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

Interstellar Scintillation of Extragalactic Radio Sources.An ASTRON / JIVE Workshop.

René Vermeulen2004 April 05 - 07, Dwingeloo, The Netherlands.

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

René VermeulenASTRON, Dwingeloo, NL



The 15 GHz VLBA and MOHAVE SurveysWork with K.I. Kellermann, M.L.Lister, D.C. Homan, M.H. Cohen,

E. Ros, M. Kadler, J.A. Zensus, Y.Y. Kovalev.

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.

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

MOHAVE Survey (Monitoring Of Jets in Active galaxies with VLBA Experiments):Sources from 15 GHz survey with total VLBA (=compact) flux densityS(15GHz) > 1.5 Jy (2 Jy for Southern sources) at any epoch 1995-2003.



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



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




0727-115: z=1.591 app=31.2 0.62223-052: z=1.404 app=32.5 6.0




0727-115: z=1.591 app=31.2 0.62223-052: z=1.404 app=32.5 6.0

(0716+714: if at z=0.3, app=13)




• 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.





• 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.



Brightness Temperature Histograms

VLBA at 15 GHz; N=19 VSOP at 5 GHz; N=59(Hirabayashi et al. 2000)

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





Can then derive Doppler factor struc

if intrinsic temperature is assumed: Tb,struc= struc Tb,int



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= 3var Tb,int



Variability Doppler Factor Histogram

Lähteenmäki & Valtaoja 1999; N=81; assuming Tb,int= 5 x 1010 K

From flux density outburst in a given time derive Tb,var

Can then derive Doppler factor var

if intrinsic temperature is assumed: Tb,var= 3var Tb,int



Brightness Temperatures and Doppler FactorsTb,var = 3

var Tb,int Tb,struc= struc Tb,int

Comparison yields Tb,int ~ 1011 K (e.g. Lähteenmäki et al. 1999)



Brightness Temperatures and Doppler Factors

Now we can use app as a new estimator, involving veloc ,and depending on: Lorentz factor angle to the line-of-sight

Tb,var = 3var Tb,int

Tb,struc= struc Tb,int













and not known in individualcases but for sources with bothapp and var can match statisticaldistribution to Monte Carlo.






Doppler favouritism in simple beaming models combines withsolid 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 envelopesThis is not seen !

Motion Statistics, Upper Envelopes, and Beaming



Instead, the actual distribution could indicate: Broad distribution of jet bulk Lorentz factors in the population Reflected by shape of velocity-apparent luminosity diagram ?

Motion Statistics, Upper Envelopes, and BeamingDoppler favouritism in simple beaming models combines withsolid 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 envelopesThis is not seen !



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.









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





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 !





and not known in individualcases but for sources with bothapp and var can match statisticaldistribution to Monte Carlo.







• 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



Lorentz Factors

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



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.

Documents

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