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Using Lithium and Beryllium to Study Structure and Evolution of Rotating Stars: Spite Plateau of Halo Stars

By employing stellar models that incorporate rotation, magnetic fields, gravitational settling, and diffusion, this study demonstrates that the observed Spite plateau and subsequent lithium depletion in Galactic halo stars can be explained by stellar evolution processes, thereby resolving the cosmological lithium problem without invoking new physics.

Original authors: Wuming Yang, Shuya Dou, Xiangcun Meng, Yaqian Wu, Shaolan Bi

Published 2026-02-27

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CC BY 4.0

Original authors: Wuming Yang, Shuya Dou, Xiangcun Meng, Yaqian Wu, Shaolan Bi

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

The Cosmic Mystery: The "Missing" Lithium

Imagine the universe as a giant bakery that opened 13.8 billion years ago. When it first opened, the "Big Bang" baked a specific recipe of ingredients. According to the master bakers (physicists who study the Big Bang), the recipe should have produced a lot of Lithium (a light, fragile element).

However, when we look at the oldest stars in our galaxy (the "halo stars"), they seem to have only about one-third of the Lithium that the recipe predicted. It's like baking a cake that should have 12 eggs, but when you cut it open, you only find 4. This is known as the "Cosmological Lithium Problem."

For decades, scientists wondered: Did the Big Bang recipe get it wrong? Or is something happening to the stars that is hiding the Lithium?

The Solution: The Stellar "Mixing Bowl"

This paper argues that the Big Bang recipe was actually correct. The missing Lithium isn't gone; it's just been hidden or destroyed inside the stars themselves.

To understand this, imagine a star is like a giant, swirling pot of soup (the Convection Zone).

The Surface: The top of the soup is cool and safe.
The Deep: The bottom of the pot is incredibly hot. If you drop a piece of Lithium into the deep, hot part, it gets "burned up" (destroyed) instantly.

In the old models, scientists thought the soup was just sitting there, and the Lithium stayed safely on top. But this paper says: No, the soup is being stirred.

The New Theory: The "Stirring Spoon" (Rotation and Magnetism)

The authors used a super-computer to simulate stars that are spinning and have magnetic fields. They found that these two forces act like a giant stirring spoon inside the star.

Here is how the "Stirring Spoon" solves the mystery:

The Gravity Sink: Inside the star, heavy elements (like Lithium) naturally want to sink to the bottom, like sand in water. This is called gravitational settling. In a non-spinning star, the Lithium sinks down, gets burned, and disappears from the surface.
The Stirring Effect: But in a spinning star, the rotation and magnetic fields create turbulence. This turbulence acts like a spoon, constantly stirring the soup. It pulls the Lithium that is trying to sink back up to the surface, and pushes fresh Lithium down to be burned.
The Balance: The paper shows that for the oldest stars (which are spinning slowly), this stirring is just strong enough to keep the Lithium level steady at about 2.0 to 2.4 (on a logarithmic scale). It doesn't let it drop to zero, but it prevents it from staying at the original "Big Bang" level of 2.72.

The Analogy: Think of a child trying to keep a toy boat (Lithium) floating in a bathtub.

Old Theory: The child does nothing. The boat sinks to the bottom and gets crushed.
New Theory: The child gently stirs the water. The boat keeps sinking, but the stirring keeps bringing it back up. The boat never stays at the bottom long enough to be crushed, but it never stays perfectly at the surface either. It hovers in a "Goldilocks zone."

Why Do Some Stars Have Less Lithium?

The paper also explains why some stars have even less Lithium than others. It depends on the size of the star and how metal-poor it is.

The "Shallow Pot": Hotter, more massive stars have a very shallow "soup pot" (a thin outer layer). Because the pot is shallow, the "stirring spoon" can't reach deep enough to save all the Lithium. The Lithium sinks too fast and gets burned. These stars end up with very low Lithium.
The "Deep Pot": Cooler, smaller stars (like our Sun) have a deep soup pot. The Lithium has to travel a long way to get burned. The stirring helps, but because the pot is so deep, the Lithium still gets depleted significantly. This explains why our Sun has very little Lithium left.

The "Spite Plateau" and the "Meltdown"

The paper successfully recreates a famous observation called the Spite Plateau.

