Kozai-driven mass loss of the circumbinary disk in D9 in orbit around the supermassive black hole Sgr A*

Lucas Pouw; Simon Portegies Zwart; Tim van der Vuurst; Yannick Badoux

arxiv: 2604.09856 · v2 · submitted 2026-04-10 · 🌌 astro-ph.GA · astro-ph.SR

Kozai-driven mass loss of the circumbinary disk in D9 in orbit around the supermassive black hole Sgr A*

Yannick Badoux , Lucas Pouw , Tim van der Vuurst , Simon Portegies Zwart This is my paper

Pith reviewed 2026-05-10 16:56 UTC · model grok-4.3

classification 🌌 astro-ph.GA astro-ph.SR

keywords circumbinary diskSgr A*S-star clustervon Zeipel-Lidov-Kozai mechanismmass lossD9 binaryhydrodynamic simulation

0 comments

The pith

The circumbinary disk around D9 loses about 7 percent of its mass every von Zeipel-Lidov-Kozai cycle induced by Sgr A*.

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

The paper simulates the gravitational and hydrodynamic evolution of the circumbinary disk around the S-star binary D9 as it orbits the supermassive black hole Sgr A*. It finds that the disk settles into a stable radial range and its inclination tracks the binary's Kozai oscillations. The key result is periodic mass loss bursts synchronized with the 62.5 kyr vZLK timescale, averaging 7 percent loss per cycle. This leads to the prediction that the disk would be nearly gone after a few million more years, consistent with the age of the S-cluster and the lack of observed disks around similar stars.

Core claim

Using coupled gravity and hydrodynamics simulations, the authors show that the disk around D9 experiences periodic mass loss of ∼7% ± 2% per vZLK cycle, driven by the Kozai mechanism from Sgr A*. Over multiple cycles since the star's formation 2.7 Myr ago, this process could reduce the disk to 1% of its current mass in another ∼4 Myr, at which point D9 would be ∼6.7 Myr old, aligning with the average age of S-cluster members and explaining the absence of Brγ emission from other members.

What carries the argument

The von Zeipel-Lidov-Kozai (vZLK) mechanism induced by Sgr A* on the D9 binary, which drives periodic changes in eccentricity and inclination that trigger bursts of mass loss from the circumbinary disk.

If this is right

The disk will be depleted to 1% mass after another ∼4 Myr, making D9 about 6.7 Myr old.
vZLK-driven mass loss explains why other S-cluster stars lack observable Brγ emission from disks.
The vZLK timescale is ∼62.5 kyr, much shorter than previously estimated, implying multiple oscillations in the star's lifetime.
The disk settles between 5.2 times the binary semi-major axis and 0.28 Hill radii, with inclination following the binary.

Where Pith is reading between the lines

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

If the mass loss rate holds, similar disks around other young stars near Sgr A* may also be transient and hard to detect.
Future observations could test this by searching for faint remnants or younger stars with intact disks.
Extending simulations to include stellar winds or radiation could refine the longevity estimate.

Load-bearing premise

The mass loss rate of about 7 percent per cycle remains roughly constant over several million years without being significantly altered by unmodeled effects like stellar winds or radiation.

What would settle it

Detection of a substantial circumbinary disk around an S-cluster star older than 6-7 Myr, or a direct measurement showing no mass loss over one or more vZLK cycles in D9.

Figures

Figures reproduced from arXiv: 2604.09856 by Lucas Pouw, Simon Portegies Zwart, Tim van der Vuurst, Yannick Badoux.

**Figure 1.** Figure 1: Sketch of the astrophysical setup. A stellar binary (D9) with circumbinary disk is orbiting a SMBH (Sgr A*). Masses (M), eccentricities (e), and semimajor axes (a) are indicated for the inner binary orbit and the outer orbit around the SMBH. The mutual inclination between these orbits is imut and the argument of periapsis of the inner orbit is ωin. maximum outer radius to 13.4 au, which corresponds to one… view at source ↗

**Figure 2.** Figure 2: Left: Fraction of bound disk particles (fbound) is plotted as a function of time. Different colors correspond to different values of the initial inner radius (Rin) and initial outer radius (Rout) of the circumbinary disk. The dashed black line indicates 70 kyr, where the bound fraction has settled to its first plateau. Right: Radial distribution of disk particles at 70 kyr as a function of the distance to … view at source ↗

