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

Submillimeter signatures from growing supermassive black holes before reionization