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Recent Developments in Self-Induced Supernova Neutrino Flavor Conversions

SUPERNOVA NEUTRINO OBSERVATIONS (SNOBs) Mainz, 9-13 October 2017. Recent Developments in Self-Induced Supernova Neutrino Flavor Conversions. Alessandro MIRIZZI University of BARI & Sez. INFN Bari, Italy. OUTLINE. Self-induced neutrino oscillations in SNe.

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Recent Developments in Self-Induced Supernova Neutrino Flavor Conversions

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  1. SUPERNOVA NEUTRINO OBSERVATIONS (SNOBs) Mainz, 9-13 October 2017 Recent Developments in Self-Induced Supernova Neutrino Flavor Conversions Alessandro MIRIZZI University of BARI & Sez. INFN Bari, Italy

  2. OUTLINE Self-induced neutrino oscillations in SNe Spontaneous symmetry breaking effects Fast conversions near SN core Conclusions Alessandro Mirizzi SNOBs Mainz, 11/10/2017

  3. M2 = - , + , ± Dm2 “solar” “atmospheric” n3 • Dm2 inverted hierarchy n1 • dm2/2 n1 • dm2/2 n2 n2 -dm2/2 -dm2/2 dm2 dm2 2 2 n3 -Dm2 normal hierarchy 3n FRAMEWORK Mixing parameters:U = U (q12, q13, q23, d)as for CKM matrix c12= cos q12, etc., d CP phase Mass-gap parameters: Alessandro Mirizzi SNOBs Mainz, 11/10/2017

  4. GLOBAL OSCILLATION ANALYSIS (2017) [Capozzi et al., arXiv:1703.0447] Alessandro Mirizzi SNOBs Mainz, 11/10/2017

  5. SNAPSHOT OF SN DENSITIES [Tomas et al., astro-ph/0407132] • Matter bkg potential • n-ninteraction Equivalentn density ~R2 ~R-3 ~R-2 • Vacuum oscillation frequencies When m>>l, SN n oscillations dominated by n-n interactions Collective flavor transitions at low-radii [O (102 – 103 km)] Alessandro Mirizzi SNOBs Mainz, 11/10/2017

  6. Collective Supernova Nu Oscillations since 2006 Two seminal papers in 2006 triggered a torrent of activities Duan, Fuller, Qian, astro-ph/0511275, Duan et al. astro-ph/0606616 Balantekin, Gava & Volpe [0710.3112]. Balantekin & Pehlivan [astro-ph/0607527]. Blennow, Mirizzi & Serpico [0810.2297]. Cherry, Fuller, Carlson, Duan & Qian [1006.2175, 1108.4064]. Cherry, Wu, Fuller, Carlson, Duan & Qian [1109.5195]. Cherry, Carlson, Friedland, Fuller & Vlasenko [1203.1607]. Chakraborty, Choubey, Dasgupta & Kar [0805.3131]. Chakraborty, Fischer, Mirizzi, Saviano, Tomàs [1104.4031, 1105.1130]. Choubey, Dasgupta, Dighe & Mirizzi [1008.0308]. Dasgupta & Dighe [0712.3798]. Dasgupta, Dighe & Mirizzi [0802.1481]. Dasgupta, Dighe, Raffelt & Smirnov [0904.3542]. Dasgupta, Dighe, Mirizzi & Raffelt [0801.1660, 0805.3300]. Dasgupta, Mirizzi, Tamborra & Tomàs [1002.2943]. Dasgupta, Raffelt & Tamborra [1001.5396]. Dasgupta, O'Connor & Ott [1106.1167]. Duan, Fuller, Carlson & Qian [astro-ph/0608050, 0703776, 0707.0290, 0710.1271]. Duan, Fuller & Qian [0706.4293, 0801.1363, 0808.2046, 1001.2799]. Duan, Fuller & Carlson [0803.3650]. Duan & Kneller [0904.0974]. Duan & Friedland [1006.2359]. Duan, Friedland, McLaughlin & Surman [1012.0532]. Esteban-Pretel, Mirizzi, Pastor, Tomàs, Raffelt, Serpico & Sigl [0807.0659]. Esteban-Pretel, Pastor, Tomàs, Raffelt & Sigl [0706.2498, 0712.1137]. Fogli, Lisi, Marrone & Mirizzi [0707.1998]. Fogli, Lisi, Marrone & Tamborra [0812.3031]. Friedland [1001.0996]. Gava & Jean-Louis [0907.3947]. Gava & Volpe [0807.3418]. Galais, Kneller & Volpe [1102.1471]. Galais & Volpe [1103.5302]. Gava, Kneller, Volpe & McLaughlin [0902.0317]. Hannestad, Raffelt, Sigl & Wong [astro-ph/0608695]. Wei Liao [0904.0075, 0904.2855]. Lunardini, Müller & Janka [0712.3000]. Mirizzi, Pozzorini, Raffelt & Serpico [0907.3674]. Mirizzi & Serpico [1111.4483]. Mirizzi & Tomàs [1012.1339]. Pehlivan, Balantekin, Kajino & Yoshida [1105.1182]. Pejcha, Dasgupta & Thompson [1106.5718]. Raffelt [0810.1407, 1103.2891]. Raffelt & Sigl [hep-ph/0701182]. Raffelt & Smirnov [0705.1830, 0709.4641]. Raffelt & Tamborra [1006.0002]. Sawyer [hep-ph/0408265, 0503013, 0803.4319, 1011.4585]. Sarikas, Raffelt, Hüdepohl & Janka [1109.3601]. Sarikas, Tamborra, Raffelt, Hüdepohl & Janka [1204.0971]. Saviano, Chakraborty, Fischer, Mirizzi [1203.1484]. Wu & Qian [1105.2068]………………………..