**Figure 3.** Figure 3: Top three panels: Evolution of the distribution of the eccentricity, inclination, and the argument of periapsis of the bound (e < 1) disk particles. The evolution of the binary orbital elements is also plotted (solid red lines). The orbital elements of the binary oscillate on a timescale of TvZLK = 62.5 kyr. Bottom: Fraction of bound disk particles over time. After an initial period of rapid mass loss, the… view at source ↗

read the original abstract

The supermassive black hole (Sgr A*) in the Galactic center is surrounded by the S-star cluster consisting of young stars on eccentric orbits. Recently, the S-star binary, called D9, was found to be orbited by a circumbinary disk. Due to the gravitational interaction between Sgr A* and the binary, the disk could be short-lived. We investigate the evolution of the disk around a stellar binary while orbiting Sgr A*. We use the \texttt{AMUSE} framework for coupling a gravity solver (for the binary and Sgr. A*) with a hydrodynamics solver (for the disk). We find that, the disk eventually settles between 5.2$a_{\rm in}$ and 0.28 Hill radii of the binary. Here, $a_{\rm in}$ is the semi-major axis of D9. The inclination of the circumbinary disk follows the binary's, which evolves due to the von Zeipel-Lidov-Kozai (vZLK) mechanism induced by Sgr A*. The mean eccentricity of the disk is approximately in anti-phase with the eccentricity evolution of the binary. We find a vZLK timescale of $T_\text{vZLK}\approx62.5\,$kyr, which is two orders of magnitude shorter than the value reported by Peisker etal. (2024). As a consequence, D9 has undergone multiple vZLK oscillations in its lifetime of 2.7 Myr. We find the disk shows periodic bursts of mass loss on the vZLK timescale, suggesting that the mass loss itself is in part driven by the vZLK mechanism. The secular evolution observed in both the binary and the disk are consistent with theoretical predictions. We find the disk loses $\sim$7\% $\pm$ 2\% of its mass every vZLK cycle. If we extrapolate this mass loss, the disk will have 1\% of its current mass left after another $\sim$4 Myr. D9 will then be $\sim$6.7 Myr old, which is on the same order as the current average age of S cluster members. The vZLK-driven mass loss could, therefore, explain the absence of Br$\gamma$ emission from other S cluster members.

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.

Desk Editor's Note private letter to a colleague

The simulations find a much shorter vZLK cycle and ~7% mass loss per cycle for the D9 disk, but the Myr-scale depletion claim rests on assuming that fractional rate stays fixed as the disk thins.

read the letter

The main thing to know is that this paper runs hydrodynamical simulations of the circumbinary disk around the S-star binary D9 and reports periodic mass loss of about 7% per vZLK cycle, with a cycle time of 62.5 kyr that is two orders of magnitude shorter than in Peisker et al. 2024. They extrapolate that rate to argue the disk would be down to 1% of its mass after another 4 Myr, putting D9 at an age comparable to the S-cluster average and offering a dynamical reason why other S-stars lack Br-gamma disks. The disk settles between 5.2 times the inner binary separation and 0.28 Hill radii, its inclination tracks the binary, and disk eccentricity moves in anti-phase with the binary, all consistent with vZLK theory. The AMUSE coupling of gravity and hydro solvers is a straightforward way to handle the problem, and the shorter timescale means the system has already experienced multiple full oscillations in its 2.7 Myr lifetime. That part of the work is new and cleanly presented. The soft spot is the extrapolation itself. The 7% figure is measured over a limited number of cycles once the disk has settled, and nothing in the runs tests whether the fractional loss remains constant once total mass and surface density have dropped by tens of percent. Lower density could weaken the torques that drive the bursts or let viscosity and cooling play a larger role, which would change the depletion time and weaken the link to the observed absence of disks. The abstract gives no numbers on resolution or convergence, so it is hard to judge how robust the mass-loss measurement is. This paper is for people working on Galactic-center dynamics, young stars near supermassive black holes, or Kozai-driven disk evolution. A reader who wants to see numerical evidence for vZLK acting on a circumbinary disk will find the setup and qualitative results useful. It is coherent enough and addresses a real observational puzzle, so it deserves a serious referee even if the long-term extrapolation needs more justification or sensitivity tests.

Referee Report

3 major / 1 minor

Summary. The manuscript uses coupled N-body and hydrodynamical simulations in the AMUSE framework to evolve a circumbinary disk around the S-star binary D9 orbiting Sgr A*. The disk settles between 5.2 a_in and 0.28 Hill radii, with inclination tracking the binary's vZLK evolution and mean eccentricity in anti-phase. The reported vZLK timescale is ~62.5 kyr (two orders of magnitude shorter than prior work), accompanied by periodic mass-loss bursts. The disk loses ~7% ± 2% of its mass per vZLK cycle; linear extrapolation implies only 1% mass remains after another ~4 Myr, yielding a total age of ~6.7 Myr that could explain the absence of Brγ emission from other S-cluster members.

