Photohadronic processes and neutrinosLecture 2
Summer school “High energy astrophysics”August 22-26, 2011
Weesenstein, Germany
Walter Winter
Universität Würzburg
2
Contents
Lecture 1 (non-technical)
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 fluxes Glashow resonance? (pp versus p) Neutrinos and the multi-messenger connection
Repetition and some tools
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Photohadronics (primitive picture)
Delta resonance approximation:
+/0 determines ratio between neutrinos and gamma-rays
High energetic gamma-rays;might cascade down to lower E
If neutrons can escape:Source of cosmic rays
Neutrinos produced inratio (e::)=(1:2:0)
Cosmic messengers
Cosmogenic neutrinos
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Inverse timescale plots
Quantify contribution of different processes as a function of energy. Example: (not typical!)
(from: Murase, Nagataki, 2005)
Acceleration rate
decreases with energy
Photohadronicprocesses
limit maximalenergy
Other cooling processes
subdominant
Inve
rse
times
cale
/rat
e
(might be a function of time)
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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
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Energy losses and escape
Depend on particle species and model Typical energy losses (= species unchanged):
Synchrotron cooling Photohadronic cooling (e.g. p p ) Adiabatic cooling …
Typical escape processes: Leave interaction region Decay into different species Interaction (e.g. p n ) …
~ E
~ E, const, …
~ const
~ const
~ 1/E
~ E, const, …
Energydependence
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Relativistic dynamics (simplified picture)
Transformation into observer‘s frame:
Flux [GeV-1 cm-2 s-1 (sr-1)] from neutrino injection Q[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
Observer
Observereff
Photohadronic interactions, pp 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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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?Mean angle cos ~ 0
Threshold ~ 150 MeV
-Peak ~ 350 MeV
r
The truth isin between:Exercises!
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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 …
Details: Exercises
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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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) 034018
Ratio +:-:0 ~ 1:1:1Charged to neutral pion ratio similar to pHowever: + and - produced in equal ratiosGlashow resonance as discriminator? (later)
meson etc. contributions …Kelner, Aharonian, Bugayov, Phys.Rev. D74 (2006) 034018; also: Kamae et al, 2005/2006
A toy model:magnetic field and flavor effects in neutrino fluxes
(… to demonstrate the consequences)
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A self-consistent approach Target photon field typically:
1) Put in by hand (e.g. obs. spectrum: GRBs)2) Thermal target photon field3) From synchrotron radiation of co-accelerated
electrons/positrons (AGN-like)4) 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 !?
?
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Opticallythin
to neutrons
Model summary
Hümmer, Maltoni, Winter, Yaguna,
Astropart. Phys. 34 (2010) 205
Dashed arrow: Steady stateBalances injection with energy losses and escape
Q(E) [GeV-1 cm-3 s-1] per time frameN(E) [GeV-1 cm-3] steady spectrum
Injection Energy losses Escape
Dashed arrows: include cooling and escape
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An example: Primaries
Hümmer, Maltoni, Winter, Yaguna, 2010
TP =2, B=103 G, R=109.6 km
Maximum energy: e, p Maximal energy of primaries (e, p) by balancing energy loss and acceleration rate
Hillas condition often necessary, but not sufficient!
Hillas cond.
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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 …
Hümmer, Maltoni, Winter, Yaguna, 2010
(Hillas) UHECRprot.?
Auger
Only fewprotons?
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An example: Secondaries
Hümmer et al, Astropart. Phys. 34 (2010) 205
=2, B=103 G, R=109.6 km
Cooling: charged , , K Secondary spectra (, , K)
become loss-steepend abovea critical energy
Ec depends on particle physics only (m, 0), and B
Leads to characteristic flavor composition
Any additional cooling processes mainly affecting the primaries willnot affect the flavor composition
Flavor ratios most robustpredicition for sources?
The only way to directly measure B?
Ec
Ec Ec
Pile-up effect Flavor ratio!
Spectralsplit
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Astrophysical neutrino sources producecertain flavor ratios of neutrinos (e::):
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 p (also possible: photo-dissociationof heavy nuclei)
At the source: Use ratio e/ (nus+antinus added)
Flavor composition at the source(Idealized – energy independent) REMINDER
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However: flavor composition is energy dependent!
(from Hümmer, Maltoni, Winter, Yaguna, 2010; see also: Kashti, Waxman, 2005; Kachelriess, Tomas, 2006, 2007; Lipari et al, 2007)
Muon beam muon damped
Undefined(mixed source)
Pion beam
Pion beam muon damped
Behaviorfor small
fluxes undefined
Typicallyn beamfor low E(from p)
Energywindow
with largeflux for
classification
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Parameter space scan
All relevant regions recovered
GRBs: in our model =4 to reproduce pion spectra; pion beam muon damped (confirms Kashti, Waxman, 2005)
Some dependence on injection index
Hümmer, Maltoni, Winter, Yaguna, 2010
=2
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Individual spectra
Differential limit 2.3 E/(Aeff texp)illustrates what spectra thedata limit best
Auger 2004-2008 Earth skimming
(Winter, arXiv:1103.4266)
IC-40
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Constraints to energy flux density
Which point sources can specific data constrain best?
(Winter, arXiv:1103.4266)
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Neutrino propagation (vacuum)
Key assumption: Incoherent propagation of neutrinos
Flavor mixing: Example: For 13 =0, 23=/4:
NB: No CPV in flavor mixing only!But: In principle, sensitive to Re exp(-i ) ~ cos
(see Pakvasa review, arXiv:0803.1701,
and references therein)
REMINDER
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At the detector: define observables which take into account the unknown flux normalization take into account the detector properties
Example: Muon tracks to showersDo not need to differentiate between electromagnetic and hadronic showers!
