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

In this paper we study scenarios of the super-Eddington accretion onto black holes at high redshifts z > 10, which are expected to be seeds to evolve to supermassive black holes until redshift z similar to 7. For a initial mass, MBH,ini less than or similar to 2 x 103 M circle dot of a seed black hole (BH), we definitely need the super-Eddington accretion, which can be applicable to both astrophysical and primordial origins. Such an accretion disk inevitably emitted highenergy photons which had heated the cosmological plasma of the inter-galactic medium continuously from high redshifts. In this case, cosmic history of cosmological gas temperature is modified, by which the absorption feature of the cosmological 21-cm lines are suppressed. By comparing theoretical predictions of the 21-cm line absorption with the observational data at z similar to 17, we obtain a cosmological upper bound on the massaccretion rate as a function of the seed BH masses. In order to realize MBH similar to 109 M circle dot at z similar to 7 by a continuous mass accretion on to a seed BH, to be consistent with the cosmological 21-cm line absorption at z similar to 17, we obtained an severe upper bound on the initial mass of the seed BH to be MBH,ini less than or similar to 102 M circle dot (MBH,ini less than or similar to 106 M circle dot) when we assume a seed BH with its comoving number density nseed,0 similar to 10-3 Mpc-3 (nseed,0 similar to 10-7 Mpc-3). We also discuss some implications for application to primordial black holes as the seed black holes.