1. The Lorentz Factor Distribution and Luminosity Function of Relativistic Jets in AGN
Yuan Liu and Shuang Nan Zhang
Center for Astrophysics Tsinghua University

2. Introduction FR II FSRQ Radio luminosity function of AGN
Doppler beaming effect
FR II (as the intrinsic luminosity function)
beamed luminosity function
FR II
FSRQ
(Urry & Padovani
1991, 1992, 1995)

3. Introduction Luminosity function Flux limit
Lorentz factor distribution
Flux limit
(Lister & Marscher 1997, Simulation results)

4. Introduction
-1.75< a< -1.5

5. For a single power law intrinsic luminosity functon
The inverse problem
The maximum likelihood method
The probability density function of apparent velocity for the given observed luminosity and redshift
The observed luminosity function
For a single power law intrinsic luminosity functon
“3=1+2”

6. Examples
deboosting

7. Examples

8. The luminosity and redshift sample (MOJAVE survey 15GHz)

9. The result of the apparent velocity

10. The result of the apparent velocity
Different parent populations?

11. The result of the observed luminosity
z>0.1

12. The goodness of fit

13. The goodness of fit

14. The goodness of fit

15. Comparison with previous studies
Padovani & Urry (1995)
Lister (1997) < a< Simulation results

16. Application Intrinsic luminosity function
Kinetic luminosity function +Black hole mass density
Jet production efficiency
(Heinz et al. 2007)

17. Summary
We determine simultaneously the intrinsic luminosity function and the Lorentz factor distribution.
The shape of the intrinsic luminosity function is the same with the observed luminosity function of FR II
The low and high redshift groups divided by z = 0.1 are likely to be from different parent populations.