Radiation Processes in
High Energy Astrophysics
Lecture 3: basic processes and concepts
Felix Aharonian
Dublin Institute for Advanced Studies, Dublin
Max-Planck Institut fuer Kernphysik, Heidelberg
interactions with matter
E-M:
bremsstrahlung:
pair production
e+e- annihilation
e N(e) => e’  N (e)
 N(e) => e+e- N (e)
e+e- =>  (511 keV line)
pp () => , K,  …
, K,  =>  e
 => 
also in the low energy region
Nuclear:
p A => A* => A’ n
Strong:
n p => D  (2.2 MeV line)
interactions with radiation and B-fields
Radiation field
E-M processes:
inverse Compton:
 pair production
e  (B) => e’ 
  (B) => e+e-
p > , K,  …
, K,  =>  e
 => 
’ 
B-field
synchrotron
e (p) B => 
S processes:
pair production
 B => e+e-
leptonic or hadronic?
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
S
are calculated with high accuracy and confirmed experimentally
are well studied experimentally and explained theoretically
calculations of gamma-ray energy spectra and fluxes
one needs two functions:
differential cross-section
energy distribution of parent particles
Differential cross section:
Integral cross section:
Particle Distribution:
Cross-sections, mean free paths, cooling times
cross-section
<==> probability of interaction
(E), (E,E’) [cm2]
f - coefficient of inelasticity:
mean free path:
cooling time:
= d n 
f=(Ei-Ef)/Ei
=1/( n)
[cm]
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.)
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
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
an example: SNR RXJ1713
> 40 TeV gamma-rays and sharper shell
type morphology: acceleration of p or e
in the shell to energies exceeding 100TeV
almost constant
photon index !
2003-2005 data
can be explained by -rays from pp->o ->2
problems with IC because of KN effect
an example: diffusive shock acceleration of electrons
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
V.Zirakashvili, FA 2007
(*)
it is very different from the the “standard” assumption E exp[-E/E0]
electron energy distributions and and synch. and IC radiation spectra at shock front
e
synch. rad.
upstream
=4, B1= B2
electrons
IC on 2.7 MBR
Sy
Thompson!
upstream
upstream
perfect fit of the X-ray spectrum of RXJ1713 with just one parameter
; since v=3000 km/s => Bohm diffusion with
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
quick estimates of -ray fluxes and spectra
this can be done, in many cases with a surprisingly good accuracy,
using cooling times (for energy fluxes)
F = Wp(e)/4d2tcool
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
bremsstrahlung and pair-production*: total cross-sections
ee
ee
 e
eee
at E>> mec2 “e=”
f =1/137 - fine structure constant
re=2.82 10-13 cm - electron classical radius
* “Bethe-Heitler processes”
Differential cross-sections of B-H processes
Bremsstrahlung
Pair-production
Bethe-Heitler processes
Differential cross-sections normalized to 4re2
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
some basic features of bremsstrahlung
cooling time:
spectrum of -rays from a single electron: 1/E
power-law distribution of electrons:
-ray spectrum:
an example: interstellar medium:
repeats the shape of electrons!
electron injection spectrum
(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)
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
pp -> 0 ->  - a major gamma-ray
production mechanism s
relativistic protons and nuclei produce high energy in inelastic collisions
with 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
the 0-deacy bump at mc2/2 = 67.5 MeV (in diff. spectrum)
p=2
p=2.5
p=2.7
in the F presentation (SED) the peak is moved to 1 GeV
energy spectra of - and  mesons at proton-proton interactions
histograms – SIBYLL code, solid lines – analitical parametrization
decay modes: o
, +/-
+/ +/
e+/- e 
P
energy distributions of stable
decay-producs –
, e
lepton/photon ratios for power-law
energy distributions of p-mesons
analytical presentations of energy spectra of
, e, 
energy spectra of secondary gamma-rays, electrons and neutrinois
total inelastic pp cross-section
and
production rates of  and  for
power-law spectrum of protons
nH wp=1 erg/cm-6
interactions with photon fields
photon-photon pair production and Compton scattering
two processes are tightly coupled - both have large crosssections 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: EE >m2c4(1-cos)-1
in radiation-dominated environments both processes work together
supporting the transport of high energy radiation via electromagnetic
Klein-Nishin Cascades
integral cross-sections
differential cross-sections
energy spectra and cooling times
for electron spectrum
IC -ray spectrum in nonrealistic (Thompson) limit
IC -ray spectrum in realistic (Klein-Nishina) limit
energy loss time:
cooling time:
some interesting features related to Klein-Nishina effect
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
interactions of protons with radiation
photomeson processes: p => N +np
Eth=mc2 (1+m/2mp)=145 MeV
plus
pair production: p  => e+ethreshold: 2mec2=1 MeV
distributions of photons and leptons: E=1020 eV
distributions of photons and leptons: E=1021eV
Energy losses of EHE CRs in 2.7 K CMBR due to
pair production and photomeson processes
1 - pair production, 2 - photomeson
lifetime of protons in IGM
a - interaction rate, b- inelasticity
electrons
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
gamma-radiation spectra of secondary electrons
E*=3 1020 eV
interactions with magnetic field
photon-photon pair production and Compton scattering
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 Bfield 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
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
differential spectra of secondary products produced in
magnetic field
at curves are shown values of  parameter