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arxiv: 2604.14555 · v1 · submitted 2026-04-16 · 🌌 astro-ph.EP

Recognition: unknown

Misaligned circumbinary discs around unequal-mass eccentric binaries: alignment, morphology, and binary accretion variability

Ruiqi Yang , Jeremy L. Smallwood , Hongping Deng , Ya-Ping Li , Alessia Franchini , Ruobing Dong , Shang-Fei Liu
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Pith reviewed 2026-05-10 10:26 UTC · model grok-4.3

classification 🌌 astro-ph.EP
keywords circumbinary discsmisaligned discsbinary accretiondisc alignmentaccretion variabilityeccentric binarieshydrodynamical simulations
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The pith

Initial tilt and mass ratio set which star accretes most from a misaligned circumbinary disc around an eccentric binary.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper runs 3D hydrodynamical simulations of circumbinary discs starting at tilts from 0° to 180° around eccentric binaries whose secondary-to-primary mass ratios range from 0.11 to 0.67. It tracks how these discs align over time and measures the resulting time-averaged accretion rates onto each star. Discs that settle into polar or coplanar retrograde orientations preferentially feed the primary, while those reaching coplanar prograde orientations feed the secondary more. The ratio of secondary accretion to total binary accretion, η, changes non-monotonically with mass ratio depending on the tilt regime. These patterns also link disc warping and breaking to faster mass loss.

Core claim

Simulations reveal that both initial disc tilt and binary mass ratio control long-term accretion variability: polar and coplanar retrograde alignments favor accretion onto the primary while coplanar prograde alignments favor the secondary, and the preferential accretion ratio η is a non-monotonic function of mass ratio that increases with decreasing mass ratio for near-prograde discs but decreases for intermediate tilts.

What carries the argument

3D hydrodynamical simulations that evolve disc tilt, morphology, and time-averaged mass accretion rates onto each binary component for varied initial tilts and mass ratios.

If this is right

  • Discs near coplanar prograde alignment show stronger secondary accretion preference as the mass ratio decreases.
  • Discs with initial tilts 30°–135° show weaker secondary preference at smaller mass ratios.
  • Polar configurations produce the lowest overall disc mass-loss rates, slightly below those of prograde coplanar discs.
  • Retrograde discs lose mass faster than prograde ones.
  • Strong warping or breaking of the disc causes rapid mass loss.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same tilt-dependent accretion rules could influence where planets form and grow in circumbinary systems.
  • Changing the viscosity law or adding magnetic fields might shift the reported alignment endpoints and η values.
  • Targeted observations of accretion signatures in known misaligned binaries could map tilt to dominant accretor.

Load-bearing premise

The alignment pathways and accretion preferences depend on the chosen initial disc conditions, binary eccentricity, and numerical hydrodynamical setup including viscosity.

What would settle it

Long-term monitoring of accretion rates onto each component in an eccentric binary with a measured disc tilt and mass ratio would test whether the predicted primary-versus-secondary preferences hold.

Figures

Figures reproduced from arXiv: 2604.14555 by Alessia Franchini, Hongping Deng, Jeremy L. Smallwood, Ruiqi Yang, Ruobing Dong, Shang-Fei Liu, Ya-Ping Li.

