No collective neutrino flavor conversions during the supernova accretion phase
Sovan Chakraborty, Tobias Fischer, Alessandro Mirizzi, Ninetta Saviano, Ricard Tomas
aa r X i v : . [ h e p - ph ] O c t No collective neutrino flavor conversions during the supernova accretion phase
Sovan Chakraborty, Tobias Fischer,
2, 3
Alessandro Mirizzi, Ninetta Saviano, and Ricard Tom`as II Institut f¨ur Theoretische Physik, Universit¨at Hamburg,Luruper Chaussee 149, 22761 Hamburg, Germany GSI, Helmholtzzentrum f¨ur Schwerionenforschung GmbH, Planckstraße 1, 64291 Darmstadt, Germany Technische Universit¨at Darmstadt, Schlossgartenstraße 9, 64289 Darmstadt, Germany
We perform a dedicated study of the SN neutrino flavor evolution during the accretion phase, usingresults from recent neutrino radiation hydrodynamics simulations. In contrast to what expected inthe presence of only neutrino-neutrino interactions, we find that the multi-angle effects associatedwith the dense ordinary matter suppress collective oscillations. The matter suppression impliesthat neutrino oscillations will start outside the neutrino decoupling region and therefore will havea negligible impact on the neutrino heating and the explosion dynamics. Furthermore, the possibledetection of the next galactic SN neutrino signal from the accretion phase, based on the usualMikheyev-Smirnov-Wolfenstein effect in the SN mantle and Earth matter effects, can reveal theneutrino mass hierarchy in the case that the mixing angle θ is not very small. PACS numbers: 14.60.Pq, 97.60.Bw
Introduction.—
Neutrinos emitted from core-collapsesupernovae (SNe) represent a crucial tool to get valuableinformation about the mixing parameters and an insightinto the dynamics of the exploding stellar core [1]. SNneutrinos not only interact with the stellar medium viathe Mikheyev-Smirnov-Wolfenstein (MSW) effect [2], butalso with other neutrinos ( ν ) and antineutrinos ( ν ). Itwas pointed out that large ν densities in the deepest stel-lar regions can result in significant coherent ν – ν forwardscatterings [3, 4], which give rise to collective ν flavor os-cillations inside the SN [5–7] (see [8] for a recent review).The development of these self-induced ν transforma-tions crucially depends on the primary SN ν spectra (see,e.g., [9, 10]). At this regard the post-bounce accretionphase of core-collapse SNe, lasting few tens of millisec-onds (for low mass O-Ne-Mg-core progenitors) up to sev-eral hundreds of milliseconds (for more massive iron-coreprogenitors), might seem the best opportunity to detectsignatures of collective ν flavor oscillations. Indeed, theabsolute ν fluxes are large during the accretion phasewith significant spectral differences between the differ-ent ν species, and a flux order F ν e > F ν e ≫ F ν x . Thisscenario has been often taken as a benchmark for the de-scription of the self-induced effects. Notably, these latterwould leave the ν spectra unaffected in normal mass hier-archy (NH: ∆ m = m − m , > ν mass hierarchy (IH: ∆ m < ν e and ¯ ν x spectra, and a spec-tral split in the energy distributions of the ν ’s [9]. Thisseemingly robust and clear behavior has been proposedas an unique way to determine the ν mass hierarchy evenif the leptonic 1–3 mixing angle θ is too small to be de-tected in terrestrial ν oscillation experiments [11, 12].The implicit assumption in this picture is related to theflavor evolution in the deepest SN regions being drivenby only large neutrino densities n ν . However, duringthe accretion phase also the net electron density n e isexpected to be large, as documented by many differentSN simulations [13–16]. This is a generic feature that ap- plies to SNe of massive iron-core progenitors. As recentlypointed out in [17] and confirmed in [18], when n e is notnegligible with respect to n ν , the large phase dispersioninduced by the matter for ν ’s traveling in different di-rections, will partially or totally suppress