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

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

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

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 physics Mücke, Rachen, Engel, Protheroe, Stanev, 2000 Limitations: Monte Carlo, somtimes too slow, helicity dep. muon decays! Parameterizations based on SOPHIA Kelner, Aharonian, 2008 Fast, but no intermediate muons, pions (cooling cannot be included) Hümmer, Rüger, Spanier, Winter, 2010 Fast (~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

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

Applications: Neutrinos Neutrino flavor composition on 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 from 10000 individual GRBs Baerwald, Hümmer, Winter, Astropart. Phys. 35 (2012) 508

NeuCosmA Neutrinos from Cosmic Accelerators Not-yet-public C-code designed specifically for CR source simulation fitting the requirements of neutrinos Current features: Photohadronic processes based on Hümmer, 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 …

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

Treatment of spectral effects Energy losses in continuous limit: b(E)=-E t-1loss Q(E,t) [GeV-1 cm-3 s-1] injection per time frame N(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

Photohadronic interactions

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 section Photon energy in nucleon rest frame:  CM-energy: g p q er

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 b Caveat: ignores more complicated kinematics … Relationship to inelasticity K (fraction of proton energy lost by interaction):

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

Different interaction processes Resonances Different characteristics (energy loss of protons; energy dep. cross sec.) D res. Multi-pion production er (Photon energy in nucleon rest frame) Direct (t-channel) production (Mücke, Rachen, Engel, Protheroe, Stanev, 2008; SOPHIA; Ph.D. thesis Rachen)

Factorized response function Assume: can factorize response function in 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

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

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

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)

Comparison with SOPHIA Example: GRB Model Sim-B matches sufficiently well: Hümmer, Rüger, Spanier, Winter, ApJ 721 (2010) 630

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, …

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

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

Limitations, modifications Some particle species (e.g. e+, e-, K0) not built in yet Effort for extensions proportional to interaction types x particle species (need to develop individual kinematics description/interaction type splitting manually) Significant deviations from SOPHIA for “extreme“ spectra, such as protons with sharp 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

Summary Efficient description of photohadronic processes by single integral evaluation over appropriate number of interaction types Hümmer, 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

BACKUP

Threshold issues In principle, two extreme cases: Processes start at (heads-on-collision at threshold) but that happens only in rare cases! g p q g p q er Threshold ~ 150 MeV

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