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Weakened Inspirals I: High Mass Ratio Common Envelope Interactions in RGB Stars

This study utilizes 3D hydrodynamical simulations to demonstrate that while high mass-ratio common envelope interactions in red giant branch stars produce wider post-interaction separations and stable fallback-formed circumbinary discs, the resulting orbital distances remain too small to explain the existence of observed wide post-giant binaries.

Original authors: Jack Nibbs, Orsola De Marco, Lionel Siess, Ryosuke Hirai, Daniel Price

Published 2026-04-20

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CC BY 4.0

Original authors: Jack Nibbs, Orsola De Marco, Lionel Siess, Ryosuke Hirai, Daniel Price

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine two stars dancing in a cosmic waltz. One is a giant, bloated old star (a Red Giant), and the other is a smaller, tighter companion. Usually, when the giant gets too big, it swallows its partner, leading to a chaotic crash that shrinks their orbit until they are almost touching. This is called a Common Envelope (CE) event.

However, astronomers have found many of these "post-giant" pairs that are still dancing far apart, with wide orbits and a ring of gas around them. This is a mystery: if they went through a crash, they should be much closer together.

This paper asks a simple question: What if the partner star is much heavier than we thought?

Here is the story of their investigation, explained through everyday analogies.

1. The Setup: The "Heavy Partner" Experiment

The researchers used a supercomputer to simulate this dance. They took a standard Red Giant (about the size of our Sun's orbit, but very fluffy) and paired it with companions of different weights.

The Variable: They changed the Mass Ratio ( $q$ ). Think of this as the weight difference between the two dancers.
- Low $q$ : The partner is light (like a child dancing with an adult).
- High $q$ : The partner is heavy (like two adults, or even a heavyweight champion dancing with the giant).

They ran 12 different simulations, some with "light" partners and some with "heavy" partners, to see if a heavier partner changes the outcome of the crash.

2. The Dance: What Happened?

When the giant star starts to overflow its "rope" (the Roche lobe) and spill gas onto the partner, two things can happen:

The Crash (Standard CE): The gas drags the partner in, they spiral together violently, and the orbit shrinks massively.
The Stabilized Dance (The Goal): The partner is heavy enough to handle the gas without spiraling in immediately.

The Findings:

Heavier Partners = Slower Crashes: When the partner was heavier (high mass ratio), the spiral-in happened much more slowly. It was like the heavy partner had better "grip" on the dance floor, resisting the drag.
The "Pre-Crash" Phase: Before the actual crash, there was a long period of stable mass transfer. The heavier the partner, the longer this stable phase lasted.
The Result: Even with the heaviest partners, the final orbit was still too small to explain the real stars astronomers see in the sky. The simulations showed the stars ending up about 50 times the size of our Sun apart, but the real stars are often 100 to 200 times that size.

The Analogy: Imagine trying to stop a runaway train (the giant star) by throwing a heavy anchor (the companion) on the tracks. A heavier anchor slows the train down more effectively, but in this simulation, even the heaviest anchor couldn't stop the train from crashing completely; it just made the crash less violent.

3. The Ring of Gas: Did a Disc Form?

Astronomers also see a ring of gas (a circumbinary disc) around these stars. There are two ways this ring could form:

Spilling Over the Side: Gas spills out the back of the system (through Lagrange points L2 and L3) and forms a ring immediately.
The "Fall-Back": Gas is ejected during the crash, but some of it doesn't escape completely. It loops back around and settles into a ring.

The Findings:

Spilling Over: The simulations showed that when gas spills out the back, it usually gets blasted away by the subsequent crash. It's like trying to build a sandcastle while a tsunami is coming; the wave (the crash) sweeps the sand (the gas) away.
The Fall-Back: This was the winner. About 1% to 5% of the giant's gas didn't escape. It fell back toward the stars over a few hundred years.
The Result: This falling gas formed a ring. Interestingly, the simulations predicted rings that look very much like the ones we observe in real life (spreading out to about 1 to 20 times the Earth-Sun distance).

4. The Big Picture: Why This Matters

The paper concludes that while having a heavy companion helps stabilize the dance and creates wider orbits than usual, it isn't the magic bullet that explains all the wide-orbit stars we see. The orbits in the simulation were still too tight.

However, the study confirmed that:

Heavy partners make the crash "weaker."
The "fall-back" mechanism is a very likely way to create the gas rings we see around these stars.

The Takeaway

Think of this paper as testing different "brakes" for a runaway cosmic dance. The researchers found that a heavier partner acts like a better brake, slowing the crash and leaving a nice gas ring behind. But even with the best brakes they tested, the dance floor was still too small compared to what we see in the universe.

This suggests that while heavy partners help, there might be other factors (like the specific type of giant star, or how the gas cools down) that we need to understand in future studies to solve the full mystery of these wide-orbit stellar couples.

1. Problem Statement

Post-red giant branch (post-RGB) and post-asymptotic giant branch (post-AGB) binary systems with main-sequence companions are observed to have wide orbital separations ( $\sim$ 0.5–4 au), significant eccentricities (up to 0.6), and circumbinary discs. Standard Common Envelope (CE) evolution models predict that when a giant star fills its Roche lobe, the resulting unstable mass transfer leads to a rapid dynamical inspiral, leaving the binary with a much tighter orbit (typically $<30 R_\odot$ ) and a circularized orbit.