the collectiveoscillations through peculiar multi-angle effects.Motivated by this insight, we have performed a de-tailed study of the SN ν flavor evolution during the ac-cretion phase, characterizing the ν signal and the matterdensity profiles by means of recent neutrino radiation hy-drodynamics simulations. Contrarily to what shown inprevious studies based on the only ν - ν interaction ef-fects, we find that the presence of a dominant matterterm inhibits the development of collective flavor con-versions. The matter suppression ranges from completeto partial, producing intriguing time-dependent features.In particular, when it is complete (for post-bounce times t pb ∼ < . ν signal will be processedonly by the usual MSW effect in the SN mantle and Earthmatter effects. This was the usual description before theinclusion of collective phenomena. This d´ej`a vu wouldreopen the possibility, prevented by self-induced effects,to reveal the neutrino mass hierarchy through the Earthmatter effect on the next galactic SN neutrino burst, inthe case θ is not very small [19]. ν signal from the accretion phase.— We take as bench-mark for our study the results of the recent long-term SNsimulations, described in [20]. These are based on radia-tion hydrodynamics that employs three flavor Boltzmannneutrino transport in spherical symmetry. Figure 1 showsthe evolution of the ν number fluxes F ν α for the differentneutrino flavors ν α up to 0.6 seconds after core bounce,for the 10.8 M ⊙ iron-core progenitor model. Enhanced ν heating was applied, because a neutrino-driven explosioncannot be obtained in spherical symmetry for such a pro-genitor (for details, see [20]). The first phase after corebounce lasts only ∼ .
02 s, where large numbers of elec-tron captures release a flare of ν e with luminosities on theorder of 10 erg/s. It is followed by the accretion phase FIG. 1: ν fluxes during the accretion phase of the 10.8 M ⊙ SN explosion model. that can last up to several hundred milliseconds. Afterthe onset of the explosion, mass accretion vanishes atthe neutrinospheres (i.e., ν last-scattering surfaces) andthe neutrino luminosities are determined by diffusion. Itresults in a sharp drop of the fluxes after the explosionshock crosses a distance of 500 km, where the fluxes aremeasured in a co-moving reference frame. The fluxes ofall flavors decrease continuously on a longer timescale of O (10 s), indicating the beginning of the cooling phase. Setup of the flavor evolution.—
Our description ofthe ν flavor conversions is based on a two-flavor sce-nario, driven by the atmospheric mass-square difference∆ m ≃ . × − eV and by a small (matter sup-pressed) in-medium mixing θ eff = 10 − [21]. Three-flavoreffects, associated with the solar sector, are small for the ν flux ordering expected during the accretion phase [22].We will always refer to the inverted mass hierarchy wherefor the assumed spectral ordering collective oscillationsare possible [9, 22]. The impact of the non-isotropic na-ture of the ν emission on the flavor conversions is takeninto account by “multi-angle” simulations [6], where onefollows a large number [ O (10 )] of interacting ν modes.The ν ’s emitted from a SN core naturally have a broadenergy distribution. However, this is largely irrelevantfor our purposes, since large matter effects would locktogheter the different neutrino energy modes, both incase of supression [17] and of decoherence [23] of collec-tive oscillations. Therefore, to simplify the complexity ofthe numerical simulations, we assume all ν ’s to be repre-sented by a single energy, that we take E = 15 MeV.The strength of the ν – ν interaction is given by µ r = √ G F [ n ν e ( r ) − n ν x ( r )] [23], where n ν α ( r ) = F ν α / πr isthe number density of the ν species ν α . The ν – ν poten-tial is normalized at the neutrinosphere, where ν ’s areassumed to be half-isotropically emitted [23]. We de-termine the neutrinospheres from the core-collapse SNsimulations, where during the accretion phase the neu-trinosphere radius is at r ν ∼ O (10 ) km. The matterpotential is represented by λ r = √ G F n e ( r ) [24], encod-ing the net electron density, n e ≡ n e − − n e + . Matter and neutrino densities.—
