

While studying the directional dependence of theneutrino signal, we stumbled over a completely new andunexpected effect: the lepton-number flux (νe minus νe)is primarily emitted in one hemisphere. The neutrino-hydrodynamical instability responsible for this surpris-ing phernomenon has been termed LESA for Lepton-Emission Self-sustainded Asymmetry [31, 32].

2. Lepton-emission asymmetry

Neutrino trapping during collapse causes the proto-neutron star (PNS) to contain a large e− and νe fraction.Moreover, during the accretion phase, additional leptonnumber is advected. Therefore, the number flux of νeexceeds that of νe from collapse all the way to the PNScooling phase tens of seconds after bounce. In contrastto what is naively expected, however, the lepton num-ber is not isotropically emitted, but rather develops apronounced dipole pattern during the first 150 ms aftercore bounce.

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Figure 2: IceCube and Hyper-Kamiokande detection rates R for the 3D Garching models with 27, 20 and 11.2 M� SN progenitors at a distance of10 kpc [32]. The rates are shown for νe and for νx (i.e., assuming full swap by flavor conversion). For the 27 and 20 M� progenitors, the observerdirection is close to the SASI plane where the signal modulation is strong.

G.G. Raffelt / Nuclear and Particle Physics Proceedings 265–266 (2015) 81–8682


Figure 3: Lepton-number flux (νe minus νe) for the 11.2 M� model as a function of direction for the indicated times post bounce [31]. The flux ineach panel is normalized to its 4π average. The lepton-number emission asymmetry is a large-scale feature, which at later times has clear dipolecharacter. The black dots indicate the positive dipole direction, the black crosses mark the negative dipole direction. The dipole track between 70and 340 ms is shown as a dark-gray line. Once the dipole is strongly developed, its direction remains essentially stable and shows no correlationwith the numerical grid. The polar hot spots are an artifact connected with the coordinate singularity of the polar grid.

We show several snap shots of the lepton-number fluxas a function of emission direction in Fig. 3. We alsoshow the track of the dipole direction and conclude thatthe LESA dipole, once established, maintains a ratherstable direction which is not correlated with the coordi-nate grid. In those models that develop SASI, its plane isuncorrelated with the LESA dipole. The three available3D Garching models do not explode, but we speculatethat the LESA dipole decays within some 100 ms afterthe explosion has taken off.

In Fig. 4 we show the evolution of the lepton-numberflux and its dipole component for the 11.2 M� Garchingmodel which does not show SASI. The two other avail-able 3D models (20 and 27 M�) do develop strong SASIactivity, but apart from a small modulation, the lepton-number dipole evolution looks very similar and appearsto be a generic phenomenon.

The emission of the other neutrino flavors and theoverall neutrino luminosity remain spherically symmet-ric within a few percent. In particular, LESA does notcause a significant neutron-star recoil.

In Fig. 5 we show the flavor-dependent spectra in thetwo extreme directions at 210 ms post bounce. Thespectral shape is similar in both directions, but the over-all amplitude, especially of νe, is very different. Thiseffect also implies a very different impact of flavor os-

cillations in the two directions. In the direction of max-imum lepton-number flux, the νe and νx flux spectra arevery similar so that flavor-swaps would have no effect,in the opposite direction the effect would be large. It isclear that during the accretion phase, the neutrino signalfrom a SN not only depends strongly on the progenitormass and structure, but also on observer direction.

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Figure 4: Evolution of lepton-number emission (νe minus νe) for the11.2 M� model [31]. The overall flux is AMonopole + ADipole cosϑ incoordinates aligned with the dipole direction.

G.G. Raffelt / Nuclear and Particle Physics Proceedings 265–266 (2015) 81–86 83


0 10 20 30 40Neutrino Energy [MeV]

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Figure 5: Energy spectra of νe, νe, and νx for the 11.2 M� model at210 ms post bounce [31]. The spectra are for directions of maximal(black) and minimal (red) lepton-number flux, evaluated at a distanceof 400 km in the comoving frame of the accretion flow. We provide themonochromatic energy moment J = ΔE c/(4πΔεν) with ΔE being theenergy density in neutrino energy bin Δεν. The tick marks at the upperedge of the plot mark the rms energies. The neutrino spectral shape isvery similar in these opposite directions for each species, whereas thedifferences in overall normalization reflect the LESA effect.

