Wind Roche Lobe Overflow (WRLOF) Dynamics

• WRLOF is a binary mass-transfer process where the donor’s slow, dust-driven wind is gravitationally confined and focused through the inner Lagrangian point.
• The regime employs geometric criteria based on the ratio of the dust-formation radius to the Roche-lobe radius, often modeled with a capped quadratic efficiency function.
• WRLOF significantly influences binary evolution, enabling enhanced mass transfer in AGB systems and affecting the orbital dynamics and evolutionary outcomes.

Wind Roche-Lobe Overflow (WRLOF) is a binary mass-transfer regime in which the donor star does not fill its Roche lobe with its photosphere, yet the wind acceleration or dust-formation zone becomes comparable to the donor Roche-lobe radius, so the outflow remains slow enough to be gravitationally confined within the donor’s Roche geometry and focused through the inner Lagrangian region toward the companion. In the modern literature, WRLOF is treated as an intermediate regime between classical Roche-lobe overflow (RLOF) and ordinary Bondi–Hoyle–Lyttleton (BHL) wind accretion, but later work has emphasized that the transition can be evolutionary, geometry-dependent, and, in compact systems, intermittent rather than steady (Vathachira et al., 13 Jan 2025, Maldonado et al., 8 Aug 2025).

1. Physical definition and conceptual framework

WRLOF was proposed for binaries in which the donor launches a slow, dense wind over an extended acceleration region, so that the outflow has not yet become a freely escaping fast wind when it reaches the scale of the Roche lobe. In the canonical AGB-star picture, the relevant control variable is the ratio of the wind acceleration or dust-formation radius to the donor Roche-lobe radius. When that scale is large enough, the binary potential reshapes the outflow and channels material through $L_1$, producing a flow topology that is distinct from both fast-wind BHL capture and photospheric RLOF (Sun et al., 2023, Abate et al., 2013).

This distinction is not merely one of efficiency. In BHL accretion, the donor wind is treated as approximately isotropic and already fast enough to escape the donor Roche lobe, so the accretor intercepts only a small fraction of the outflow. In classical RLOF, the stellar surface itself reaches the Roche lobe and matter is transferred directly through $L_1$. WRLOF occupies the intermediate regime: the donor remains formally detached, but the wind is still slow and confined on the scale of the Roche lobe, so the Roche potential shapes the flow and greatly enhances transfer (Vathachira et al., 13 Jan 2025, Abate et al., 2013).

The physical setting in which WRLOF was first emphasized is the cool, dust-driven wind of an AGB donor. Observed AGB wind speeds are typically $5$–$30~\mathrm{km\,s^{-1}}$, while orbital speeds in relevant binaries can be of order $\sim 10~\mathrm{km\,s^{-1}}$, so the fast-wind assumption underlying canonical BHL accretion is often poor (Abate et al., 2013). In wide symbiotics, this led to an important clarification: WRLOF is not the same as tidal enhancement of the donor mass-loss rate. In that formulation, the donor wind is not initially altered by the accretor; rather, the already-launched wind is later funneled because the wind itself fills the donor’s Roche lobe (Ilkiewicz et al., 2018).

Recent symbiotic literature also uses the shorter label “WRLO,” especially when the regime is activated by an explicit switch criterion in orbital integrations rather than diagnosed hydrodynamically (Maldonado et al., 8 Aug 2025).

2. Geometric criteria and standard parameterizations

A widely used WRLOF prescription is the Abate et al. fit, implemented in later binary-evolution calculations as a capped quadratic function of the ratio between the dust-formation radius and the donor Roche-lobe radius. In one common form,

$$\beta_{\rm WRLOF}= \min\left\{ \frac{25}{9}q^2\left[c_1x^2+c_2x+c_3\right], \beta_{\rm WRLOF,max} \right\},$$

with $x=R_{\rm d}/R_{\rm RL,1}$, $q=M_2/M_1$, $c_1=-0.284$, $c_2=0.918$, $L_1$0, and $L_1$1. In this implementation, WRLOF can never exceed $L_1$2 efficiency (Sun et al., 2023).

For dust-driven AGB winds, the dust-formation radius is commonly written as

$L_1$3

with $L_1$4 for carbon-rich dust and $L_1$5 for oxygen-rich dust. In carbon-rich AGB stars, $L_1$6 during most of the AGB phase, so WRLOF is favored when the Roche-lobe scale is not much larger than the stellar radius (Abate et al., 2013).

A different, explicitly regime-classifying approach treats WRLOF as the case in which an accelerating wind has still not reached escape speed by the time it reaches the donor Roche lobe. In that formulation, WRLOF holds when

$L_1$7

and the resulting critical separation $L_1$8 divides WRLOF-dominated from BHL-dominated systems. Across a grid of 375 WD–AGB configurations, the corresponding boundary lies roughly in the range $L_1$9, increasing with donor mass, donor radius, and WD mass (Vathachira et al., 13 Jan 2025).

Compact-symbiotic work has used a more operational switch. There, the donor dust-condensation radius

$5$0

is compared directly with the donor Roche-lobe radius, and WRLO is activated whenever $5$1. This criterion