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Radiation Processes in High Energy Astrophysics
Lecture 3: basic processes and concepts
Felix Aharonian Dublin Institute for Advanced Studies, DublinMax-Planck Institut fuer Kernphysik, Heidelberg
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interactions with matter
E-M:bremsstrahlung: e N(e) => e’ N (e)pair production N(e) => e+e- N (e)e+e- annihilation e+e- => (511 keV line)
Strong: pp () => , K, … , K, => e => also in the low energy region Nuclear: p A => A* => A’ n
n p => D (2.2 MeV line)
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interactions with radiation and B-fields
Radiation fieldE-M processes:inverse Compton: e (B) => e’ pair production (B) => e+e-
S processes: p > , K, … , K, => e =>
’ B-fieldsynchrotron e (p) B =>
pair production B => e+e-
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gamma-rays produced by electrons and protons/nuclei often are (wrongly) called
leptonic and hadronic interactions
but it is more appropriate to call them as E-M (electromagnetic) and S (strong)
examples:
(i) synchrotron radiation of protons - pure electromagnetic process
interaction of hadrons without production of neutrinos
(ii) photon-photon annihilation => +- => neutrinos, antineutrinos
production of neutrinos by photons as parent particles
E-M are calculated with high accuracy and confirmed experimentally
S are well studied experimentally and explained theoretically
leptonic or hadronic?
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calculations of gamma-ray energy spectra and fluxes
one needs two functions:
differential cross-section
energy distribution of parent particles
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Differential cross section:
Integral cross section:
Particle Distribution:
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Cross-sections, mean free paths, cooling times
cross-section <==> probability of interaction (E), (E,E’) [cm2] = d n
f - coefficient of inelasticity: f=(Ei-Ef)/Ei
mean free path: =1/( n) [cm]
cooling time: tcool=1/(f n c) [s]
effective mechanism of production?
When tcool is smaller than (1) the timescales characterizing other radiative and non-radiative (e.g. adiabatic, escape time, etc.) losses, and (2) the intrinsic dynamical timescales characterizing the source (acceleration time, age of the source, etc.)
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distributions of charged parent particles
three different approaches:(i) assume a production mechanism and then adopt a particle (electron or
proton) energy spectrum, dN/dE, to fit the data
should be treated no more than a fit
(ii) assume an injection spectrum of particles, Q(E), calculate the particle spectrum, dN/dE, at given time for given radiative (e.g. synchrotron IC, photomeson, etc.), and non-radiative (e.g. adiabatic, escape) losses, and see weather can you explain the gamma-ray (radio , X-ray) data
works if the particle acceleration and -ray production regions are separated
(iii) assume an acceleration process (e.g. diffusive shock acceleration, turbulent acceleration, etc.), derive and solve the relevant equation(s), obtain the particle spectrum, dN/dE, and see
weather can you explain the gamma-ray (radio, X-ray, …) data
in many cases the only correct approach to follow
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general kinetic equation that describes the evolution of particle distribution
f(E,r,t) including the diffusion, convection, energy losses and the acceleration terms
(e.g. Ginzburg & Sirovatskii 1964),
in many cases the acceleration and radiation production regions are separated, then
where
steady-state solution
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an example: SNR RXJ1713 > 40 TeV gamma-rays and sharper shelltype morphology: acceleration of p or e
in the shell to energies exceeding
100TeV
2003-2005 data
almost constant
photon index !
can be explained by -rays from pp->o ->2
problems with IC because of KN effect
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in the Bohm diffusion regime; losses dominated by synchrotron radiation
E0 almost coincides with the value derived from tacc = t synch
the spectrum of synchrotron radiation at the shock front
Synchrotron cutoff energy approximately 10 times h
(*) it is very different from the the “standard” assumption E exp[-E/E0]
V.Zirakashvili, FA 2007
an example: diffusive shock acceleration of electrons
(*)
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electron energy distributions and and synch. and IC radiation spectra at shock front
-function
al
approx. upstream
electrons
synch. rad.
dow
nstream
upstream
downstrea
m
e
Sy IC on 2.7 MBR
upstream
=4, B1= B2
Thompson!
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perfect fit of the X-ray spectrum of RXJ1713 with just one parameter ; since v=3000 km/s => Bohm diffusion with
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energy distibutions of particles
acceleration (injection) spectrum of particles; generally power-law with
high-energy cutoff determined by the condition
“acceleration rate=energy loss rate” or taa=tcool
later (in the gamma-ray production region) the particle energy psectrum
is changed due to energy losses:
the steady state solutions for power-law injection (e.g. bremsstrahlung, pp, adiabatic) - no spectral change
(e.g. synchrotron, IC (Tompson)) - steeper
(e.g. ionozation) -harder
(e.g. IC Klein-Nishina) - much harder
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this can be done, in many cases with a surprisingly good accuracy,
using cooling times (for energy fluxes)
F = Wp(e)/4d2tcool
and -functional approximation (for energy spectra) using the relation
<E>=f(Ep(e))
but be careful with -functional approximations …
this may lead to wrong results
quick estimates of -ray fluxes and spectra
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bremsstrahlung and pair-production*: total cross-sections
f =1/137 - fine structure constant
re=2.82 10-13 cm - electron classical radius
e e e e
e e e e
* “Bethe-Heitler processes”
at E>> mec2 “e=”
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Pair-production
Bremsstrahlung
Differential cross-sections of B-H processes
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Bethe-Heitler processes
two processes together effectively support E-M cascades in cold matter
while pair-production in matter is not very important in astrophysics,
bremsstrahlung is very important especially at intermediate energies
Differential cross-sections normalized to 4re2
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some basic features of bremsstrahlung
cooling time:
spectrum of -rays from a single electron: 1/E
power-law distribution of electrons:
-ray spectrum: repeats the shape of electrons!