A full physical explanation of LESA does not yet ex-ist. However, a feed-back loop has been identified thatcould explain the instability of a spherically-symmetricsolution and the self-sustained nature of the dipole pat-tern (see Fig. 6). The main idea is that a deformation ofthe stalling shock front deflects the accretion flow, lead-ing to asymmetric advection of lepton-rich matter. Theresulting modified νe and νe fluxes lead to asymmetricheating rates beneath the shock by inverse beta decayreactions, enhancing the shock-wave deformation.

However, this picture is certainly incomplete becausethe asymmetry actually arises deep below the neutrinosphere as shown in Fig. 7. In these layers, there is strongPNS convection with asymmetric strength and also astrong hemispheric asymmetry of the electron density.It is unclear at present how exactly the PNS convectionbelow the neutrino sphere communicates with large-scale convection and shock-wave deformation.

The final verdict on LESA will depend on a true phys-ical understanding and on a systematic observation ofthis effect in a broader range of 3D simulations. Ap-parently the authors of Ref. [33] have also found in-dications of LESA in their 3D models. On the otherhand, in the 2D models of Ref. [34] no indication forlepton-number emission asymmetry was found. Thereare many physical and numerical difference betweenthese models, so it is not clear at present where thesedifferent conclusions come from.

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Figure 6: Visualization of the proposed feedback loop causing theself-sustained lepton-emission asymmetry [31]. The outer thick blackline is the accretion shock with an exaggerated dipole deformation.The dotted circular line is the gain radius and the inner dashed circularline the neutrino spheres close to the PNS surface. Deeper inside, thebright-red and inner dark-red circular regions indicate the sphericaldensity distribution around the mass center (black dot), whereas thedisplaced, blue circular shapes indicate schematically the deformationof the Ye distribution. The black elliptical loops interior to the neu-trino spheres visualize PNS convection, whereas the light gray loopsvisualize convective overturn between gain radius and shock. PNSconvection is stronger in the lower hemisphere, whereas gain-regionconvection is more powerful on the opposite side. The red lines markaccretion-stream lines, which are deflected by the deformed shockfront. The brown and magenta arrows show the hemispheric asym-metry of the νe and νe energy fluxes.

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Figure 7: Radial evolution of the lepton-number emission in the hemi-sphere where the lepton flux is maximal (black) and minimal (red) forthe 11.2 M� simulation at 210 ms p.b. [31]. The lepton-number fluxasymmetry originates mostly from deep inside the PNS, i.e., from thehot PNS mantle below the neutrinosphere that is located at approxi-mately 35 km, whereas a more spherically symmetric component ofthe lepton-number flux develops in the surrounding, semi-transparentcooling layer and is fed by the accretion of lepton-rich material.



3. Self-induced flavor conversion

The LESA phenomenon prompts us to investigateif self-induced flavor conversion would be instigatedby a nearly symmetric distribution between νe and νe.In an isotropic neutrino gas or in the single-angle ap-proximation of SN neutrinos, a distribution which issymmetric between neutrinos and anti-neutrinos is en-tirely unstable with regard to self-induced flavor con-version [35, 36, 37, 38]. However, multi-angle effectscaused by matter or by neutrinos themselves can sup-press the instability [8, 9, 10, 11, 12, 13, 14].

In this context we mention another case of sponta-neous symmetry breaking which strongly changes theparadigm of self-induced flavor conversion. The neu-trino flux streaming from a SN core was always as-sumed to be axially symmetric around the radial di-rection. The usual “bimodal instability” which leadsto self-induced flavor conversion in the inverted masshierarchy preserves this symmetry. However, in nor-mal hierarchy, a completely new class of solutions wasrecently discovered, i.e., an instability which sponta-neously breaks azimuthal symmetry [39, 40, 41, 42]; ithas been termed multi-azimuth-angle (MAA) instabil-ity. If local axial symmetry is broken, global sphericalsymmetry is also broken, but an understanding of suchglobal solutions has not yet been developed.

The MAA instability is harder to suppress by multi-angle matter effects. Therefore, it is conservative to usethis case for a linearized stability analysis. Based on aschematic model for SN neutrino emission, this ques-tion was recently investigated in Ref. [43]. They useda simplified single-energy neutrino spectrum and per-formed a stability analysis for different chosen values ofthe asymmetry ε between the νe and νe fluxes. A typicalresult is shown in Fig. 8 where contours of the region areshown where run-away solutions exist in neutrino flavorspace. The parameter plane is spanned by the electrondensity and thus the multi-angle matter effect λ and theeffective neutrino-neutrino interaction strength μ whichis proportional to r−4.

