Photohadronic processes and neutrinos Lecture 2 Summer school High energy astrophysics August 22-26,...

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

4

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

5

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)

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 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

7

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

8

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

11

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

12

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!

13

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

15

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

17

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


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Pion production: Sim-B

Pion production efficiency

Consequence: Charged to neutral pion ratio


19

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:


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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?


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.

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 …


(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

32

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

33

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


=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

37

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

38

Parameter uncertainties

Basic dependencerecovered afterflavor mixing


However: mixing parameter knowledge ~ 2015 (Daya Bay, T2K, etc) required

Glashow resonance?

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

40

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

43

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)

44

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

50

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.)

Photohadronic processes and neutrinos Lecture 2 Summer school High energy astrophysics August 22-26,...

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