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Efficient computation of photohadronic interactions

Efficient computation of photohadronic interactions. HAP Theory Code Retreat September 13, 2012 DESY Zeuthen , Germany Walter Winter Universität Würzburg. TexPoint fonts used in EMF: A A A A A A A A. Contents. Introduction Motivation, requirements, applications

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Efficient computation of photohadronic interactions

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  1. Efficient computation of photohadronic interactions HAP Theory Code Retreat September 13, 2012 DESY Zeuthen, Germany Walter Winter Universität Würzburg TexPoint fonts used in EMF: AAAAAAAA

  2. Contents • Introduction • Motivation, requirements, applications • Photohadronic interactions: • Principles • Our method • Comparison with SOPHIA • Summary

  3. Cosmic ray source(illustrative proton-only scenario, pg interactions) If neutrons can escape:Source of cosmic rays Neutrinos produced inratio (ne:nm:nt)=(1:2:0) Delta resonance approximation: High energetic gamma-rays;cascade down to lower E Cosmic messengers

  4. Meson photoproduction • Often used: D(1232)-resonance approximation • Limitations: • No p- production; cannot predict p+/ p- ratio (affects neutrino/antineutrino) • High energy processes affect spectral shape (X-sec. dependence!) • Low energy processes (t-channel) enhance charged pion production • Solutions: • SOPHIA: most accurate description of physicsMücke, Rachen, Engel, Protheroe, Stanev, 2000Limitations: Monte Carlo, somtimes too slow, helicity dep. muon decays! • Parameterizations based on SOPHIA • Kelner, Aharonian, 2008Fast, but no intermediate muons, pions (cooling cannot be included) • Hümmer, Rüger, Spanier, Winter, 2010Fast (~1000 x SOPHIA), including secondaries and accurate p+/ p- ratios; also individual contributions of different processes (allows for comparison with D-resonance!) from:Hümmer, Rüger, Spanier, Winter, ApJ 721 (2010) 630 T=10 eV

  5. Motivation and requirements • Exact method, no Monte Carlo • Accurate enough to predict well enough neutrino spectra including • Multi-pion processes • Helicity dependent muon decays • Neutrino flavor composition and neutrino-antineutrino ratios (need pions, muons, kaons explicitely, compute secondary cooling!) • Fast enough for large parameter space scans, time-dependent codes from: Baerwald, Hümmer, Winter,Astropart. Phys. 35 (2012) 508

  6. Applications: Neutrinos Neutrino flavor compositionon Hillas plot Burst-by-burst flux predictions in large stacking samples (Hümmer, Baerwald, Winter, Phys. Rev. Lett. 108 (2012) 231101) Hümmer, Maltoni, Winter, Yaguna, Astropart. Phys. 34 (2010) 205 Diffuse fluxes from10000 individual GRBs Baerwald, Hümmer, Winter,Astropart. Phys. 35 (2012) 508

  7. NeuCosmANeutrinos from Cosmic Accelerators • Not-yet-public C-code designed specifically for CR source simulation fitting the requirements ofneutrinos • Current features: • Photohadronic processes based onHümmer, Rüger, Spanier, Winter, ApJ 721 (2010) 630  this talk • Weak decays • Kinetic equation solvers for p, n, secondary pions, muons, kaons, etc. • Several boost and normalization functions, source models, etc • In progress: • UHECR proton propagation from source to detector(idea: use same method for photohadronic CIB interactions, cosmogenic neutrino production)  Mauricio‘s talk • New models for CR escape from source  Philipp Baerwald • Potential further directions/collaborations: • Role of different CIB evolution models for cosmogenic neutrinos • Systematics in photohadronic interactions/updates of model • Effects of heavier nuclei • …

  8. “Minimal“ (top down) n model Q(E) [GeV-1 cm-3 s-1] per time frameN(E) [GeV-1 cm-3] steady spectrum Dashed arrows: include cooling and escape Input: B‘ Opticallythinto neutrons from: Baerwald, Hümmer, Winter,Astropart. Phys. 35 (2012) 508

  9. 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

  10. Photohadronic interactions

  11. 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

  12. 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):

  13. Results • 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

  14. 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)

  15. 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

  16. 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

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

  18. 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)

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

  20. 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, …

  21. 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

  22. 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

  23. Limitations, modifications • Limitations: • Some particle species (e.g. e+, e-, K0) not built in yet • Effort for extensions proportional tointeraction types x particle species(need to develop individual kinematics description/interaction type splitting manually) • Significant deviations from SOPHIA for“extreme“ spectra, such as protons withsharp cutoff on 10 eV (105 K) thermal photon spectrum • Advantages: • Separate evaluation of different interaction types • Use systematical errors on cross sections etc. • Adjust cross sections etc. by more recent measurements

  24. Summary • Efficient description of photohadronic processes by single integral evaluation over appropriate number of interaction typesHümmer, Rüger, Spanier, Winter, ApJ 721 (2010) 630 • Perpectives for collaborations: • Role of different CIB evolution models for cosmogenic neutrinos • Systematics in photohadronic interactions/updates of model • Effects of heavier nuclei • … • Method public, C-code not (yet) • Example application: CR propagation  Mauricio

  25. BACKUP

  26. 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

  27. Threshold issues (2) • Better estimate:Use peak at 350 MeV?but: still heads-on-collisions only! • Discrepancies with numerics! • Even better estimate?Use peak of f(y)! er D-Peak ~ 350 MeV Threshold ~ 150 MeV

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