One finds that the instability region is indeed signifi-cantly extended when the asymmetry is small, but into aregion of small matter density. Typical SN density pro-files are also shown where, in particular, one can clearlysee the dramatic density drop at the shock front. A re-duced lepton-number flux actually shifts and extendsthe instability region toward the lower-left direction ofFig. 8, i.e., away from those conditions which are rele-vant in the SN core.

One concludes that LESA does not change the cur-rent paradigm that self-induced flavor conversion does

Ε � �0.05Ε � 0.00Ε � 0.05Ε � 0.20

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Figure 8: Instability region (κ > 0.01 km−1) for the forward-peakedangular distribution of Ref. [43]. The vertical axis represents themulti-angle matter effect λ =

√2GFneR2/2r2 where R = 35 km is

the neutrino-sphere radius. The horizontal axis is related to the ef-fective neutrino-neutrino interaction strength through μ = μ0(R/r)4

with μ0 = 2 × 105 km−1. Contours refer to different cases of asym-metry with ε = (Fνe − Fνe )/Fνe . Representative SN density profilesat 150 ms and 350 ms p.b. are shown by continuous red and dashedblack curves, respectively, from the 11.2 M� Garching model.

not operate behind the shock wave and thus is not rele-vant for the explosion mechanism. Of course, this con-clusion may be revised as our theoretical understandingof the effects of neutrino-neutrino refraction develops.

4. Discussion

Observing a high-statistics SN neutrino signal re-mains the most coveted goal of low-energy neutrino as-tronomy. Taking advantage of such a once-in-a-lifetimeopportunity requires the long-term operation of large-scale detectors. The neutrino sky has been continu-ously observed since 1980 when the Baksan ScintillatorTelescope turned on. Thus far SN neutrinos have beenobserved only from SN 1987A, statistically in agree-ment with the expectation of a galactic core-collapseSN every few decades. However, given the optimisticprospects of large-scale detector operation over a longtime, an eventual high-statistics observation appearspractically guaranteed. Since the distance distributionis rather broad, one danger is that the SN might be tooclose and could saturate the data acquisition system. In-strumental measures should be taken to avoid the disas-ter of a detector blinded by neutrinos.

Over the years, the expectations of what to learn froma high-statistics SN signal have evolved. Learning aboutneutrino mixing parameters is no longer the focus ofinterest because, after the measurement of a relativelylarge θ13 value, all active-neutrino properties are acces-sible in the laboratory. Of course, there is always room

G.G. Raffelt / Nuclear and Particle Physics Proceedings 265–266 (2015) 81–86 85


for surprises in the form of sterile neutrinos becominga reality with a possibly dramatic impact on SNe or theappearance of other novel neutrino properties.

At the same time, our understanding of neutrinoflavor evolution in the SN context, where neutrino-neutrino refraction is important, has also evolved in thesense that we are less confident about our overall un-derstanding of this problem. Many complications haveappeared and the question of flavor evolution has be-come almost as challenging as the SN explosion mech-anism itself. However, the two issues are probably notconnected in the sense that neutrino flavor conversionwithin the shock-wave radius is suppressed by mattereffects. Still, flavor oscillations are a strong effect forthe observable SN neutrino signal, but a correct inter-pretation requires significantly more theoretical work.

Recently, the first 3D numerical SN simulations withsophisticated neutrino transport have been producedby the Garching group and suggest the possible ap-pearance of intriguing time-dependent features of theneutrino signal imprinted by hydrodynamical instabil-ities during the accretion phase. A completely newneutrino-hydrodynamical instability has appeared, theLESA phenomenon. It has not yet been fully under-stood and an exploration of its consequences has onlyjust begun. It is clear, however, that during the accretionphase, the expected neutrino signal strongly depends onthe observer direction relative to the SN.

While we wait for the next galactic SN, life is notboring because both numerical simulations and theoreti-cal studies of flavor-dependent neutrino propagation arechallenging topics that remain full of surprises.

Acknowledgments

Partial support by the Deutsche Forschungsgemein-schaft (DFG) under Grant No. EXC-153 (ExcellenceCluster “Universe”) and by the Research ExecutiveAgency (REA) of the European Union under Grant No.PITN-GA-2011-289442 (FP7 Initial Training Network“Invisibles”) is acknowledged.

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