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

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)

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

Introduction -1.75< a< -1.5

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”

Examples deboosting

Examples

The luminosity and redshift sample (MOJAVE survey 15GHz)

The result of the apparent velocity

The result of the apparent velocity Different parent populations?

The result of the observed luminosity z>0.1

The goodness of fit

The goodness of fit

The goodness of fit

Comparison with previous studies Padovani & Urry (1995) Lister (1997) -1.75< a< -1.5 Simulation results

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

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.