The Plateau: Imagine a flat table. Most old stars have the exact same amount of Lithium, no matter how old they are. The paper shows that the "stirring" creates this flat table.
The Meltdown: If you look at stars that are extremely metal-poor (very old and pure), the "pot" gets so shallow that the stirring can't save the Lithium anymore. The Lithium level crashes. The paper predicts this crash, matching what astronomers see in the most ancient stars.

The Beryllium Connection

The paper also looked at Beryllium (a cousin of Lithium). Beryllium is even tougher to burn than Lithium; it needs a hotter fire.

Because it needs more heat to burn, Beryllium survives deeper in the star.
The "stirring" affects Beryllium differently, creating a slightly different pattern. The paper's models successfully predicted these patterns too, proving that the "stirring" theory works for multiple elements, not just Lithium.

The Big Conclusion

The authors conclude that we don't need new physics to explain the missing Lithium. We don't need to rewrite the laws of the Big Bang.

Instead, the "missing" Lithium is simply a result of stellar housekeeping. The stars are spinning, they have magnetic fields, and they are constantly mixing their interiors. This process slowly eats away at the Lithium over billions of years, leaving us with the lower levels we see today.

In short: The universe baked the right amount of Lithium. The stars just ate most of it before we could count it.

1. Problem Statement

The paper addresses the Cosmological Lithium Problem, a long-standing discrepancy in astrophysics.

The Discrepancy: Standard Big Bang Nucleosynthesis (BBN) combined with Cosmic Microwave Background (CMB) data predicts a primordial Lithium-7 ( $^7$ Li) abundance of $A(\text{Li}) \approx 2.72$ dex. However, observations of metal-poor Galactic halo stars (Population II) reveal a nearly constant surface abundance known as the Spite Plateau, with values ranging only from 2.0 to 2.4 dex.
The Challenge: This observed value is approximately a factor of three lower than the BBN prediction. The lack of dispersion along the plateau and the existence of a "meltdown" (a sharp drop in Li) in extremely metal-poor stars ( $[\text{Fe/H}] \lesssim -3$ ) and deviations in Beryllium (Be) abundances suggest that standard stellar models are insufficient.
The Question: Can the same physical mechanisms responsible for solar lithium depletion (gravitational settling, diffusion, rotation, and magnetic fields) explain the Spite Plateau and the observed Li/Be distributions in halo stars, thereby resolving the cosmological Li problem without invoking new physics?

2. Methodology

The authors employed the Yale Rotating Stellar Evolution Code (YREC) to compute detailed stellar evolutionary models.

Physics Inputs:
- Equation of State & Opacity: OPAL EOS2005 and OPAL opacity tables (supplemented by Ferguson et al. low-T tables), reconstructed for specific mixtures (including $\alpha$ -element enhancement).
- Transport Mechanisms: The models explicitly include gravitational settling, diffusion (using Thoul et al. coefficients), rotational mixing, and magnetic fields.
- Angular Momentum Transport: Treated as a diffusion process involving dynamical instabilities, secular shear instability, and magnetic fields (Spruit's dynamo).
- Boundary Conditions: A tachocline (width $0.05R$ ) is assumed below the convection zone (CZ). Magnetic braking and disk-locking (5 Myr timescale) are included for the pre-main sequence (pre-MS) phase.
- Nuclear Burning: Li, Be, and B burning rates are computed as functions of temperature, assuming complete destruction above $10^7$ K.
Model Parameters:
- Initial Conditions: Initial Li abundance set to the BBN prediction ($2.72$ dex). Initial Be and B abundances assumed to follow solar values or a metallicity-dependent relation.
- Stellar Properties: Models cover masses $M < 1.0 M_\odot$ , initial metallicities $[\text{Fe/H}]_0$ from $-0.7$ to $-2.0$, and ages up to 13 Gyr.
- Calibration: Mixing efficiency parameters ( $f_\Omega, f_c, f_m, f_{cm}$ ) are calibrated to reproduce the solar rotation profile, surface helium abundance, and observed solar Li/Be depletion.
Comparative Approach: The study compares Rotating Models (RMs) against Non-Rotating Models (NMs) to isolate the effects of rotation and magnetic fields.

