The shockwave impact upon the Diffuse Supernova Neutrino Background GDR Neutrino, Ecole Polytechnique Sébastien GALAIS S. Galais, J. Kneller, C. Volpe and J. Gava Phys.Rev.D81:053002,2010 / arxiv: [hep-ph]

Plan  Diffuse Supernova Neutrino Background (DSNB)  Motivations o Introduction  The neutrino self-interaction  The shockwave effects in supernova o Theoretical Framework  on the fluxes  on the events rates o Results o Simplified model to reproduce the shockwave effects

Introduction Introduction Theoretical Framework Results Simplified Model Conclusions neutrinos Neutron Star  1.The interaction : neutrinos interact each other giving rise to collective effects. - J. T. Pantaleone, Phys. Rev. D (1992). - S. Samuel, Phys. Rev. 48, 1462 (1993). - G. Sigl and G. G. Raffelt, Nucl. Phys. B (1993). - Y. Z. Qian and G. M. Fuller, Phys. Rev. D (1995). - H. Duan, G. M. Fuller, J. Carlson, and Y.-Z. Qian, Phys. Rev. 74, (2006), ,… Neutrino -sphere Core-collapse supernova explosion 99 % of the energy is released by (anti)neutrinos of all flavors (about ergs for about 10 seconds).

Introduction neutrinos Neutron Star  matter 2. The shockwave effects : The shock will modify the density profile and therefore the MSW resonance. - R. C. Schirato and G. M. Fuller (2002), C. Lunardini and A. Y. Smirnov, JCAP 0306, 009 (2003), G. L. Fogli, E. Lisi, A. Mirizzi, and D. Montanino, Phys. Rev. 68, (2003), J. P. Kneller, G. C. McLaughlin, and J. Brockman, Phys. Rev. 77, (2008), … Neutrino -sphere MSW Introduction Theoretical Framework Results Simplified Model Conclusions

Diffuse Supernova Neutrino Background (DSNB) Supernova explosion  Neutrinos are emitted with a Fermi-Dirac distribution: from a localized region. during a finite time. Introduction Theoretical Framework Results Simplified Model Conclusions

 Neutrinos are emitted with a Fermi-Dirac distribution: from all directions (past and invisible SN). the background is there. DSNB  Energies are redshifted due the distance between the SN and Earth: Much progress have been done on its ingredients such as star formation rate. - S. Ando and K. Sato, New Journal of Physics 6, 170 (2004), L. E. Strigari, J. F. Beacom, T. P. Walker and P. Zhang, JCAP 0504, 017 (2005), C. Lunardini, Astroparticle Physics 26, 190 (2006), H. Yüksel and J. F. Beacom, Phys. Rev. 76, (2007), ) - … Introduction Theoretical Framework Results Simplified Model Conclusions

Motivations  Numerical simulations are close to the upper limits for relic neutrinos fluxes (Super Kamiokande, LSD).  Detection window for relic neutrinos. Introduction Theoretical Framework Results Simplified Model Conclusions

 Future observatories should be able to observe these fluxes. MEMPHYS: 440 kTon Water Čerenkov detector. Main detection channel: GLACIER: 100 kTon liquid argon detector. Main detection channel: Our aim is to explore: 1)the shockwave effects (in the supernova) upon the DSNB. 2)the sensitivity to the oscillations parameters (Hierarchy,  13,  phase). LENA: 44 kTon scintillator detector. Main detection channel: Introduction Theoretical Framework Results Simplified Model Conclusions

z: redshift : energy of the neutrino at emission (neutrinosphere) R SN : core-collapse supernova rate per unit comoving volume : differential spectra emitted by the supernova Theoretical framework Diffuse Supernova Neutrino Background (DSNB) flux at Earth. Flat universe and ΛCDM model: Ω Λ =0.7Ω m =0.3H 0 =70 km s -1 Mpc -1 Introduction Theoretical Framework Results Simplified Model Conclusions Supernova Rate R SN. Many constraints ( Gamma-ray bursts, rest-frame UV, NIR H α, and FIR/sub-millimeters observations )

Star Formation Rate (R SF ) Star formation rate R SF from [1], where R SF is divided in three parts. [1] H. Yuksel, M. D. Kistler, J. F. Beacom, and A. M. Hopkins, Astrophys. J. 683, L5 (2008). with Introduction Theoretical Framework Results Simplified Model Conclusions

The propagation in supernovae e  e-e- Neutron Star MSW effect interaction Vacuum osc Introduction Theoretical Framework Results Simplified Model Conclusions