Figure 1
Figure 1. Figure 1: Analytically estimated timescales for coplanar and polar align￾ments as a function of binary mass ratio 𝑞b. The blue (orange) curve shows the analytically calculated polar (coplanar) alignment timescale, 𝜏p (𝜏c). The timescales for both alignments increase monotonically with smaller mass ra￾tios, and the polar alignment consistently occurs faster than coplanar align￾ment. where Ω = p 𝐺(𝑀1 + 𝑀2)/𝑟 3 is the … view at source ↗
Figure 2
Figure 2. Figure 2: The evolution of binary-disc tilt for four binary mass ratios: 𝑞b = 0.67 (top left), 𝑞b = 0.43 (top right), 𝑞b = 0.25 (bottom left) and 𝑞b = 0.11 (bottom right), in units of initial binary orbital period 𝑃b. Different colours represent various initial binary-disc tilts (𝑖0): greens and blues indicate discs evolving towards coplanar prograde and retrograde alignments, respectively; reds and purples represen… view at source ↗
Figure 3
Figure 3. Figure 3: The 𝑖 cos 𝜙 − 𝑖 sin 𝜙 phase spaces for four binary mass ratios: 𝑞b = 0.67 (top left), 𝑞b = 0.43 (top right), 𝑞b = 0.25 (bottom left) and 𝑞b = 0.11 (bottom right). Different coloured curves correspond to various initial binary-disc tilts, consistent with the definition in [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: The evolution of reference radius 𝑟20%, as a function of binary orbital periods (𝑃b). 𝑟20% is the reference radius where the surface density reaches its 20% of the maximum. Different curve colours represent simula￾tions with varying initial binary-disc tilts for a binary mass ratio of 𝑞b = 0.67. than the coplanar prograde case. Like the coplanar retrograde disc, its 𝑟20% also gradually expands outward over… view at source ↗
Figure 4
Figure 4. Figure 4: Surface density snapshots of circumbinary discs with different in￾stantaneous binary-disc tilts 𝑖 at 1000 binary orbital periods, viewed opposite to the direction of the disc’s angular momentum. From top left to bottom right, 𝑖 are: 0.1 ◦ (0p67i0), 16.3 ◦ (0p67i15), 28.2 ◦ (0p67i30), 57.3 ◦ (0p67i135), 89.2 ◦ (0p67i90), 147.8 ◦ (0p67i150), 160.4 ◦ (0p67i165), 179.9 ◦ (0p67i180). The two red markers indicat… view at source ↗
Figure 7
Figure 7. Figure 7: The evolution of the surface density Σ, amplitude of the warp 𝜓, eccentricity 𝑒, binary-annulus tilt 𝑖bd, and longitude of the ascending node 𝜙, as a function of radius 𝑟, for the case of 𝑖0 = 45◦ in 𝑞b = 0.67. Different colours, from dark red to ocean blue, denote different time, from 𝑡 = 500𝑃b to 1200𝑃b, with intervals of 100𝑃b. With the disc break propagating outward, the inner disc pumps its eccentrici… view at source ↗
Figure 8
Figure 8. Figure 8: The accretion rate 𝑀¤ i (where i = 1, 2 correspond to primary and secondary), and cavity eccentricity 𝑒 (𝑟 = 𝑟cav ), as a function of time in units of initial binary orbital period 𝑃b, for 𝑞b = 0.67 and different initial binary-disc tilts. Red and blue curves use the left 𝑦-axis, representing the primary and secondary accretion rates, respectively. Purple curves use the right 𝑦-axis, denoting the cavity ec… view at source ↗
Figure 9
Figure 9. Figure 9: Comparison of the preferential accretion ratio 𝜂 = h𝑀¤ 2 i/h𝑀¤ b i for two accretion radii. The larger and smaller scatters correspond to simulations with 𝑟acc = 0.25 and 𝑟acc = 0.025, respectively. Note that for each initial condition, values of 𝜂 for both accretion radii are averaged over the simulation duration of the 𝑟acc = 0.025𝑎b runs. disc, preventing the presence of prograde resonances (e.g., Li et… view at source ↗
Figure 10
Figure 10. Figure 10: Preferential accretion ratio 𝜂 = h𝑀¤ 2 i/h𝑀¤ b i as a function of initial binary-disc tilt 𝑖0 for four different binary mass ratios, denoted by different colours. Background shading marks the types of alignment. Solid and dotted lines correspond to simulations with accretion radii of 𝑟acc = 0.25𝑎b and 0.025𝑎b, respectively. For the 𝑟acc = 0.25𝑎b runs, the averaging time for 𝜂 is chosen separately for each… view at source ↗
Figure 11
Figure 11. Figure 11: Disc mass 𝑀d as a function of initial binary-disc tilt 𝑖0 at 5000 binary orbital periods for four distinct mass ratios, represented by varying colours. The left 𝑦-axis is normalised to the total disc mass, while the right 𝑦-axis is expressed as a percentage. or breaking and therefore retain more disc mass. Nevertheless, their mass loss rates remain higher than those of discs at other initial tilts within … view at source ↗
Figure 12
Figure 12. Figure 12: The evolution of disc warp amplitude 𝜓 as a function of radius 𝑟 for initial binary-disc tilts 𝑖0 = 45◦ , 135◦ , and 150◦ across four binary mass ratios, 𝑞b = 0.67, 0.43, 0.25, 0.11. Note that we select different time intervals for each tilt. of the disc are radially extended significantly. When the disc under￾goes strong warping, disc breaking can occur, splitting the disc into separate rings [PITH_FULL… view at source ↗
read the original abstract

