Weesenstein Lecture 2 - uni
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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