[Paper Review] Further Evidence of Modified Spin-down in Sun-like Stars: Pileups in the Temperature-Period Distribution

Trevor J. David, Ruth Angus+6 more|arXiv (Cornell University)|Mar 16, 2022

Stellar, planetary, and galactic studies107 references36 citations

TL;DR

This study provides further evidence for modified magnetic braking in Sun-like stars by identifying distinct pileups in the temperature-period distribution of Kepler stars. Using precise spectroscopic temperatures and rotation periods, it shows that both long- and short-period pileups align with constant Rossby number curves, supporting astrophysical origins over observational biases, with the long-period pileup linked to weakened magnetic braking and the short-period feature possibly due to core-envelope decoupling.

ABSTRACT

We combine stellar surface rotation periods determined from NASA's Kepler mission with spectroscopic temperatures to demonstrate the existence of pileups at the long-period and short-period edges of the temperature-period distribution for main-sequence stars with temperatures exceeding $\sim 5500$K. The long-period pileup is well-described by a curve of constant Rossby number, with a critical value of $\mathrm{Ro_{crit}} \lesssim 2$. The long-period pileup was predicted by van Saders et al. (2019) as a consequence of weakened magnetic braking, in which wind-driven angular momentum losses cease once stars reach a critical Rossby number. Stars in the long-period pileup are found to have a wide range of ages ($\sim 2-6$Gyr), meaning that, along the pileup, rotation period is strongly predictive of a star's surface temperature but weakly predictive of its age. The short-period pileup, which is also well-described by a curve of constant Rossby number, is not a prediction of the weakened magnetic braking hypothesis but may instead be related to a phase of slowed surface spin-down due to core-envelope coupling. The same mechanism was proposed by Curtis et al. (2020) to explain the overlapping rotation sequences of low-mass members of differently aged open clusters. The relative dearth of stars with intermediate rotation periods between the short- and long-period pileups is also well-described by a curve of constant Rossby number, which aligns with the period gap initially discovered by McQuillan et al. (2013a) in M-type stars. These observations provide further support for the hypothesis that the period gap is due to stellar astrophysics, rather than a non-uniform star-formation history in the Kepler field.

Motivation & Objective

• To investigate the astrophysical origin of observed pileups in the temperature–rotation period distribution of Sun-like stars.
• To test whether the long-period and short-period pileups in the Teff–Prot plane are due to physical processes or observational biases.
• To examine whether the pileups align with constant Rossby number curves, supporting the weakened magnetic braking hypothesis.
• To determine if the period gap between pileups is a physical feature or an artifact of star-formation history.
• To assess the role of core–envelope coupling in shaping the short-period pileup and period gap.

Proposed method

• Combined rotation periods from the Kepler mission with high-precision spectroscopic temperatures from multiple large-scale surveys (CKS, LAMOST, APOGEE, Gaia).
• Constructed Gaussian kernel density estimates of the Teff–Prot distribution to identify overdensities (pileups) in the data.
• Fitted constant Rossby number curves to the observed pileups to test their physical consistency.
• Evaluated the possibility that the short-period pileup is a harmonic of the long-period pileup due to period measurement errors.
• Used visual inspection and statistical comparison to rule out aliasing or detection bias as the sole explanation for the short-period feature.
• Cross-validated results across multiple independent data samples (e.g., CKS, LAMOST, APOGEE) to ensure robustness.

Experimental results

Research questions

• RQ1 Do pileups exist at both the long- and short-period edges of the temperature–rotation period distribution for Sun-like stars?
• RQ2 Are these pileups consistent with constant Rossby number curves, indicating a physical origin?
• RQ3 Is the long-period pileup consistent with the weakened magnetic braking hypothesis?
• RQ4 Can the short-period pileup be explained by period measurement artifacts or harmonics of the long-period feature?
• RQ5 Is the observed period gap between the pileups a physical feature or an artifact of non-uniform star formation in the Kepler field?

Key findings

• A long-period pileup is observed in the Teff–Prot distribution for stars with Teff > 5500 K, well-described by a constant Rossby number curve with Rocrit ≲ Ro⊙, supporting the weakened magnetic braking hypothesis.
• The long-period pileup spans a wide age range (∼2–6 Gyr), indicating that rotation period is a strong predictor of temperature but a weak predictor of age for stars along this feature.
• A short-period pileup is also observed, particularly for hotter stars (Teff > 6000 K), and is well-described by a constant Rossby number curve, suggesting a physical origin distinct from detection bias.
• The short-period pileup is not a harmonic of the long-period pileup, as shown by period folding and kernel density analysis, ruling out simple aliasing from period measurement errors.
• The relative dearth of stars with intermediate periods (the period gap) is also well-described by a constant Rossby number curve, aligning with the gap first reported by McQuillan et al. (2013a) in M-dwarfs.
• The results collectively support the hypothesis that the period gap and pileups are physical features driven by stellar astrophysics—specifically, modified magnetic braking and core–envelope coupling—rather than non-uniform star-formation history in the Kepler field.