In Fig. 2 we showthe net electron density n e (left panel) and the ratio R = n e / ( n ν e − n ν x ) between electron and neutrino den-sities entering the potentials (right panel), at selectedpost-bounce times. One can recognize the abrupt dis-continuity in n e associated with the SN shock-front thatpropagates in time. From the ratio R at the differentpost-bounce times, we realize that n e is always largerthan or comparable to n ν e − n ν x , suggesting that mattereffects cannot be ignored during the accretion phase. De-pending on the strength of the matter density, the mattersuppression can be total, when n e ≫ n ν , or partial whenthe matter dominance is less pronounced. Finally, when n e ∼ > n ν the interference of the two comparable potentialsleads to a flavor equilibrium with a complete mixture ofelectron and non-electron species [17]. Neutrino flavor conversions.—
In order to have a quan-titative description of these matter effects, we performeda multi-angle numerical study of the ν flavor evolutionin the schematic model described above. In Fig. 3 weshow the radial evolution of the ¯ ν e survival probability P ee for the same post-bounce times as in Fig. 2. Forcomparison, we also show the example of what is ex-pected in the case of n e = 0 (light curve for t pb = 0 . t pb = 0 . , . n e ≫ n ν the flavor conversions are completely blocked ( P ee = 1).Conversely, at t pb = 0 . n e ≃ n ν in the con-versions region, the matter suppression is only partialgiving a final P ee ≃ .
75. Finally, at t pb = 0 . n e ∼ > n ν , matter effects produce a complete flavor mix-ture ( P ee = 1 / (i) a complete matter suppression ofthe self-induced transformations for t pb ∼ < . (ii) par-tial matter suppression for 0 . ∼ < t pb ∼ < .
35 s, and (iii) again complete suppression for 0 .
35 s ∼ < t pb ∼ < . ν con-versions, i.e. complete-partial-complete suppression.The behavior, analyzed for this specific example of the10.8 M ⊙ SN explosion model, is generic also for moremassive iron-core SNe. It is independent from the explo-sion scenarios and applies also for non-exploding models.Indeed, in any case the density of the material, enclosedinside the standing bounce shock, can only increase dueto mass accretion from the iron-core envelope. Only af-ter the onset of an explosion, when mass accretion van-ishes, the matter density decreases. However, for thelow-mass O-Ne-Mg-core SNe, where the matter densityprofile is very steep, the suppression is never complete.As a consequence, the different features induced by thedense matter effects on the oscillations may allow to dis-tinguish iron-core SNe from O-Ne-Mg-core SNe [25].Our results have been obtained considering a spheri-cally symmetric neutrino emission. All the previous anal-ysis in the field have relied on this assumption to makethe flavor evolution equations numerically tractable. Itremains to be investigated if the removal of a perfectspherical symmetry can provide a different behavior in
FIG. 2: Radial profiles of the net electron density n e (left panel) and of the ratio R = n e / ( n ν e − n ν x ) (right panel), at selectedpost-bounce times for the 10.8 M ⊙ SN model. the flavor evolution [26]. Moreover, in multi-dimensionalSN models density fluctuations are expected behind thestanding bounce shock, due to the presence of convectionand hydro instabilities. These can range at most between10% to a factor 2-3 (see, e.g., [14, 27]). Therefore, even inthis case, the matter suppression of the collective oscilla-tions will still remain relevant. This claim is supportedby a recent analysis of the matter suppression, performedwith two-dimensional SN simulations [28].
