The estimation of γ-ray Doppler factor forFermi/LAT-detected blazars

Abstract

Blazars are a subclass of active galactic nuclei with extreme observation properties, which is caused by the beaming effect, expressed by a Doppler factor ( $\delta$ ), in a relativistic jet. Doppler factor is an important parameter in the blazars paradigm to indicate all of the observation properties, and many methods were proposed to estimate its value. In this paper, we present a method following Mattox et al. to calculate the lower limit on $\gamma$ -ray Doppler factor ( $\delta_{\gamma}$ ) for 809 selected Fermi/LAT-detected $\gamma$ -ray blazars by adopting the available $\gamma$ -ray and X-ray data. Our sample included 342 flat-spectrum radio quasars (FSRQs) and 467 BL Lac objects (BL Lacs), out of which 507 sources are compiled with available radio core-dominance parameter (R) from our previous study. Our calculation shows that the average values of the lower limit on $\delta_{\gamma}$ for FSRQs and BL Lacs are $\left\langle\delta_{\gamma}|_{\textrm{FSRQ}}\right\rangle = 6.87 \pm 4.07$ and $\left\langle\delta_{\gamma}|_{\textrm{BL\ Lac}}\right\rangle=4.31 \pm 2.97$ , respectively. We compare and discuss our results with those from the literature. We found that the derived lower limit on $\delta_{\gamma}$ for some sources is higher than that from the radio estimation, which could be possibly explained by the jet bending within those blazars. Our results also suggest that the $\gamma$ -ray and radio regions perhaps share the same relativistic effects. The $\gamma$ -ray Doppler factor has been found to be correlated with both the $\gamma$ -ray luminosity and core-dominance parameter, implying that the jet is possibly continuous in the $\gamma$ -ray bands, and R is perhaps an indicator for a beaming effect.

A study of Intrinsic $γ$-ray Emission for {\it Fermi}/LAT-detected BL Lacs

“…From Pei et al (2020), we obtained 467 Fermi BL Lacs. Then we checked in the latest Fermi/LAT incremental Data Release (4FGL-DR2, for Data Release 2) for the power law spectrum (Abdollahi et al 2020) Pei et al (2020), Col. 8-13 for the corresponding γ-ray emissions.…”

“…2 classification, LBL for LSP BL Lac, IBL for ISP BL Lac, HBL for HSP BL Lac, Col. 3 redshift, z, Col. 4 photon spectral index, α ph , Col. 5 the integral photon flux (N ) for 1 -100 GeV in units of 10 −10 photons/cm 2 /s, Col. 6 the γ-ray Doppler factor for q = 2 from Pei et al (2020). Col. 7 the γ-ray Doppler factors for q = 3 from Pei et al (2020).…”

“…2 classification, LBL for LSP BL Lac, IBL for ISP BL Lac, HBL for HSP BL Lac, Col. 3 redshift, z, Col. 4 photon spectral index, α ph , Col. 5 the integral photon flux (N ) for 1 -100 GeV in units of 10 −10 photons/cm 2 /s, Col. 6 the γ-ray Doppler factor for q = 2 from Pei et al (2020). Col. 7 the γ-ray Doppler factors for q = 3 from Pei et al (2020). Col. 8 the observed flux density, f ob γ at E = 50 GeV in units of 10 −5 pJy, Col. 9 the intrinsic flux density (f in2 γ ) for q = 2 in units of 10 −5 pJy, Col. 10 the intrinsic flux density (f in3 γ ) for q = 3 in units of 10 −5 pJy, Col. 11 the logarithm of observed luminosity in units of erg s −1 , Col. 12 the logarithm of intrinsic luminosity for q = 2 in units of erg s −1 , Col. 13 logarithm of the intrinsic luminosity for q = 3 in units of erg s −1 .…”

“…The clouds of gas near the SMBH are radiating strong optical and ultraviolent emissions, the so-called broad line region (BLR), while those clouds of gas far away from the SMBH producing narrow lines is called the narrow line region (NLR) (Urry and Padovani 1995). Blazars are a subclass of AGNs with following observational properties, such as rapid variability superimposed on the slow longterm variation, high and variable polarization, apparent superluminal motion, radio core dominance, and strong γ-ray emissions (Sillanpaa et al 1988;Wills et al 1992;Dondi and Ghisellini 1995;Fan et al 1998;Hartman et al 1999;Xiao et al 2019;Abdollahi et al 2020;Otero-Santos et al 2020;Pei et al 2020;Fan et al 2021;Raiteri et al 2021;Yuan and Fan 2021). Based on the feature of emission lines, blazars can be classified as BL Lacs and flat spectrum radio quasars (FSRQs).…”

“…Since it is difficult to obtain the viewing angle and the bulk velocity, one can not obtain the Doppler factor from observations directly. Fortunately, many indirect methods have been proposed to estimate the Doppler factor, such as Doppler factor estimation from radio flux density variation or variability brightness temperature (Lähteenmäki and Valtaoja 1999;Fan et al 2009;Hovatta et al 2009;Liodakis et al 2018), from the combination between X-ray emissions and synchrotron Self-Compton (SSC) modal (Ghisellini et al 1993), from pair-production opacity in the high energy emission (Mattox et al 1993;Fan et al 2013Fan et al , 2014Pei et al 2020), from broadband SED fitting (Chen 2018). Recently, Zhang et al (2020) proposed a new method using both the γ-ray luminosity and BLR luminosity to estimate Doppler factor for a sample of 350 blazars.…”