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 in ratio (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 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

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 composition on Hillas plot
Burst-by-burst flux predictions in large stacking samples
(Hümmer, Baerwald, Winter, Phys. Rev. Lett (2012) )
Hümmer, Maltoni, Winter, Yaguna, Astropart. Phys. 34 (2010) 205
Diffuse fluxes from individual GRBs
Baerwald, Hümmer, Winter, Astropart. Phys. 35 (2012) 508

7. 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 …

8. “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

9. 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

10. Photohadronic interactions

11. 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

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 b Caveat: 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
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)

15. 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

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 GeV protons (mostly)

19. Comparison with SOPHIA Example: 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) ; also: Kelner, Aharonian, Bugayov, Phys.Rev. D74 (2006) , …

21. 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

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
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

24. 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

25. BACKUP

26. 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

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