We present a model-dependent method to estimate the redshifts of three TeV BL Lac objects ( BL Lacs ) through fitting their ( quasi- ) simultaneous multi-waveband spectral energy distributions ( SEDs ) by one-zone leptonic synchrotron self-Compton ( SSC ) model .
Considering the impact of electron energy distributions ( EEDs ) on the results , we use three types of EEDs , such as the power-law EED with exponential cut-off ( PLC ) , the log-parabola ( PLLP ) and the broken power-law ( BPL ) EEDs , to fit the SEDs .
We also use a parameter \alpha to describe the uncertainties of the extragalactic background light ( EBL ) models , as in ( 2 ) .
We then use Markov Chain Monte Carlo ( MCMC ) method to explore multi-dimensional parameter space and obtain the uncertainties of the model parameters based on the observational data .
We apply our method to obtain the redshifts of three TeV BL Lac objects in the marginalized 68 % confidence , and find that the PLC EED does not fit the SEDs .
For 3C66A , the redshift is 0.14 - 0.31 and 0.16 - 0.32 in the BPL and PLLP EEDs ; for PKS1424+240 , the redshift is 0.55 - 0.68 and 0.55 - 0.67 in the BPL and PLLP EEDs ; for PG1553+113 , the redshift is 0.22 - 0.48 and 0.22 - 0.39 in the BPL and PLLP EEDs .
We also estimate the redshift of PKS1424+240 in the high stage to be 0.46 - 0.67 in the PLLP EED , roughly consistent with that in the low stage .