Evolution of Shocks in Blazar Jets Geoffrey Bicknell Research - - PDF document

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Evolution of Shocks in Blazar Jets Geoffrey Bicknell Research - - PDF document

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Evolution of Shocks in Blazar Jets Geoffrey Bicknell Research School of Astronomy & Astrophysics Australian National University Stefan Wagner Landessternwarte, Heidelberg 1 Current phenomenology and implied parameters for (TeV) blazars

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SLIDE 1

Evolution of Shocks in Blazar Jets

Geoffrey Bicknell Research School of Astronomy & Astrophysics Australian National University Stefan Wagner Landessternwarte, Heidelberg

2

1 Current phenomenology and implied parameters for (TeV) blazars Spherical homogeneous blob representing region following shock 10 20 –

  • Synchrotron and inverse

Compton radiation R 1016 cmUB 10 4

– ergs cm 3 –

  • p

10 2

–

1 – ( ) dyn cm 2

–

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SLIDE 2

3

Large Doppler factor

  • Synchrotron (and inverse Compton cooling rate) cooling

constraint – Doppler factor compensates for required low mag- netic field

  • Pair opacity
  • seems large in view of lack of superluminal

velocities seen in MKN 501

  • pair

R16

1 –

  • 10
  • 4

–

  • TeV
  • 0.5
  • 20
  • 10
  • (

)

4

Examples of models

1e+03 1e+05 1e+07 1e+09 1e+11 1e+13 1e+00 1e+01 1e+02 1e+03 Energy (eV) Fluence (ev cm -2 s-1) X-Rays TeV

  • rays

X-ray epoch 6 and TeV epoch 6 B = 0.06 G Ke = 4.4 103 cm-3

  • 2 = 3 106

R = 1.4 1016 cm

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SLIDE 3

5

Tev data corrected for absorption by DIRB ( )

  • 10

=

1e+03 1e+05 1e+07 1e+09 1e+11 1e+13 1e+00 1e+01 1e+02 1e+03

  • (eV)
  • 2 dN/(dt d

dA) (eV cm -2 s-1) B=0.1 Gauss Ke = 4.3x10 5 cm -3

  • 2 = 3x10 6

R= 5.3x10 15 cm

6

Constraint from spectral breaks

1e+03 1e+04 1e+05 1e+02 1e+03

  • (eV)
  • 2 N

(eV cm -2 s-1) Epoch 10 of RXTE data on MKN 501

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SLIDE 4

7

If synchrotron cooling dominates: Criterion for spectral break: Travel time across region Cooling time

  • sh

Shock R 5

15

×10 cm

  • sh B

0.1G

  • 3 2

/ –

1 z + ( ) 1 2

/ –

  • 10
  • 1 2

/

  • b

keV

  • 1 2

/ –

8

Constraints from pair opacity

  • pair

2.6 c

  • ( )

T

dL

2

R

  • 2 3

+ ( ) –

F

  • me

2c4

  • Svensson (1987)

Flux density at fiducial energy Energy of -ray

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SLIDE 5

9

For MKN 501, 421 type parameters: R 2

15

×10

  • 10
  • 4.2

–

  • 0F

0 keV

( ) 100 eV cm 2

– s 1 –

  • TeV
  • 0.6

>

10

Constraints from spectral breaks and pair opacity satisfied by

high Doppler factor. Require , . Gauss

  • B

Ke p B2 8 ( ) ⁄ R Rpair Rsynch cm 3

–

dyn cm 2

–

ergs cm 3

–

1015cm 10 0.1 4.3

5

×10 0.59 4

4 –

×10 5.3 8.3 1.5 20 0.2 2.6

6

×10 3.6 2

3 –

×10 0.87 0.46 0.75 R Rpair > R Rsynch

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SLIDE 6

11

2 Production of shocks in jets Shocks resulting from variation in flow velocity Forward shock Reverse shock Contact discontinuity

  • 1
  • 2
  • CD
  • 2 sh

,

  • 1 sh

,

Shocked fast- moving gas Shocked slow- moving gas

12

Frame of contact discontinuity (used for calculating emissivity)

Parameters of shocks depend upon relative velocity

and pressure ratio of two streams . (Ultrarelativistic equation of state.)

