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Spectral index-mass accretion rate correlation and evaluation of black hole masses in AGNs 3C~454.3 and M87

We present the discovery of correlations between the X-ray spectral (photon) index and mass accretion rate observed in active galactic nuclei (AGNs) 3C~454.3 and M87. We analyzed spectral transition episodes observed in these AGNs using Chandra, Swift, Suzaku, BeppoSAX, ASCA and RXTE data. We applied a scaling technique for a black hole (BH) mass evaluation which uses a correlation between the photon index (Gamma) and normalization of the seed component which is proportional to a disk mass accretion rate Mdot. We developed an analytical model that shows that Gamma of the BH emergent spectrum undergoes an evolution from lower to higher values depending on Mdot. To estimate a BH mass in 3C~454.3 we consider extra-galactic SMBHs NGC~4051 and NGC~7469 as well as Galactic BHs Cygnus X--1 and GRO~J1550--564 as reference sources for which distances, inclination angles are known and the BH masses are already evaluated. For M87 on the other hand, we provide the BH mass scaling using extra-galactic sources (IMBHs: ESO 243-49 HLX 1 and M 101 ULX--1) and Galactic sources (stellar mass BHs: XTE J1550-564, 4U 1630-472, GRS 1915+105 and H 1743-322) as reference sources. Application of the scaling technique for the photon index-Mdot correlation provides estimates of the BH masses in 3C 454.3 and M87 to be about 3.4x10^9 and 5.6 x10^7 solar masses, respectively. We also compared our scaling BH mass estimates with a recent BH mass estimate of M_{87}=6.5x 10^9 M_{\odot} made using the {Event Horizon Telescope} which gives an image at 1.3 mm and is based on the angular size of the `BH event horizon'. Our BH mass estimate in M87 is at least two orders of magnitude lower than that made by the EHT team.