electron injection spectruman example: interstellar medium:
(1) at low energies -1 because losses are dominated by ionization
(2) at intermediate energies because losses are dominated Bremsstrahung
(3) at very high energies +1 because losses are dominated Synch./IC
(4) at very low (keV) energies - only <10-5 (because of ionization losses)
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annihilation of electron-positron pairs
astrophysical significance of this process - formation of mec2=0.511MeV
line gamma-ray emission at annihilation of thermalized positrons
however if positrons are produced with relativistic energies, a significant fraction - 10 to 20 % of positrons annihilate in flight before they cool down to the temperature of the thermal background gas (plasma)
power-law spectrum of positrons E+
total cross-section:
cooling time:
for positrons energies annihilation dominates over bremsstrahlumg
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pp -> 0 -> - a major gamma-ray production mechanism s
relativistic protons and nuclei produce high energy in inelastic collisionswith ambient gas due to the production and decay of secondary particles pions, kaons and hyperons
neutral 0-mesons provide the main channel of gamma-ray production
• production threshold
• the mean lifetime of 0-mesons
• three types of pions are produced with comparable probabilities
• spectral form of pions is generally determined by number o a few (one or two) leading particles (carrying significant fraction of the nucleon energy)
• cooling (radiation) time: tpp = 1015 (n/1cm-3)-1 s
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the 0-deacy bump at mc2/2 = 67.5 MeV (in diff. spectrum)
p=2.5
p=2.7
p=2
in the F presentation (SED) the peak is moved to 1 GeV
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energy spectra of - and mesons at proton-proton interactions
histograms – SIBYLL code, solid lines – analitical parametrization
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energy distributions of stable
decay-producs – , e
decay modes: , +/- e+/- e
lepton/photon ratios for power-law energy distributions of p-mesons
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analytical presentations of energy spectra of , e,
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energy spectra of secondary gamma-rays, electrons and neutrinois
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total inelastic pp cross-section and production rates of and for
power-law spectrum of protons nH wp=1 erg/cm-6
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interactions with photon fields photon-photon pair production and Compton scattering
two processes are tightly coupled - both have large cross-sections and work effectively everywhere in the Universe from compact objects like pulsars, Black Holes and Active Galactic Nuclei to large scale structures as clusters of galaxies
IC - production process - no energy threshold
PP - absorption process: threshold: EE >m2c4(1-cos)-1
in radiation-dominated environments both processes work together supporting the transport of high energy radiation via electromagnetic
Klein-Nishin Cascades
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integral cross-sections
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differential cross-sections
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for electron spectrum
IC -ray spectrum in nonrealistic (Thompson) limit
IC -ray spectrum in realistic (Klein-Nishina) limit
energy loss time:
energy spectra and cooling times
cooling time:
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if IC losses dominate over synchrotron losses K-N effect makes electron spectrum harder ( => -1)
but gamma-ray spectrum steeper (-1+1 -> ) for IC -rays it operates twice in opposite ways => hard -ray
spectrum for Synchrotron it works only once => very hard synchrotron spectrum
if synchrotron losses dominate over IC losses Synch losses make electron spectrum steeper ( => +1)
K-N effect makes gamma-ray spectrum steeper (1+1 -> ) => very steep -ray spectrum: +2
=> standard synchrotron spectrum: /2
some interesting features related to Klein-Nishina effect
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interactions of protons with radiation
photomeson processes: p => N +np Eth=mc2 (1+m/2mp)=145 MeV
pair production: p => e+e-
threshold: 2mec2=1 MeV
plus
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distributions of photons and leptons: E=1020 eV
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distributions of photons and leptons: E=1021eV
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Energy losses of EHE CRs in 2.7 K CMBR due topair production and photomeson processes
1 - pair production, 2 - photomeson
a - interaction rate, b- inelasticitylifetime of protons in IGM
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electrons
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production of electrons in IGM
spectrum of protons: power-law with an exponential cutoff with power-law index a=2 and cutoff Ecut=kE*; E*=3 1020 eV
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gamma-radiation spectra of secondary electrons
E*=3 1020 eV
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many important results of synchrotron theory are obtained within
the framework of classical electrodynamics, i.e.
or
where - critical magnetic field
Classical regime: energy of synch. photons << energy of electrons Quantum regime: energy of synch photon is close to electron energy and gamma-rays start effectively interact with B- field and produce electron-positron pairs
probabilities of both processes depend on a single parameter
two are tightly coupled and lead to effective pair-cascade development
interactions with magnetic field photon-photon pair production and Compton scattering
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synchrotron radiation and pair-production in quantum regime
analog of 0 and s0 parameters for
IC and processes in the photon field
prob. of synch.rad. - constant
prob of B:
prob. of B: maximum
prob. of both:
with synch a factor of 3 higher
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differential spectra of secondary products produced in magnetic field
at curves are shown values of parameter