Submillimeter signatures from growing supermassive black holes before
  reionization
  The presence of supermassive black holes (SMBHs) with masses up to
$M_\bullet\sim10^9M_\odot$ at redshifts $z\simeq7.5$ suggests that their seeds
may have started to grow long before the reionization in ambient medium with
pristine chemical composition. During their latest 500Myr episode of growing
from $z\geq10$ to $z\sim7$ the black holes shine as luminous as
$10^{11}\hbox{--}10^{12}L_\odot$, with a cumulative spectrum consisting of the
intrinsic continuum from hot accretion disk, nebular hydrogen and helium
spectral lines and free-free continuum from gas of host halos. Here we address
the question of whether such a plain spectrum would allow us to trace evolution
of these growing SMBHs. In our calculations we assume that host galaxies have
stellar populations with masses smaller than the mass of their central black
holes -- the so-called obese black hole galaxies. Within this model we show
that for a sufficiently high mass of gas in a host galaxy -- not smaller than
the mass of a growing black hole, the cumulative spectrum in the far-infrared
reveals a sharp transition from a quasi-blackbody Rayleigh-Jeans spectrum of
the black hole $\propto\lambda^{-2}$ to a flat free-free nebular continuum
$\lambda^{0.118}$ on longer wavelength limit. Once such a transition in the
spectrum is resolved, the black hole mass can be inferred as a combination of
the observed wavelength at the transition $\lambda_k$ and the corresponding
spectral luminosity. Possible observability of this effect in spectra of
growing high-$z$ SMBHs and determination of their mass with the upcoming JWST
and the planned space project Spektr-M is briefly discussed.
