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Stellar Obliquity Excitation via Disk Dispersal-Driven Resonances in Binaries

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Pith's one-line read Disk dispersal-driven secular resonance crossing broadly misaligns stars with planets beyond about 0.1 au, but a photoevaporatively opened gap keeps warm planets aligned with the stellar spin.

arxiv 2411.08094 v2 pith:WLKOQ2G7 submitted 2024-11-12 astro-ph.EP astro-ph.SR

Yubo Su , Dong Lai This is my paper · ORCID
classification astro-ph.EPastro-ph.SR
keywords stellarbinarydiskobliquitiescompanionsevolutionobliquitysystem
verification ladder T0 review T1 audit T2 compute T3 formal

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

The reading

Most stars are born with a disk of gas and dust around them, and roughly half have a distant stellar companion. If the companion's orbit is tilted to the disk, the star and the disk exert torques on each other and the star slowly wobbles. As the disk loses mass and fades, the wobble rates change, and at a particular moment the system crosses a resonance: the stellar spin axis can be knocked far out of alignment with the disk and any planets forming in it. This paper computes, analytically and numerically, what final tilts such a mechanism produces. For an idealized disk that shrinks as a rigid plate, the calculation predicts that most stars with planets beyond about 0.1 au end up tilted by 60 to 180 degrees, potentially explaining many misaligned exoplanet systems. The authors then add a realistic wrinkle: photoevaporation often carves a gap in the disk at about 2 au, splitting it into an inner and outer disk. With this gap, the inner disk and its close-in planets drain quickly, before the resonance can act, so warm planets inside about 1 au stay aligned with the star, consistent with the observed alignment of warm super-Earths. A second, weaker resonance can still misalign planets beyond 0.3 au if the gap opens very early, but for typical gap-opening times this effect is too weak to matter.
Extended reading notes

Core claim

For idealized, homologously dissipating disk models, adiabatic resonance crossing produces final stellar obliquities broadly distributed between 60 degrees and 180 degrees for most warm and cold planets; and non-homologous disk dissipation via a photoevaporatively opened gap at about 2 au maintains orbital alignment of warm planets with a_p less than about 1 au, independent of planet mass. (Abstract and Section 4.)

Load-bearing premise

The disk is assumed to dissipate homologously as a single rigid, warpless precessing plane with the planet's orbital axis perfectly locked to the disk axis (Section 2.1, Eq. 23). This underpins the headline 60 to 180 degree obliquity distribution. Real protoplanetary disks can warp, open gaps, or clear inside-out, and the paper itself shows that a photoevaporative gap materially changes the warm-planet outcome, indicating the broad-distribution claim is sensitive to the rigid-disk idealization.

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Assumptions & free parameters 6 free parameters · 6 assumptions · 0 invented entities

The central results are derived from classical rigid-body secular dynamics. The paper introduces no new physical entities. The inputs are fiducial astrophysical parameters chosen from observations, not fitted to the target obliquity distribution. The main assumptions are the rigid-disk model, initial spin-disk alignment, adiabatic crossing, and an assumed initial distribution of disk-binary misalignment.

free parameters (6)
  • Disk dissipation e-folding time tau_d = 1 Myr (fiducial)
    Sets the rate of adiabatic resonance crossing; taken from typical protoplanetary disk lifetimes (Bertout et al. 2007).
  • Initial disk mass M_d,i = 0.1 M_sun
    Used in the homologous single-disk model (Eq. 23); chosen from standard disk-mass estimates.
  • Inner disk clearing timescale tau_d,i = 0.1 Myr (fiducial)
    Governing warm-planet alignment in the broken-disk model; adopted from photoevaporation models of transition disks (Alexander et al. 2014).
  • Initial inner disk mass M_i,i = 10^-3 M_sun
    Mass inside the photoevaporative gap; fiducial choice for the broken-disk model (Section 4.1).
  • Gap radius r_gap = about 2 au
    Location of the photoevaporatively-opened gap separating inner and outer disks (Section 4.1).
  • Stellar spin period P_star = 3 days (fiducial)
    Sets the spin angular momentum S; typical of young FGK stars (Kounkel et al. 2023).
assumptions (6)
  • domain assumption The protoplanetary disk evolves as a single rigid, warpless precessing body with surface density Sigma proportional to r_in/r (Eq. 2), and the planet's orbital axis remains perfectly aligned with the disk axis at all times.
    Invoked in Section 2.1 and underpins the single-disk equations of motion (Eqs. 5 and 9); warps and disk-planet decoupling are neglected.
  • domain assumption The stellar spin and disk axes are initially aligned (theta_sl,i = 0).
    Assumed at the start of Section 3.2; any initial misalignment from accretion or magnetic processes is ignored.
  • domain assumption The disk dissipation is adiabatic: the e-folding time tau_d is much longer than the precession timescales, so phase-space area is conserved during resonance crossing.
    Assumed in Section 3.2 and quantified in Eq. (38); the analytic obliquity formula (Eq. 26) follows from the adiabatic invariant.
  • domain assumption The initial distribution of disk-binary misalignment angles theta_lb,i is isotropic (uniform in cos theta_lb,i), with tests of a prograde distribution (Eq. 36).
    Needed to convert single-system outcomes into a predicted population obliquity distribution (Section 3.4); the paper acknowledges observational preference for alignment at a_b less than about 500 au.
  • domain assumption The binary companion is an equal-mass star on a fixed circular orbit, and higher-order (octupole) terms are negligible.
    Assumed in Eqs. (11) and (12) and throughout; the binary precession axes are treated as fixed.
  • standard math Standard Hamiltonian dynamics of Colombo's Top and the theory of adiabatic phase-space area conservation.
    The calculation relies on known results from Colombo (1966), Peale (1969), and Ward and Hamilton (2004) without re-derivation.

