1. 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: AAAAAAAA

2. Contents Lecture 1 (non-technical) Lecture 2 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 in ratio (ne:nm:nt)=(1:2:0)
Cosmogenic neutrinos
Delta resonance approximation:
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 rate decreases with energy
(might be a function of time)
Photohadronic processes limit maximal energy
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-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

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
Energy dependence
~ const
~ 1/E
~ E, const, …

8. 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 G
Observer

9. Photohadronic interactions, pp interactions

10. 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

11. 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

12. The truth is in between: Exercises!
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 is in 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 b Caveat: ignores more complicated kinematics
Relationship to inelasticity K (fraction of proton energy lost by interaction):

14. Results Production of secondaries: With “response function“:
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
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)

16. 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

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 GeV protons (mostly)

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

22. 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

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)
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) ; 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. Hümmer, Maltoni, Winter, Yaguna, Astropart. Phys. 34 (2010) 205
Model summary
Dashed arrows: include cooling and escape
Dashed arrow: Steady state Balances injection with energy losses and escape Q(E) [GeV-1 cm-3 s-1] per time frame N(E) [GeV-1 cm-3] steady spectrum
Optically thin to neutrons
Injection
Energy losses
Escape
Hümmer, Maltoni, Winter, Yaguna, Astropart. Phys. 34 (2010) 205

28. Hümmer, Maltoni, Winter, Yaguna, 2010
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 few protons?
(Hillas)
UHECR prot.?
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 above a 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 will not affect the flavor composition
Flavor ratios most robust predicition for sources?
The only way to directly measure B?
Cooling: charged m, p, K
Spectral split
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 produce certain 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-dissociation of heavy nuclei)
At the source: Use ratio ne/nm (nus+antinus added)

32. However: flavor composition is energy dependent!
Muon beam  muon damped
Pion beam
Energy window with large flux for classification
Typically n beam for low E (from pg)
Undefined (mixed source)
Pion beam  muon damped
Behavior for small fluxes undefined
(from Hümmer, Maltoni, Winter, Yaguna, 2010; see also: Kashti, Waxman, 2005; Kachelriess, Tomas, 2006, 2007; Lipari et al, 2007)

33. Hümmer, Maltoni, Winter, Yaguna, 2010
Parameter space scan
All relevant regions recovered
GRBs: in our model a=4 to reproduce pion spectra; pion beam  muon damped (confirms Kashti, 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 the data limit best
Auger Earth skimming nt
IC-40 nm
(Winter, arXiv: )

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: )

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: , 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 showers Do 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 ; 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 dependence recovered after flavor mixing
However: mixing parameter knowledge ~ 2015 (Daya Bay, T2K, etc) required
Hümmer, Maltoni, Winter, Yaguna, 2010

39. Sensitive to neutrino-antineutrino ratio, since only e- in water/ice!
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/ )
May identify “pg optically thin source“ with about 20% contamination from p-, but cannot establish pp source!
Glashow res.
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 connection Example: GRB neutrino fluxes

43. Example: GRB stacking Idea: Use multi-messenger approach
Predict neutrino flux from observed photon fluxes burst by burst
quasi-diffuse flux extrapolated
(Source: IceCube)
(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: )

44. Gamma-ray burst fireball model: IC-40 data meet generic bounds
(arXiv: , PRL 106 (2011) )
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/(ng s); need estimates for ng, which contains the size of the acceleration region]
½ (charged pions) x ¼ (energy per lepton)
Energy in protons
Energy in neutrinos
Fraction of p energy converted into pions fp
Energy in electrons/ photons
(Description in arXiv: ; see also Guetta et al, astro-ph/ ; Waxman, Bahcall, astro-ph/ )

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

47. (Baerwald, Hümmer, Winter, arXiv:1107.5583)
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: )

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

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

51. Re-analysis of fireball model
Correction factors from:
Cosmological expansion (z)
Some crude estimates, e.g. for fp (frac. of E going pion production)
Spectral corrections (compared to choosing the break energy)
Neutrinos from pions/muons
Photohadronics and magnetic field effects change spectral shape Baerwald, Hümmer, Winter, PRD83 (2011)
Conclusion (this parameter set): Fireball flux ~ factor of five lower than expected, with different shape
(one example)
Preliminary
(Hümmer, Baerwald, Winter, in prep.)

52. Systematics in aggregated fluxes
IceCube: Signal from 117 bursts “stacked“ (summed) for current limit (arXiv: )
Is that sufficient?
Some results:
z ~ 1 “typical“ redshift of a GRB
Peak contribution in a region of low statistics
Systematical error on quasi-diffuse flux (90% CL)
50% for 100 bursts
35% for 300 bursts
25% for 1000 bursts
Need O(1000) bursts for reliable stacking extrapolations!
Weight function: contr. to total flux
Distribution of GRBs following star form. rate
(strong evolution case)
10000 bursts
(Baerwald, Hümmer, Winter, arXiv: )

53. G-distr. as model discriminator?
Fireball pheno; bursts alike in SRF (Liso‘, B‘, Dd‘, …)
Fireball pheno; bursts alike at detector (Liso, tv, T90, G, …)
Contribution from G~400 dominates
Contribution from G~200 dominates
Spectral features + sharp flavor ratio transition
No spec. features + wide flavor ratio transition
Plausible?
Typical assumption in n literature
(Baerwald, Hümmer, Winter, arXiv: )

54. Why is FB-S interesting?
(arXiv: )
If properties of bursts alike in comoving frame:
Liso ~ G2 and Epeak ~ G generated by different Lorentz boost
Epeak ~ (Liso)0.5 (Yonetoku relationship; Amati rel. by similar arguments)
Neutrinos sensitive to this approach!

55. Summary (lecture 2)
Efficient and accurate parameterization for photohadronic interactions is key issue for many state-of-the-art applications, e.g.,
Parameter space scans
Time-dependent simulations
Peculiarity of neutrinos: magnetic field effects of the secondaries, which affect spectral shape and flavor composition
Do not integrate out secondaries!
May even be used as model discriminators
Flavor ratios, though difficult to measure, are interesting because
they may be the only way to directly measure B (astrophysics)
they are useful for new physics searches (particle physics)
they are relatively robust with respect to the cooling and escape processes of the primaries (e, p, g)

56. BACKUP

57. Revised fireball normalization (compared to IceCube approach)
Normalization corrections:
fCg: Photon energy approximated by break energy (Eq. A13 in Guetta et al, 2004)
fS: Spectral shape of neutrinos directly related to that of photons (not protons) (Eq. A8 in arXiv: )
fs, f≈, fshift: Corrections from approximations of mean free path of protons and some factors approximated in original calcs
Preliminary
(Hümmer, Baerwald, Winter, in prep.)