  7. arXiv:1508.00785 [astro-ph.HE]

  8. DENSITY MATRIX FOR THE NEUTRINO ENSEMBLE Diagonal elements related to flavor content Off-diagonal elements responsible for flavor conversions In 2n scenario (Dm2atm, q13). Decompose density matrix over Pauli matrices to get the “polarization” (Bloch) vector P. Survival probability Pee =1/2(1+Pz) . Pz = -1 -> Pee =0 ; Pz = 0 -> Pee =1/2 (flavor decoherence) The EOMs for the time evolution in a homogeneous medium are the Liouville equations (e.g. Early Universe) Alessandro Mirizzi SNOBs Mainz, 11/10/2017

  9. EQUATIONS OF MOTION FOR A DENSE NEUTRINO GAS [Sigl & Raffelt, 1992; Vlasenko, Fuller, Cirigliano, 1309.2628 Volpe, Vaananen, Espinoza, 1302.2374] Liouville operator Hamiltonian (see talk of Cristina Volpe) Explicit time evolution Drift term due to space inhomogeneities Force term acting on neutrinos (negligible) 7-dimensional problem. Never solved in its complete form. Symmetries have been used to reduce the complexity of the problem. Alessandro Mirizzi SNOBs Mainz, 11/10/2017

  10. SPACE/TIME HOMOGENEITIY Space Homogeneity: Pure temporal evolution (Neutrinos in Early Universe) Time Homogeneity: Stationary space evolution (SN neutrinos) Alessandro Mirizzi SNOBs Mainz, 11/10/2017

  11. MULTI-ANGLE (M.A.) EOMs FOR SN NEUTRINOS Evolution in space for n’s streaming from a SN core in quasi-stationary situation Liouville operator for free streaming n MULTI-ANGLE n-n HAMILTONIAN

  12. BULB MODEL [see, e.g., Duan et al., astro-ph/0606616] First large-scale multi-angle simulations zenith angle Azimuthal angle Neutrinos are emitted uniformly and (half)-isotropically from the surface of a sphere (n-sphere), like in a blackbody. Physical conditions depend only on the the distance r from the center of the star (azimuthal symmetry) Only multi-zenith-angle (MZA) effects in terms of u = sin2qR Project evolution along radial direction (ODE problem)

  13. MULTI-ANGLE LARGE SCALE SIMULATIONS First multi-angle simulations in 2006 by Duan, Fuller, Qian (2006). Major breakthrough! Anti-neutrino Neutrino Normal hierarchy Survival probability of ne vs E and emission angle cos q Inverted hierarchy Significant angular dependence on the Pee Convergence required > 103 angular bins Large scale numerical simulations

  14. MULTI-ANGLE SIMULATIONS BY DIFFERENT GROUPS Duan, Fuller, Carlson & Qian, astro-ph/0606616, 0608050 Fogli, Lisi, Marrone & A.M., 0707.1998, Fogli, Lisi, Marrone, A.M & Tamborra, 0808.0807; Esteban-Pretel, Pastor, Tomas, Raffelt & Sigl, 0706.2498 Duan & Friedland, 1006.2359 A.M. & Tomas, 1012.1339 Cherry, Fuller, Carlson, Duan, Qian, 1006.2175 Alessandro Mirizzi SNOBs Mainz, 11/10/2017

