Modeling Rotation in the Old, Cold Domain: Implications on Gyrochronology and the Stellar Magnetic Wind

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This study investigates stellar spin-down in the previously under-constrained old field star regime using gyro-kinematic ages to explore this formerly inaccessible domain. The research aims to move beyond purely empirical approaches by employing forward modeling techniques that relax strict Rossby scaled assumptions, providing a more physical understanding of stellar rotation.

Methodology and Data

The observational dataset combines open cluster period measurements (starting at 10 Myr) with field star gyro-kinematic ages, spanning an age range up to approximately 9 Gyr. The sample covers masses from 0.5 M to 1.05 M. The rotational evolution is modeled using the YREC stellar evolution code and the forward modeling code, Rotevol, which tracks the angular momentum evolution of partially-convective stars under various physical constraints, including inertial changes and magnetic wind torques (Eq. 1).

** Key Findings: Limitations of Current Models**

The study demonstrates that a standard, solar-calibrated wind model is fundamentally unable to be extrapolated to the old field star domain. The reduced chi squared statistic disfavors this model across all masses (Section 6.1). Furthermore, the paper finds that a standard Rossby scaling does not capture the full mass-dependence of stellar spin down (Section 7).

** Wind Dominated Domain and Physical Constraints**

The researchers identified a specific, mass-dependent age domain where stellar wind spin down can be isolated from other physical effects.

1. Lower Age Limits: For lower masses, the treatment of internal angular momentum transport leaves a lasting imprint on the later rotational evolution of the star, with core-envelope coupling being a significant factor (Section 5.1).

2. Upper Age Limits: For higher mass stars, evolutionary radius expansion acts as the greatest limiting factor in spin down (Section 5.1).

The study highlights that stars between about 0.7 - 0.9 M represent a sweet spot for fitting these models (Section 5.1).

** Results from Analytical and Forward Modeling**

When fitting the mass sequences:

• Analytical Models: A mean super-Skumanich spin down index of 0.746 plus or minus 0.053 was found over the wind-dominated domain in the 0.70 - 0.90 M range (Section 5.2).

• Forward Models: The data is equally well represented by a model which allows for a variable torque scaling factor, Fk, or a changing wind-induced spin down slope (Section 5.3).

Solutions to Mass Dependence

The findings suggest two viable physical explanations for the observed mass dependence in spin down:

1. Torque Scaling: The first solution requires that the torques in the least massive partially-convective stars are a factor of about 2 greater than a solar-calibrated model. This could be explained by a correction term to the convective turnover timescale, thereby altering the Rossby number.

2. Dynamo Scaling: The second solution suggests that the dynamo scalings have a mass dependence, meaning the relationship between the magnetic field strength and angular velocity is not linear but decreases from a value near 1.6 for 0.5 M stars to less than 0.5 in higher mass sequences (Section 6.2).

** Implications and Conclusion**

The study concludes that gyrochronology is best approached using forward modeling techniques as opposed to simple analytic relations due to its superior ability to trace physical effects governing stellar spin down (Abstract/Section 7). The research provides a framework for future work, noting that the kinematic ages allow researchers to measure the efficacy of standard, solar scaled stellar spin down models as a function of mass and that this can be further vetted using model predictions of the width of rotation period distributions as a function of age (Section 7). The study also recovers a qualitatively consistent trend in core-envelope coupling timescales with literature estimates, despite differences in the assumed spin down indices (Section 6.3).

The following improvements represent specific architectural and algorithmic enhancements to an AI system designed for stellar chronometry and astrophysics, leveraging the physical insights presented in this paper.

• Implementation: The core architecture must move beyond fitting empirical power-laws (like Skumanich's) to incorporate a multi-physics forward modeling framework (e.g., utilizing Rotevol/YREC structure). This requires the the AI system to treat physical parameters (alpha, b, F k) as variables rather than fixed constants.

• Specific Component: A dedicated Structural Evolution Module must be integrated, allowing the AI to calculate how radius expansion and mass loss (*) influence angular momentum conservation throughout the main sequence.

• Implementation: The AI must utilize a non-solid body approximation for stellar interiors, treating tau CE (core-envelope coupling timescale) as a dynamic variable rather than an assumption.

• Specific Component: A dedicated Decoupling Subroutine capable of modeling the transient stalling and subsequent recovery of the core and envelope. This subroutine must be parameterized to handle mass-dependent behavior, where tau CE acts differently for low-mass stars (e.g., M3.65) versus higher mass stars (M 0.85 M).

• Implementation: The AI must abandon the assumption of a uniform, solar-calibrated wind torque (F k) and instead treat the wind index (alpha wind) and torque scaling factor as functions of mass.

• Specific Component: A Mass-Scaling Optimizer that allows both a (mass loss index) and b (field efficiency parameter) to be optimized simultaneously, recovering the necessary increase in required torque for lower-mass stars relative to higher-mass stars.

• Implementation: The AI must utilize a Residual Analysis Engine that separates the signal of wind spin-down (wind) from the signal of inertial/structural changes (inertial).

• Specific Component: A dedicated module to identify and isolate the Wind-Dominated Domain (the green region in Figure 5), allowing the AI to determine which parts of a dataset are reliable for gyrochronology and which are corrupted by structural evolution.

1. Accurately Date Old, Cold Field Stars: The system can provide robust age estimates for stars in the old field star regime (up to 9 Gyr), where current empirical models fail, by integrating tau CE and structural evolution into its calculations.

2. Determine Physical Parameters of Stellar Winds: The AI can not only estimate an age but also output the specific physical parameters of the stellar wind—namely, the mass-dependent torque scaling factor (F k) and the required changes in dynamo scaling (field strength vs. omega) necessary to match observed rotation distributions.

3. Validate/Refute Existing Literature: The system can test whether existing empirical gyrochronological models are fundamentally flawed by comparing their predictions against the observed wind-dominated domain and the calculated residuals (chi squared), identifying where structural effects (e.g., C-E coupling) are dominating the signal.

4. Forecast Rotational Behavior: It can predict how rotation period distributions will evolve over time, specifically predicting a narrower range of rotation periods at late ages due to the combined effects of C-E coupling and weakened magnetic braking (omega WMB), providing a testable metric for future kinematic surveys.

Gyrochronology ties stellar rotation periods to ages. It is well studied in the young, open cluster age domain, but there are few constraints on gyrochronology in the old field star regime. In this work we use gyro-kinematic ages to explore the spin down of stars in this formerly inaccessible domain. Using forward modeling techniques which relax strict Rossby scaled assumptions, we find evidence for a departure from a standard spin down models. This departure can be explained with a mass-dependent term either in the global strength of the stellar wind or in the relationship between angular velocity and wind strength. Models with this additional mass- dependence help explain prior difficulty in fitting open cluster rotation distributions across the full mass range. Additionally, we use rotation models to identify an mass-dependent age domain over which wind driven stellar spin down can be isolated from other physical effects. For lower mass stars, this age domain is most affected by the core-envelope coupling timescale, where as higher mass stars are more subject to inertial effects late in their main sequence lifetimes. Using simple, analytic models of stellar spin down in this domain is unable to determine whether the stellar wind has a mass-dependence or if the stellar wind is strictly Skumanich-like in nature. In future studies of rotational and dynamo evolution we advocate for a forward modeling approach to gyrochronology over purely empirical approaches due to its superior ability to trace physical effects governing stellar spin down.