  Self-gravitating accretion discs have only been studied in a few nearby
objects using maser spots at the parsec-scale. We find a new spectral window
for observing the self-gravitating accretion disc in super-Eddington accreting
Active Galactic Nuclei (AGNs). This window is determined by calculating the
outermost radius (rsg) of a non self-gravitating disc and the corresponding
emission wavelength (lsg) as a function of various disc parameters. We find
that lsg reaches ~ 4000 AA for alpha=0.1, when Mdot > 70 (M_BH / 10^7 M_Sun)^-1
L_Edd/c^2 (where alpha, Mdot, M_BH and L_Edd are, respectively, the viscosity
parameter, gas accretion rate onto the central black hole (BH), the BH mass and
the Eddington luminosity). Moreover, lsg is as small as 1500 AA for alpha =
0.001, which is the smallest alpha case in this study. Therefore, the window
for observing the self-gravitating part of an AGN accretion disc is from 2
micron to lsg. Incidentally, rsg can be less than the photon trapping radius
for Mdot >~ 10^3.3 L_Edd/c^2. Namely, a self-gravitating, optically-thick,
advection-dominated accretion disc is expected to appear in the extremely high
accretion rate regime.
  Next, we demonstrate that the Mid-Infrared to X-ray spectrum of a bright,
well-studied Narrow-Line Seyfert 1 galaxy, Ton S 180, is indeed well fitted by
the spectrum arising from the following three components: an inner slim disc
(with a corona), an outer, self-gravitating non-Keplerian disc and a dusty
torus. The total mass, BH mass plus the entire disc mass, is found to be about
(1.4 - 8.0) M_BH. If the surface density varies with radius r in proportion to
r^-0.6, the total mass is consistent with the central mass estimated by H_beta
and [O III] widths.