The propagation in supernovae e  e-e- Neutron Star MSW effect interaction Vacuum osc Hierarchy  13 Introduction Theoretical Framework Results Simplified Model Conclusions

The propagation in supernovae e  e-e- Neutron Star MSW effect interaction Vacuum osc SHOCK Hierarchy  13 Introduction Theoretical Framework Results Simplified Model Conclusions

Our simulation We use a 3 flavour code in which we solve the propagation of the amplitudes. We include the interaction (single angle approximation). J. Gava, C. Volpe, Phys.Rev.D78:083007(2008), Inverted hierarchy;  13 =9 ,  23 =40  Movies realized by S. Galais. Introduction Theoretical Framework Results Simplified Model Conclusions

Synchronized region Bipolar oscillations Spectral split region Inverted hierarchy;  13 =9 ,  23 =40  Our simulation J. Gava, C. Volpe, Phys.Rev.D78:083007(2008), Movies realized by S. Galais. Introduction Theoretical Framework Results Simplified Model Conclusions

Inverted hierarchy;  13 =9 ,  23 =40  Our simulation J. Gava, C. Volpe, Phys.Rev.D78:083007(2008), Movies realized by S. Galais. Introduction Theoretical Framework Results Simplified Model Conclusions

Inverted hierarchy;  13 =9 ,  23 =40  Synchronized region Bipolar oscillations Spectral split region Our simulation J. Gava, C. Volpe, Phys.Rev.D78:083007(2008), Movies realized by S. Galais. Introduction Theoretical Framework Results Simplified Model Conclusions

Shockwave effects in supernovae E =20 MeV Evolution of the density profile with time in the MSW region. 1. Before the shock (adiabatic propagation). Without. Impact on the probability. Introduction Theoretical Framework Results Simplified Model Conclusions

E =20 MeV 2. The shock arrives (non-adiabatic prop.). Without. Shockwave effects in supernovae Evolution of the density profile with time in the MSW region. 1. Before the shock (adiabatic propagation). Impact on the probability. Introduction Theoretical Framework Results Simplified Model Conclusions

E =20 MeV 3. Phase effects appear. Without. Shockwave effects in supernovae 2. The shock arrives (non-adiabatic prop.). Evolution of the density profile with time in the MSW region. 1. Before the shock (adiabatic propagation). Impact on the probability. Introduction Theoretical Framework Results Simplified Model Conclusions

Without. E =20 MeV 4. Post-shock propagation. Shockwave effects in supernovae 3. Phase effects appear. 2. The shock arrives (non-adiabatic prop.). Evolution of the density profile with time in the MSW region. 1. Before the shock (adiabatic propagation). Impact on the probability. Introduction Theoretical Framework Results Simplified Model Conclusions

A complete calculation including the shockwave has been realized. Now we’re aiming at:  seeing its impacts on the fluxes and events rates.  exploring the sensitivity to oscillations parameters:   13,  hierarchy.

Normal Hierarchy for.Inverted Hierarchy for. + shock (numerical). RESULTS: relic electron (anti-)neutrino fluxes For  13 we have two cases: L and S. + no shock (analytical).  13 Small. Results for  13 large are valid for the range: (MeV -1 cm -2 s -1 )  13 Small. + no shock. + shock. (MeV -1 cm -2 s -1 ) Chooz limitBest limit for future facilities exp window (argon detector) exp window (Čerenkov detector) Normal Hierarchy for.Inverted Hierarchy for. Introduction Theoretical Framework Results Simplified Model Conclusions

+ shock. + no shock. Here is plotted the ratio Shockwave impacts:  10-20% effect from numerical calculations. + no shock. + shock. NHIH Introduction Theoretical Framework Results Simplified Model Conclusions

+ shock. + no shock. Here is plotted the ratio Shockwave impacts:  10-20% effect from numerical calculations. + no shock. + shock. NHIH reduction of the sensitivity to  13. Introduction Theoretical Framework Results Simplified Model Conclusions

Water Čerenkov, scintillator detectors and Inverted Hierarchy (with ) Analytical (no shock)Numerical (shock) N events Detection windowLL MeV Argon detectors and Normal Hierarchy MeV DSNB event rates (per kTon per year) +18% -11%  10-20% variation only due to the presence of the shock. Introduction Theoretical Framework Results Simplified Model Conclusions

