🔭 astrophysics

Building three-dimensional giant stellar models for common envelope simulations

This paper presents a method for constructing three-dimensional red supergiant models for common envelope simulations by transporting 1D data to a 3D grid and mimicking nuclear heating and photospheric cooling, demonstrating that this approach yields stable, vigorously convective stars with realistic pulsations without the need for model relaxation.

Original authors: Ron Schreier (Technion, Israel), Shlomi Hillel (Technion, Israel), Noam Soker (Technion, Israel)

Published 2026-06-11

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CC BY 4.0

Original authors: Ron Schreier (Technion, Israel), Shlomi Hillel (Technion, Israel), Noam Soker (Technion, Israel)

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 trying to simulate a cosmic dance where a small star spirals into the giant, bloated envelope of a massive red star. This event, called a "Common Envelope Evolution," is incredibly complex. To understand it, scientists need a 3D computer model of that giant star that behaves like the real thing.

For a long time, computer models of these stars were like stiff mannequins. Scientists would take a 1D blueprint of a star, put it into a 3D grid, and then "relax" it—essentially forcing the star to stand perfectly still and calm before starting the simulation. The problem? Real giant stars are never still; they pulse, breathe, and churn with convection. When scientists forced the models to be calm, the star's natural movements died out almost immediately, leaving a boring, unrealistic simulation.

The New Approach: Let the Star "Live"
In this paper, the researchers (Schreier, Hillel, and Soker) decided to stop forcing the star to be calm. Instead, they built a model that lets the star do what it naturally does: pulsate and convect.

Think of the star as a giant, glowing balloon. To make their computer model behave like a real balloon, they added two simple "ingredients":

The "Cooling Fan" (Photospheric Cooling): Real stars lose heat from their surface (photosphere). In the computer, the researchers set a rule: any part of the gas that gets too thin (like the outer edge of the balloon) gets cooled down to a chilly 1,000 Kelvin. This mimics the star radiating heat into space.
The "Internal Heater" (Nuclear Energy): Real stars generate massive energy in their cores. The researchers mimicked this by pumping energy into a specific inner shell of the model, matching the exact power output of the real star.

What Happened?
They ran two types of simulations to see how these ingredients changed the star's behavior:

Scenario A: Just the Cooling Fan. When they only cooled the outer edges, the star still pulsed, but the movements slowly faded away, like a swing being pushed once and then slowly stopping.
Scenario B: The Heater AND the Cooling Fan. When they added the internal energy source and the cooling, the star came alive. The pulsations didn't die out; they actually grew slightly stronger over time. The star began to "breathe" with a rhythm of about one year per cycle.

The "Churn" and the "Wobble"
The model didn't just breathe in and out; it also showed convection. Imagine a pot of boiling water where hot bubbles rise and cool water sinks. The researchers saw this same vigorous churning inside their star model.

Furthermore, the star wasn't a perfect sphere. It wobbled and changed shape in complex ways. The researchers noticed that the energy peaks in their data had "split" (like a double peak), suggesting that while the star had a main "heartbeat" (radial pulsation), it was also vibrating in other, more complex directions (non-radial modes). It was like a drum being hit not just in the center, but also off to the side, creating a complex vibration pattern.

The Big Conclusion
The most important takeaway is simple: Don't try to calm the star down.

Previous methods tried to "relax" the model to start with zero movement, but this killed the star's natural life. The authors found that the best way to prepare a giant star for these simulations is to:

Pump energy into the core (to mimic nuclear burning).
Cool the outer edges (to mimic heat loss).
Let it pulsate naturally.

There is no need to force the star to be still. By letting the model pulse and churn just like a real Red Supergiant, the simulation becomes a much more accurate representation of the chaotic, dynamic environment where these cosmic collisions happen.

