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Superluminal Velocity Surveys, Lorentz Factors, Doppler Factors, and Brightness Temperatures.

Superluminal Velocity Surveys, Lorentz Factors, Doppler Factors, and Brightness Temperatures. René Vermeulen ASTRON, Dwingeloo, NL. The 15 GHz VLBA and MOHAVE Surveys. Work with K.I. Kellermann, M.L.Lister, D.C. Homan, M.H. Cohen, E. Ros, M. Kadler, J.A. Zensus, Y.Y. Kovalev.

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Superluminal Velocity Surveys, Lorentz Factors, Doppler Factors, and Brightness Temperatures.

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  1. Superluminal Velocity Surveys, Lorentz Factors, Doppler Factors, and Brightness Temperatures. René Vermeulen ASTRON, Dwingeloo, NL

  2. The 15 GHz VLBA and MOHAVE Surveys Work with K.I. Kellermann, M.L.Lister, D.C. Homan, M.H. Cohen, E. Ros, M. Kadler, J.A. Zensus, Y.Y. Kovalev. Kellermann et al., 2004, ApJ, in press for July 10 Cohen et al., 2004, Proc. 2003 JENAM, in press Cohen et al., 2003, ASP Conf. Ser. 300, 27 Zensus et al., 2003, AJ, 124, 662 Kellermann et al., 1998, AJ, 115, 1295 15 GHz VLBA Survey: From complete 5 GHz survey (Kühr et al., Stickel et al.), plus additions. Total flux density S(15GHz) > 1.5 Jy (2 Jy for Southern sources). Flat spectrum ( > 0.5) anywhere above 500 MHz. MOHAVE Survey (Monitoring Of Jets in Active galaxies with VLBAExperiments): Sources from 15 GHz survey with total VLBA (=compact) flux density S(15GHz) > 1.5 Jy (2 Jy for Southern sources) at any epoch 1995-2003.

  3. The 15 GHz VLBA Proper Motion Survey • 29 observing sesions 1994 – 2001 • 208 components in 110 sources • 79 Q, 18 BL, 13 G • Typically 3 – 7 sessions per source

  4. Velocity Histograms • Mostly 0 < app < 15, tail to app ~ 34.

  5. Velocity Histograms • Mostly 0 < app < 15, tail to app ~ 34. 0727-115: z=1.591 app=31.2  0.6 2223-052: z=1.404 app=32.5  6.0

  6. Velocity Histograms • Mostly 0 < app < 15, tail to app ~ 34. (0716+714: if at z=0.3, app=13) 0727-115: z=1.591 app=31.2  0.6 2223-052: z=1.404 app=32.5  6.0

  7. Velocity Histograms • Mostly 0 < app < 15, tail to app ~ 34. • BL-Lacs and Galaxies: app < 6 many are not superluminal; differ from Q at 98% confidence.

  8. Velocity Histograms • Mostly 0 < app < 15, tail to app ~ 34. • BL-Lacs and Galaxies: app < 6 many are not superluminal; differ from Q at 98% confidence. • EGRET sources: faster than non-EGRET at 90% confidence.

  9. Velocity Histograms • Mostly 0 < app < 15, tail to app ~ 34. • BL-Lacs and Galaxies: app < 6 many are not superluminal; differ from Q at 98% confidence. • EGRET sources: faster than non-EGRET at 90% confidence. • In 5 GHz CJ-Survey: velocity distributions similar in shape, but roughly a factor 2 slower.

  10. Brightness Temperature Histograms From flux density originating in a given area derive Tb,struc. VLBA at 15 GHz; N=19 VSOP at 5 GHz; N=59 (Hirabayashi et al. 2000)

  11. Brightness Temperature Histograms From flux density originating in a given area derive Tb,struc. VLBA at 15 GHz; N=19 VSOP at 5 GHz; N=59 (Hirabayashi et al. 2000) Can then derive Doppler factor struc if intrinsic temperature is assumed: Tb,struc= struc Tb,int

  12. Brightness Temperature Histograms From flux density originating in a given area derive Tb,struc. Can then derive Doppler factor struc if intrinsic temperature is assumed: Tb,struc= struc Tb,int

  13. Variability Doppler Factor Histogram From flux density outburst in a given time derive Tb,var Can then derive Doppler factor var if intrinsic temperature is assumed: Tb,var= 3varTb,int

  14. Variability Doppler Factor Histogram From flux density outburst in a given time derive Tb,var Lähteenmäki & Valtaoja 1999; N=81; assuming Tb,int= 5 x 1010 K Can then derive Doppler factor var if intrinsic temperature is assumed: Tb,var= 3varTb,int

  15. Brightness Temperatures and Doppler Factors Tb,var = 3varTb,int Tb,struc= struc Tb,int Comparison yields Tb,int ~ 1011 K (e.g. Lähteenmäki et al. 1999)

  16. Brightness Temperatures and Doppler Factors Tb,var = 3varTb,int Tb,struc= struc Tb,int Comparison yields Tb,int ~ 1011 K (e.g. Lähteenmäki et al. 1999) Now we can use app as a new estimator, involving veloc , and depending on: Lorentz factor  angle to the line-of-sight 

