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# Weakened magnetic braking supported by asteroseismic rotation rates of Kepler dwarfs

## Abstract

Studies using asteroseismic ages and rotation rates from star-spot rotation have indicated that standard age–rotation relations may break down roughly half way through the main sequence lifetime, a phenomenon referred to as weakened magnetic braking. Although rotation rates from spots can be difficult to determine for older, less active stars, rotational splitting of asteroseismic oscillation frequencies can provide rotation rates for both active and quiescent stars, and so can confirm whether this effect really takes place on the main sequence. We obtained asteroseismic rotation rates of 91 main sequence stars showing high signal-to-noise modes of oscillation. Using these new rotation rates, along with effective temperatures, metallicities and seismic masses and ages, we built a hierarchical Bayesian mixture model to determine whether the ensemble more closely agreed with a standard rotational evolution scenario, or one where weakened magnetic braking takes place. The weakened magnetic braking scenario was found to be 98.4% more likely for our stellar ensemble, adding to the growing body of evidence for this stage of stellar rotational evolution. This work presents a large catalogue of seismic rotation rates for stars on the main sequence, which opens up possibilities for more detailed ensemble analysis of rotational evolution with Kepler.

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## Data availability

The core input data and results are summarized in Supplementary Table 1, which is available in a machine-readable format as Supplementary Data 1. Larger data files, such as stellar model populations and individual posterior distribution chains from the asteroseismic and gyrochronology model fitting are fully available on request from the corresponding author. This work made use of publicly available data. Kepler power spectral densities were obtained from the KASOC webpages for the majority of stars, and from the MAST for 16 Cyg A and B. This work used asteroseismic data from refs. 7,22,23,24. Parameter distributions of the Kepler field used to alter our stellar population models were taken from ref. 36.

## Code availability

The code required to replicate our results has been placed in a curated online repository at www.github.com/ojhall94/halletal2021. All code written in the duration of this project, along with a full commit history, can be found in an uncurated online repository at www.github.com/ojhall94/malatium. The code used to construct the stellar population models used in this work is available upon request from the corresponding author.

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## Acknowledgements

We thank S. Matt, E. Avallone, A. Dixon, W. Ball and B. Morris for helpful discussions. O.J.H., G.R.D. and W.J.C. acknowledge support from the UK Science and Technology Facilities Council (STFC). J.v.S. acknowledges support from the TESS Guest Investigator Program (grant number 80NSSC18K18584). M.B.N. acknowledges support from the UK Space Agency. This work has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (CartographY GA. 804752). Funding for the Stellar Astrophysics Centre is provided by The Danish National Research Foundation (Grant agreement number DNRF106). L.A., A.A.B. and V.S. acknowledge funding from the ERC under the European Union’s Horizon 2020 research and innovation program (grant agreement number 682393 AWESoMeStars). A.A.B. also acknowledges support from the College of Engineering, Mathematics and Physical Sciences at the University of Exeter. R.A.G. acknowledges support from the PLATO and GOLF CNES grants. J.T. acknowledges that support for this work was provided by NASA through NASA Hubble Fellowship grant number 51424 awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract number NAS5-26555. The computations described in this paper were performed using the University of Birmingham’s BlueBEAR HPC service. This paper includes data collected by the Kepler mission and obtained from the MAST data archive at the Space Telescope Science Institute (STScI). Funding for the Kepler mission is provided by the NASA Science Mission Directorate. STScI is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract number NAS 5-26555.

## Author information

Authors

### Contributions

O.J.H. led the project, with help from G.R.D., J.v.S., M.B.N. and W.J.C. J.v.S. also led the development of the stellar population models. M.N.L., R.A.G. and S.K. provided data or stellar models and, along with J.T., assessed the validity of our asteroseismic results. L.A., A.A.B. and V.S. provided the assessment of the theoretical implications of the gyrochronology results. All authors have contributed to the interpretation of the data and the results, and all discussed and provided comments for all drafts of the paper.

### Corresponding author

Correspondence to Oliver J. Hall.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review informationNature Astronomy thanks Cecilia Garraffo and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Extended data

### Extended Data Fig. 1 A probabilistic graphical model (PGM) represented algebraically in Equation 2.

The shaded circle indicates observed data, and solid black points represent other fixed information, such as the KDEs and observational uncertainties. The remaining circles represent parameters. The underline indicates that the symbol represents a set of parameters or data. Here, κs and κWMB represent the KDEs of standard and WMB model populations respectively. QWMB is the mixture model weighting factor. The latent parameters θ, our observations $${\mathcal{D}}$$ and their uncertainties $${\sigma }_{{\mathcal{D}}}$$ include temperature Teff), mass (M), log-age ($$\mathrm{ln}\,(t)$$), metallicity [Fe/H]) and log-rotation ($$\mathrm{ln}\,(P)$$). This model is hierarchical, as all the latent parameters are drawn from the common probability distribution set by QWMB and described in Equation (3).

## Supplementary information

### Supplementary Information

Supplementary Figs. 1–5, Table 1 and asteroseismic model, verifying asteroseismic results and verifying consequences for gyrochronology sections.

### Supplementary Data 1

A .csv file with the contents of Supplementary Table 1.

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Hall, O.J., Davies, G.R., van Saders, J. et al. Weakened magnetic braking supported by asteroseismic rotation rates of Kepler dwarfs. Nat Astron 5, 707–714 (2021). https://doi.org/10.1038/s41550-021-01335-x