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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: AAAAAAAA

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**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

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**Repetition and some tools**

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**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

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**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)

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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 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

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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. 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, …

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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 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

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**Photohadronic interactions, pp interactions**

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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

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**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

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**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!

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**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):

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**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

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**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)

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**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

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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

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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 GeV protons (mostly)

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

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**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

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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) 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

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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: 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!? ?

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**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

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**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

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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 … Only few protons? (Hillas) UHECR prot.? Auger Hümmer, Maltoni, Winter, Yaguna, 2010

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**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

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**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)

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**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)

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**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

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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: )

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**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: )

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**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)

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**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…)

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**Parameter uncertainties**

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

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**Sensitive to neutrino-antineutrino ratio, since only e- in water/ice!**

Glashow resonance? Sensitive to neutrino-antineutrino ratio, since only e- in water/ice!

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**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

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**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

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**Neutrinos and the multi-messenger connection Example: GRB neutrino fluxes**

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**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: )

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**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)

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**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/ )

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**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)

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**(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: )

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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**

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)

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**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

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**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.)

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**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: )

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**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: )

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**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!

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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, g)

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BACKUP

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**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.)

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