Flavor ratios have recently been discussed for many particle physics applications
Flavor ratios at detector
(for flavor mixing and decay: Beacom et al 2002+2003; 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…)
REMINDER
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Parameter uncertainties
Basic dependencerecovered afterflavor mixing
Hümmer, Maltoni, Winter, Yaguna, 2010
However: mixing parameter knowledge ~ 2015 (Daya Bay, T2K, etc) required
Glashow resonance?
Sensitive to neutrino-antineutrino ratio, since only e- in water/ice!
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Glashow resonance… at source
pp: Produce + and - in roughly equal ratio and in equal ratios
p: Produce mostly + Glashow resonance (6.3 PeV, electron
antineutrinos) as source discriminator?
Caveats: Multi-pion processes produce -
If some optical thickness, n “backreactions“ equilibrate + and -
Neutron decays fake - contribution Myon decays from pair production of high E
photons (from 0)(Razzaque, Meszaros, Waxman, astro-ph/0509186)
May identify “p optically thin source“ with about 20% contamination from -, but cannot establish pp source!
Sec. 3.3 in Hümmer, Maltoni, Winter, Yaguna, 2010; see also Xing, Zhou, 2011
Glashowres.
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Additional complications: Flavor mixing
(electron antineutrinos from muon antineutrinos produced in + decays)
Have to know flavor composition(e.g. a muon damped pp source can be mixed up with a pion beam p source)
Have to hit a specific energy (6.3 PeV), which may depend on of the source
Glashow resonance… at detector
Sec. 4.3 in Hümmer, Maltoni, Winter, Yaguna, 2010
Neutrinos and the multi-messenger connection
Example: GRB neutrino fluxes
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Idea: Use multi-messenger approach
Predict neutrino flux fromobserved photon fluxesburst by burst
quasi-diffuse flux extrapolated
Example: GRB stacking
(Source: NASA)
GRB gamma-ray observations(e.g. Fermi GBM, Swift, etc)
(Source: IceCube)
Neutrino observations
(e.g. IceCube, …)Coincidence!
(Example: IceCube, arXiv:1101.1448)
Observed:broken power law(Band function)
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Gamma-ray burst fireball model:IC-40 data meet generic bounds
(arXiv:1101.1448, PRL 106 (2011) 141101)
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)
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IceCube method …normalization
Connection -rays – neutrinos
Optical thickness to p interactions:
[in principle, p ~ 1/(n ); need estimates for n, which contains the size of the acceleration region]
(Description in arXiv:0907.2227; see also Guetta et al, astro-ph/0302524; Waxman, Bahcall, astro-ph/9701231)
Energy in electrons/photons
Fraction of p energyconverted into pions f
Energy in neutrinos
Energy in protons½ (charged pions) x
¼ (energy per lepton)
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IceCube method … spectral shape
Example:
First break frombreak in photon spectrum
(here: E-1 E-2 in photons)
Second break frompion cooling (simplified)
3-
3-
3-+2
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Numerical approach Use spectral shape of observed -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:1107.5583)
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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
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Effect of photohadronics
Reproduced original WB flux with similar assumptions
Additional charged pion production channels included, also -!
~ factor 6
Baerwald, Hümmer, Winter, Phys. Rev. D83 (2011) 067303
decays only
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Fluxes before/after flavor mixing
e
Baerwald, Hümmer, Winter, Phys. Rev. D83 (2011) 067303; see also: Murase, Nagataki, 2005; Kashti, Waxman, 2005;
Lipari, Lusignoli, Meloni, 2007
BEFORE FLAVOR MIXINGAFTER FLAVOR MIXING
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Re-analysis of fireball model
Correction factors from: Cosmological expansion (z) Some crude estimates, e.g.
for f(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) 067303
Conclusion (this parameter set): Fireball flux ~ factor of five lower than expected, with different shape (Hümmer, Baerwald, Winter, in prep.)
(one example)
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Systematics in aggregated fluxes
IceCube: Signal from 117 bursts “stacked“ (summed) for current limit (arXiv:1101.1448) Is that sufficient?
Some results: z ~ 1 “typical“ redshift of
a GRB Peak contribution in a region of
low statisticsSystematical 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!
Distribution of GRBsfollowing star form. rate
Weight function:contr. to total flux
10000 bursts
(Baerwald, Hümmer, Winter, arXiv:1107.5583)
(strongevolution
case)
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-distr. as model discriminator?
Fireball pheno;bursts alike
in SRF(Liso‘, B‘, d‘, …)
(Baerwald, Hümmer, Winter, arXiv:1107.5583)
Fireball pheno;bursts alike at detector
(Liso, tv, T90, , …)
Contribution from dominates
Plausible?
Contribution from dominates
Typicalassumption in
literature
Spectral features+ sharp flavorratio transition
No spec. features+ wide flavor
ratio transition
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Why is FB-S interesting?
If properties of bursts alike in comoving frame:
Liso ~ 2 and Epeak ~ generated by different Lorentz boost
Epeak ~ (Liso)0.5 (Yonetoku relationship; Amati rel. by similar arguments)
Neutrinos sensitive to this approach!
(arXiv:1107.4096)
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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, )
BACKUP
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Revised fireball normalization(compared to IceCube approach)
Normalization corrections: fC: 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:0907.2227)
f, f≈, fshift: Corrections from approximations of mean free path of protons and some factors approximated in original calcs
(Hümmer, Baerwald, Winter, in prep.)