Local simulations of common-envelope dynamical inspiral. Impact of rotation, accretion, and stratification

TL;DR

This paper investigates the near-field gas dynamics during common-envelope inspiral by performing three-dimensional local hydrodynamic simulations in a frame rotating with the companion. It systematically isolates and combines the effects of rotation, stratification, and accretion on flow morphology, gravitational drag, lift forces, and the companion’s spin-up, using high-resolution Athena++ simulations. Key findings include that stratification induces inward forces while rotation generates outward lift, accretion disrupts quasi-hydrostatic bubbles and injects heat, and drag remains largely governed by gravity with revised prescriptions for both drag and lift. The results motivate future magnetohydrodynamic studies to assess magnetic amplification, angular-momentum transfer, and their feedback on mass loss and orbital evolution during CEE.

Abstract

Common envelope evolution (CEE) is a crucial phase in binary stellar evolution. Current global three-dimensional simulations lack the resolution to capture the small-scale dynamics around the embedded companion, while local wind-tunnel simulations always approximate the companion's orbital motion as linear rather than as rotation around the center of mass. We investigate how rotation, accretion, and stratification influence small-scale gas dynamics, gravitational drag and lift forces, and the spin-up rate of the companion. We perform three-dimensional local hydrodynamic simulations of a $0.2\, M_\odot$ compact companion plunging into the envelope of a $2\, M_\odot$ red giant in a reference frame rotating at the companion's orbital angular velocity, using the Athena++ code. The presence of stratification generates an inward-directed force, partially opposed by a rotation-induced outward lift force. Both the resulting inward directed force and the drag force, strongly influenced by stratification, would affect the evolution of the binary separation. We propose revised semi-analytical prescriptions for both drag and lift forces. Without accretion and for sufficiently small gravitational softening radii, a quasi-hydrostatic bubble forms around the companion, while accretion prevents its formation and converts kinetic energy into heat that could contribute to the envelope ejection. Drag and lift forces are only marginally affected by accretion. The companion spin-up rate varies non-monotonically in time, first increasing and then decreasing as it plunges deeper into the envelope. These results motivate future magnetohydrodynamic simulations to investigate how accretion, rotation, and stratification affect magnetic amplification, and how magnetic fields, in turn, influence mass and angular momentum accretion rates, as well as the drag and lift force exerted on the companion.

Figures (18)

• Figure 1: Density and pressure profiles from the $2\,M_\odot$ red giant MESA model of Ohlmann2016b, shown as a function of the radius. Dashed lines indicate the polytropic reconstruction used as initial conditions, computed around the location where $\epsilon_\rho = 3$, which is marked by red crosses. The vertical line marks the radius where $\epsilon_\rho = 10$ in the reconstructed stellar structure. The red curve shows the stratification parameter ($\epsilon_\rho$) as a function of radius for the MESA model, while black dots indicate the $\epsilon_\rho$ values employed in our simulations.
• Figure 2: Density (panel a), pressure (panel b), normalized hydrostatic balance residual $R_{\rm HSE} = \left\lVert \nabla P + \rho \, \nabla \Phi_2 \right\rVert/\max \left( \lVert \nabla P \rVert, \; \lVert \rho \, \nabla \Phi_2 \rVert \right)$ (panel c), and Bernoulli parameter (panel d) profiles along radial rays from the companion for a nonrotating, non-stratified, and non-accreting simulation with $\mathcal{M}_\infty = 4$. Gray lines indicate the analytical solutions for density and pressure (Eqs. \ref{['eq:rho_HSE']}, \ref{['eq:P_HSE']}) and the hydrostatic Bernoulli parameter $\mathcal{B}_{\rm HSE}$ (Eq. \ref{['eq:BHSE']}). The vertical dashed line marks the predicted shock radius, $d_s$ (Eq. \ref{['eq:Rs']}). All quantities are averaged over a duration of $\Delta t = R_a / u_\infty$ once a quasi-steady state has been reached.
• Figure 3: Zoomed-in snapshots in the $xy$ plane of the density, pseudo-entropy, and Mach number at $t = 100\, R_a/u_\infty$ for non-stratified simulations with $h_s = 0.05\, R_a$ and $\mathcal{M}_\infty = 4$. First row: Non-accreting case. Second row: Accreting case with $\gamma = 100$ and $\delta = 0$.
• Figure 4: Time evolution of the radial and drag forces exerted by the gas on the companion in non-stratified simulations with ${\rm Ro}= 5.5$ and $\mathcal{M}_\infty = 4$, with and without accretion. Forces are integrated within a sphere of radius $3\, R_a$. The shaded regions indicate the $3\sigma$ range (see Appendix \ref{['app:stat']}).
• Figure 5: Zoomed-in density, pseudo-entropy, and Mach number snapshots at $t = 100\, R_a/u_\infty$ in the $xy$ plane for non-stratified simulations with ${\rm Ro} = 5.5$ and $\mathcal{M}_\infty = 2$. The top panel includes rotation; the bottom does not. White lines indicate streamlines.