Water Čerenkov, scintillator detectors Inverted Hierarchy (with ) N events Detection window L (no shock) L (shock)S MeV Argon detectors and Normal Hierarchy MeV The sensitivity to  13 is reduced.  10-20% variation only due to the presence of the shock. -12% +14% DSNB event rates (per kTon per year) -26% -28% Introduction Theoretical Framework Results Simplified Model Conclusions

Loss of the sensitivity to collective effects in the L case. The sensitivity to  13 is reduced.  10-20% variation only due to the presence of the shock. Water Čerenkov, scintillator detectors Inverted Hierarchy (with shock) N events Detection window L (with )L (without ) MeV MeV % DSNB event rates (per kTon per year) Introduction Theoretical Framework Results Simplified Model Conclusions

What have we learnt?  one should include the shockwave in future simulations because its effects are significant. To do so, we propose a simplified model to account for these effects.

1. From the numerical evolution of, we extract the 3 times. t s : shock arrives t p : phase effects t ∞ : post-shock 2. We average the value of in each part because is  independent of the energy. A simplified model to account for the shockwave This model based upon the general behaviour of the shockwave in supernova to calculate the flux. Introduction Theoretical Framework Results Simplified Model Conclusions

1. From the numerical evolution of, we extract the 3 times. t s : shock arrives t p : phase effects t ∞ : post-shock 2. We average the value of in each part because is  independent of the energy. A simplified model to account for the shockwave This model based upon the general behaviour of the shockwave in supernova to calculate the flux. Introduction Theoretical Framework Results Simplified Model Conclusions

Survival probability evolution with times and energy. A simplified model to account for the shockwave Introduction Theoretical Framework Results Simplified Model Conclusions

Interval0→t s t s →t p t p →t  t→t→ With Without Times fitting with polynomials functions. The simulations using these functions reproduce the full calculation to less than 2%. Introduction Theoretical Framework Results Simplified Model Conclusions

Conclusions  First complete calculation with interaction and shockwave for relic supernova neutrinos.  The shock affects significantly the DSNB fluxes and event rates.  We propose a model that can be used in future calculations to include shockwave effects. S. Galais, J. Kneller, C. Volpe and J. Gava, Phys.Rev.D81:053002,2010 / arxiv: [hep-ph] Introduction Theoretical Framework Results Simplified Model Conclusions

Our predictions for future observatories after 10 years MEMPHYS, UNO 440 kTon 290 < N events < 392 LENA 50 kTon 84 < N events < 96 GLACIER 100 kTon 58 < N events < 66 IH NH S. Galais, J. Kneller, C. Volpe and J. Gava, Phys.Rev.D81:053002,2010 / arxiv: [hep-ph]

Simplified model VS Numerical calculation Here is plotted the ratio

Modification of the parameters Variation of the cooling time . Addition of a temporal offset  t to t i. Luminosity decreases like: Change the arrival time of the shock. Results are robust to variations of the cooling time and the arrival time. Introduction DSNB Motivations Theoretical Framework Results Simplified Model Conclusions

interaction as a pendulum S. Hannestad, G. G. Raffelt, G. Sigl, and Y. Y. Y. Wong, Phys. Rev. 74, (2006),

Inverted Hierarchy: with  without  N events Detection windowLS MeV0.078 (0.078)0.089 (0.066) MeV0.211 (0.210)0.224 (0.196) Normal Hierarchy Detection windowL or S MeV MeV0.196 Inverted Hierarchy: with  without  N events Detection windowL or S MeV0.059 (0.058) MeV0.099 (0.096) Normal Hierarchy Detection windowLS MeV MeV

A simplified model to account for the shockwave SHOCK NO SHOCK

A simplified model to account for the shockwave NO SHOCK N events (without ) > N events (with )

A simplified model to account for the shockwave SHOCK

A simplified model to account for the shockwave SHOCK N events (with ) increases N events (without ) decreases  N events (with )  N events (without )

Interval0→t s t s →t p t p →t  t→t→ With Without Timesa0a0 a1a1 a2a2 a3a3 a4a4 a5a5 tsts 1.02       tptp 9.83       tt   This model can be used in future calculations of DSNB fluxes and rates to include shockwave effects.