Technical Summary: Building Three-Dimensional Giant Stellar Models for Common Envelope Simulations

Problem Statement
Common envelope evolution (CEE) simulations face significant challenges due to the vast dynamical range required to resolve both the bloated envelope of an evolved primary star (RGB, AGB, or RSG) and the compact secondary companion. Existing numerical codes often struggle to simultaneously resolve the large envelope, convection, accretion processes, and potential jet launching. A critical limitation in current methodologies is the treatment of the initial stellar model. Many studies transport a 1D stellar model to a 3D grid and then "relax" the model (damping velocities) to start simulations with zero envelope velocity. This approach suppresses the natural pulsations and convection inherent to giant stars, which are known to influence mass loss, accretion rates, and the onset of CEE. Furthermore, previous attempts to simulate unperturbed 3D models without energy input resulted in the rapid decay of oscillations after only two periods, failing to sustain the dynamic state of a real giant star.

Methodology
The authors developed a new approach to constructing 3D red supergiant (RSG) models for CEE simulations using the hydrodynamical code FLASH. The methodology involves transporting a 1D RSG model (derived from MESA, with an initial mass of $15 M_\odot$ and evolved to $12.5 M_\odot$ with a radius of $881 R_\odot$ ) onto a 3D Cartesian grid. Key numerical ingredients include:

No Relaxation: Unlike previous studies, the model is not relaxed; it is allowed to evolve with its natural velocities, permitting pulsation.
Inert Core: To save computational time, an inner inert sphere ( $R_{inert} = 0.2 R_{RSG}$ ) is kept static, while the envelope is evolved dynamically.
Mimicking Photospheric Cooling: To simulate radiative energy loss, numerical cells with densities below a set "numerical photospheric density" ( $\rho_{ph} = 2 \times 10^{-9}$ g cm $^{-3}$ ) are cooled to a "numerical chromospheric temperature" ( $T_{ch} = 1000$ K).
Mimicking Nuclear Energy: To simulate core nuclear power, energy is deposited at a rate equal to the 1D stellar luminosity ( $L \approx 7 \times 10^4 L_\odot$ ) into an inner shell located just above the inert core ( $201 R_\odot < r < 230 R_\odot$ ).
Boundary Conditions: A spherical numerical boundary is imposed at $1.63 R_{*,0}$ to prevent grid boundary effects, with a slow radial outflow velocity set beyond this radius to mimic a wind (though detailed wind modeling is reserved for future work).

The study compares two primary scenarios: one with only photospheric cooling and one with both photospheric cooling and energy deposition.

Key Results

Sustained Pulsation: In simulations lacking energy deposition, oscillations decayed after approximately two periods (roughly 3 years). However, when both photospheric cooling and energy deposition were included, the oscillations did not decay; instead, their amplitude slowly increased over time.
Pulsation Period: The main pulsational period was found to be approximately 1 year, comparable to the stellar dynamical time ( $\tau_d \approx 0.76$ yr), suggesting a fundamental radial pulsation mode.
Non-Radial Modes: The stellar model exhibited non-spherical structures and rapid, low-amplitude temporal variations in the average stellar radius. Analysis of kinetic energy graphs revealed splitting of peaks and troughs, which the authors attribute to the presence of non-radial oscillation modes superimposed on the fundamental radial mode.
Convection: The models successfully reproduced vigorous convection, characteristic of RSG stars. Tracer maps indicated that convection mixed the envelope gas on a timescale of approximately 3 years (about four dynamical times), rendering initially distinct shells indistinguishable.
Velocity Structure: Velocity maps showed magnitudes of $30-50$ km s $^{-1}$ , consistent with Keplerian velocities at the stellar surface, confirming the development of vigorous convection.

Significance and Claims
The paper concludes that the optimal method for preparing a giant star for CEE and grazing-envelope evolution simulations is to deposit energy in an inner shell to mimic nuclear luminosity and cool the outer low-density numerical shell to mimic photospheric emission. Crucially, the authors assert that there is no need to relax the model. Allowing the stellar model to pulsate naturally, rather than damping it to a static state, provides a more realistic representation of the dynamic environment (pulsation and convection) that influences mass accretion and interaction with a companion. This approach addresses the need for realistic initial conditions in simulations that aim to study the complex interplay of jets, accretion, and envelope ejection in binary systems.

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