Efficient computation of photohadronic interactions

HAP Theory Code RetreatSeptember 13, 2012

DESY Zeuthen, Germany

Walter Winter

Universität Würzburg

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Contents

Introduction Motivation, requirements, applications Photohadronic interactions:

Principles Our method Comparison with SOPHIA

Summary

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Cosmic ray source(illustrative proton-only scenario, p interactions)

Delta resonance approximation:

High energetic gamma-rays;cascade down to lower E

If neutrons can escape:Source of cosmic rays

Neutrinos produced inratio (e::)=(1:2:0)

Cosmic messengers

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Often used: (1232)-resonance approximation

Limitations:- No - production; cannot predict / - 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, 2000Limitations: 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 / - ratios; also individual contributions of different processes (allows for comparison with -resonance!)

Meson photoproduction

T=10 eV

from:Hümmer, Rüger, Spanier, Winter,

ApJ 721 (2010) 630

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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

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Applications: Neutrinos

Baerwald, Hümmer, Winter, Astropart. Phys. 35 (2012) 508

Hümmer, Maltoni, Winter, Yaguna, Astropart. Phys. 34 (2010) 205

(Hümmer, Baerwald, Winter,

Phys. Rev. Lett. 108 (2012) 231101)

Neutrino flavor compositionon Hillas plot

Burst-by-burst flux predictions in large stacking samples

Diffuse fluxes from10000 individual GRBs

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NeuCosmANeutrinos from Cosmic Accelerators

Not-yet-public C-code designed specifically for CR source simulation fitting the requirements ofneutrinos

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 …

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Opticallythin

to neutrons

“Minimal“ (top down) model

from:

Baerwald, Hümmer, Winter, Astropart. Phys. 35 (2012) 508

Dashed arrows: include cooling and escape Q(E) [GeV-1 cm-3 s-1] per time frame

N(E) [GeV-1 cm-3] steady spectrum

Input: B‘

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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 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 EscapeEnergy losses

often: tesc ~ R

Photohadronic interactions

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: cross sectionPhoton energy

in nucleon rest frame:

CM-energy:

Principles

Production rate of a species b:

(: Interaction rate for a b as a fct. of E; IT: interact. type)

Interaction rate of nucleons (p = nucleon)

p

n: Photon density as a function of energy (SRF), angle

r

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Typical simplifications

The angle is distributed isotropically Distribution of secondaries (Ep >> ):

Secondaries obtain a fraction of primary energy. Mb: multiplicity of secondary species bCaveat: ignores more complicated kinematics …

Relationship to inelasticity K (fraction of proton energy lost by interaction):

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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

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Different interaction processes

(Photon energy in nucleon rest frame)

(Mücke, Rachen, Engel, Protheroe, Stanev, 2008; SOPHIA;

Ph.D. thesis Rachen)

Multi-pionproduction

Differentcharacteristics(energy lossof protons;

energy dep.cross sec.)

res.

r

Direct(t-channel)production

Resonances

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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

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Examples

Model Sim-C: Seven IT for direct

production Two IT for resonances Simplified multi-pion

production with =0.2

Model Sim-B:As Sim-C, but 13 IT for multi-pion processes

Hümmer, Rüger, Spanier, Winter, ApJ 721 (2010) 630

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Pion production: Sim-B

Pion production efficiency

Consequence: Charged to neutral pion ratio

Hümmer, Rüger, Spanier, Winter, ApJ 721 (2010) 630

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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)

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Comparison with SOPHIAExample: GRB

Model Sim-B matches sufficiently well:

Hümmer, Rüger, Spanier, Winter, ApJ 721 (2010) 630

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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, …

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Where impacts?

Hümmer, Rüger, Spanier, Winter, ApJ 721 (2010) 630

Spectral shapeNeutrino-

antineutrino ratioFlavor composition

-approximation:Infinity

-approximation:~ red curve

-approx.: 0.5.Difference to

SOPHIA:Kinematics ofweak decays

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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

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Limitations, modifications Limitations:

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 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

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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

BACKUP

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Threshold issues In principle, two extreme cases:

Processes start at

(heads-on-collision atthreshold)but that happens onlyin rare cases!

p

p

r

Threshold ~ 150 MeV

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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)!

Threshold ~ 150 MeV

-Peak ~ 350 MeV

r