Survival probability evolution with times and energy. Introduction DSNB Motivations Theoretical Framework Results Simplified Model Conclusions A simplified model to account for the shockwave

Evolution of times with energy. Introduction DSNB Motivations Theoretical Framework Results Simplified Model Conclusions BUT the luminosity decreases So we must do : A simplified model to account for the shockwave AND

1.The interaction. - J. T. Pantaleone, Phys. Rev. D (1992). - S. Samuel, Phys. Rev. 48, 1462 (1993). - G. Sigl and G. G. Raffelt, Nucl. Phys. B (1993). - Y. Z. Qian and G. M. Fuller, Phys. Rev. D (1995). - S. Pastor, G. G. Raffelt, and D. V. Semikoz, Phys. Rev. 65, (2002), H. Duan, G. M. Fuller, J. Carlson, and Y.-Z. Qian, Phys. Rev. 74, (2006), S. Hannestad, G. G. Raffelt, G. Sigl, and Y. Y. Y. Wong, Phys. Rev. 74, (2006), A. B. Balantekin and Y. Pehlivan, J. Phys. 34, 47 (2007), G. G. Raffelt and A. Y. Smirnov, Phys. Rev. 76, (2007), … Recent developments in neutrino propagation in SN: After the explosion of the star, the neutrinos density is so high that neutrinos interact each other giving rise to collective effects like synchronization, bipolar oscillations and spectral split. Introduction

2. The shockwave effects. - R. C. Schirato and G. M. Fuller (2002), C. Lunardini and A. Y. Smirnov, JCAP 0306, 009 (2003), K. Takahashi, K. Sato, H. E. Dalhed, and J. R. Wilson, Astropart. Phys. 20, 189 (2003), G. L. Fogli, E. Lisi, A. Mirizzi, and D. Montanino, Phys. Rev. 68, (2003), R. Tomas, M. Kachelrieß, G. Raffelt, A. Dighe, H.-T. Janka, and L. Scheck, JCAP 0409, 015 (2004), G. L. Fogli, E. Lisi, A. Mirizzi, and D. Montanino, JCAP 4, 2 (2005), S. Choubey, N. P. Harries, and G. G. Ross, Phys. Rev. D74, (2006), B. Dasgupta and A. Dighe, Phys. Rev. 75, (2007), S. Choubey, N. P. Harries, and G. G. Ross, Phys. Rev. 76, (2007), J. P. Kneller, G. C. McLaughlin, and J. Brockman, Phys. Rev. 77, (2008), J. P. Kneller and G. C. McLaughlin, Phys. Rev. 73, (2006), … Introduction The shock propagates through the matter in which it will modify the density profile and therefore the MSW resonance. Introduction DSNB Motivations Theoretical Framework Results Conclusions

- … - I.K. Baldry and K. Glazebrook, Astrophys. J. 593, 258 (2003). - S. Ando and K. Sato, New Journal of Physics 6, 170 (2004), L. E. Strigari, J. F. Beacom, T. P. Walker and P. Zhang, JCAP 0504, 017 (2005), C. Lunardini, Astroparticle Physics 26, 190 (2006), H. Yüksel and J. F. Beacom, Phys. Rev. 76, (2007), S. Chakraborty, S. Choubey, B. Dasgupta, and K. Kar, JCAP 0809, 013 (2008), … 3. Progress on the Diffuse Supernova Neutrino Background (DSNB). Introduction There have been much progress on the ingredients of the DSNB such as star formation rate, initial mass function.

Normal HierarchyAnalytic (no shock)Numeric (shock) N events Detection windowLL MeV MeV Argon detectors. Inverted Hierarchy: with Analytic (no shock)Numeric (shock) N events Detection windowLL MeV MeV Water Cerenkov and scintillator detectors. per kTon per year DSNB event rates in -observatories +18% +8% - 9% -11%  10% variation only due to the presence of the shock.

Inverted Hierarchy: with + shock N events Detection windowLS MeV MeV Normal Hierarchy N events Detection windowLS MeV MeV Argon detectors. per kTon per year DSNB event rates in -observatories Water Cerenkov and scintillator detectors. +14% - 6% -12% Same variation due to  13.  10% variation only due to the presence of the shock.

Inverted Hierarchy: with + shock N events Detection window L (with  L (without  MeV MeV Normal Hierarchy N events Detection windowL MeV MeV0.106 Argon detectors. per kTon per year DSNB event rates in -observatories Water Cerenkov and scintillator detectors. Loss of the sensitivity to collective effects in the L case. Same variation due to  %  10% variation only due to the presence of the shock.

The method used We use a 3 flavour code in which we solve the propagation of the amplitudes. We include the interaction (single angle approximation). J. Gava, C. Volpe, Phys.Rev.D78:083007(2008), Spectral split. This gives our at the supernova. interaction Inverted Hierarchy. 1. Synchronized region. 2. Bipolar oscillations. MSW effect DSNB Motivations Theoretical Framework Results Conclusions