3. Key Contributions

Unified Explanation: The paper demonstrates that the Spite Plateau and the solar Li depletion can be explained by the same physical mechanisms (gravitational settling + rotational mixing + magnetic fields), suggesting the Li problem is astrophysical rather than cosmological.
Mechanism of Plateau Formation: It identifies that the Spite Plateau is not a primordial constant but a result of a dynamic equilibrium where rotational mixing partially counteracts gravitational settling, smoothing the Li gradient below the convection zone.
Reproduction of Complex Features: The models successfully reproduce not only the main Spite Plateau but also:
- The "meltdown" of the plateau in very metal-poor stars.
- The deviation in Be abundances for stars with $[\text{Fe/H}] \approx -3$ .
- The second Li plateau observed in Red Giant Branch (RGB) stars ( $A(\text{Li}) \approx 1.0$ dex).
Role of Metallicity: The study clarifies how metallicity affects the depth of the convection zone (CZ), thereby altering the efficiency of gravitational settling and the resulting Li abundance trends.

4. Key Results

Formation of the Spite Plateau:
- For stars with ages 8–13 Gyr and effective temperatures $T_{\text{eff}} \in [5900, 6400]$ K, RMs predict Li abundances between 2.0 and 2.4 dex.
- Mechanism: In these stars, gravitational settling creates a negative Li gradient below the CZ. Rotational mixing (calibrated to the Sun) transports Li from deeper layers back into the CZ, mitigating depletion and smoothing the gradient. This results in a nearly flat Li profile that remains stable for gigayears.
- Contrast with NMs: Non-rotating models fail to reproduce the plateau; they predict a steep decline in Li followed by a sharp rise as the CZ deepens (dredge-up), inconsistent with observations.
Temperature and Mass Dependence:
- Hotter Dwarfs ( $T_{\text{eff}} \gtrsim 6000$ K): Shallow CZs lead to strong gravitational settling. Rotation mitigates this, keeping Li high.
- Cooler Dwarfs ( $T_{\text{eff}} \lesssim 5800$ K): Deeper CZs and higher base temperatures ( $T_{\text{BCZ}}$ ) allow rotational mixing to transport Li into hotter regions where it is efficiently burned, enhancing depletion. This explains why cooler dwarfs have lower Li.
Metallicity Effects:
- Lower metallicity leads to shallower CZs and more efficient gravitational settling.
- Very metal-poor stars ( $[\text{Fe/H}] \lesssim -2.5$ ) exhibit Li abundances below the plateau (the "meltdown") because the CZ is too shallow for rotational mixing to counteract settling effectively.
- The slope of the Spite Plateau ( $A(\text{Li})$ vs. $T_{\text{eff}}$ ) becomes steeper at lower metallicities.
Beryllium and Boron:
- Be and B have higher burning temperatures than Li. Consequently, their dilution occurs at lower $T_{\text{eff}}$ (later in evolution).
- The models reproduce the observed Be plateau and its deviation in extremely metal-poor stars, confirming that Be depletion is driven by the same rotational/settling physics.
RGB Evolution:
- As stars evolve to the RGB, the CZ deepens rapidly, diluting surface Li. RMs predict a second plateau at $A(\text{Li}) \approx 1.0$ dex for $T_{\text{eff}} \lesssim 5200$ K, consistent with observations.

5. Significance

Resolution of the Li Problem: The study provides strong evidence that the cosmological Li problem arises from stellar depletion processes rather than new physics or errors in BBN. The initial Li abundance of 2.72 dex is preserved in the models, but stellar evolution reduces the surface abundance to the observed Spite Plateau level.
Stellar Physics Validation: By calibrating rotation and magnetic field parameters to the Sun and successfully applying them to halo stars, the work validates the universality of these transport mechanisms across different stellar populations.
Diagnostic Power: The paper highlights that Li, Be, and B abundances serve as powerful tracers for internal stellar structure, specifically the depth of the convection zone and the efficiency of mixing processes.
Implications for Chemical Evolution: The successful reproduction of Li and Be distributions in metal-poor stars supports the use of these elements to constrain Galactic chemical evolution models, provided stellar depletion is accurately accounted for.

In conclusion, the authors demonstrate that a comprehensive stellar model incorporating rotation, magnetic fields, and diffusion can naturally explain the Spite Plateau, the Li/Be deviations in metal-poor stars, and the solar Li depletion, unifying these phenomena under a single physical framework.