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O-axis emission from relativistic jets

E. Derishev, Vl. Kocharovsky
Institute of Applied Physics RAS, Russia

F. Aharonian
Max-Planck-Institut fur Kernphysik, Germany


Standard acceleration mechanism

v = c/3

v=c

Downstream rest frame
Lorentz transformation Isotropization Lorentz transformation

Upstream rest frame



+

Bending of trajectories


Converter acceleration mechanism

v = c/3

v=c

Downstream rest frame
Lorentz transformation

Upstream rest frame

Isotropization + conversion Lorentz transformation

+

Conversion and bending
2



Energy gain is g = () /2 Complete isotropization upstream results in 1 hence g 2 in every acceleration cycle. Particle distribution:

dN d

-

with

=1-

ln pcn ln g


Electron-photon conversion



e
+ _

+ _

electron _

e

e

electron/ positron

high-energy photon

e+
positron

-25

cm cross-section, 10 8 6 4 2 0.5 1.0 center-of-momentum energy, MeV (log scale)

2

e


+ _


Proton-neutron conversion

cm cross-section, 10

proton
u
+2/3

2 -28

d

-1/3



6

u

+2/3

4

resonance

_ u d d+1/3 -1/3 d u+2/3
+2/3

-1/3

2 150 340 center-of-momentum energy, MeV

u

+2/3

d

-1/3

d

-1/3

u _+1/3 d

+2/3

neutron



+

pion

Active Galactic Nuclei Luminosity/ Energy release Distance Avrg. photon energy Conversion threshold Optical depth: p L p E or Rc 4 R 2 L 1044 erg/s

Gamma-Ray Bursts E 1052 erg

BLR

Xray

R 3 в 1017 cm 6 eV 1015 eV 0.07


R 3 в 1016 cm 600 keV 1012 eV 2 в 10
-4


Deection in the magnetic eld uniform: turbulent: Catch-up condition shock: shear ow:

= 0 + /rg
2 = 0 + c 2 /rg

(

0

+ )=
0

0

cos 0 +
0

0

cos d

sin 0 =

sin d

· Shock and uniform magnetic eld


( 0)



30 rg 2

1/3

1 = eB R

2 = eB R

· Shock and turbulent magnetic eld


( 0)



2c0 2 rg 2

1/4

1 = 2 = eB R

c

· Shear ow and uniform magnetic eld


( 0)



20 rg

1/2

1 = 2 = eB R

· Shear ow and turbulent magnetic eld


( 0)



3 2 2 rg

1/3 c 0

1 = eB R

c

2 =

3/2

eB R

c


Lorentz transformations

Comoving frame

Observer's frame





v~c
· Angles: · Brightness: · Frequency: cos = - cos ; 1 - cos cos = - cos 1 - cos

L( ) = 3 в L( ) =в
is the Doppler factor.

Here = (1 - cos ) For smal l angles one can use



2 ( ) + 1
2



( )2 + 1 2


Is it always correct that ...
the apparent brightness of an off-axis jet decreases as L ~ ( )
-6

the peak (cut-off) frequency in the spectrum decreases as ( )
-2


Is it always correct that ...
the apparent brightness of an off-axis jet decreases as L ~ ( )
-6

No No

the peak (cut-off) frequency in the spectrum decreases as ( )
-2


Is it always correct that ...
the apparent brightness of an off-axis jet decreases as L ~ ( )
-6

No No

the peak (cut-off) frequency in the spectrum decreases as ( )
-2

Does the apparent brightness decrease with observation angle? - Yes, but maybe much slower than you would expect. Does the peak (cut-off) energy decrease with observation angle? - Not always.


Changes in the emission beam-pattern
Downstream frame Observer's frame

· Low-energy particles,



cr

· Critical-energy particles,





cr

· High-energy particles,





cr

3 mec2 cr = 3/2 1/2 2e B

2

if the synchrotron energy losses dominate




Vjet
log L


angle-averaged brightness

cr



max

log
Given injection, dN /d -s , and cooling time, tc() , nd cooling distribution: dN/d tc-s tc L( ) tc 2


-s+3 2 -s+3 2

<

cr max

cr < <

=

( ) 2 cr cr

,


Dependence of -ray spectrum on observation angle (Unidentied EGRET sources)

lg vFv

lg vFv

lg v
On-axis view

lg v
O-axis view