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Photohadronic processes and neutrinos Lecture 2

Photohadronic processes and neutrinos Lecture 2. Summer school “High energy astrophysics” August 22-26, 2011 Weesenstein , Germany Walter Winter Universität Würzburg. TexPoint fonts used in EMF: A A A A A A A A. Contents. Lecture 1 (non-technical) Introduction, motivation

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Photohadronic processes and neutrinos Lecture 2

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  1. Photohadronic processes and neutrinosLecture 2 Summer school “High energy astrophysics” August 22-26, 2011 Weesenstein, Germany Walter Winter Universität Würzburg TexPoint fonts used in EMF: AAAAAAAA

  2. Contents • Lecture 1 (non-technical) • Introduction, motivation • Particle production (qualitatively) • Neutrino propagation and detection • Comments on expected event rates • Lecture 2 • Tools (more specific) • Photohadronic interactions, decays of secondaries, pp interactions • A toy model: Magnetic field and flavor effects in n fluxes • Glashow resonance? (pp versus pg) • Neutrinos and the multi-messenger connection

  3. Repetition and some tools

  4. Photohadronics (primitive picture) If neutrons can escape:Source of cosmic rays Neutrinos produced inratio (ne:nm:nt)=(1:2:0) Delta resonance approximation: Cosmogenic neutrinos p+/p0 determines ratio between neutrinos and gamma-rays High energetic gamma-rays;might cascade down to lower E Cosmic messengers

  5. Inverse timescale plots • Quantify contribution of different processes as a function of energy. Example: (not typical!) Acceleration ratedecreases with energy (might be a function of time) Photohadronicprocesses limit maximalenergy Inverse timescale/rate Other cooling processes subdominant (from: Murase, Nagataki, 2005)

  6. Treatment of spectral effects • Energy losses in continuous limit:b(E)=-E t-1lossQ(E,t) [GeV-1 cm-3 s-1] injection per time frameN(E,t) [GeV-1 cm-3] particle spectrum including spectral effects • For neutrinos: dN/dt = 0 (steady state) • Simple case: No energy losses b=0 Injection Energy losses Escape often: tesc ~ R

  7. Energy losses and escape • Depend on particle species and model • Typical energy losses (= species unchanged): • Synchrotron cooling • Photohadronic cooling (e.g. pg p ) • Adiabatic cooling • … • Typical escape processes: • Leave interaction region • Decay into different species • Interaction (e.g. pg n ) • … ~ E ~ E, const, … ~ const Energydependence ~ const ~ 1/E ~ E, const, …

  8. G Relativistic dynamics (simplified picture) • Transformation into observer‘s frame:Flux [GeV-1 cm-2 s-1 (sr-1)] from neutrino injection Qn [GeV-1 cm-3 s-1]N: Normalization factor depending on volume of interaction region and possible Lorentz boost • Spherical emission, relativistically boosted blob: • Relativistic expansion in all directions:(“fireball“): typically via calculation of isotropic luminosity (later) • Caveat: Doppler factor more general Geff Observer Observer

  9. Photohadronic interactions, pp interactions

  10. g q p Principles • Production rate of a species b:(G: Interaction rate for a  b as a fct. of E; IT: interact. type) • Interaction rate of nucleons (p = nucleon) ng: Photon density as a function of energy (SRF), angle s: cross sectionPhoton energy in nucleon rest frame: CM-energy: er

  11. q p g g q p Threshold issues • In principle, two extreme cases: • Processes start at(heads-on-collision atthreshold)but that happens onlyin rare cases! er Threshold ~ 150 MeV

  12. Threshold issues (2) • Better estimate:Use peak at 350 MeV?but: still heads-on-collisions only! • Discrepancies with numerics! • Even better estimate?Mean angle cos q ~ 0 er D-Peak ~ 350 MeV Threshold ~ 150 MeV The truth isin between:Exercises!

