Wave-Mediated Boundary Layers of Accretion Discs: Role of Internal Structure of the Accretor

TL;DR

The paper investigates how the internal structure of a star with a surface influences wave-driven boundary-layer accretion in discs. By modeling the accretor as a polytropic sphere with index $n$ and running 2D hydrodynamic simulations, the authors quantify how acoustic modes excite mass and angular-momentum transport across the BL, finding that transport strength correlates strongly with the total mass inside the domain and increases with $n$, while the mode mix remains robustly wave-driven. The study reveals a largely global, mass-dependent mechanism for transport in 2D, with the BL width showing weak dependence on $n$ and scaling primarily with Mach number; preliminary 3D results suggest additional complexities due to vertical structure and replenishment processes. These findings refine the understanding of wave-mediated BL transport and provide insight into how an accretor's internal structure can shape accretion dynamics and disc–star coupling in various astrophysical systems.

Abstract

Disc accretion onto astrophysical objects with a material surface proceeds through the boundary layer (BL) -- a radially narrow region in the inner disc where the incoming gas must slow down its rotation before settling onto the surface of the accretor. Here we numerically study a BL in which the angular momentum transport in the layer is accomplished via the excitation of global acoustic waves. While the earlier studies of such wave-mediated BLs typically modeled the internal structure of the central object as a globally isothermal sphere with sharply rising density profile, here we explore the effect of other internal density and temperature profiles on the mode operation. We model the inner structure of an accretor as a polytropic sphere, allowing a shallower increase of density and a non-trivial temperature profile inside the object. While the mix of acoustic modes observed in our long-duration (1000 inner orbits long) 2D hydrodynamic simulations is a weak function of the polytropic index $n$ of the accretor's structure, the mass accretion rate and the angular momentum flux across the BL show a clear dependence on $n$, both decreasing in amplitude as $n$ is lowered. Interestingly, in 2D these transport metrics are better correlated not with $n$ but with a total mass inside the central object contained within the simulation domain. These results improve our understanding of the wave-mediated BL accretion by quantifying the effect of the inner structure of the accretor on the excitation and propagation of acoustic modes mediating the BL transport.

Figures (19)

• Figure 1: Profiles of (a) surface density $\Sigma(r)$ and (b) temperature $T(r)$ for $\mathcal{M}=10$ defined by equations (\ref{['eq:T_s']})-(\ref{['eq:T']}) and used in this work, plotted for several values of the polytropic index of the stellar structure, $n=1.5, 3, 10, \infty$.
• Figure 2: Snapshots of ${rv_r\sqrt{\Sigma}}$, which is a proxy for the wave action, in the $(r,\phi)$ plane. (a): A typical upper mode from the globally isothermal simulation Ninf.b at ${t/2\pi=95}$ when ${\Omega_\mathrm{max}=0.880}$. This mode has ${m=15}$, ${\Omega_\mathrm{p} = 0.828}$. (b): A typical lower mode from the globally isothermal simulation Ninf.a at ${t/2\pi=650}$ (${\Omega_\mathrm{max}}=0.849$). This mode has ${m=13}$, ${\Omega_\mathrm{p} = 0.494}$. (c): A mixed mode from the globally isothermal simulation Ninf.a at ${t/2\pi=150}$ when ${\Omega_\mathrm{max}}=0.852$. This mode has ${m=17}$, ${\Omega_\mathrm{p} = 0.674}$. In each panel, the vertical dotted line shows the location of $r=1$. The dashed line shows the predicted shape of the wavefront, calculated using eq. \ref{['eq:WKB']} and \ref{['eq:wavefront']}, with $m$ and $\Omega_\mathrm{p}$ measured directly from the data. The vertical solid line is the corotation radius, and the short vertical line at the bottom of each figure the Keplerian value (i.e. the corotation radius if ${\Omega=\Omega_K}$. The vertical dot-dashed lines are the limits of the region where $k_r^2<0$. The corresponding short lines at the bottom of each panel are the Keplerian Lindblad Resonances.
• Figure 3: Temporal and radial evolution of various quantities for the ${\mathcal{M}=10}$ globally isothermal simulation Ninf.a. All panels show azimuthally averaged quantities. (a): The local accretion rate at $r=1.1$ (b): The angular velocity (c): The fractional change in the surface density, compared to that at ${t=0}$ (d): $\alpha_\mathrm{stress}$ as defined in eq. \ref{['eq:alpha_stress']} (e): $\alpha_\mathrm{acc}$ as defined in eq. \ref{['eq:alpha_acc']}. Panels (a), (d) and (e) are smoothed temporally with a box function of width ${t/2\pi=5}$.
• Figure 4: Summary snapshots for a $\mathcal{M}=10$ simulation (Ninf.a) with a $n=\infty$ (globally isothermal) star. Snapshots are shown at intervals $t/2\pi=50$, at times indicated in the upper left corner of the (c) panel. At each time, Panel (a) shows the change in vortensity compared to $t=0$. Panels (b) and (c) show the wave action $rv_r\sqrt{\Sigma}$. Panel (b) shows the inner region $r<2.25$ in the $(r,\phi)$ plane while Panel (c) shows the entire disc. See Section \ref{['sec:ninf']} for details.
• Figure 5: Same as Figure \ref{['fig:Ninf_profiles']} but for the $n=1.5$ simulation N1.5.a.