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Physical limit to variability timescale
1 1 2
The central engine can change its state in a time Rg /c Rg ­ Schwarzschild radius The faster blob catches up with the slower one at the distance Lin Lsh = c 2 2 Lin 1 v2 - v1

L in ~ R g 2 >> 1

L sh

The minimum apparent duration of the light burst (at = 0): Lsh Rg 2 2 c c


Geometrical implications
Instantaneous and synchronous (in the lab frame) release of energy by the sho ck results in a light pulse apparently spread over = Lsh Lsh cos - c c

delay

L

Under nominal assumptions, the observer sees a bright sp ot subtending a small angle 1/

sh

Then, the apparent time spread is Lsh/22c



Relating the sho ck distance to the size of the central engine, we get Rg /c


-!
· -,

Lsh 2
·

wph 1 L 2 4 L2 c sh L 4 (c )26c

L ­ the isotropic luminosity

·


...
(1) = 2 eB mc

(2) B2 wph = 1 8 4 2 9 me c
e2 mc2 2

(3)

B2


­ ­ ­ ­

L wph = 4 (2c )3

- -


... .
Derishev, Ko charovsky, Ko charovsky, A&A 372, 1071 (2001) Begelman, Fabian, Rees, MNRAS Letters 384, L19 (2008)

: B (1) (3) (2) (3) : -
1/16 11/38 e14 2 L3 2 < 34 1 2 2 (mec2)10 c7 2

1 55 3 4 1 2



1/16

6

1/8

3

1/8

L45

3/16








me c2 2 e




( ) Nph() R

1 e Nph() c 2
( > /t)

R 1

ct



(/2) > 2 e ()
Nph () ­







(1) = 4 eB mc

(2) B2 wph = 1 8 4 2 9 me c 4 1/2 2 1 9 me c
e2 mc2 2

(3)

B2



e2 mc2

2

B2


- ( )

36 223/316 e30 2 L7 < 7 8 2 1 2 (mec2)22 c15 6



1

1 21 7 8 1 2 - 1 1400 7 8 1 2
1/36 1/36

12

1/18

3

1/6

L45

7/36

6

1/18

1/6 -3

L51

7/36




( ) 13 2 mec2 5B6 1 3 = Ї sin6 2 15 2 315 me c2 Bcr



< c/R



: R3 B 2 6 35 (5 2) 3 < 4 2
1

W=

3 13

2 3

me c2 R 3 c

8




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