  13. Typical simplifications • The angle q is distributed isotropically • Distribution of secondaries (Ep >> eg):Secondaries obtain a fraction c of primary energy. Mb: multiplicity of secondary species bCaveat: ignores more complicated kinematics • Relationship to inelasticity K (fraction of proton energy lost by interaction):

  14. Results Details: Exercises • Production of secondaries: • With “response function“: • Allows for computation with arbitrary input spectra! But: complicated, in general … from:Hümmer, Rüger, Spanier, Winter, ApJ 721 (2010) 630

  15. Different interaction processes Resonances Differentcharacteristics(energy lossof protons;energy dep.cross sec.) Dres. Multi-pionproduction er (Photon energy in nucleon rest frame) Direct(t-channel)production (Mücke, Rachen, Engel, Protheroe, Stanev, 2008; SOPHIA;Ph.D. thesis Rachen)

  16. Factorized response function • Assume: can factorize response functionin g(x) * f(y): • Consequence: • Fast evaluation (single integral)! • Idea: Define suitable number of IT such that this approximation is accurate! (even for more complicated kinematics; IT ∞ ~ recover double integral) Hümmer, Rüger, Spanier, Winter, ApJ 721 (2010) 630

  17. Examples • Model Sim-C: • Seven IT for direct production • Two IT for resonances • Simplified multi-pion production with c=0.2 • Model Sim-B:As Sim-C, but 13 IT for multi-pion processes Hümmer, Rüger, Spanier, Winter, ApJ 721 (2010) 630

  18. Pion production: Sim-B • Pion production efficiency • Consequence: Charged to neutral pion ratio Hümmer, Rüger, Spanier, Winter, ApJ 721 (2010) 630

  19. Interesting photon energies? • Peak contributions: • High energy protons interact with low energy photons • If photon break at 1 keV, interaction with 3-5 105 GeV protons (mostly)

  20. Comparison with SOPHIAExample: GRB • Model Sim-B matches sufficiently well: Hümmer, Rüger, Spanier, Winter, ApJ 721 (2010) 630

  21. Decay of secondaries • Description similar to interactions • Example: Pion decays: • Muon decays helicity dependent! Lipari, Lusignoli, Meloni, Phys.Rev. D75 (2007) 123005; also: Kelner, Aharonian, Bugayov, Phys.Rev. D74 (2006) 034018, …

  22. Where impacts? Neutrino-antineutrino ratio Spectral shape Flavor composition D-approx.: 0.5.Difference to SOPHIA:Kinematics ofweak decays D-approximation:Infinity D-approximation:~ red curve Hümmer, Rüger, Spanier, Winter, ApJ 721 (2010) 630

  23. Cooling, escape, re-injection • Interaction rate (protons) can be easily expressed in terms of fIT: • Cooling and escape of nucleons: (Mp + Mp‘ = 1) • Also: Re-injection p  n, and n  p … Primary loses energy Primary changes species

  24. Comments on pp interactions • Similar analytical parameterizations of “response function“ exist, based on SIBYLL, QGSJET codes(secondaries not integrated out!) Kelner, Aharonian, Bugayov, Phys.Rev. D74 (2006) 034018 • Ratio p+:p-:p0 ~ 1:1:1 • Charged to neutral pion ratio similar to pg • However: p+ and p- produced in equal ratios • Glashow resonance as discriminator? (later) • h meson etc. contributions … Kelner, Aharonian, Bugayov, Phys.Rev. D74 (2006) 034018; also: Kamae et al, 2005/2006

  25. A toy model:magnetic field and flavor effects in neutrino fluxes(… to demonstrate the consequences)

  26. A self-consistent approach • Target photon field typically: • Put in by hand (e.g. obs. spectrum: GRBs) • Thermal target photon field • From synchrotron radiation of co-accelerated electrons/positrons (AGN-like) • From more complicated combination of radiation processes • Approach 3) requires few model params, mainly • Purpose: describe wide parameter ranges with a simple model; minimal set of assumptions for n!? ?

  27. Model summary Dashed arrows: include cooling and escape Dashed arrow: Steady stateBalances injection with energy losses and escapeQ(E) [GeV-1 cm-3 s-1] per time frameN(E) [GeV-1 cm-3] steady spectrum Opticallythinto neutrons Injection Energy losses Escape Hümmer, Maltoni, Winter, Yaguna, Astropart. Phys. 34 (2010) 205

  28. An example: Primaries TP 3: a=2, B=103 G, R=109.6 km • Maximal energy of primaries (e, p) by balancing energy loss and acceleration rate • Hillas condition often necessary, but not sufficient! Maximum energy: e, p Hillas cond. Hümmer, Maltoni, Winter, Yaguna, 2010

