Pfrommer: Particle Acceleration and Radiation from Galaxy Clusters
Particle Acceleration
8
Particle Acceleration The observation of high-energy -rays from space implies that particles must be accelerated to very high energies (up to ~ 10 20 eV to explain highest-energy cosmic rays). Power-law spectra observed in many objects indicate that acceleration mechanisms produce power-law particle spectra, N() ~ -p Generally, d(mv) = e (E + v x B) No strong, static electric fields (most of the regular matter in the Universe is completely ionized) => Acceleration may be related to induced electric fields (time-varying
description
0. The observation of high-energy g -rays from space implies that particles must be accelerated to very high energies (up to ~ 10 20 eV to explain highest-energy cosmic rays). Particle Acceleration. - PowerPoint PPT Presentation
Transcript of Particle Acceleration
Particle AccelerationThe observation of high-energy -rays from space implies that particles must be accelerated to very high energies (up to ~ 1020 eV to explain highest-energy cosmic rays).
Power-law spectra observed in many objects indicate that acceleration mechanisms produce
power-law particle spectra,
N() ~ -p
Generally,
d(mv) = e (E + v x B)
No strong, static electric fields (most of the regular matter in the Universe is completely ionized)
=> Acceleration may be related to induced electric fields (time-varying or moving magnetic fields)
Particle Acceleration at Strong ShocksGeneral Idea:
Particles bouncing back and forth across shock front:
At each pair of shock crossings, particles gain energy
<E / E> = (4/3) V/c = U/c
p2, 2 p1, 1
U
Stationary frame of ISM
v2 = (1/4) v1 v1 = U
Shock rest frame
v1 1 = v2 2
1 / 2 = 1/4
Rest frame of shocked material
v2 ‘ = (3/4) Uv1‘ = (3/4) U
Write E = E0 = (1 + U/c) E0 ; = 1 + U/c
Particle Acceleration at Strong Shocks (cont.)
Flux of particles crossing the shock front in either direction:
Fcross = ¼ Nc
Downstream, particles are swept away from the front at a rate :
NV = ¼ NU
p2, 2 p1, 1
U
Stationary frame of ISM
v2 = (1/4) v1 v1 = U
Shock rest frame
v1 1 = v2 2
1 / 2 = 1/4
Rest frame of shocked material
v2 ‘ = (3/4) Uv1‘ = (3/4) U
Probability of particle to remain in the acceleration region:
P = 1 - (¼ NU)/(¼ Nc) = 1 – (U/c)
Particle Acceleration at Strong Shocks (cont.)
Energy of a particle after k crossings:
E = k E0
=> ln (N[>E]/N0) / ln (E/E0) = lnP / ln
or N(>E)/N0 = (E/E0)lnP/ln
Number of particles remaining:
N = Pk N0
=> N(E)/N0 = (E/E0)-2
More General CasesWeak nonrelativistic shocks
p > 2
Relativistic parallel shocks:
p = 2.2 – 2.3
Relativistic oblique shocks:
p > 2.3
U
BU
U B U
Effects of Cooling and Escape
= - ( ne) + Qe (,t) - ______ __∂ne (,t)
∂t∂
∂.
Radiative and adiabatic losses
Escape
______ne (,t)tesc,e
Particle injection (acceleration on very
short time scales)
Evolution of particle spectra is governed by the Continuity Equation:
Effects of Cooling and Escape (cont.)
Assume rapid particle acceleration:
Q(, t) = Q0 -q 1 < < 2
Fast Cooling :
tcool << tdyn, tesc for all particles
N(
)
(q+1)
F(
)
q/2
Particle spectrum:Synchrotron or
Compton spectrum:
Effects of Cooling and Escape (cont.)
Assume rapid particle acceleration:
Q(, t) = Q0 -q 1 < < 2
Slow Cooling :
tcool << tdyn, tesc only for particles with > b
N(
)
q
(q+1)
b
F(
)
q
q/2
b
Particle spectrum:Synchrotron or
Compton spectrum:
11