  17. Brightness Temperatures and Doppler Factors Tb,var = 3varTb,int Tb,struc= struc Tb,int Comparison yields Tb,int ~ 1011 K (e.g. Lähteenmäki et al. 1999) Now we can use app as a new estimator, involving veloc , and depending on: Lorentz factor  angle to the line-of-sight 

  18. Brightness Temperatures and Doppler Factors Tb,var = 3varTb,int Tb,struc= struc Tb,int Comparison yields Tb,int ~ 1011 K (e.g. Lähteenmäki et al. 1999) Now we can use app as a new estimator, involving veloc , and depending on: Lorentz factor  angle to the line-of-sight   and  not known in individual cases but for sources with both app and var can match statistical distribution to Monte Carlo.

  19. Motion Statistics, Upper Envelopes, and Beaming Doppler favouritism in simple beaming models combines with solid angle available to predict many sources oriented at  ~ 1/  , corresponding to maximal velocities: Velocity distributions sharply peaked at the high end Crowding towards well-defined upper envelopes This is not seen !

  20. Motion Statistics, Upper Envelopes, and Beaming Doppler favouritism in simple beaming models combines with solid angle available to predict many sources oriented at  ~ 1/  , corresponding to maximal velocities: Velocity distributions sharply peaked at the high end Crowding towards well-defined upper envelopes This is not seen ! Instead, the actual distribution could indicate: Broad distribution of jet bulk Lorentz factors in the population Reflected by shape of velocity-apparent luminosity diagram ?

  21. Velocity is Correlated with Apparent Luminosity • Upper envelope of app distribution rises with Lobs(15GHz). • app and Lobs could really be correlated: pattern and bulk motion in the same jet flow, with similar Lorentz factor . • Or it could be the result of Malmquist bias: if high  jets are fairly rare, e.g. N()  -1.5 , none may be seen at low L = low z, where there is not much volume.

  22. Motion Statistics, Upper Envelopes, and Beaming Doppler favouritism in simple beaming models combines with solid angle available to predict many sources oriented at  ~ 1/  , corresponding to maximal velocities: Velocity distributions sharply peaked at the high end Crowding towards well-defined upper envelopes This is not seen ! Instead, the actual distribution could indicate: Broad distribution of jet bulk Lorentz factors in the population Reflected by shape of velocity-apparent luminosity diagram ?

  23. Motion Statistics, Upper Envelopes, and Beaming Doppler favouritism in simple beaming models combines with solid angle available to predict many sources oriented at  ~ 1/  , corresponding to maximal velocities: Velocity distributions sharply peaked at the high end Crowding towards well-defined upper envelopes This is not seen ! Instead, the actual distribution could indicate: Broad distribution of jet bulk Lorentz factors in the population Reflected by shape of velocity-apparent luminosity diagram ? Decoupling between source selection and component motions Pattern motions (shocks moving in fluid) Jet curvature (between core and moving knot) Different beaming cones between core and jet components

  24. Motion Statistics, Upper Envelopes, and Beaming Doppler favouritism in simple beaming models combines with solid angle available to predict many sources oriented at  ~ 1/  , corresponding to maximal velocities: Velocity distributions sharply peaked at the high end Crowding towards well-defined upper envelopes This is not seen ! Instead, the actual distribution could indicate: Broad distribution of jet bulk Lorentz factors in the population Reflected by shape of velocity-apparent luminosity diagram ? Decoupling between source selection and component motions Pattern motions (shocks moving in fluid) Jet curvature (between core and moving knot) Different beaming cones between core and jet components 6cm velocities statistically 2x slower than 2cm !

  25. Brightness Temperatures and Doppler Factors Tb,var = 3varTb,int Tb,struc= struc Tb,int Comparison yields Tb,int ~ 1011 K (e.g. Lähteenmäki et al. 1999) Now we can use app as a new estimator, involving veloc , and depending on: Lorentz factor  angle to the line-of-sight   and  not known in individual cases but for sources with both app and var can match statistical distribution to Monte Carlo.

  26. Brightness Temperatures and Doppler Factors • Top-left panels: Monte-Carlo simulation using N() ~ -1.5 , max=30 (N=100) • Other panels: Measured app (N=30) against var , assuming Tb,int = 4x109 K, 2x1010 K, 1011 K

  27. Lorentz Factors Using Tb,int = 2x1010 K, can then derive Lorentz factor distribution:

  28. Summary • At 15 GHz, mostly 0 < app < 15, tail to app ~ 34. • Motions are statistically slower at 5 GHz, possibly faster at higher frequencies: deceleration, decollimation, bending, “banana-trunk” jets, ... • Motion distributions, correlations with luminosity may show a steep intrinsic Lorentz factor distribution, N() ~ -1.5 , max=30. • If variability and 15 GHz superluminal motions are closely linked, then perhaps typically Tb,int ~ 2x1010 K.

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