  29. Maximal proton energy (general) • Maximal proton energy (UHECR) often constrained by proton synchrotron losses • Sources of UHECR in lower right corner of Hillas plot? • Caveat: Only applies to protons, but … Only fewprotons? (Hillas) UHECRprot.? Auger Hümmer, Maltoni, Winter, Yaguna, 2010

  30. An example: Secondaries a=2, B=103 G, R=109.6 km • Secondary spectra (m, p, K) become loss-steepend abovea critical energy • Ec depends on particle physics only (m, t0), and B • Leads to characteristic flavor composition • Any additional cooling processes mainly affecting the primaries willnot affect the flavor composition • Flavor ratios most robustpredicition for sources? • The only way to directly measure B? Cooling: charged m, p, K Spectralsplit Pile-up effect Flavor ratio! Ec Ec Ec Hümmer et al, Astropart. Phys. 34 (2010) 205

  31. Flavor composition at the source(Idealized – energy independent) REMINDER • Astrophysical neutrino sources producecertain flavor ratios of neutrinos (ne:nm:nt): • Pion beam source (1:2:0)Standard in generic models • Muon damped source (0:1:0)at high E: Muons lose energy before they decay • Muon beam source (1:1:0)Cooled muons pile up at lower energies (also: heavy flavor decays) • Neutron beam source (1:0:0)Neutron decays from pg(also possible: photo-dissociationof heavy nuclei) • At the source: Use ratio ne/nm (nus+antinus added)

  32. However: flavor composition is energy dependent! Pion beam Muon beam muon damped Energywindowwith largeflux for classification Typicallyn beamfor low E(from pg) Pion beam muon damped Undefined(mixed source) Behaviorfor smallfluxes undefined (from Hümmer, Maltoni, Winter, Yaguna, 2010; see also: Kashti, Waxman, 2005; Kachelriess, Tomas, 2006, 2007; Lipari et al, 2007)

  33. Parameter space scan • All relevant regions recovered • GRBs: in our model a=4 to reproduce pion spectra; pion beam  muon damped (confirmsKashti, Waxman, 2005) • Some dependence on injection index a=2 Hümmer, Maltoni, Winter, Yaguna, 2010

  34. Individual spectra • Differential limit 2.3 E/(Aeff texp)illustrates what spectra thedata limit best Auger 2004-2008 Earth skimming nt IC-40 nm (Winter, arXiv:1103.4266)

  35. Which point sources can specific data constrain best? Constraints to energy flux density Inaccessible (atm. BG) Inaccessible (atm. BG) Deep Core IC cascades? ANTARES Auger North? Radio Radio FUTURE/OTHER DATA? (Winter, arXiv:1103.4266)

  36. Neutrino propagation (vacuum) REMINDER • Key assumption: Incoherent propagation of neutrinos • Flavor mixing: • Example: For q13 =0, q23=p/4: • NB: No CPV in flavor mixing only!But: In principle, sensitive to Re exp(-i d) ~ cosd (see Pakvasa review, arXiv:0803.1701, and references therein)

  37. Flavor ratios at detector REMINDER • At the detector: define observables which • take into account the unknown flux normalization • take into account the detector properties • Example: Muon tracks to showersDo not need to differentiate between electromagnetic and hadronic showers! • Flavor ratios have recently been discussed for many particle physics applications (for flavor mixing and decay: Beacom et al 2002+2003; Farzan and Smirnov, 2002; Kachelriess, Serpico, 2005; Bhattacharjee, Gupta, 2005; Serpico, 2006; Winter, 2006; Majumar and Ghosal, 2006; Rodejohann, 2006; Xing, 2006; Meloni, Ohlsson, 2006; Blum, Nir, Waxman, 2007; Majumar, 2007; Awasthi, Choubey, 2007; Hwang, Siyeon,2007; Lipari, Lusignoli, Meloni, 2007; Pakvasa, Rodejohann, Weiler, 2007; Quigg, 2008; Maltoni, Winter, 2008; Donini, Yasuda, 2008; Choubey, Niro, Rodejohann, 2008; Xing, Zhou, 2008; Choubey, Rodejohann, 2009; Esmaili, Farzan, 2009; Bustamante, Gago, Pena-Garay, 2010; Mehta, Winter, 2011…)

  38. Parameter uncertainties • Basic dependencerecovered afterflavor mixing • However: mixing parameter knowledge ~ 2015 (Daya Bay, T2K, etc) required Hümmer, Maltoni, Winter, Yaguna, 2010

