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The YREC Stellar Evolution Code: Public Data Release

This paper announces the public release of the Yale Rotating Evolution Code (YREC), a versatile stellar evolution tool covering brown dwarfs and stars from pre-main sequence to helium burning, accompanied by comprehensive documentation, input libraries, and educational resources.

Original authors: Marc H. Pinsonneault, Jennifer L. van Saders, Lyra Cao, Jamie Tayar, Franck Delahaye, Leslie M. Morales, Rachel A. Patton, Matthew C. Rendina, Joel C. Zinn, Zachary R. Claytor, Amanda L. Ash, Susan By

Published 2026-03-30

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CC BY 4.0

Original authors: Marc H. Pinsonneault, Jennifer L. van Saders, Lyra Cao, Jamie Tayar, Franck Delahaye, Leslie M. Morales, Rachel A. Patton, Matthew C. Rendina, Joel C. Zinn, Zachary R. Claytor, Amanda L. Ash, Susan Byrom, Kaili Cao, Vincent A. Smedile

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 you have a time machine, but instead of visiting the past, you can fast-forward or rewind the life of a star. You want to see how a baby star is born, how it grows up, how it ages, and how it eventually dies.

This paper is essentially the user manual and public release for a very sophisticated time machine called YREC (Yale Rotating Evolution Code). For over 60 years, scientists have used this code to simulate the lives of stars, but until now, it was like a secret recipe kept in a locked kitchen. The authors are now throwing open the doors, handing out the recipe, the ingredients, and the instructions so anyone can cook up their own stellar simulations.

Here is a breakdown of what this paper is about, using some everyday analogies:

1. What is YREC? (The Star Simulator)

Think of a star as a giant, glowing pressure cooker. Inside, it's a chaotic mix of nuclear explosions (fusion), gravity trying to crush it, and heat trying to blow it apart. YREC is a computer program that solves the math equations describing this pressure cooker.

The Scope: It can simulate stars from the size of Jupiter (brown dwarfs) all the way up to massive giants, covering their entire life from "birth" (pre-main sequence) to "retirement" (burning helium).
The Goal: The authors want to show that this code is fast, accurate, and ready for both professional researchers and students to use.

2. How Does It Work? (The Puzzle Solver)

Simulating a star is like trying to solve a massive, shifting jigsaw puzzle where the pieces keep changing shape.

The "Relaxation" Method: Imagine you have a wobbly table. You keep adjusting the legs until it's perfectly flat. YREC does this with stars. It starts with a guess, calculates the physics, sees where the balance is off, and tweaks the numbers until the star is in perfect "hydrostatic equilibrium" (gravity and pressure are perfectly balanced).
The Layers: Stars have layers like an onion. The code calculates what's happening in the core, then the middle, then the surface, and repeats this process billions of times to see how the star changes over millions of years.

3. What Makes YREC Special? (The Customizable Engine)

The paper highlights that YREC isn't just a "one-size-fits-all" engine. It's highly customizable, like a video game where you can change the physics rules.

Spinning Stars: Real stars spin, and that spinning changes their shape and how they mix their ingredients. YREC can simulate this "dance," including how fast they spin down as they age.
Sunspots (The Freckles): Just like the Sun has dark spots, other stars have them too. These spots can make a star look cooler or bigger than it really is. YREC can add these "freckles" to the simulation to see how they affect the star's life.
The "Secret Sauce" (Microphysics): The code uses detailed tables for things like how light moves through gas (opacity) and how atoms behave under pressure. The authors updated these tables to be the best available science.

4. The "Test Drive" (Proving It Works)

You wouldn't buy a car without a test drive. The authors ran YREC on a "Test Suite" to prove it works.

The Solar Calibration: They ran a simulation of our own Sun. The result? It matched the real Sun's size, brightness, and even the neutrinos (ghostly particles) it emits almost perfectly.
Comparing to Rivals: They compared YREC to other famous star codes (like MESA). They found that YREC is often much faster (sometimes 8 to 50 times faster!) while still being just as accurate for most stars. It's like YREC is a sports car, while others are heavy trucks.
The "Hard" Stuff: They showed it can handle tricky situations, like the "Helium Flash" (a violent explosion in the core of aging stars) and the complex lives of red giants.

