Spectral index−mass accretion rate correlation and evaluation of black hole masses in AGNs 3C 454.3 and M 87

Abstract

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 M 87. 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 and normalization of the seed (disk) component which is proportional to a mass accretion rate. We developed an analytical model that shows that the photon index of the BH emergent spectrum undergoes an evolution from lower to higher values depending on disk mass accretion rate. 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 M 87 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−mass accretion rate correlation provides estimates of the BH masses in 3C 454.3 and M 87 to be about 3.4 × 109 and 5.6 × 107 solar masses, respectively. We also compared our scaling BH mass estimates with a recent BH mass estimate of M87 = 6.5 × 109 M⊙ 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 M 87 is at least two orders of magnitude lower than that made by the EHT team.