Disk-Overflow Accretion Dynamics

• Disk-overflow accretion is a regime characterized by anisotropic, midplane-dominant mass transfer that departs from classical symmetric models.
• It operates under distinct sub-thermal and super-thermal regimes, where parameters like disk scale height, critical radius, and Hill radius govern the flow dynamics.
• Observational diagnostics from AGN disks, intermediate polars, and high-mass cataclysmic variables reveal its impact on mass transfer efficiency and binary evolution.

Disk-overflow accretion refers to a class of hydrodynamic mass-transfer regimes where accreting flow exceeds the simple, symmetric geometry assumed in classical disk-driven or Roche-lobe overflow. In disk-overflow modes, material may be funneled, diverted, or accreted preferentially along non-spherical, anisotropic channels—often in the presence of competing tidal, magnetic, or radiative forces—yielding rapid, midplane-dominant, or highly variable rates of accretion. Manifestations include super-thermal channeling in AGN disks, magnetic curtain overflow in intermediate polars, disk-to-disk transfer via decretion flows in high-mass cataclysmic variables, and transitions between conservative and non-conservative flow in binary black hole progenitors. Disk-overflow accretion bridges classical Bondi, wind, or RLO models and introduces complex dependencies on disk geometry, mass ratio, orbital eccentricity, and radiative feedback.

1. Physical Principles and Regimes of Disk-Overflow Accretion

Disk-overflow accretion is governed by the interplay of accretion flow geometry, channel confinement, and feedback mechanisms. The regime hinges on several characteristic length scales:

• Supersonic (critical) radius $R_{\mathrm{crit}}$: In isotropic, spherical flow, the critical radius inside which infall velocity exceeds the local sound speed is $R_{\mathrm{crit}} \simeq (1-\lambda)GM_\star/c_s^2$ (where $\lambda$ is the Eddington ratio). Under stratified disk background, this sets the core sphere of influence (Chen et al., 20 May 2025).
• Hill radius $R_H$: The tidal (Hill) radius delineates the region within which the accretor dominates gravitationally: $R_H = a(M_\star/3M_{\mathrm{BH}})^{1/3}$ for a star orbiting a supermassive black hole.
• Disk scale height $H$: Vertical hydrostatic equilibrium yields $H = c_s/\Omega$, with $\Omega$ the orbital angular frequency and $c_s$ the local sound speed; $H$ sets the vertical thickness of the disk.

Regimes are classified as:

• Sub-thermal (thick disk): $H > R_{\mathrm{crit}}$—Accretion remains nearly isotropic, feedback is symmetric, and the inflow matches Bondi-like spherical scaling.
• Super-thermal (thin disk): $H < R_{\mathrm{crit}}$—Accretion localizes along the disk midplane, with escaped polar radiation driving outflows, resulting in “disk-overflow” geometry where midplane flows are shielded from Eddington feedback (Chen et al., 20 May 2025).

In intermediate polars and related systems, the truncation of accretion disks by strong magnetic fields can similarly provoke overflow modes where accretion occurs away from the nominal disk plane, with stream-fed flows and vertical overflows across the magnetic barrier (Rawat et al., 2021, Eksi et al., 2010).

2. Accretion Morphology, Dynamics, and Efficiency

The accretion cross-section and dynamical flow properties vary sharply between disk-overflow and classical models.

Regime	Dominant Cross-Section	$v_{\mathrm{eff}}$
Sub-thermal	$\sim R_{\mathrm{crit}}^2$	$\sim c_s$
Super-thermal	$\mathrm{min}(R_H, H)^2$	$\sim \Omega R_H \gg c_s$

In cold (super-thermal) disks, the mass flux is approximated as $$\dot{M} \sim \pi\rho_0[\mathrm{min}(R_H, H)]^2v_{\mathrm{eff}}$$, with midplane density $\rho_0$ and relevant infall velocity. The disk-overflow regime exhibits accretion rates $\lesssim 0.02\,M_\odot/\mathrm{yr}$ and accretion $\alpha \sim 10^{-1}$ for AGN star capture scenarios at $T_0 = (3–7)\times10^4\,\mathrm{K}$ and $\rho_0 \sim 10^{-10}$ g/cm$^3$ (Chen et al., 20 May 2025).

By contrast, in semidetached binaries undergoing Roche-lobe overflow, the overfilling factor $f = R_\mathrm{donor,ecl}/R_\mathrm{RL,ecl}$ sets the accretion mode: “barely-overflowing” ($f\sim1.01$) produces non-conservative transfer (only $\sim$86% of stream accretes; the remainder escapes via outflow), while “extreme overflow” ($f\sim1.1$) yields fully conservative accretion, with all transfered mass and angular momentum ending up on the compact object (Dickson, 2024).

3. Key Systems and Observational Diagnostics

AGN Embedded Stars

The interaction of massive stars embedded within AGN disks proves a laboratory for disk-overflow physics. When the disk is sufficiently cool and thin, anisotropic accretion channels form in the midplane, while polar regions experience radiative blowout and super-Eddington outflows. Spiral density waves inside the Hill sphere efficiently transport angular momentum at $\alpha_{\mathrm{eff}}\sim0.1$–1, facilitating rapid midplane accretion (Chen et al., 20 May 2025).