5. Why Should You Care? (Education and Discovery)

The paper emphasizes that this isn't just for PhDs in dark rooms.

For Students: They created a web version called "yreclab." Imagine a website where you can click buttons to change a star's mass or spin, hit "Run," and watch it evolve in real-time right in your browser. It's like a virtual science lab for anyone with an internet connection.
For Researchers: They released scripts (automated tools) that let scientists run thousands of simulations at once to build "isochrones" (charts that help astronomers figure out the age of star clusters).

6. The "Fine Print" (Limitations)

The authors are honest about the code's flaws.

It's not magic: If you ask it to simulate a star that spins so fast it flies apart, it will crash. It follows the rules you give it, even if those rules are silly.
Specific Domains: It works best for low-to-medium mass stars. For the most massive, violent stars, or the very smallest brown dwarfs, you have to be careful with the settings.
Old Code: The code is written in an older programming language (Fortran). It's powerful but can be a bit clunky to modify compared to modern software. The authors promise to make it easier to tweak in the future.

The Big Picture

This paper is an invitation. The authors are saying, "We've built a powerful tool to understand the universe's most beautiful objects. We've tested it, we've fixed the bugs, and we've made it easy to use. Now, it's your turn to explore the stars."

Whether you are a student trying to understand why stars shine, or an astronomer trying to date a distant galaxy, YREC is now open for business.

1. Problem Statement

Stellar structure and evolution theory relies on solving complex systems of differential equations involving conservation laws, thermodynamics, nuclear physics, and fluid dynamics. While numerous stellar evolution codes have been developed over the last 60 years, the landscape of publicly available, open-source tools remains limited. Major codes like MESA (Modules for Experiments in Stellar Astrophysics) are widely used, but others (e.g., CESAM, Eggleton STARS, ESTER) are either less accessible or have different optimization goals.

There is a specific need for a robust, fast, and precise code optimized for hydrostatic stars ranging from brown dwarfs to intermediate-mass stars, covering evolution from the pre-main sequence (pre-MS) through core helium burning. Existing public tools often lack specific capabilities regarding rotation, magnetic activity (starspots), or specific numerical efficiencies required for large-scale population studies and gyrochronology. This paper addresses the gap by releasing the Yale Rotating Evolution Code (YREC) to the public, documenting its physics, numerical methods, and performance.

2. Methodology

The paper details the architecture, physics inputs, and numerical approach of YREC, a code with origins in the 1960s that has been continuously updated.

A. Numerical Approach

Algorithm: YREC is a relaxation code utilizing the Henyey technique. It converts coupled stellar structure equations into finite difference equations.
Boundary Conditions:
- Inner: Uses Taylor series expansion at the center to avoid divergence.
- Outer: Unlike MESA, which often fits at the base of the atmosphere, YREC uses a fitting point well below the photosphere (typically $10^{-4}$ to $10^{-7} M_{\odot}$ below the surface). It integrates an envelope solution and matches it to interior solutions using an "envelope triangle" interpolation method based on $L$ and $T_{\text{eff}}$ .
Iteration: The code employs up to four iterative loops:
1. Fixed Surface Boundary Conditions (SBCs).
2. Floating SBCs (dynamic envelope triangle).
3. (Optional) Recomputing composition changes using end-of-timestep structure.
4. (Optional) Iterating between rotation, diffusion, and structure solutions.
Mesh: Adaptive meshing reallocates spatial points based on gradients in mass, luminosity, and pressure, with specific flags to prevent rezoning across discontinuities.

B. Input Physics

YREC incorporates modern microphysics with user-configurable options:

Equation of State (EoS): Supports OPAL (2005 update), SCV (Saumon-Chabrier-Van Horn), and the legacy Yale EoS. It includes a tie-breaker algorithm to switch between tables based on density and temperature regimes.
Opacity: Uses conductive opacities (Cassisi et al.), molecular opacities (Ferguson et al. for $T < 4000$ K), and atomic opacities (OPAL and OP tables).
Nuclear Reactions: Tracks non-equilibrium burning for H, He, and CNO cycles. Uses rates from Solar Fusion II (Adelberger et al.) and Solar Fusion III (Acharya et al.).
Convection: Uses Mixing Length Theory (MLT) with Schwarzschild criterion. Includes step overshoot (limited by core size) and semi-convection (Castellani et al. approach).
Rotation & Mixing:
- Treats rotation via a pseudo-2D approximation (Kippenhahn & Thomas technique) assuming uniform rotation on equipotential surfaces.
- Includes angular momentum transport via meridional circulation, shear instabilities, and Goldreich-Schubert-Fricke instability.
- Supports magnetic braking laws (Kawaler, van Saders & Pinsonneault) and star-spot physics (flux blocking and modified SBCs).
Diffusion: Includes microscopic diffusion (gravitational settling and thermal diffusion) for He and metals, following the Thoul et al. implementation of Burgers' equations.

