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We have performed a general relativistic radiative magnetohydrodynamics (GRRMHD) simulations of a stable accretion disc around a stellar-mass black hole (BH) with sub-Eddington mass accretion rates. The numerical solutions revealed an elevated vertical structure - above a dense geometrically thin core of dimensionless thickness hρ/r ∼ 0.1, resembling a classic thin accretion disc, a puffed-up, optically and geometrically thick layer of lower density and hτ/r ∼ 1.0 is formed. We refer to this solution as the Puffy disc. We discuss the observational properties of a puffy discs, in particular the geometrical obscuration at higher observing inclinations of the inner area by the puffed-up region, and collimation of radiation along the accretion disc spin axis. These effects may explain the apparent super-Eddington luminosity of some ultraluminous X-ray binaries. We also present synthetic spectra of puffy discs, and show that they are qualitatively similar to Comptonized thin disc spectra. We demonstrate that the existing XSPEC spectral models provide good fits to synthetic spectra of puffy discs but cannot correctly recover the input luminosity, nor the black hole spin. We suggest that puffy discs may correspond to X-ray binary systems in the intermediate spectral state with luminosities above 0.3 of the Eddington luminosity., {"references":["M. Wielgus, D. Lančová, O. Straub, W. Kluźniak, R. Narayan, D. Abarca, F. H. Vincent, A. Różańska, and M. Abramowicz , 2022, MNRAS","D. Lančová, D. Abarca, W. Klużniak, M. Wielgus, A. Sądowski, R. Narayan, J. Schee, G. Török & M. Abramowicz, 2019, ApJ, 884, L37","A. Sądowski, Narayan, R., Tchekhovskoy, A., & Zhu, Y., 2013a MNRAS, 429, 3533","A. Sądowski, 2016, MNRAS, 459, 4367"]}

Puffy accretion disk is model of a stable accretion disk obtained purely via a general relativistic radiative magnetohydrodynamical simulation. It combines features of the thin, slim, and thick disk models but differs in crucial respects from each of them. We expect the new solution to provide a more realistic description of black hole disks than the slim disk model. We are presenting a disk solution for a nonspinning black hole at a sub-Eddington mass accretion rate. Although the density scale-height of the disk appears to be thin with a high density core near the equatorial plane, most of the inflow occurs through a highly advective, turbulent, optically thick, Keplerian region surrounding the core. Stability of the solution is supported in large part by the magnetic field, even though the radiation pressure strongly dominates over gas pressure., This work was supported by the Student Grant Foundation of the Silesian University in Opava, Grant No. SGF/1/2020, which has been carried out within the EU OPSRE project entitled "Improving the quality of the internal grant scheme of the Silesian University in Opava", reg. number: CZ.02.2.69/0.0/0.0/19 073/0016951, the internal grant of the SU SGS/13/2019 and the Czech Science Foundation grant EXPRO 21-06825X., {"references":["D. Lančová, D. Abarca, W. Klużniak, M. Wielgus, A. Sądowski, R. Narayan, J. Schee, G. Török & M. Abramowicz, 2019, ApJ, 884, L37","A. Sądowski, Narayan, R., Tchekhovskoy, A., & Zhu, Y., 2013a MNRAS, 429, 3533","Penna R. F., Sądowski A., Kulkarni A. K., Narayan R., 2013, MNRAS, 428, 2255","A. Sądowski, Narayan, R., McKinney, J. C., & Tchekhovskoy, A., 2014b, MNRAS, 439, 503","A. Sądowski, 2016, MNRAS, 459, 4367"]}