The discrepancy between observed wide separations and the tight orbits predicted by standard CE theory suggests that the CE phase in these systems may be "weakened" or avoided entirely. Previous analytical work suggests that high mass ratios ( $q = M_{\text{companion}}/M_{\text{donor}}$ ) could stabilize mass transfer, potentially preventing a full CE inspiral. However, this hypothesis lacked rigorous 3D hydrodynamic verification. This study investigates whether high mass ratios ( $q \approx 0.68 - 1.5$ ) can lead to wider post-CE separations and the formation of circumbinary discs, thereby explaining the observed properties of post-RGB/AGB binaries.

2. Methodology

The authors performed a suite of 12 3D hydrodynamic simulations using the Smoothed Particle Hydrodynamics (SPH) code PHANTOM.

System Configuration:
- Donor: A $0.88 M_\odot$ Red Giant Branch (RGB) star with a radius of $90 R_\odot$ and a core mass of $0.392 M_\odot$ .
- Companion: Point-mass companions with varying masses to achieve mass ratios $q = M_2/M_1$ ranging from 0.68 to 1.5.
- Initial Conditions: Circular orbits ( $e=0$ ) starting exactly at Roche lobe contact.
Simulation Parameters:
- Resolution: Two resolutions were used: Low ( $\sim$ 76,000 particles) and High ( $\sim$ 531,000 particles).
- Equation of State (EoS): Two EoS models were tested:
  1. Ideal Gas: Adiabatic, no recombination energy.
  2. Tabulated (MESA): Includes recombination energy, which provides additional thermal energy to the envelope, aiding unbinding.
- Total Simulations: 4 mass ratios $\times$ 2 resolutions $\times$ 2 EoS (with some variations for specific EoS testing).

3. Key Contributions

Systematic Exploration of High $q$ : This is the first study to systematically simulate CE interactions with mass ratios up to $q=1.5$ in the context of RGB stars, moving beyond the typical $q < 1$ regime.
Resolution and EoS Dependence: The study rigorously compares how simulation resolution and the inclusion of recombination energy affect the unbinding of the envelope and the duration of the pre-inspiral phase.
Disc Formation Mechanisms: The paper distinguishes between two potential mechanisms for circumbinary disc formation: (1) mass ejection through outer Lagrange points ( $L_2/L_3$ ) during the pre-inspiral phase, and (2) the fallback of bound envelope material after the interaction.

4. Key Results

A. Orbital Evolution and Mass Transfer Stability

Pre-Insipral Phase: Higher mass ratios ( $q$ ) lead to a significantly longer stable mass transfer phase before the dynamical inspiral begins. For $q \gtrsim 1$ , the mass transfer becomes more stable, consistent with analytical predictions (Tout 1991).
Final Separation: While higher $q$ values result in wider final separations compared to low $q$ cases, the predicted maximum separation is only $\sim 50 R_\odot$ (for $q \approx 1$ ). Even the extreme $q=1.5$ simulation (150MH) only reached $\sim 140 R_\odot$ after a very shallow inspiral, which is still smaller than the observed separations of post-RGB binaries ( $\sim 100-200 R_\odot$ ).
Convergence: The duration of the pre-inspiral phase is not converged with resolution; higher resolution leads to longer stable phases. The final orbital separation, however, appears converged.

B. Envelope Unbinding

Resolution Effects: Higher resolution simulations unbind less mass than lower resolution ones (an artifact of numerical diffusion in lower resolutions).
EoS Effects: Simulations using the Tabulated EoS (including recombination energy) unbind the vast majority of the envelope, whereas Ideal Gas simulations retain more bound mass.
High $q$ Behavior: For $q=1.5$ , the envelope can be unbound almost entirely without a deep dynamical inspiral, suggesting that stable mass loss driven by recombination energy could strip the giant's envelope in real systems.

C. Circumbinary Disc Formation

L2/L3 Ejection: The study found that mass ejected through the $L_2$ and $L_3$ Lagrange points during the pre-inspiral phase is largely unbound (especially in Tabulated EoS simulations) or swept away by the subsequent CE ejecta. Consequently, disc formation via direct $L_2/L_3$ ejection is unlikely to survive the CE phase.
Fallback Discs: The primary mechanism for disc formation identified is the fallback of bound material after the interaction.
- Timescales: Fallback occurs on timescales of a few hundred to $\sim 1000$ years.
- Disc Size: The resulting fallback discs have radii ranging from 0.5 to 5 au (depending on EoS and $q$ ), which aligns well with observed circumbinary discs around post-RGB/AGB stars.
- Mass: The mass of these fallback discs (0.003–0.34 $M_\odot$ ) is consistent with observed disc masses, provided a small fraction of the envelope remains bound.

5. Significance and Conclusions

Weakened CE: The study confirms that high mass ratios can "weaken" the CE interaction, extending the pre-inspiral phase and resulting in wider final separations than low-mass-ratio cases. However, even with high $q$ , the resulting separations are generally too small to fully explain the observed population of wide post-RGB binaries solely through CE evolution.
Disc Origin: The research concludes that circumbinary discs in these systems are likely formed by the fallback of bound envelope material rather than direct ejection through Lagrange points.
Future Directions: The authors suggest that the observed wide separations might require additional physics not fully captured here, such as more realistic stellar surface cooling (which could stabilize mass transfer at lower $q$ ) or interactions with AGB stars (which have lighter envelopes).
Implication: While high mass ratios help, they are likely not the sole solution to the "wide separation" problem in post-RGB binaries. The paper sets the stage for a follow-up study on AGB stars (Paper II) and suggests that a combination of high $q$ and other stabilizing mechanisms is necessary to reproduce the observed systems.