C. Software Infrastructure

Language: Written in Fortran 77 (compatible with F90).
Release: Hosted on GitHub with input tables, starting models, and documentation.
Tools: Includes Python wrappers for grid generation, solar calibration, and a WebAssembly interface (yreclab) for interactive, client-side execution.
Tracer Code: Includes rotevol, a fast tracer code that generates angular momentum evolution scenarios from pre-computed non-rotating tracks, reducing computation time by two orders of magnitude.

3. Key Contributions

Public Release of YREC: The first comprehensive public release of the code, including source, input libraries, and extensive documentation.
Performance Benchmarking: Demonstrated that YREC is significantly faster than MESA (approx. 8x faster on pre-MS, 2x on MS, and 6x on post-MS) at similar mesh resolutions, making it ideal for large population synthesis.
Starspot Physics: Detailed implementation of starspot effects (filling factors and temperature contrast) on stellar structure, crucial for modeling young, active stars and radius inflation.
Gyrochronology Framework: Provided calibrated models for angular momentum loss, including different braking laws and internal transport mechanisms, validated against open cluster data.
Isochrone Generation (ISTARY): Demonstrated the creation of isochrones using the kiauhoku interpolator, validated against open clusters (Pleiades, M67).
Educational Tools: Highlighted the utility of yreclab for teaching, allowing students to run and visualize stellar evolution in real-time via a web browser.

4. Results

Solar Models: YREC produces high-precision solar models that match helioseismic sound speed profiles and neutrino fluxes within 1% when including diffusion and appropriate mixtures (GS98).
Evolutionary Tracks:
- Low Mass ( $<1 M_{\odot}$ ): Shows good agreement with eclipsing binary data. Discrepancies with other codes (MIST, PARSEC) at the lowest masses are attributed to differences in EoS and surface boundary conditions.
- Intermediate/High Mass: Tracks for $1-9 M_{\odot}$ show consistency with PARSEC and MIST in luminosity and temperature, though differences arise in core helium burning due to overshooting treatments.
- Horizontal Branch: YREC models exhibit "breathing pulses" and stepwise helium ingestion due to overshooting, leading to longer horizontal branch lifetimes compared to PARSEC v2.0.
Rotation: Models successfully reproduce the spin-down of solar-mass stars in open clusters (gyrochronology) and the core-envelope decoupling observed in red giants via asteroseismology.
Starspots: Models with starspots successfully explain radius inflation and lithium depletion anomalies in young, active stars (e.g., in the Pleiades).

5. Significance

Research Utility: YREC fills a niche for fast, precise stellar evolution specifically optimized for low-to-intermediate mass stars. Its speed advantage over MESA makes it uniquely suited for generating large grids for galactic archaeology, exoplanet host characterization, and asteroseismic modeling where computational cost is a bottleneck.
Educational Impact: The yreclab web interface democratizes access to stellar evolution modeling, allowing for interactive learning without local compilation or high-performance computing resources.
Community Standard: By releasing the code and a comprehensive test suite, the authors provide a baseline for regression testing and code comparison, fostering transparency and reproducibility in stellar astrophysics.
Limitations & Future Work: The paper candidly outlines limitations, such as the inability to evolve through the helium flash (requiring a two-step rescaling procedure), lack of support for thermally pulsing AGB phases, and numerical challenges with microscopic diffusion in thin convective envelopes. Future updates aim to improve convective boundary treatments and mass loss physics.

In summary, this paper establishes YREC as a state-of-the-art, open-source tool for stellar astrophysics, balancing historical robustness with modern physics implementations, and offering significant advantages in speed and specific physical treatments (rotation, spots) for the community.