  15. SELF-INDUCED SPECTRAL SPLITS [Fogli, Lisi, Marrone, A.M. , arXiV: 0707.1998 [hep-ph],Duan, Carlson, Fuller, Qian, astro-ph/0703776, Raffelt and Smirnov, 0705.1830 [hep-ph],Dasgupta, Dighe, Raffelt & Smirnov, arXiv:0904.3542 [hep-ph], Duan & Friedland, arXiv: 1006.2359, A.M. & Tomas, arXiv:1012.1339, Choubey, Dasgupta, Dighe, A.M., 1008.0308....] Swap of the original SN n spectra in inverted mass hierarchy Strong dependence of collective oscillations on mass hierarchy and on the energy (‘’splits’’) Splits possible in both normal and inverted hierarchy, for n & n !! Alessandro Mirizzi SNOBs Mainz, 11/10/2017

  16. [Chakraborty, Fischer, A.M., Saviano , Tomas, arXiV:1105.1130, Dasgupta et al, 1106.1167….]

  17. HALO EFFECT Small fraction (10-3) of n undergo direction-changing scattering outside the neutrinosphere create a “neutrino halo” that can affect the flavor evolution [Cherry, Carlson, Friedland, Fuller, Vlasenko, arXiV:1203.1607] The halo converts the neutrino evolution problem from an initial value problem to a boundary value problem Stability analysis suggest small effect during accretion phase [Sarikas, Tamborra, Raffelt, Hudepohl, Janka, arXiV:1204.0971]. However possible role of inhomogeneities Effect studied during nu burst of O-Ne-Mg SNe [Cherry et al., 1302.1159]

  18. FIRST EXPLODING 3D SIMULATIONS [Lentz et al., 1504.07631] [Melson, Janka et al., 1504.07631] Shock-front 3D SN simulations show strong anisotropies and asphericities in the matter profile and in the neutrino emission. Real SN environment very far from the idealized bulb model. How deviations from the bulb model would affect the self-induced effects?

  19. MULTI-AZIMUTHAL-ANGLE (MAA) INSTABILITY Self-induced flavor conversions are associated to an instability in the flavor space [Sawyer,0803.4319; Banerjee, Dighe & Raffelt, 1107.2308] Instability required to get started (exponential growth of the off-diagonal density matrix part) The onset of the conversions can be found through a stability analysis of the linearized EoMs. In[Raffelt, Sarikas, Seixas, 1305.7140] a stability analysis of the EoMs has been performed including the azimuthal angle f of the n propagation and without enforcing axial symmetry. Also starting with an intial axial symmetric n emission..... .....A new multi-azimuthal-angle (MAA) instability has been found!! In the unstable case, numerical simulations are mandatory. Alessandro Mirizzi SNOBs Mainz, 11/10/2017

  20. SPECTRAL SPLITS FOR SN NEUTRINO FLUXES [Chakraborty, A.M., 1308.5255] ne nx Nu fluxes present a spectral split at E= 12 MeV (fixed by lepton number conservation) Antinu fluxes are swapped

  21. SPONTANEOUS SYMMETRY BREAKING IN SELF-INDUCED OSCILLATIONS Symmetries have been used to reduce the complexity of the SN n flavor evolution (e.g. the bulb model). However, n can lead to a spontaneous symmetry breaking (SSB) of the symmetry inherent to the initial conditions [Raffelt, Sarikas, Seixas, 1305.7140] . Small deviations from the space/time symmetries of the bulb model have to be expected. Can these act as seed for new instabilities? FIRST INVESTIGATIONS WITH TOY MODELS With a simple toy model in[Mangano, A.M. & Saviano, 1403.1892]it has been shown that self-interacting n can break translational symmetries in space and time. By a stability analysis in[Duan & Shalgar, 1412.7097]is has been found that self-interacting n can break the spatial symmetries of a 2D model. Alessandro Mirizzi SNOBs Mainz, 11/10/2017

  22. 2D MODEL FOR SELF-INTERACTING n FROM BULB MODEL  PLANAR MODEL [Duan & Shalgar, 1412.7097] Nu evolving in the plane (x,z) emitted from an infinite boundary at z=0, in only two directions (L and R). Excess of ne over ne . SPHERICAL TRANSLATIONAL AXIAL L-R BROKEN SYMMETRIES ? Alessandro Mirizzi SNOBs Mainz, 11/10/2017

  23. 2D MODEL FOR SELF-INTERACTING n A. M., Mangano and Saviano, [arXiv:1503.03485 [hep-ph]]. L-R TRANSLATIONAL (see talk of Ninetta Saviano) Large variations in the x direction at smaller and smaller scales. Planes of common phase broken. Coherent behavior of oscillation lost.