Oscillated SN neutrino fluxes—
Figure 4 shows the ¯ ν e distribution function at the neutrinosphere (continuousthin curve) as well as after self-induced and matter effectsat r = 2 × km (continuous thick curve). We comparethe case of complete matter suppression at t pb = 0 . t pb = 0 . n e = 0, wherea complete ¯ ν e → ¯ ν x swap occurs (dashed curve). Thedifference in the final ¯ ν e flux with/without matter sup-pression is striking. It is plausible that a high-statisticsdetection of a future galactic SN ν signal would moni-tor the abrupt spectral changes between the phases ofcomplete and partial matter suppression, probing thisscenario. These peculiar time variations in the ν signalduring the accretion would represent also a new tool toextract information on the ν mass ordering, since the ef-fects of dense matter would show up only in the case ofinverted mass hierarchy. Earth matter effect.—
A further consequence of thematter suppression is a significant change in the inter-pretation of the Earth matter effect on the SN ν signalduring the accretion phase, occurring when ν ’s oscillateinside the Earth before being detected (see, e.g., [29]).In the case of complete matter suppression of the self-induced oscillations (at t pb ∼ < . ν fluxes at Earth have been already calcu-lated in the literature, antecedent to the inclusion of thecollective effects. For definiteness, here we consider theEarth effects on the ¯ ν e spectrum, observable through in-verse beta decay reactions ¯ ν e + p → n + e + at large volumeCherenkov or scintillation detectors (see, e.g., [19]).The ¯ ν e flux at Earth F D ¯ ν e in NH for any value ofthe mixing angle θ is given by F D ¯ ν e = cos θ F ¯ ν e +sin θ F ¯ ν x [19], where θ is the 1–2 mixing angle, with FIG. 3: Radial profiles of the ν e survival probability P ee atselected post-bounce times from multi-angle simulations inmatter (black continuous curves) and for n e = 0 (light curve).FIG. 4: Distribution functions for ¯ ν e at the neutrinosphere(continuous thin curve) and after self-induced and matter ef-fects at r = 2 × km (continuous thick curve), in the caseof complete matter suppression ( P ee = 0 at t pb = 0 . P ee = 1 / t pb = 0 . ν e spectra ob-tained for n e = 0 are also shown (dashed thin curve). sin θ ≃ . θ (i.e.for sin θ ∼ > − ) F D ¯ ν e = F ¯ ν x , while for “small” θ (i.e.for sin θ ∼ < − ) the flux is the same as in the case ofNH. Earth effects can be taken into account by mappingcos θ → P (¯ ν → ¯ ν e ) and sin θ → − P (¯ ν → ¯ ν e ),where P (¯ ν → ¯ ν e ) is the probability that a state enteringthe Earth as mass eigenstate ¯ ν is detected as ¯ ν e at thedetector (see, e.g., [29]).In this scenario, the presence or absence of Earth mat-ter effects at early times ( t pb ∼ < . ν mass hierarchy at large value of the mix-ing angle θ . This possibility, prevented in the previ-ous scenario with dominant self-induced effects, is par-ticularly attractive since there are already hints for a“large” θ [30, 31], promising its possible detection withthe current and upcoming reactor and accelerator exper-iments [32]. Thus for large θ , the next galactic SN ν signal would become crucial to get a determination of the ν mass hierarchy from the sky. Impact on SN heating.—
Neutrino flavor oscillationsbetween the neutrinospheres and the standing bounceshock, have long been speculated to influence the ν heat-ing and hence the SN dynamics [6, 13]. In contrast, wefind that the high matter density in the heating regioncauses complete suppression of the flavor conversion be-hind the shock-front. Hence, collective ν flavor oscilla-tions cannot help to increase the ν heating significantlyand an impact on the SN dynamics is not expected. Ourresult is in agreement with the analysis recently per-formed in [28]. In order to solve the SN problem, whichis related to the revival of the stalled bounce shock, itis possible to decouple the ν flavor evolution from thehydrodynamics aspects as well as from the ν transport. Conclusions.—