Intermediate Polars

In systems such as TX Col, TESS long-cadence photometry and frequency analysis reveal rapid day-to-day switches between disk-fed, stream-fed, and disk-overflow accretion (Rawat et al., 2021). DO accretion is marked by simultaneous detection of the WD spin frequency and beat frequency, with occasional quasi-periodic oscillations arising from diamagnetic “blobs” at the disk edge beating with the stellar spin. Classification algorithms based on amplitude ratios $R_A$ illustrate up to 71% stream-dominated DO, with parseable recurrence patterns.

High-Mass Cataclysmic Variables with Decretion Disk Overflow

FQ Circini demonstrates disk-to-disk overflow wherein a Be-star’s viscous decretion disk expands to fill its Roche lobe, then overflows through $L_1$ into the accretion disk of the WD. The observed system parameters ($M_\mathrm{comp}=13\,M_\odot$, $R_\mathrm{comp}=6.2\,R_\odot$, $R_L\simeq9.5\,R_\odot$) verify the geometric setup. Empirical signatures include ellipsoidal modulation, emission-line fills, persistent flickering, and rates consistent with nova trigger requirements ($\sim 10^{-9}$–$10^{-10}\,M_\odot$/yr) (Schaefer et al., 20 Nov 2025).

Roche-Lobe Overflow Systems and Planet-Star Accretion

3D hydrodynamic and ballistic modeling for planet-star and HMXB binaries distinguish disk-overflow, direct-impact, and self-accretion regimes via initial Jacobi constant and impact geometry (Dosopoulou et al., 2017, Dickson, 2024). Disk formation dominates for low-eccentricity ($e\lesssim0.2$), sub-synchronous systems. Advanced parameterization links $f$ to mass-transfer efficiency, angular-momentum loss, and runaway transition thresholds, delineating conservative/non-conservative transfer domains (Dickson, 2024).

Supergiant Fast X-Ray Transients

IGR J08408–4503 displays hybrid disk-overflow (RLO + wind) accretion, with periastron passages triggering Roche-lobe overflow and disk formation, and matter escaping through $L_2$ to sustain diffuse, circumbinary reservoirs (Ducci et al., 2019). Observational features include X-ray flare profiles, spectral signatures indicative of accretion disks, and phase-correlated outbursts.

4. Disk-Overflow in Magnetosphere/Spin-Down Regimes

Magnetically truncated disks in millisecond X-ray pulsars exhibit disk-overflow accretion in the “spin-down/propeller” regime, where a thick disk allows high-latitude accretion, circumventing centrifugal exclusion at the midplane. For $R_m > R_c$ (magnetospheric vs corotation radius), fraction $f \equiv \dot{M}_*/\dot{M}$ accreted scales as $$f=1-\frac{3}{2}\sqrt{1-\omega_*^{-2}}+\frac{1}{2}{(1-\omega_*^{-2})}^{3/2}$$, bridging canonical cessation with finite accretion persistence (Eksi et al., 2010). Empirical modeling successfully explains observed light curve transitions in SAX J1808.4-3658.

5. Angular Momentum Transport, Spiral Shocks, and Gap Opening

A key dynamical driver in disk-overflow systems is the excitation of non-axisymmetric spiral density waves, which propagate as shocks and facilitate angular momentum transport away from the accretor (Chen et al., 20 May 2025). Efficient transport (via large $\alpha_{\mathrm{eff}}$) accelerates midplane inflow; on longer timescales, tidal torques can open a gap, deplete co-orbital gas, and reduce accretion rates. Full quantification requires global simulations over viscous timescales exceeding $1/\alpha\Omega$.

6. Evolutionary and Astrophysical Implications

Disk-overflow accretion modulates evolutionary pathways for interacting binaries, introducing previously unappreciated stability transitions and mass-transfer feedback mechanisms. For example, as the overfilling factor $f$ increases in HMXB or black hole progenitor systems, mass transfer efficiency transitions sharply from non-conservative to conservative, with mass-transfer rates exceeding $\dot{M}_{L1}\sim10^{-6}M_\odot/\mathrm{yr}$ at $f_{\mathrm{crit}}\sim1.012$ (Dickson, 2024). Runaway unstable RLO can drive common-envelope evolution or luminous supernovae. In FQ Circini, disk-overflow transfer from decretion disk to WD promotes nova eruptions without enabling Type Ia pathways (Schaefer et al., 20 Nov 2025).

Disk-overflow accretion also informs AGN metallicity regulation, population synthesis of black hole binaries, the flare morphology in SFXTs, and the persistence of pulsations in accreting millisecond pulsars under rapidly variable flow conditions.

7. Controversies, Open Questions, and Future Directions

Numerical and observational results challenge long-standing assumptions of instantaneous disruption in Roche-lobe overflow (RLO); detailed integrators identify substantial regions of parameter space where disk formation, not direct impact, is the norm for low-eccentricity and sub-synchronous systems (Dosopoulou et al., 2017). Open questions include the impact of radiative feedback, precise flow partitioning in gap-opening and spiral-shock-dominated disks, the long-term evolutionary fate of runaway disk-overflow binaries, and the full taxonomy of magnetic and decretion-disk-mediated overflow regimes.

Hydrodynamic and MHD simulations at extreme resolution (Dickson, 2024, Chen et al., 20 May 2025), coupled with multi-wavelength, high-cadence photometry and spectroscopic campaigns (e.g., TESS for IPs and HMCVs (Rawat et al., 2021, Schaefer et al., 20 Nov 2025)), continue to refine accretion mode diagnostics and drive deeper exploration into the complex, channelized, disk-overflow domain.