  24. NON-STATIONARITY Pulsating components may have component exactly cancealing the multi-angle matter term. Time-dependent fluctuations (with frequency p) can be unstable at higher matter density and lead to flavor conversions deeper in a SN. [Dasgupta, A.M., arXiv:1509.03171] Instability starts as a small pulsating seed, and cascades down to a large steady instability [Capozzi, Dasgupta, A.M., arXiv:1603.03288] Alessandro Mirizzi SNOBs Mainz, 11/10/2017

  25. RECENT PAPERS ON SSB G. Mangano, A. M. and N. Saviano, ‘’Damping the neutrino flavor pendulum by breaking homogeneity,’’Phys. Rev. D 89, no. 7, 073017 (2014) [arXiv:1403.1892 [hep-ph]]. H. Duan and S. Shalgar, ‘’Flavor instabilities in the neutrino line model,’’ Phys. Lett. B 747, 139 (2015) [arXiv:1412.7097 [hep-ph]]. A. M., G. Mangano and N. Saviano, ‘’Self-induced flavor instabilities of a dense neutrino stream in a two-dimensional model,’’Phys. Rev. D 92, no. 2, 021702 (2015) [arXiv:1503.03485 [hep-ph]]. S. Chakraborty, R. S. Hansen, I. Izaguirre and G. Raffelt, ‘’Self-induced flavor conversion of supernova neutrinos on small scales,’’JCAP 1601, no. 01, 028 (2016) [arXiv:1507.07569 [hep-ph]]. S. Abbar and H. Duan, ‘’Neutrino flavor instabilities in a time-dependent supernova model,’’ Phys. Lett. B 751, 43 (2015) [arXiv:1509.01538 [astro-ph.HE]]. B. Dasgupta and A. M., ’‘ Temporal Instability Enables Neutrino Flavor Conversions Deep Inside Supernovae,’’ Phys. Rev. D 92, no. 12, 125030 (2015) [arXiv:1509.03171 [hep-ph]]. F. Capozzi, B. Dasgupta and A. M., ‘’Self-induced temporal instability from a neutrino antenna,’’ JCAP 1604, no. 04, 043 (2016) [arXiv:1603.03288 [hep-ph]].

  26. FLAVOR CONVERSIONS NEAR SN CORE? Most of the studies assume no flavor conversion at r < 50 km (only synchronized oscillations). After self-induced conversions develop with a rate ~√wm [see, e.g., Hannestad et al, astro-ph/0608695] However, since more than a decade Ray Sawyer is pointing out that close to nu-sphere nu angular distributions of different species are rather different. This would lead to a new flavor instability (absent assuming equal angular distributions). The outcome would be a possible complete flavor mixing of the outgoing stream just above the nu-sphere. Fast rate ~m Alessandro Mirizzi SNOBs Mainz, 11/10/2017

  27. FAST FLAVOR CONVERSIONS NEAR SN CORE

  28. WHY SHOULD WE WORRY ABOUT THESE EFFECTS? If flavor changes occur in the deepest SN regions, they would modify the neutrino heating behind the stalled shock wave, possibly helping a SN to explode. Exploding. Spectral swap (by hands) behind shock front Non-exploding [Suwa et al., 1106.5487] If flavor equilibrium would occur close to the nu-sphere, all further oscillation effects (self-indued, matter…) would be washed-out. Crucial to predict observable SN nu signal. Alessandro Mirizzi SNOBs Mainz, 11/10/2017

  29. (See talk of Manibrata Sen) + new developments…

  30. NEUTRINO ANGULAR DISTRIBUTIONS AT DECOUPLING [Dasgupta, A.M., Sen, arXiV:1609.00528] Electron flavors remain in equilibrium with matter for a longer period than the non-electron flavors, due to the largest cross-sections of CC interactions Non-electron flavors decouple deeper in the star (more fwd-peaked distributions) Neutron-richness enhances CC interactions for ne keeping them more coupled to matter (more isotropic distribution) than ne . Alessandro Mirizzi SNOBs Mainz, 11/10/2017

