Radiative GRMHD simulations of puffy accretion discs: Numerical versus analytical models of sub-Eddington accretion

Abstract

A widely accepted picture of an accretion flow in the luminous soft spectral state of X-ray binary systems is a geometrically thin disc structure much like the classic analytic solution of Shakura \& Sunyaev. Although the analytic models are troubled by instabilities and miss important aspects of physics, such as magnetic fields, they are successfully used as a framework for interpreting observational data. Here, we compare the results of general relativistic radiative magnetohydrodynamic (GRRMHD) simulations of optically thick, mildly sub-Eddington accretion on a stellar-mass black hole (the puffy disc) with established analytic and semi-analytic accretion models in the same regime. From the simulations, we find that the accretion flow is stabilised by the magnetic field, with a puffed-up, optically thick region resembling a warm corona surrounding a denser and cooler disc core. However, the stratified vertical structure of the disc significantly influences the observational picture of such a system. We analyse the inner disc structure, flow properties, effective viscosity, and inner edge position, and compare them to the predictions of standard models. We find that the simulated discs share some similarities with the models; however, they differ in several important aspects, most notably: the photosphere is geometrically thick, the inner edge is located closer to the central black hole than the analytic models assume, the surface density is significantly lower than analytically predicted, and the effective viscosity parameter is not constant but rises steeply in the innermost region.

Figures (8)

• Figure 1: The surface density to central gas temperature ratio for the thin disc model (black curve) and simulation S06 (see \ref{['tab:sims']}) of the puffy disc at $R = 10\,r_\mathrm{g}$. The size and colour of the dots correspond to different snapshots from the simulations, and time is shown on the colourbar. In the thin disc model, the upper constant part of the curve corresponds to the unstable radiation-pressure-dominated solution, and the bottom part to the stable gas-pressure-dominated branch.
• Figure 2: Morphology of puffy disc obtained from S06, averaged over time and azimuth. Two surfaces, corresponding to the density scale height (white dotted line) and the photosphere (white full line), are shown in each panel. They divide the accretion flow into three regions, denoted in the upper-left panel. Top left: gas density and magnetic field lines. Top right: local dissipation rate $\widehat{G}^0$ and streamlines of gas velocity (black) and radiation flux (yellow). Bottom left: gas temperature (discretised) and contours of $\tau=\left(0.1,1,10,100\right)$ from outside the disc towards the equator, and $\tau = 2/3$ with white dashed line. Bottom right: gas radial velocity in terms of local magnetosonic speed, the yellow contour shows the border where $|\tilde{v}^r|/c_\mathrm{ms}=1$. The yellow dashed line shows the stagnation surface (inflow/outflow boundary), where $\tilde{v}^r$ changes sign.
• Figure 3: Vertical thickness of the accretion discs. Full solid lines correspond to the thickness of the photosphere (SO6 and S09 lines nearly coincide), and the thick dashed line to the scale height from simulated discs (the lines of all four models nearly coincide), with mass accretion rate denoted by the line colours. The dotted thin lines (increasing with $\dot m$) show the thickness of the slim disc, and the dash-dotted line the thin disc. The thin and slim disc model curves were calculated for a non-rotating BH with mass $M = 10\,\mathrm{M}_\odot$, viscous $\alpha = 0.1$, and mass accretion rate the same as the corresponding simulation, denoted by the same colours. The simulated data are shown up to the radius where the quasi-stable state was reached.
• Figure 4: Top: Central gas temperature $T_c$ in simulations (full lines), slim disc (dotted lines), and thin disc (dot-dashed lines). Bottom: Vertically integrated (surface) density $\Sigma$ from simulations (full lines), slim (dotted lines), and thin (dash-dotted lines) disc. The parameters for the thin disc models are the same as in \ref{['fig:Hbyr']}.
• Figure 5: Vertical distribution of pressure and its components on four cylindrical radii in S06. The dashed grey line labels the location of the photosphere, and the dotted line is the density scale height. Grey-shaded areas are located under the photosphere.