Binary systems are ubiquitous in the Universe and often host circumbinary discs that are misaligned with the binary orbital plane. Such misalignments can affect disc evolution and binary accretion variability. We here present 3D hydrodynamical simulations of circumbinary discs with initial tilts $i_0$ from $0^\circ$ to $180^\circ$, around eccentric binaries with secondary-to-primary mass ratios of $0.11-0.67$. We find that both the initial tilt and mass ratio can affect the long-term accretion variability in our simulations. Discs evolving towards polar and coplanar retrograde generally favour accretion onto the primary star, while discs evolving towards coplanar prograde generally favour accretion onto the secondary. We find preferential accretion ratio $\eta=\langle\dot{M_2}\rangle/\langle\dot{M_\mathrm{b}}\rangle$ to be a non-monotonic function of the mass ratio. For discs close to coplanar prograde alignment, $\eta$ increases with decreasing mass ratio, whereas for discs with $30^\circ \le i_0 \le 135^\circ$, $\eta$ decreases for smaller mass ratios. Polar discs show the lowest mass loss rates, slightly lower than those of coplanar prograde discs, while retrograde discs lose mass faster than their prograde counterparts. Discs that undergo strong warping or breaking experience rapid mass loss. Our findings provide insights into observed circumbinary discs and have implications for circumbinary planet formation.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript presents 3D hydrodynamical simulations of circumbinary discs with initial tilts i0 ranging from 0° to 180° around eccentric binaries with secondary-to-primary mass ratios q = 0.11–0.67. It reports that both initial tilt and mass ratio influence long-term alignment pathways (polar, coplanar prograde, or retrograde), which in turn produce distinct accretion biases: polar and retrograde discs favor the primary while prograde discs favor the secondary. The time-averaged preferential accretion ratio η = ⟨Ṁ₂⟩/⟨Ṁ_b⟩ is found to be non-monotonic in q, with opposite trends in the low-i0 and 30°–135° regimes; polar discs exhibit the lowest mass-loss rates and strongly warped discs the highest.

Significance. If the reported trends are numerically robust, the work supplies a concrete link between initial misalignment, alignment outcome, and accretion partitioning that is directly relevant to interpreting ALMA observations of misaligned circumbinary discs and to models of circumbinary planet formation. The non-monotonic η(q) behavior and the identification of distinct accretion preferences tied to alignment state constitute falsifiable predictions that could be tested against both observations and future simulations.

major comments (2)
  1. [Numerical methods and results] The central claims on accretion preferences and the non-monotonic dependence of η on mass ratio (abstract and results section) rest on a finite suite of 3D runs. The manuscript provides no convergence tests with respect to grid resolution, artificial viscosity coefficient, or sink-particle accretion radius. In circumbinary disc simulations these choices routinely affect cavity size, warp propagation speed, and time-averaged mass flux through the inner cavity; without such tests the robustness of the reported η values and the reversal of primary/secondary preference between tilt regimes cannot be verified.
  2. [Discussion] The discussion of limitations notes that long-term evolution depends on initial disc conditions, binary eccentricity, and hydrodynamical treatment, yet no quantitative sensitivity experiments (e.g., varying the viscosity prescription or adding magnetic fields) are shown. Because the headline non-monotonic η(q) result and the alignment–accretion mapping are extracted directly from the simulation outcomes, an explicit statement of the explored numerical parameter space or a brief resolution study is required to support the conclusions.
minor comments (2)
  1. [Abstract] The abstract states that polar discs show 'slightly lower' mass-loss rates than coplanar prograde discs; a quantitative comparison (e.g., a table of time-averaged Ṁ values) would make this statement more precise.
  2. [Notation] Notation for the total binary accretion rate is introduced as Ṁ_b in the abstract but is not defined in the text until the results section; a brief parenthetical definition on first use would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thoughtful review and for highlighting the potential implications of our work for observations and planet formation. We address each major comment below and describe the revisions we will implement to improve the clarity and robustness of the numerical results.

