Far-infrared nebular spectral features from growing massive black holes
  Supermassive black holes (BHs) and their host galaxies are interlinked by
virtue of feedbacks and are thought to be co-eval across the Hubble time. This
relation is highlighted by an approximate proportionality between the BH mass
$M_\bullet$ and the mass of a stellar bulge $M_\ast$ of the host galaxy.
However, a large spread of the ratio $M_\bullet/M_\ast$ and a considerable
excess of BH mass at redshifts $z\sim8$, indicate that the coevolution of
central massive BHs and stellar populations in host galaxies may have
experienced variations in its intensity. These issues require a robust
determination of the relevant masses (BH, stars and gas), which is difficult in
the case of distant high-redshift galaxies that are unresolved. In this paper,
we seek to identify spectral diagnostics that may tell us about the relative
masses of the BH, the gas mass and stellar mass. We consider general features
of SEDs of galaxies that harbour growing massive BHs, forming stars and
interstellar/circumgalactic gas. We focus on observational manifestations of
possible predominances or intermittent variations in evolutionary episodes of
growing massive BHs and forming stellar populations. We consider simplified
scenarios for star formation and massive BHs growth, and simple models for
chemical composition of gas, for dust free gas as well as for gas with dust
mass fraction of $1/3$ of the metal content. We argue that wideband
multi-frequency observations (X-ray to submillimeter) of the composite emission
spectra of growing BH, stellar population and nebular emission of interstellar
gas are sufficient to infer their masses.
