BL Lacertae: X-ray spectral evolution and a black-hole mass estimate

We present an analysis of the spectral properties observed in X-rays from active galactic nucleus BL Lacertae using RXTE, Suzaku, ASCA, BeppoSAX, and Swift observations. The total time covered by these observations is approximately 20 yr. We show strong observational evidence that this source undergoes X-ray spectral transitions from the low hard state (LHS) through the intermediate state (IS) to the high soft state (HSS) during these observations. During the RXTE observations (1997-2001, 180 ks, for a total 145 datasets), the source was approximately similar to 75%, similar to 20% and only similar to 5% of the time in the IS, LHS, and HSS, respectively. We also used Swift observations (470 datasets, for a total 800 ks), which occurred during 12 yr (2005-2016), the broadband (0.3-200 keV) data of BeppoSAX (1997-2000, 160 ks), and the low X-ray energy (0.3-10 keV) data of ASCA (1995-1999, 160 ks). Two observations of Suzaku (2006, 2013; 50 ks) in combinations with long-term RXTE and Swift data-sets fortunately allow us to describe all spectral states of BL Lac. The spectra of BL Lac are well fitted by the so-called bulk motion Comptonization (BMC) model for all spectral states. We have established the photon index saturation level, Gamma(sat) = 2.2 +/- 0.1, in the Gamma versus mass accretion rate ((M) over dot) correlation. This Gamma - (M) over dot correlation allows us to estimate the black-hole (BH) mass in BL Lac to be M-BH similar to 3 x 10(7) M-circle dot for a distance of 300 Mpc. For the BH mass estimate, we use the scaling method taking stellar-mass Galactic BHs 4U 1543-47 and GX 339-4 as reference sources. The Gamma - (M) over dot correlation revealed in BL Lac is similar to those in a number of stellar-mass Galactic BHs and two recently studied intermediate-mass extragalactic BHs. It clearly shows the correlation along with the very extended Gamma saturation at similar to 2.2. This is robust observational evidence for the presence of a BH in BL Lac. We also reveal that the seed (disk) photon temperatures are relatively low, of order of 100 eV, which are consistent with a high BH mass in BL Lac. It is worthwhile to emphasize that we found particular events when X-ray emission anti-correlates with radio emission. This effect indicates that mass accretion rate (and thus X-ray radiation) is higher when the mass outflow is lower.