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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: A A A A A A A A. Contents. Lecture 1 (non-technical) Introduction, motivation
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Photohadronic processes and neutrinosLecture 2 Summer school “High energy astrophysics” August 22-26, 2011 Weesenstein, Germany Walter Winter Universität Würzburg TexPoint fonts used in EMF: AAAAAAAA
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 n fluxes • Glashow resonance? (pp versus pg) • Neutrinos and the multi-messenger connection
Photohadronics (primitive picture) If neutrons can escape:Source of cosmic rays Neutrinos produced inratio (ne:nm:nt)=(1:2:0) Delta resonance approximation: Cosmogenic neutrinos p+/p0 determines ratio between neutrinos and gamma-rays High energetic gamma-rays;might cascade down to lower E Cosmic messengers
Inverse timescale plots • Quantify contribution of different processes as a function of energy. Example: (not typical!) Acceleration ratedecreases with energy (might be a function of time) Photohadronicprocesses limit maximalenergy Inverse timescale/rate Other cooling processes subdominant (from: Murase, Nagataki, 2005)
Treatment of spectral effects • Energy losses in continuous limit:b(E)=-E t-1lossQ(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 Energy losses Escape often: tesc ~ R
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 Energydependence ~ const ~ 1/E ~ E, const, …
G 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 Observer
g q p 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 sectionPhoton energy in nucleon rest frame: CM-energy: er
q p g g q p Threshold issues • In principle, two extreme cases: • Processes start at(heads-on-collision atthreshold)but that happens onlyin rare cases! 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?Mean angle cos q ~ 0 er D-Peak ~ 350 MeV Threshold ~ 150 MeV The truth isin between:Exercises!
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 bCaveat: ignores more complicated kinematics • Relationship to inelasticity K (fraction of proton energy lost by interaction):
Results 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
Different interaction processes Resonances Differentcharacteristics(energy lossof protons;energy dep.cross sec.) Dres. Multi-pionproduction 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 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
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 SOPHIAExample: 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-approx.: 0.5.Difference to SOPHIA:Kinematics ofweak decays D-approximation:Infinity D-approximation:~ red curve 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
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 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) 034018; also: Kamae et al, 2005/2006
A toy model:magnetic field and flavor effects in neutrino fluxes(… to demonstrate the consequences)
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!? ?
Model summary Dashed arrows: include cooling and escape Dashed arrow: Steady stateBalances injection with energy losses and escapeQ(E) [GeV-1 cm-3 s-1] per time frameN(E) [GeV-1 cm-3] steady spectrum Opticallythinto neutrons Injection Energy losses Escape Hümmer, Maltoni, Winter, Yaguna, Astropart. Phys. 34 (2010) 205
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
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 fewprotons? (Hillas) UHECRprot.? Auger Hümmer, Maltoni, Winter, Yaguna, 2010
An example: Secondaries a=2, B=103 G, R=109.6 km • Secondary spectra (m, p, K) become loss-steepend abovea 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 willnot affect the flavor composition • Flavor ratios most robustpredicition for sources? • The only way to directly measure B? Cooling: charged m, p, K Spectralsplit Pile-up effect Flavor ratio! Ec Ec Ec Hümmer et al, Astropart. Phys. 34 (2010) 205
Flavor composition at the source(Idealized – energy independent) REMINDER • Astrophysical neutrino sources producecertain 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-dissociationof heavy nuclei) • At the source: Use ratio ne/nm (nus+antinus added)
However: flavor composition is energy dependent! Pion beam Muon beam muon damped Energywindowwith largeflux for classification Typicallyn beamfor low E(from pg) Pion beam muon damped Undefined(mixed source) Behaviorfor smallfluxes undefined (from Hümmer, Maltoni, Winter, Yaguna, 2010; see also: Kashti, Waxman, 2005; Kachelriess, Tomas, 2006, 2007; Lipari et al, 2007)
Parameter space scan • All relevant regions recovered • GRBs: in our model a=4 to reproduce pion spectra; pion beam muon damped (confirmsKashti, Waxman, 2005) • Some dependence on injection index a=2 Hümmer, Maltoni, Winter, Yaguna, 2010
Individual spectra • Differential limit 2.3 E/(Aeff texp)illustrates what spectra thedata limit best Auger 2004-2008 Earth skimming nt IC-40 nm (Winter, arXiv:1103.4266)
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:1103.4266)
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:0803.1701, and references therein)
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 showersDo 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 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…)
Parameter uncertainties • Basic dependencerecovered afterflavor mixing • However: mixing parameter knowledge ~ 2015 (Daya Bay, T2K, etc) required Hümmer, Maltoni, Winter, Yaguna, 2010
Glashow resonance? Sensitive to neutrino-antineutrino ratio, since only e- in water/ice!
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/0509186) • May identify “pg optically thin source“ with about 20% contamination from p-, but cannot establish pp source! Glashowres. Sec. 3.3 in Hümmer, Maltoni, Winter, Yaguna, 2010; see also Xing, Zhou, 2011
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
Neutrinos and the multi-messenger connectionExample: GRB neutrino fluxes
Example: GRB stacking (Source: IceCube) • Idea: Use multi-messenger approach • Predict neutrino flux fromobserved photon fluxesburst by burst • quasi-diffuse fluxextrapolated (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:1101.1448)
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)
IceCube method …normalization • Connection g-rays – neutrinos • Optical thickness to pg interactions:[in principle, lpg ~ 1/(ngs); need estimates for ng, which contains the size of the acceleration region] ½ (charged pions) x¼ (energy per lepton) Energy in protons Energy in neutrinos Fraction of p energyconverted into pions fp Energy in electrons/photons (Description in arXiv:0907.2227; see also Guetta et al, astro-ph/0302524; Waxman, Bahcall, astro-ph/9701231)
IceCube method … spectral shape • Example: 3-ag 3-bg 3-ag+2 First break frombreak in photon spectrum(here: E-1 E-2 in photons) Second break frompion cooling (simplified)
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:1107.5583)
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
Effect of photohadronics • Reproduced original WB flux with similar assumptions • Additional charged pion production channels included, also p-! p decays only ~ factor 6 Baerwald, Hümmer, Winter, Phys. Rev. D83 (2011) 067303
Fluxes before/after flavor mixing BEFORE FLAVOR MIXING AFTER FLAVOR MIXING ne nm Baerwald, Hümmer, Winter, Phys. Rev. D83 (2011) 067303; see also: Murase, Nagataki, 2005; Kashti, Waxman, 2005; Lipari, Lusignoli, Meloni, 2007