  31. FAST FLAVOR CONVERSIONS [Dasgupta, A.M., Sen, arXiV:1609.00528] ne – ne difference Nu angular distributions no crossing crossing ne survival probability Growth rate of instability

  32. LEPTON NUMBER IN SN SIMULATIONS ne – ne difference ne – ne difference 3 D simulations LESA (crossing) [Tamborra et al., 1402.5418] 1 D simulations (no crossing) [Tamborra et al., 1702.00060]

  33. LOCAL STABILITY ANALYSIS z y x Shock n n n n PNS • Small test volume O(cm3) • Homogeneous conditions • Need fn for all species • Large mean free path • What is the flavor evolution at (x,y,z,t)?

  34. EQUATIONS OF MOTION FOR A TWO FLAVOR SYSTEM [Izaguirre, Raffelt & Tamborra, 1610.01612] Liouville equations for 2x2 density matrices (Free-streaming neutrinos Collisions=0) Flavor-dependent phase-space densities Diagonal elements related to flavor content Off-diagonal elements responsible for flavor conversions Flavor evolution governed by the “Hamiltonian matrix” Vacuum oscillations MSW effect nu-nu interaction term Note the for Dm2=0 the nu-nu interaction term could still produce run-away modes (off-diagonal r) Alessandro Mirizzi SNOBs Mainz, 11/10/2017

  35. LINEAR STABILITY ANALYSIS Flavor-dependent phase-space densities Complex scalar function S(x,t) contains all information if |S|<<1 and s=1 Linearized equations of motion for Dm2=0 nu direction of motion (angular variable) Matter potential Nu potential and current Lepton number angle distribution for ne Alessandro Mirizzi SNOBs Mainz, 11/10/2017

  36. PLANE WAVE SOLUTION (FOURIER SPACE) Look for plane-wave solution of the form Eliminate the differentials Eigenvalue equation for the plane wave solutions MSW potential from (e—e+) Angle distribution for (ne-ne) Potential and current from (ne-ne) Alessandro Mirizzi SNOBs Mainz, 11/10/2017

  37. DISPERSION RELATION This equation can be schematically written as a dispersion relation D(W,K)=0 Task: Derive solution as Temporal stability analysis Spatial stability analysis Quantitative characterization of the instabilities requires study of time-asymptotic behavior Green’s function [see, e.g., Briggs 1964, Landau & Lifshitz, Physical Kinetics-Volume 10, Chapter VI, Instability Theory] See [Capozzi, Dasgupta, Lisi, Marrone, A.M., arXiV:1706.03360] for details Alessandro Mirizzi SNOBs Mainz, 11/10/2017

  38. TWO-BEAM MODEL n n Shock n n • Four modes with different intensities • neinvward, outward • neinvward, outward

  39. DISPERSION RELATION [Izaguirre, Raffelt & Tamborra, 1610.01612;Capozzi, Dasgupta, Lisi, Marrone, A.M., arXiV:1706.03360] Neutrino angular spectrum Linearized equations of motion Dispersion relation No crossing e>0 e<0 crossing Alessandro Mirizzi SNOBs Mainz, 11/10/2017

  40. oscillatory behavior, no growing mode Complete stability v1v2>0, e>0 no gap in k or w w=W(k) k=K(w) [Capozzi, Dasgupta, Lisi, Marrone, A.M., arXiV:1706.03360]

  41. Damping v1v2<0, e>0 Evanescent wave. Damped solution Complex k for real w in frequency gap w=W(k) k=K(w) gap

  42. The signal grows and is convected away from the original region Convective instability v1v2>0, e<0 Complex k for real w, complex w for real k k=K(w) w=W(k) Alessandro Mirizzi SNOBs Mainz, 11/10/2017

  43. growing disturbance that does not propagate Absolute instability v1v2<0, e<0 Complex w for real k, in the wavenumber gap w=W(k) k=K(w) Growth rate Alessandro Mirizzi SNOBs Mainz, 11/10/2017

  44. ORBIT OF THE SOLUTIONS Complete stability v1v2>0, e>0 Damping v1v2<0, e>0 Convective instability v1v2>0, e<0 Absolute instability v1v2<0, e<0

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