Comptonization in Super-Eddington Accretion Flow and Growth Timescale of Supermassive Black Holes

Super-Eddington accretion onto black holes (BHs) may occur at ultraluminous compact X-ray sources in nearby galaxies, Galactic microquasars and narrow-line Seyfert 1 galaxies (NLS1s). Effects of electron scattering (opacity and Comptonization) and the relativistic correction (gravitational redshift and transverse Doppler effect) on the emergent spectra from super-Eddington accretion flows onto non-rotating BHs are examined for 10^{1.5} and 10^{6.5} M_sun BH masses (M_BH). With mdot [= Mdot / (L_Edd / c^2), where Mdot is the accretion rate] > 100, the spectral hardening factor via electron scattering is \lesssim 2.3 - 6.5. Due to the mdot-sensitive hardening factor, the color temperature of the innermost radiation is not proportional to L^{0.25}, differing from the simplest standard accretion disk. The model is applied to optical--soft X-ray emission from NLS1s. We pick up one NLS1, namely PG 1448+273 with an inferred M_BH of 10^{6.4} M_sun, among the highest mdot candidates. The broadband spectral distribution is successfully reproduced by the model with an extremely high mdot (= 1000) and the viscosity parameter alpha of 0.01. This implies that this object, as well as some other highest mdot systems, is really young: the inferred age, M_BH / Mdot, is about 10^6 years. We also briefly discuss the distribution of mdot for transient and highly variable NLS1s, finding that those are located at 3 \lesssim mdot \lesssim 300. Such a moderately high accretion rate is indicative of thermal instability. Furthermore, mdot for a possible type-2 counterpart of NLS1s, NGC 1068, is found to be similar to mdot for NLS1s.