Transform back to jet frame

p1 p3 p2

  • 1
  • =
  • 2

CD CD

  • 2 sh

,

  • 1 sh

,

  • 1

2

– ( ) p2 p1 ⁄ ( )

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SLIDE 7

13

Rate of expansion of region of shocked gas

1 2 3 4 5 0.6 0.8 1.0 1.2 1.4 p3/p 1 Shock velocity difference p2/p 1 = 0.5 1.0 2.0 Difference in velocities of forward and reverse shocks in frame of shocked gas

14

Size of region

  • 1

2

– ( )c t

  • 1

2

– ( ) CD

  • c

t = = 2.6

14

×10

  • 1

2

– ( ) 10

  • 1

–

t day

  • cm

=

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SLIDE 8

15

Flare in MKN 501

641 642 643 644 645 646 647 0.00 0.05 0.10 0.15 0.20 JD-2,440,000 Flux 1 2 3 4 5 6 7 8 9 10 RXTE All-Sky Monitor counts

Time of outburst Epoch 6: t 640

  • t

643.7

  • t

3.7 days

  • Size of shocked gas region

at epoch 6 1.9

15

×10

  • 5
  • 1

–

cm

  • 16

3 Solutions with only one shock p1 p1 p2 p3

  • 1
  • 2
  • 1
  • 2

CD Relativistic centred sim- ple wave (Liang 1977) p1 p3 p2 CD p2

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SLIDE 9

17

Condition for single shock solution Relative velocity not high enough to support the high pressure

  • n one side of the shock.

Relative velocity 3 p2 p1 ⁄ 1 – 3p2 p1 ⁄ 1 + ( ) 3 p2 p1 ⁄ + ( )

  • <

18

1 2 3 4 5 2 4 6 8 10 12 p2/p 1 Maximun Lorentz factor 1 = 10 1 = 5 Maximum Lorentz factor for forward and reverse shock

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SLIDE 10

19

4 Indicative parameters for slab geometry For same emitting volume as homogeneous model:

  • 10

=

  • x

1.9

15

×10 cm

  • R

1.0

16

×10 cm

  • 20

Spectral break Break energy: Shock Boundary of shocked gas Spectral break at energy for which

  • tcool

=

  • b

keV

  • 1.1

3 –

×10 B 3

–

  • 2

( ) t day

  • 2

–

=

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SLIDE 11

21

1e+04 1e+05 1e+02

  • (eV)
  • 2 N

(eV cm -2 s-1) Epoch 1 Epoch 2 Epoch 3 Epoch 4 Epoch 5 Epoch 6

22

1e+03 1e+04 1e+05 1e+02

  • (eV)
  • 2 N

(ev cm -2 s-1) Epoch 6 Epoch 7 Epoch 8 Epoch 9 Epoch 10

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SLIDE 12

23

Consider spectral break at epoch 10 Pole on jet :

  • 2

9.1

2

×10 B3 t day

  • 2
  • b

keV

  • 6keV
  • 0.1G
  • 5.7days
  • 2

=

  • 4.5
  • 24

5 Pair opacity Reduction of escape length reduces pair optical depth.

  • x

1.9

15

×10 cm

  • R

1.0

16

×10 cm

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SLIDE 13

25

6 Summary

Both double and single shock structures can be produced in

jets with variable flow velocity

Relative velocities greater than a critical value produce two

shocks

Initial stage of a flare may be the result of the increase in

volume of the emitting region

Estimate of the size of the shocked plasma in MKN 501 con-

sistent with estimates based on the spherical homogeneous model.

26

Constraints on Doppler factor due to cooling and pair opac-

ity relaxed as result of slab geometry

Estimate of spectral break in MKN 501 consistent with

,

  • 5
  • 10