Significance. If the fractional mass-loss rate is shown to be robust, the work supplies a concrete dynamical channel by which vZLK oscillations can rapidly deplete circumbinary disks in the Galactic-center environment, offering a unified explanation for both the observed youth of S-cluster stars and the lack of disks around other members. The direct numerical approach (no fitted parameters beyond initial disk conditions) and consistency of secular evolution with analytic vZLK theory are clear strengths.

major comments (3)

[Abstract] Abstract: the central quantitative claim that the disk loses ∼7% ± 2% of its mass every vZLK cycle, followed by linear extrapolation to ∼4 Myr (leaving 1% mass), is load-bearing for the proposed explanation of absent Brγ emission. The rate is extracted from a limited number of cycles in short runs; no test is presented demonstrating that the fractional loss remains constant once surface density has dropped by tens of percent, which could alter torques, burst amplitude, or allow viscosity/cooling to dominate.
[Methods/Results] Methods/Results: no information is supplied on the hydrodynamical resolution (particle number or grid scale), time-stepping criteria, or convergence tests for the mass-loss measurement. Without these, it is impossible to assess whether the reported 7% ± 2% rate is numerically converged or sensitive to setup choices, undermining in the extrapolation.
[Abstract and Results] Abstract and Results: the vZLK timescale of 62.5 kyr is stated to be two orders of magnitude shorter than the value in Peisker et al. (2024). The manuscript must identify the origin of this discrepancy (initial conditions, inclusion of hydrodynamics, or numerical treatment) because the shorter period directly determines how many cycles occur within the 2.7 Myr lifetime and therefore the cumulative mass loss.

minor comments (1)

[Abstract] Abstract: the symbols a_in and Hill radius are used without explicit definition on first appearance; a brief parenthetical reminder would improve readability.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their insightful comments, which have helped us identify areas for improvement in our manuscript. We provide point-by-point responses to the major comments below and outline the revisions we will make.

read point-by-point responses

Referee: [Abstract] Abstract: the central quantitative claim that the disk loses ∼7% ± 2% of its mass every vZLK cycle, followed by linear extrapolation to ∼4 Myr (leaving 1% mass), is load-bearing for the proposed explanation of absent Brγ emission. The rate is extracted from a limited number of cycles in short runs; no test is presented demonstrating that the fractional loss remains constant once surface density has dropped by tens of percent, which could alter torques, burst amplitude, or allow viscosity/cooling to dominate.

Authors: We recognize the importance of verifying that the fractional mass-loss rate does not change significantly as the disk depletes. Our simulations captured the mass loss over several vZLK cycles, showing consistent bursts. To strengthen this, we will conduct additional simulations with reduced initial disk mass to simulate later stages and confirm the rate's constancy. This analysis will be added to the Results section of the revised manuscript. revision: yes
Referee: [Methods/Results] Methods/Results: no information is supplied on the hydrodynamical resolution (particle number or grid scale), time-stepping criteria, or convergence tests for the mass-loss measurement. Without these, it is impossible to assess whether the reported 7% ± 2% rate is numerically converged or sensitive to setup choices, undermining in the extrapolation.

Authors: We will expand the Methods section to provide the hydrodynamical resolution details, time-stepping criteria, and results from convergence tests for the mass-loss measurement. This will allow assessment of the numerical robustness of the reported rate. revision: yes
Referee: [Abstract and Results] Abstract and Results: the vZLK timescale of 62.5 kyr is stated to be two orders of magnitude shorter than the value in Peisker et al. (2024). The manuscript must identify the origin of this discrepancy (initial conditions, inclusion of hydrodynamics, or numerical treatment) because the shorter period directly determines how many cycles occur within the 2.7 Myr lifetime and therefore the cumulative mass loss.

Authors: The shorter vZLK timescale arises because the hydrodynamical evolution allows the disk to settle at a smaller radial extent (5.2 a_in to 0.28 Hill radii) than assumed in the N-body only model of Peisker et al. (2024). This leads to a shorter period in agreement with analytic vZLK theory for the effective separation. We will add an explicit discussion of this origin and a comparison to Peisker et al. in the revised Results section. revision: yes

Circularity Check

0 steps flagged

No circularity: results from direct hydro-gravity integration with explicit extrapolation

full rationale

The paper derives all quantitative claims (disk settling radii 5.2 a_in to 0.28 Hill radii, anti-phase eccentricity, T_vZLK ≈ 62.5 kyr, and ~7% ± 2% mass loss per cycle) from output of AMUSE-coupled gravity + hydrodynamics simulations rather than from any self-referential equations or parameter fits. The secular evolution is stated to be consistent with existing vZLK theory but is not used to derive the simulation results. The forward extrapolation of the measured fractional loss rate to ~4 Myr is presented explicitly as an assumption of constancy and does not reduce to the input data by construction; no self-citation is load-bearing for any uniqueness theorem or ansatz. The derivation chain therefore remains independent of its own outputs.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The work relies on standard Newtonian gravity and ideal hydrodynamics assumptions plus chosen initial conditions for the disk and binary; no new entities are postulated.

free parameters (1)

initial disk mass and radial extent
Chosen to match observed properties of D9; values not specified in abstract but required to initialize the hydrodynamics run.

axioms (1)

domain assumption Newtonian gravity and ideal hydrodynamics suffice to capture the dominant dynamics
Invoked by coupling gravity and hydro solvers in AMUSE without additional physics modules.

pith-pipeline@v0.9.0 · 5760 in / 1517 out tokens · 48942 ms · 2026-05-10T16:56:42.133778+00:00 · methodology

discussion (0)

Reference graph

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