Revealing the structure of the lensed quasar Q 0957+561: III. SMBH mass
  via gravitational redshift
  We intend to use the impact of microlensing on the Fe III emission line blend
along with a measure of its gravitational redshift to estimate the mass of the
quasar's central supermassive black hole (SMBH). We fit the Fe III feature in
multiple spectroscopic observations between 2008 and 2016 of the
gravitationally lensed quasar Q 0957+561 with relatively high signal-to-noise
ratios (at the adequate wavelength). Based on the statistics of microlensing
magnifications, we used a Bayesian method to derive the size of its emitting
region. The Fe III spectral feature appears systematically redshifted in all
epochs of observation by a value of 17 angstroms on average. We find clear
differences in the shape of the Fe III line blend between images A and B.
Measuring the strength of those magnitude differences, we conclude that this
blend may arise from a region of half-light radius of 15 lt-days, which is in
good agreement with the accretion disk dimensions for this system. We obtain a
mass for the central SMBH of (1.5 +/- 0.5) x 10^9 solar masses, consistent
within uncertainties with previous mass estimates based on the virial theorem.
The relatively small uncertainties in the mass determination (< 35%) make this
method a compelling alternative to other existing techniques (e.g., the virial
plus reverberation mapping based size) for measuring black hole masses.
Combining the Fe III redshift-based method with the virial, we estimate a
virial factor in the 1.2 to 1.7 range for this system.
