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

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 � � – ergs cm 3 10 16 cm U B 10 4 – R � ( ) dyn cm 2 10 2 – – – 1 p � 10 � Spherical homogeneous blob – 20 representing region following shock Synchrotron and inverse Compton radiation 2

� � � �� � Large Doppler factor �� Synchrotron (and inverse Compton cooling rate) cooling constraint – Doppler factor compensates for required low mag- netic field �� Pair opacity � 0.5 � � � � 4 – � � � � – 1 R 16 - - - - - - - - - - - - - - - - � � � � pair 10 TeV � 20 � ( � ) 10 seems large in view of lack of superluminal velocities seen in MKN 501 3 Examples of models 1e+03 X-ray epoch 6 and TeV epoch 6 X-Rays TeV � - rays Fluence (ev cm -2 s -1 ) B = 0.06 G 1e+02 10 3 cm -3 K e = 4.4 2 = 3 10 6 � R = 1.4 10 16 cm 1e+01 1e+00 1e+03 1e+05 1e+07 1e+09 1e+11 1e+13 Energy (eV) 4

� Tev data corrected for absorption by DIRB ( ) = 10 1e+03 dA) (eV cm -2 s -1 ) 1e+02 2 dN/(dt d � B=0.1 Gauss K e = 4.3x10 5 cm -3 1e+01 2 = 3x10 6 � � R= 5.3x10 15 cm 1e+00 1e+03 1e+05 1e+07 1e+09 1e+11 1e+13 � (eV) 5 Constraint from spectral breaks 1e+03 (eV cm -2 s -1 ) Epoch 10 of RXTE data on MKN 501 2 N � � 1e+02 1e+03 1e+04 1e+05 � (eV) 6

Shock � sh � Criterion for spectral break: � Travel time across region Cooling time If synchrotron cooling dominates: � � 1 2 – / � � 3 2 – / 1 2 / � � � � sh � B 15 b � � × 10 ( ) 1 2 – / - - - - - - - - - - - - - - - - - - - - - - - - - - - - R 5 cm 1 + z � � � � � � 0.1G 10 keV 7 Constraints from pair opacity � Energy of -ray � � 0 � 2 � � d L � 2.6 - � 2 � 3 ( ) � � - �� ( ) � – + � � - - - - - - - - - - - - - - - - - - - - - - - - F � pair T � � c R 2 c 4 m e 0 Svensson (1987) Flux density at fiducial energy � 0 8

For MKN 501, 421 type parameters: � ( ) � � 0 F � 0 keV � � 0.6 � � � 4.2 – � � 15 > × 10 � � - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - R 2 � � � � � – s 1 � 10 100 eV cm 2 – TeV 9 �� Constraints from spectral breaks and pair opacity satisfied by high Doppler factor. ⁄ ( 8 � ) R pair R synch B 2 K e � p R B cm 3 – dyn cm 2 – ergs cm 3 – 10 15 cm Gauss 10 0.1 5 0.59 – 4 5.3 8.3 1.5 × 10 × 10 4.3 4 20 0.2 6 3.6 – 3 0.87 0.46 0.75 × 10 × 10 2.6 2 � > Require R R pair , R R synch . 10

2 Production of shocks in jets Shocks resulting from variation in flow velocity Shocked fast- Shocked slow- moving gas moving gas � � � � � , , 2 sh 1 sh 2 1 CD Reverse shock Forward shock Contact discontinuity 11 Frame of contact discontinuity (used for calculating emissivity) p 3 CD � � � � � 1 � , , 1 sh 2 sh p 1 � 2 � p 2 � � = 0 CD �� Parameters of shocks depend upon relative velocity � 1 � � 2 � ( ) ( ⁄ ) – and pressure ratio of two streams . p 2 p 1 (Ultrarelativistic equation of state.) �� Transform back to jet frame 12

Rate of expansion of region of shocked gas 1.4 Difference in velocities of forward and reverse shocks in frame of shocked gas 1.2 Shock velocity difference 2.0 1.0 1.0 p 2 /p 1 = 0.5 0.8 0.6 1 2 3 4 5 p 3 /p 1 13 � 1 � � 2 � ( ) – ( � 1 � � 2 � ) c � t � - c � - - - - - - - - - - - - - - - - - - - - - - - - - Size of region = – = t � CD ) � � � 1 – � � t 14 × 10 ( � 1 � � 2 � = 2.6 – - - - - - - - - - - - - - - cm � � � � 10 day 14

� Flare in MKN 501 0.20 Time of outburst 9 10 1 2 � 8 t 640 0.15 4 3 5 7 6 Epoch 6: Flux 0.10 � t 643.7 RXTE All-Sky Monitor counts � � 0.05 t 3.7 days 0.00 641 642 643 644 645 646 647 JD-2,440,000 Size of shocked gas region �� 1 – 15 � × 10 1.9 - - - cm �� 5 at epoch 6 15 3 Solutions with only one shock p 3 p 2 p 2 � 1 � � 1 � � 2 � � 2 � p 1 p 1 p 2 CD p 3 Relativistic centred sim- p 1 ple wave (Liang 1977) CD 16

Condition for single shock solution ⁄ p 2 p 1 – 1 < Relative velocity 3 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ( ⁄ ) 3 ( ⁄ ) 3 p 2 p 1 + 1 + p 2 p 1 Relative velocity not high enough to support the high pressure on one side of the shock. 17 12 Maximum Lorentz factor for forward and reverse shock 10 Maximun Lorentz factor � 1 = 10 8 6 � 1 = 5 4 2 0 1 2 3 4 5 p 2 /p 1 18

4 Indicative parameters for slab geometry � For same emitting volume as = 10 homogeneous model: 16 � × 10 1.0 cm R 15 � � × 10 x 1.9 cm 19 Spectral break Spectral break at Boundary of Shock energy for which shocked gas � = t cool Break energy: � � 2 – � – 3 t b � × 10 ( ) B 3 – � 2 - - - - - - - - - - = 1.1 - - - - - - - - � � keV day 20

(eV cm -2 s -1 ) Epoch 1 Epoch 2 2 N � Epoch 3 � Epoch 4 Epoch 5 Epoch 6 1e+02 1e+04 1e+05 � (eV) 21 (ev cm -2 s -1 ) Epoch 6 2 N � Epoch 7 Epoch 8 � Epoch 9 Epoch 10 1e+02 1e+03 1e+04 1e+05 � (eV) 22

� Consider spectral break at epoch 10 � 6keV � 0.1G � 2 � � � � t 2 b � � × 10 B 3 � 2 - - - - - - - - - - - - - - - - - - 9.1 � � � � day keV � 5.7days � Pole on jet = 2 � : � 4.5 23 5 Pair opacity 16 � × 10 R 1.0 cm � 15 � � × 10 x 1.9 cm Reduction of escape length reduces pair optical depth. 24

� 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. 25 �� 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 � � 10 � 5 , 26