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In this paper, we study scenarios of the super-Eddington accretion onto blackholes at high redshifts $z > 10$, which are expected to be seeds to evolve tosupermassive black holes until redshift $z \sim 7$. For an initial mass,$M_{\rm BH, ini} \lesssim 2 \times 10^{3} M_{\odot}$ of a seed BH, wedefinitely need the super-Eddington accretion, which can be applicable to bothastrophysical and primordial origins. Such an accretion disk inevitably emittedhigh-energy photons which had heated the cosmological plasma of theinter-galactic medium continuously from high redshifts. In this case, thecosmic history of cosmological gas temperature is modified, by which theabsorption feature of the cosmological 21 cm lines is suppressed. By comparingtheoretical predictions of the 21cm line absorption with the observational dataat $z\sim17$, we obtain a cosmological upper bound on the mass-accretion rateas a function of the seed BH masses. In order to realize $M_{\rm BH} \sim 10^9M_{\odot}$ at $z \sim 7$ by a continuous mass-accretion on to a seed BH, to beconsistent with the cosmological 21cm line absorption at $z \sim 17$, weobtained an severe upper bound on the initial mass of the seed BH to be $M_{\rmBH, ini} \lesssim 10^2 M_{\odot}$ ($M_{\rm BH, ini} \lesssim 10^6 M_{\odot}$)when we assume a seed BH with its comoving number density $n_{\rm seed,0} \sim10^{-3} {\rm Mpc}^{-3}$ ($n_{\rm seed,0} \sim 10^{-7} {\rm Mpc}^{-3}$). We alsodiscuss some implications for application to primordial black holes as the seedblack holes.

physical review. d/physical review. d.

Cosmological 21cm line observations to test scenarios of super-Eddington  accretion on to black holes being seeds of high-redshifted supermassive black  holes