Using the Markov Chain Monte Carlo method to study the physical properties GeV-TeV BL Lac objects

Abstract

We fit the spectral energy distributions (SEDs) of 46 GeV - TeV BL Lac objects in the frame of leptonic one-zone synchrotron self-Compton (SSC) model and investigate the physical properties of these objects. We use the Markov Chain Monte Carlo (MCMC) method to obtain the basic parameters, such as magnetic field (B), the break energy of the relativistic electron distribution ($\gamma'_{\rm{b}}$) and the electron energy spectral index. Based on the modeling results, we support the following scenarios on GeV-TeV BL Lac objects: (1) Some sources have large Doppler factors, implying other radiation mechanism should be considered. (2) Comparing with FSRQs, GeV-TeV BL Lac objects have weaker magnetic field and larger Doppler factor, which cause the ineffective cooling and shift the SEDs to higher bands. Their jet powers are around $4.0\times 10^{45}~\rm{ erg\cdot s}^{-1}$, comparing with radiation power, $5.0\times 10^{42}~\rm{ erg\cdot s}^{-1}$, indicating that only a small fraction of jet power is transformed into the emission power. (3) For some BL Lacs with large Doppler factors, their jet components could have two substructures, e.g., the fast core and the slow sheath. For most GeV-TeV BL Lacs, Kelvin-Helmholtz instabilities are suppressed by their higher magnetic fields, leading few micro-variability or intro-day variability in the optical bands. (4) Combined with a sample of FSRQs, an anti-correlation between the peak luminosity $L_{\rm {pk}}$ and the peak frequency $\nu_{\rm {pk}}$ is obtained, favoring the blazar sequence scenario. In addition, an anti-correlation between the jet power $P_{\rm {jet}}$ and the break Lorentz factor $\gamma_{\rm {b}}$ also supports the blazar sequence.