Jet formation in BL Lacertae objects with different accretion modes

Abstract

We estimate the masses of massive black holes in BL Lac objects from their host galaxy luminosity. The power of jets and central optical ionizing luminosity for a sample of BL Lac objects are derived from their extended radio emission and the narrow-line emission, respectively. The maximal jet power can be extracted from a standard thin accretion disk/spinning black hole is calculated as a function of dimensionless accretion rate $\dot{m}$ ($\dot{m}=\dot{M}/\dot{M}_{\rm Edd}$). Comparing with the derived jet power, we find that the accretion disks in most BL Lac objects should not be standard accretion disks. For a pure advection dominated accretion flow (ADAF), there is an upper limit on its optical continuum luminosity due to the existence of an upper limit $\dot{m}_{\rm crit}$ on the accretion rate. It is found that a pure ADAF is too faint to produce the optical ionizing luminosity of BL Lac objects derived from their narrow-line luminosity. We propose that an ADAF is present in the inner region of the disk and it becomes a standard thin disk in the outer region in most BL Lac objects, i.e., ADAF+SD(standard disk) scenario. This ADAF+SD scenario can explain both the jet power and optical ionizing continuum emission of these BL Lac objects. The inferred transition radii between the inner ADAF and outer SD are in the range of $40-150 GM_{bh}/c^2$, if the disks are accreting at the rate $\dot{m}=0.01$.