  Numerical general relativistic radiative magnetohydrodynamic simulations of
accretion disks around a stellar mass black hole with a luminosity above 0.5 of
the Eddington value reveal their stratified, elevated vertical structure. We
refer to these thermally stable numerical solutions as puffy disks. Above a
dense and geometrically thin core of dimensionless thickness $h/r \sim 0.1$,
crudely resembling a classic thin accretion disk, a puffed-up, geometrically
thick layer of lower density and $h/r \sim 1.0$ is formed. We discuss the
observational properties of puffy disks, in particular the geometrical
obscuration of the inner disk by the elevated puffy region at higher observing
inclinations, and collimation of the radiation along the accretion disk spin
axis, which may explain the apparent super-Eddington luminosity of some X-ray
objects. We also present synthetic spectra of puffy disks, and show that they
are qualitatively similar to those of a Comptonized thin disk. We demonstrate
that the existing xspec spectral fitting models provide good fits to synthetic
observations of puffy disks, but cannot correctly recover the input black hole
spin. The puffy region remains optically thick to scattering; in its spectral
properties the puffy disk roughly resembles that of a warm corona sandwiching
the disk core. We suggest that puffy disks may correspond to X-ray binary
systems of luminosities above 0.3 of the Eddington luminosity in the
intermediate spectral states.
