2003A&A...398..927W

We present a detailed model of an extreme slim disk (ESD) with a hot corona around a massive black hole with dimensionless accretion rate {dot}(m) in the range 2.5≪{dot}(m)≤100. We assume that a fraction f of the gravitational energy is released in the hot corona and the rest is released in the ESD. The energy equation of the ESD is dominated by advection and the spectrum shows a broad ``hump'' caused by saturated Comptonization with monochromatic luminosity given by νL_ν∝ν⁰. This relationship enables us to estimate the black hole mass from the ESD luminosity. The spectrum of the hot corona is sensitive to the parameter f{dot}(M) and the viscosity and shows a Comptonized power-law with a high-energy cutoff. The model is used to explain the spectral properties of narrow line Seyfert 1 galaxies (NLS1s). In particular, it can explain the spectrum of extreme NLS1s like NLS1 RE J1034+396. Our spectral estimate of the black hole mass in this source is in good agreement with the mass obtained by applying the reververation mapping correlation. We also examine the Eddington ratios in a large NLS1 sample and find that most objects show super-Eddington accretion rates. We argue that soft X-ray humps in NLS1s are natural consequences of super-Eddington accretion in such objects.