Constraining the redshifts of TeV BL Lac objects

Abstract: We present a model-dependent method to estimate the redshifts of three TeV BL Lac objects (BL Lacs) through fltting 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-ofi (PLC), the log-parabola (PLLP) and the broken power-law (BPL) EEDs, to flt the SEDs. We also use a parameter fi to describe the uncertainties of the extragalactic background light (EBL) models, as in (Abdo et al. 2010b). 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% confldence, and flnd that the PLC EED does not flt 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.