Filling the Gap: Calibrating Gyrochronology at 1.3 Gyr with the Benchmark Cluster NGC-752

Empirical gyrochronology relies on co-eval stellar associations to map stellar rotation as a function of mass and age. The accuracy of its age predictions is therefore limited by the number and quality of benchmark rotation sequences. The well-characterized clusters NGC-6811 (t ≈ 1 Gyr) and NGC-6819 (t ≈ 2.5 Gyr) bracket an intermediate-age interval in which stellar spin-down remains poorly constrained due to lack of available rotation data. At t ≈ 1.3 Gyr, NGC-752 provides a critical benchmark within this gap, but previous measurements could not define the G- and K-dwarf rotation sequence needed for calibration. Here, we combine Gaia-based NGC-752 membership lists with literature rotation periods to map NGC-752’s slow-rotator sequence for the first time. We identify a well-defined sequence intermediate between those of NGC-6811 and NGC-6819. Stars near Teff ≈ 4500 K rotate more slowly than their counterparts in NGC-6811, indicating that stars experiencing stalled spin-down at ≈ 1 Gyr have resumed appreciable spin-down by the age of NGC-752. Adopting an age of 1.3 Gyr for NGC-752, we further show that existing empirical gyrochronology models overestimate the ages of many G and early-K dwarfs by 20–50% because they lack intermediate-age calibration data, although uncertainty in the absolute age of NGC-752 may account for part of this offset. NGC-752 therefore provides a necessary anchor for improving rotational age estimates. This calibration is especially timely because Gaia DR4, Roman, and PLATO are expected to yield rotation periods for tens of millions of stars, making the age coverage of benchmark sequences a principal limitation on large-scale gyrochronology.

Improvements to AI Systems:

1. Age-Calibration-Aware Gyrochronology Models

• Improvement: Incorporate NGC-752’s newly mapped G/K-dwarf rotation sequence as an explicit intermediate-age anchor (t ≈ 1.3 Gyr) into empirical gyrochronology training data.

• What the improved AI can do: Predict stellar ages for G and early-K dwarfs with 20–50% reduced systematic bias, correcting the current overestimation caused by missing intermediate-age benchmarks.

2. Uncertainty-Propagating Age Estimators

• Improvement: Add a Bayesian layer that treats the absolute age of NGC-752 (and other anchors) as a free parameter with prior distributions, rather than fixed values.

• What the improved AI can do: Output age posteriors that explicitly account for anchor-age uncertainty, allowing users to see how much of the age offset is due to calibration vs. intrinsic spin-down physics.

3. Mass-Dependent Spin-Down Transition Detector

• Improvement: Train a classifier or regression model on the rotation–Teff sequences of NGC-6811, NGC-752, and NGC-6819 to detect the onset and rate of resumed spin-down after stalled phases (e.g., near Teff ≈ 4500 K).

• What the improved AI can do: Automatically identify stars in the “stall-then-resume” regime and assign them more accurate ages than models assuming monotonic spin-down, improving age estimates for field stars in the 1–2.5 Gyr range.

4. Benchmark-Gap-Aware Data Augmentation

• Improvement: Use NGC-752’s sequence to generate synthetic rotation–age pairs for the previously unconstrained 1.3–2.5 Gyr interval, then augment training sets for deep learning gyrochronology models.

• What the improved AI can do: Produce robust age predictions for stars in this gap without requiring new observations, reducing reliance on sparse cluster data.

5. Multi-Survey Fusion for Large-Scale Gyrochronology

• Improvement: Build a transfer-learning pipeline that uses NGC-752’s calibration to correct systematic biases in rotation periods from Gaia DR4, Roman, and PLATO (which will observe tens of millions of stars).

• What the improved AI can do: Deliver age maps for entire stellar populations (e.g., Galactic disk surveys) with uniform accuracy, avoiding the current limitation where benchmark sequence coverage is the primary bottleneck.

6. Physical Consistency Checker

• Improvement: Integrate NGC-752’s observed spin-down rate into a physics-based loss function that penalizes AI models for predicting rotation evolution inconsistent with the new intermediate-age data.

• What the improved AI can do: Reject implausible age predictions that violate known spin-down behavior, improving reliability for exoplanet host star ages and Galactic archaeology studies.

Empirical gyrochronology relies on co-eval stellar associations to map stellar rotation as a function of mass and age. The accuracy of its age predictions is therefore limited by the number and quality of benchmark rotation sequences. The well-characterized clusters NGC-6811 (t 1 Gyr) and NGC-6819 (t 2.5 Gyr) bracket an intermediate-age interval in which stellar spin-down remains poorly constrained due to lack of available rotation data. At t 1.3 Gyr, NGC-752 provides a critical benchmark within this gap, but previous measurements could not define the G- and K-dwarf rotation sequence needed for calibration. Here, we combine Gaia-based NGC-752 membership lists with literature rotation periods to map NGC-752's slow-rotator sequence for the first time. We identify a well-defined sequence intermediate between those of NGC-6811 and NGC-6819. Stars near Teff 4500 K rotate more slowly than their counterparts in NGC-6811, indicating that stars experiencing stalled spin-down at 1 Gyr have resumed appreciable spin-down by the age of NGC-752. Adopting an age of 1.3 Gyr for NGC-752, we further show that existing empirical gyrochronology models overestimate the ages of many G and early-K dwarfs by 20--50% because they lack intermediate-age calibration data, although uncertainty in the absolute age of NGC-752 may account for part of this offset. NGC-752 therefore provides a necessary anchor for improving rotational age estimates. This calibration is especially timely because Gaia DR4, Roman, and PLATO are expected to yield rotation periods for tens of millions of stars, making the age coverage of benchmark sequences a principal limitation on large-scale gyrochronology.