read point-by-point responses

  1. Referee: The central claims on accretion preferences and the non-monotonic dependence of η on mass ratio (abstract and results section) rest on a finite suite of 3D runs. The manuscript provides no convergence tests with respect to grid resolution, artificial viscosity coefficient, or sink-particle accretion radius. In circumbinary disc simulations these choices routinely affect cavity size, warp propagation speed, and time-averaged mass flux through the inner cavity; without such tests the robustness of the reported η values and the reversal of primary/secondary preference between tilt regimes cannot be verified.

    Authors: We agree that dedicated convergence tests would strengthen confidence in the quantitative η values. Our simulations employed a uniform grid resolution, a fixed artificial viscosity coefficient, and a standard sink accretion radius chosen to be consistent with earlier circumbinary disc studies in the literature. Across the full suite of runs spanning q = 0.11–0.67 and i0 = 0°–180°, the qualitative trends in accretion preference (polar/retrograde favouring the primary, prograde favouring the secondary) and the non-monotonic behaviour of η(q) remain consistent, which we interpret as supporting robustness. Nevertheless, to directly address the concern we will add a dedicated subsection (or appendix) that (i) tabulates the exact numerical parameters used, (ii) reports a limited resolution study for two representative models (one polar, one prograde) run at 1.5× higher resolution, and (iii) discusses the impact on time-averaged mass fluxes. These additions will be included in the revised manuscript. revision: yes

  2. Referee: The discussion of limitations notes that long-term evolution depends on initial disc conditions, binary eccentricity, and hydrodynamical treatment, yet no quantitative sensitivity experiments (e.g., varying the viscosity prescription or adding magnetic fields) are shown. Because the headline non-monotonic η(q) result and the alignment–accretion mapping are extracted directly from the simulation outcomes, an explicit statement of the explored numerical parameter space or a brief resolution study is required to support the conclusions.

    Authors: We accept that the current discussion would benefit from a more explicit enumeration of the numerical parameter space that was actually explored. In the revised version we will expand the limitations paragraph to include a concise table or bullet list of the fixed and varied parameters (grid resolution, viscosity coefficient, sink radius, binary eccentricity held at the value used throughout, and the range of q and i0). We will also note that magnetic fields and alternative viscosity prescriptions lie outside the scope of the present hydrodynamical study but are natural extensions for future work. A brief resolution comparison (as described in response to the first comment) will be referenced here as well. These changes will better contextualise the reported η(q) behaviour without overstating the generality of the results. revision: yes

Circularity Check

0 steps flagged

No circularity: results are direct outputs of forward hydrodynamical simulations

full rationale

The paper reports outcomes from 3D hydrodynamical simulations initialized with specified tilts, mass ratios, and binary eccentricities. All reported alignment pathways, accretion variability, and the non-monotonic η function emerge from numerical evolution under standard hydro equations; no analytic derivation, parameter fitting to target data, or self-citation chain is used to obtain the central claims. The abstract and methods describe direct simulation results without reducing any prediction to its own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claims rest on standard 3D hydrodynamical evolution of inviscid or viscous discs under gravity from an eccentric binary; no new physical entities are introduced and no parameters are fitted to data.

axioms (2)
  • standard math The evolution of the disc is governed by the standard equations of hydrodynamics in three dimensions under the gravitational potential of the binary.
    Invoked throughout the simulation description in the abstract.
  • domain assumption Initial disc conditions (surface density profile, temperature, tilt) remain representative of long-term behavior without additional physics such as magnetic fields or self-gravity.
    Implicit in the choice of simulation setup and reported outcomes.

pith-pipeline@v0.9.0 · 5602 in / 1483 out tokens · 30460 ms · 2026-05-10T10:26:09.989439+00:00 · methodology

discussion (0)

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Reference graph

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