  39. Glashow resonance? Sensitive to neutrino-antineutrino ratio, since only e- in water/ice!

  40. Glashow resonance… at source • pp: Produce p+ and p- in roughly equal ratio  and in equal ratios • pg: Produce mostly p+  • Glashow resonance (6.3 PeV, electron antineutrinos) as source discriminator? Caveats: • Multi-pion processes produce p- • If some optical thickness, ng “backreactions“ equilibrate p+ and p- • Neutron decays fake p- contribution • Myon decays from pair production of high E photons (from p0)(Razzaque, Meszaros, Waxman, astro-ph/0509186) • May identify “pg optically thin source“ with about 20% contamination from p-, but cannot establish pp source! Glashowres. Sec. 3.3 in Hümmer, Maltoni, Winter, Yaguna, 2010; see also Xing, Zhou, 2011

  41. Glashow resonance… at detector • Additional complications: • Flavor mixing(electron antineutrinos from muon antineutrinos produced in m+ decays) • Have to know flavor composition(e.g. a muon damped pp source can be mixed up with a pion beam pg source) • Have to hit a specific energy (6.3 PeV), which may depend on G of the source Sec. 4.3 in Hümmer, Maltoni, Winter, Yaguna, 2010

  42. Neutrinos and the multi-messenger connectionExample: GRB neutrino fluxes

  43. Example: GRB stacking (Source: IceCube) • Idea: Use multi-messenger approach • Predict neutrino flux fromobserved photon fluxesburst by burst • quasi-diffuse fluxextrapolated (Source: NASA) Coincidence! Neutrino observations(e.g. IceCube, …) GRB gamma-ray observations(e.g. Fermi GBM, Swift, etc) Observed:broken power law(Band function) (Example: IceCube, arXiv:1101.1448)

  44. Gamma-ray burst fireball model:IC-40 data meet generic bounds (arXiv:1101.1448, PRL 106 (2011) 141101) • Generic flux based on the assumption that GRBs are the sources of (highest energetic) cosmic rays (Waxman, Bahcall, 1999; Waxman, 2003; spec. bursts:Guetta et al, 2003) IC-40 stacking limit • Does IceCube really rule out the paradigm that GRBs are the sources of the ultra-high energy cosmic rays?(see also Ahlers, Gonzales-Garcia, Halzen, 2011 for a fit to data)

  45. IceCube method …normalization • Connection g-rays – neutrinos • Optical thickness to pg interactions:[in principle, lpg ~ 1/(ngs); need estimates for ng, which contains the size of the acceleration region] ½ (charged pions) x¼ (energy per lepton) Energy in protons Energy in neutrinos Fraction of p energyconverted into pions fp Energy in electrons/photons (Description in arXiv:0907.2227; see also Guetta et al, astro-ph/0302524; Waxman, Bahcall, astro-ph/9701231)

  46. IceCube method … spectral shape • Example: 3-ag 3-bg 3-ag+2 First break frombreak in photon spectrum(here: E-1 E-2 in photons) Second break frompion cooling (simplified)

  47. Numerical approach • Use spectral shape of observed g-rays (Band fct.) • Calculate bolometric equivalent energy from bolometric fluence (~ observed) [assuming a relativistically expanding fireball] • Calculate energy in protons/photons and magnetic field using energy equipartition fractions • Compute neutrino fluxes with conventional method (Baerwald, Hümmer, Winter, arXiv:1107.5583)

  48. Differences (qualitatively) • Magnetic field and flavor-dependent effects included in numerical approach • Multi-pion production in numerical approach • Different spectral shapes of protons/photons taken into account • Pion production based on whole spectrum, not only on photon break energy • Adiabatic losses of secondaries can be included

  49. Effect of photohadronics • Reproduced original WB flux with similar assumptions • Additional charged pion production channels included, also p-! p decays only ~ factor 6 Baerwald, Hümmer, Winter, Phys. Rev. D83 (2011) 067303

  50. Fluxes before/after flavor mixing BEFORE FLAVOR MIXING AFTER FLAVOR MIXING ne nm Baerwald, Hümmer, Winter, Phys. Rev. D83 (2011) 067303; see also: Murase, Nagataki, 2005; Kashti, Waxman, 2005; Lipari, Lusignoli, Meloni, 2007

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