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Pith. "Pith review of Stellar Obliquity Excitation via Disk Dispersal-Driven Resonances in Binaries." pith.science (2026). https://pith.science/paper/WLKOQ2G7

@misc{pith2026241108094,
  author       = {Pith},
  title        = {Pith review of: Stellar Obliquity Excitation via Disk Dispersal-Driven Resonances in Binaries},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WLKOQ2G7}},
  note         = {Machine review of arXiv:2411.08094}
}
abstract

The stellar obliquity of a planetary system is often used to help constrain the system's formation and evolution. One of the mechanisms to reorient the stellar spin involves a secular resonance crossing due to the dissipation of the protoplanetary disk when the system also has an inclined, distant ($\sim 300\;\mathrm{AU}$) binary companion. This mechanism is likely to operate broadly due to the $\sim 50\%$ binary fraction of FGK dwarfs and can play an important role in setting the initial stellar obliquities prior to any dynamical evolution. In this work, we revisit this mechanism analytically for idealized, homologously evolving disk models and show that the resulting stellar obliquities are broadly distributed between $60^\circ$ and $180^\circ$ for most warm and cold planets. We further show that non-homologus disk dissipation, such as the development of a photoevaporatively-opened gap at $\sim 2\;\mathrm{AU}$, can help maintain orbital alignment of warm planets, in agreement with observations. Our results represent the proper primordial obliquities for planetary systems with distant binary companions. They also represent the obliquities of stars with no present-day binary companions if these companions are dynamically unbound during the birth cluster phase of evolution, a process that occurs on a comparable timescale as the disk-driven obliquity excitation.

Figures

Figures reproduced from arXiv: 2411.08094 by the authors.

Figure 1
Figure 1. Phase portrait of the stellar spin dynamics when 𝑆/𝐿 ≪ 1 for a few values of 𝜂 (Eq. 16). Here, we have taken 𝜃lb = 5 ◦ , for which 𝜂c ≈ 0.77. The contours depict level curves of the conserved Hamiltonian given by Eq. (18), which are also the trajectories along which the spin evolves. Note that we have labelled as colored dots the four Cassini States for 𝜂 < 𝜂c and the two for 𝜂 > 𝜂c (lower right panel). In these fir… view at source ↗
Figure 2
Figure 2. Cassini State-like equilibria for 𝜃lb = 10◦ , obtained by solving Eq. 22 for the labeled values of 𝑆/𝐿. The top panel shows the equilibria for 𝜙sl = 𝜋 (including CS2 for 𝑆 = 𝐿 = 0) and the bottom panel shows the equilibria for 𝜙sl = 0 (including CSs 1, 3, and 4 for 𝑆/𝐿 = 0). With increasing 𝑆/𝐿, the classical four CSs are slightly modified while new equilibria appear. shown in [PITH_FULL_IMAGE:figures/full_fig_p005… view at source ↗
Figure 4
Figure 4. Phase space evolution corresponding to [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figures from the paper (7 more)
Figure 5
Figure 5. Figure 5: The final misalignment angles 𝜃sb,f , 𝜃lb,f , and 𝜃sl,f (Eqs. 15) after the protoplanetary disk has dissipated (evaluated at 10 Myr) for 2000 values of the initial disk-binary misalignment angle 𝜃lb,i . The spin and disk are initially aligned (𝜃sl,i = 0). We use a disk…
Figure 7
Figure 7. Figure 7: Same as [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]
Figure 8
Figure 8. Figure 8: Plots for the final obliquities 𝜃sl,f as a function of the initial 𝜃lb,i for a Jupiter-mass planet (black) and 2𝑀⊕-mass planet (blue) located at 𝑎p = 0.5 au. Following the results of Section 3.5, it can be seen that 𝜃sl,f = 𝜃lb,i and 180◦ − 𝜃lb,i (the two black dashed …
Figure 9
Figure 9. Figure 9: Parameter space that are relevant for the resonant obliq￾uity excitation, which requires that the ratio 𝜂 (Eq. 16) cross 1 adia￾batically, for a Jupiter-mass planet (top) and a 2𝑀⊕ planet (bottom). The blue lines denote 𝜂max = 1, and the black line denotes the adia￾bat…
Figure 10
Figure 10. Figure 10: Left: The top panel shows the evolution of the misalignment angles between the spin (s), planet+inner disk (l), outer disk (o), and binary (b) for a 2𝑀⊕ planet located at 0.2 au. It can be seen that an early misalignment between the stellar spin and outer disk (𝜃so, b…
Figure 11
Figure 11. Figure 11: Left: The top panel shows the final obliquity 𝜃sl for a 2𝑀⊕-mass planet as a function of the planet’s semimajor axis when assuming the two-disk evolution model described in Section 4.1. The bottom panel shows several critical precession frequency ratios as obtained fr…
Figure 12
Figure 12. Figure 12: Same as the left panels of [PITH_FULL_IMAGE:figures/full_fig_p015_12.png]

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  1. From Misaligned Sub-Saturns to Aligned Brown Dwarfs: The Highest $M_{\rm p}/M{_*}$ Systems Exhibit Low Obliquities, Even around Hot Stars

    astro-ph.EP 2024-12 conditional novelty 4.0 of 10

    Single-star exoplanet systems with planet-to-star mass ratios above roughly 2e-3 are preferentially spin-orbit aligned, even for hot stars, suggesting a primordial formation boundary.

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