In early, schematic investigations, theaccretion phase seemed particularly promising to probethe development of the collective ν transformations.However, by analyzing state-of-the art simulations, wepointed out that the presence of a large matter densitypiled-up above the neutrinosphere can take its revengeover the ν – ν interactions, producing a significant sup- pression of the self-induced flavor conversions. The pres-ence of a large matter density during the accretion phaseis a robust feature of SN simulations [13–16]. However,its impact on the self-induced oscillations was estimatedmost often negligible in previous studies (see, e.g. [8, 10]).Even if the matter suppression would prevent collec-tive effects on the ν signal during the accretion phase, itspresence will result in various benefits. In particular, thedetection of the Earth matter effect on the SN ν burstduring the accretion may allow to extract the ν masshierarchy, if θ is not too small. Moreover, the mat-ter suppression of oscillations at high densities decouplesthe problem of the ν flavor mixing in SNe from the ν transport and impact on the matter heating/cooling.Collective oscillations may remain possible during thecooling phase, when the matter effects become sub-dominant due to the continuously decreasing matter den-sity. However, the characterization of these effects inthe presence of small flux differences and of matter tur-bulences is far from being settled. Further studies arecrucial to understand possible effects of self-induced ν oscillations and imprinted observable signatures. Acknowledgements
We thank M. Liebend¨orfer, E. Lisi, C. Ott, G. Raffelt,S. Sarikas, P. D. Serpico, G. Sigl and I. Tamborra forhelpful comments on the manuscript. We also acknowl-edge B. Dasgupta and T. Janka for important discus-sions. The work of S.C., A.M., N.S. was supported bythe German Science Foundation (DFG) within the Col-laborative Research Center 676 “Particles, Strings andthe Early Universe”. T.F. acknowledges support fromHIC for FAIR project no. 62800075. [1] G. G. Raffelt, Prog. Part. Nucl. Phys. , 393 (2010).[2] L. Wolfenstein, Phys. Rev. D , 2369 (1978); S.P. Mikheev and A. Y. Smirnov, Sov. J. Nucl. Phys. ,913 (1985).[3] J. Pantaleone, Phys. Lett. B , 128 (1992).[4] Y. Z. Qian and G. Fuller, Phys. Rev. D , 1479 (1995).[5] H. Duan et al. , Phys. Rev. D , 123004 (2006).[6] H. Duan et al. , Phys. Rev. D , 105014 (2006).[7] S. Hannestad et al. , Phys. Rev. D , 105010 (2006)[Erratum-ibid. D , 029901 (2007)].[8] H. Duan et al. , Ann. Rev. Nucl. Part. Sci. , 569 (2010).[9] G. L. Fogli et al. , JCAP , 010 (2007).[10] B. Dasgupta et al. , Phys. Rev. Lett. , 051105 (2009).[11] H. Duan et al. , Phys. Rev. Lett. , 241802 (2007).[12] B. Dasgupta et al. , Phys. Rev. Lett. , 171801 (2008).[13] G. M. Fuller et al. , Astrophys. J. , 517 (1992).[14] R. Tomas et al. , JCAP , 015 (2004).[15] R. Buras et al. , Astron. Astrophys. , 1049 (2006).[16] M. Liebendoerfer et al. , Astrophys. J. , 840 (2005).[17] A. Esteban-Pretel et al. , Phys. Rev. D , 085012 (2008). [18] H. Duan et al. , J. Phys. G , 105003 (2009).[19] A. S. Dighe et al. , JCAP , 006 (2003).[20] T. Fischer et al. , Astron. Astrophys. , A80 (2010).[21] T. Schwetz et al. , arXiv:1103.0734 [hep-ph].[22] A. Mirizzi and R. Tomas, arXiv:1012.1339 [hep-ph].[23] A. Esteban-Pretel et al. , Phys. Rev. D , 125018 (2007).[24] A. S. Dighe and A. Y. Smirnov, Phys. Rev. D , 033007(2000).[25] S. Chakraborty et al. , arXiv:1105.1130 [hep-ph].[26] R. F. Sawyer, Phys. Rev. D , 105003 (2009).[27] L. Scheck et al. , Astron. Astrophys. , 963 (2006).[28] B. Dasgupta et al. , arXiv:1106.1167 [astro-ph.SR].[29] C. Lunardini and A. Y. Smirnov, Nucl. Phys. B , 307(2001).[30] G. L. Fogli et al. , Phys. Rev. Lett. , 141801 (2008).[31] K. Abe et al. [T2K Collaboration], arXiv:1106.2822.[32] M. Mezzetto and T. Schwetz, J. Phys. G37