A tight correlation between gamma-ray and radio emission is found for a
sample of BL Lacertae (BL Lac) objects detected by Fermi Gamma-ray Space
Telescope (Fermi) and the Energetic Gamma-Ray Experiment Telescope (EGRET). The
gamma-ray emission of BL Lac objects exhibits strong variability, and the
detection rate of gamma-ray BL Lac objects is low, which may be related to the
gamma-ray duty cycle of BL Lac objects. We estimate the gamma-ray duty cycle ~
0.11, for BL Lac objects detected by EGRET and Fermi. Using the empirical
relation of gamma-ray emission with radio emission and the estimated gamma-ray
duty cycle, we derive the gamma-ray luminosity function (LF) of BL Lac objects
from their radio LF. Our derived gamma-ray LF of BL Lac objects can almost
reproduce that calculated with the recently released Fermi bright active
galactic nuclei (AGN) sample. We find that about 45% of the extragalactic
diffuse gamma-ray background (EGRB) is contributed by BL Lac objects. Combining
the estimate of the quasar contribution to the EGRB in the previous work, we
find that about 77% of the EGRB is contributed by BL Lac objects and radio
quasars.Comment: 12 pages, 4 figures, submitte
