Cosmological 21cm 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 ~ 7. Such an accretion disk
inevitably emitted high-energy 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 21cm line absorption with the observational
data, we can obtain a cosmological upper bound on the mass-accretion rate as a
function of the seed BH masses. In order to realize $M_{\rm BH} \sim 10^9
M_{\odot}$ at $z \sim 7$ by a continuous mass-accretion on to a seed BH, to be
consistent with the cosmological 21cm line absorption at $z \sim 17$, we
obtained an upper bound on the initial mass of the seed BH to be $M_{\rm BH,
ini} \lesssim 10^2 M_{\odot}$ ($M_{\rm BH, ini} \lesssim 10^6 M_{\odot}$) for a
seed BH with its comoving number density $n_{\rm seed,0} \sim 10^{-3} {\rm
Mpc}^{-3}$ ($n_{\rm seed,0} \sim 10^{-7} {\rm Mpc}^{-3}$).
