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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 $\proptoλ^{-2}$ to a flat free-free nebular continuum $λ^{0.118}$ 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 $λ_k$ 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.