Transcript Weesenstein Lecture 2 - uni

Photohadronic processes and neutrinos
Lecture 2
Summer school
“High energy astrophysics”
August 22-26, 2011
Weesenstein, Germany
Walter Winter
Universität Würzburg
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
2
Repetition and some tools
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
4
Inverse timescale plots
 Quantify contribution of different processes
as a function of energy. Example: (not typical!)
Inverse timescale/rate
Acceleration
rate
decreases
with energy
(might be a function of time)
Photohadronic
processes
limit maximal
energy
Other cooling
processes
subdominant
(from: Murase,
Nagataki, 2005)
5
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)
Injection
Energy losses
Escape
 Simple case: No energy losses b=0
often: tesc ~ R
6
Energy losses and escape
 Depend on particle species and model
 Typical energy losses (= species unchanged):




Synchrotron cooling ~ E
Photohadronic cooling (e.g. pg  p
Adiabatic cooling ~ const
…
~ E, const, …
 Typical escape processes:




)
Energy
dependence
Leave interaction region ~ const
Decay into different species ~ 1/E
Interaction (e.g. pg  n ~ E, const, … )
…
7
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:
Geff
 Relativistic expansion in all directions:
(“fireball“): typically via calculation of
isotropic luminosity (later)
G
Observer
Observer
 Caveat: Doppler factor more general
8
Photohadronic interactions,
pp interactions
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
g
s: cross section
Photon energy
in nucleon rest frame:
q
p
 CM-energy:
er
10
Threshold issues
 In principle, two extreme cases:
g
q
q
p
p
g
 Processes start at
(heads-on-collision at
threshold)
but that happens only
in rare cases!
er
Threshold ~ 150 MeV
11
Threshold issues (2)
 Better estimate:
Use peak at 350 MeV?
but: still heads-oncollisions 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!
12
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):
13
Results
Details: Exercises
 Production of secondaries:
 With “response function“:
from:
Hümmer, Rüger,
Spanier, Winter,
ApJ 721 (2010) 630
 Allows for computation with arbitrary input spectra! But:
complicated, in general …
14
Different interaction processes
Resonances
Different
characteristics
(energy loss
of protons;
energy dep.
cross sec.)
D
res.
Multi-pion
production
er
Direct
(t-channel)
production
(Photon energy in
nucleon rest frame)
(Mücke, Rachen, Engel, Protheroe,
Stanev, 2008; SOPHIA;
Ph.D. thesis Rachen)
15
Factorized response function
 Assume: can factorize response function
in g(x) * f(y): Hümmer, Rüger, Spanier, Winter, ApJ 721 (2010) 630
 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)16
Examples
 Model Sim-C:
 Seven IT for direct
production
 Two IT for resonances
 Simplified multi-pion
production with c=0.2
 Model Sim-B:
Hümmer, Rüger, Spanier,
Winter, ApJ 721 (2010) 630
As Sim-C, but 13 IT for multi-pion processes
17
Pion production: Sim-B
 Pion production efficiency
 Consequence: Charged to neutral pion ratio
Hümmer, Rüger, Spanier,
Winter, ApJ 721 (2010) 630
18
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)
19
Comparison with SOPHIA
Example: GRB
 Model Sim-B matches sufficiently well:
Hümmer, Rüger, Spanier, Winter, ApJ 721 (2010) 630
20
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, …
21
Where impacts?
Neutrinoantineutrino ratio
D-approximation:
Infinity
Spectral shape
D-approximation:
~ red curve
Hümmer, Rüger, Spanier, Winter,
ApJ 721 (2010) 630
Flavor composition
D-approx.: 0.5.
Difference to
SOPHIA:
Kinematics of
weak decays
22
Cooling, escape, re-injection
 Interaction rate (protons) can be easily
expressed in terms of fIT:
 Cooling and escape of nucleons:
Primary loses energy
Primary changes species
(Mp + Mp‘ = 1)
 Also: Re-injection p  n, and n  p …
23
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
24
A toy model:
magnetic field and flavor effects in neutrino fluxes
(… to demonstrate the consequences)
A self-consistent approach

Target photon field typically:
1) Put in by hand (e.g. obs. spectrum: GRBs)
?
2) Thermal target photon field
3) 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 n!?
26
Model summary
Dashed arrows: include cooling and escape
Dashed arrow: Steady state
Balances injection with energy losses and escape
Optically
thin
Injection
to neutrons
Energy losses
Escape
Q(E) [GeV-1 cm-3 s-1] per time frame
N(E) [GeV-1 cm-3] steady spectrum
Hümmer, Maltoni,
Winter, Yaguna,
Astropart. Phys. 34 (2010) 205
27
An example: Primaries
TP 3: a=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
Hillas cond.
sufficient!
Hümmer, Maltoni, Winter, Yaguna, 2010
28
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)
Only few
protons?
UHECR
prot.?
Auger
Hümmer, Maltoni, Winter, Yaguna, 2010
29
An example: Secondaries
a=2, B=103 G, R=109.6 km
 Secondary spectra (m, p, K)
become loss-steepend above
a critical energy
Cooling: charged m, p, K
Spectral
split
Pile-up effect
 Flavor ratio!
 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?
Ec
Ec
Ec
Hümmer et al,
Astropart. Phys. 34 (2010) 205
30
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)
31
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)
32
Parameter space scan
 All relevant regions
recovered
 GRBs: in our model
a=4 to reproduce
pion spectra; pion
beam  muon
damped
a=2
(confirms Kashti, Waxman,
2005)
 Some dependence
on injection index
Hümmer, Maltoni, Winter, Yaguna, 2010
33
Individual
spectra
 Differential limit 2.3 E/(Aeff texp)
illustrates what spectra the
data limit best
Auger 2004-2008 Earth skimming nt
IC-40 nm
(Winter, arXiv:1103.4266)
34
Which point sources can specific
data constrain best?
Constraints to energy flux density
(Winter, arXiv:1103.4266)
35
REMINDER
Neutrino propagation (vacuum)
 Key assumption: Incoherent propagation of
neutrinos
(see Pakvasa review,
arXiv:0803.1701,
and references therein)
 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
36
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 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…)
37
Parameter uncertainties
 Basic dependence
recovered after
flavor mixing
 However: mixing
parameter knowledge ~
2015 (Daya Bay, T2K,
etc) required
Hümmer, Maltoni, Winter, Yaguna, 2010
38
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)
Glashow
res.
(Razzaque, Meszaros, Waxman, astro-ph/0509186)
 May identify “pg optically thin source“ with
about 20% contamination from p-, but cannot
establish pp source!
Sec. 3.3 in Hümmer, Maltoni, Winter, Yaguna, 2010; see also Xing, Zhou, 2011
40
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
41
Neutrinos and the multimessenger connection
Example: GRB neutrino fluxes
Example: GRB stacking
 Idea: Use multi-messenger approach
(Source: IceCube)
(Source: NASA)
Coincidence!
Neutrino
observations
(e.g. IceCube, …)
GRB gamma-ray observations
(e.g. Fermi GBM, Swift, etc)
 Predict neutrino flux from
observed photon fluxes
burst by burst
 quasi-diffuse flux
extrapolated
Observed:
broken power law
(Band function)
(Example: IceCube, arXiv:1101.1448)
43
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
IC-40
stacking limit
(Waxman, Bahcall, 1999;
Waxman, 2003; spec. bursts:
Guetta et al, 2003)
 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)
44
IceCube method …normalization
 Connection g-rays – neutrinos
½ (charged pions) x
¼ (energy per lepton)
Energy in neutrinos
Energy in protons
Fraction of p energy
converted into pions fp
Energy in electrons/
photons
 Optical thickness to pg interactions:
[in principle, lpg ~ 1/(ng s); need estimates for ng, 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)
45
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)
46
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)
47
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
48
Effect of photohadronics
p decays only
~ factor 6
 Reproduced
original WB flux
with similar
assumptions
 Additional
charged pion
production
channels
included, also p-!
Baerwald, Hümmer, Winter, Phys. Rev. D83 (2011) 067303
49
Fluxes before/after flavor mixing
BEFORE
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
50
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
(one example)
 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.)
51
Systematics in aggregated fluxes
 IceCube: Signal from
117 bursts “stacked“
(summed) for current limit
Weight function:
contr. to total flux
Distribution of GRBs
following star form. rate
(arXiv:1101.1448)
(strong
evolution
case)
 Is that sufficient?
 Some results:
 z ~ 1 “typical“ redshift of
a GRB
 Peak contribution in a region of
low statistics
 Systematical error on quasidiffuse flux (90% CL)
10000 bursts
- 50% for 100 bursts
- 35% for 300 bursts
- 25% for 1000 bursts
 Need O(1000) bursts for
reliable stacking
extrapolations!
(Baerwald, Hümmer, Winter, arXiv:1107.5583)
52
G-distr. as model discriminator?
Fireball pheno;
bursts alike
in SRF
Fireball pheno;
bursts alike
at detector
(Liso‘, B‘, Dd‘, …)
(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:1107.5583)
53
Why is FB-S interesting?
(arXiv:1107.4096)
 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!
54
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)
55
BACKUP
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:0907.2227)
 fs, f≈, fshift:
Corrections from
approximations of
mean free path of
protons and some
factors approximated
in original calcs
(Hümmer, Baerwald, Winter, in prep.)
57