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# Common dynamo scaling in slowly rotating young and evolved stars

## Abstract

One interpretation of the activity and magnetism of late-type stars is that these both intensify with decreasing Rossby number up to a saturation level1,2,3, suggesting that stellar dynamos depend on both rotation and convective turbulence4. Some studies have claimed, however, that rotation alone suffices to parametrize this scaling adequately5,6. Here, we tackle the question of the relevance of turbulence to stellar dynamos by including evolved, post-main-sequence stars in the analysis of the rotation–activity relation. These stars rotate very slowly compared with main-sequence stars, but exhibit similar activity levels7. We show that the two evolutionary stages fall together in the rotation–activity diagram and form a single sequence in the unsaturated regime in relation only to Rossby numbers derived from stellar models, confirming earlier preliminary results that relied on a more simplistic parametrization of the convective turn-over time8,9. This mirrors recent results of fully convective M dwarfs, which likewise fall on the same rotation–activity sequence as partially convective solar-type stars10,11. Our results demonstrate that turbulence plays a crucial role in driving stellar dynamos and suggest that there is a common turbulence-related dynamo mechanism explaining the magnetic activity of all late-type stars.

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## Data availability

The MWO HK Project data are available online at ftp://solis.nso.edu/MountWilson_HK/, and Gaia Data Release 2 from the Gaia Archive at http://gea.esac.esa.int/archive/. The YaPSI stellar models are available at http://www.astro.yale.edu/yapsi/. The adopted and derived astrophysical parameters for the stellar sample used in this study are available in online tables at the Strasbourg Astronomical Data Center via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/other/NatAs.

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## Acknowledgements

This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement. The chromospheric activity data derive from the Mount Wilson Observatory HK Project, which was supported by both public and private funds through the Carnegie Observatories, the Mount Wilson Institute and the Harvard-Smithsonian Center for Astrophysics, starting in 1966 and continuing for over 36 years. These data are the result of work by O. Wilson, A. Vaughan, G. Preston, D. Duncan, S. Baliunas and others. The work has made use of the SIMBAD database at CDS, Strasbourg, France, and NASA’s Astrophysics Data System (ADS) services. J.J.L. acknowledges financial support from the Independent Max Planck Research Group ‘SOLSTAR’. F.S. acknowledges the support of the German space agency (Deutsches Zentrum für Luft- und Raumfahrt) under PLATO Data Center grant 50OO1501. M.J.K., N.O. and P.J.K. acknowledge the support of the Academy of Finland ReSoLVE Centre of Excellence (grant no. 307411). P.J.K. acknowledges support from DFG Heisenberg (grant no. KA 4825/2-1). This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Project UniSDyn, grant agreement no. 818665).

## Author information

Authors

### Contributions

All authors contributed to the research and its design. J.J.L. and N.O. led the data analysis of the observations. F.S. led the stellar structure modelling. M.J.K. and P.J.K. led the theoretical interpretation of the obtained results. All authors contributed to the discussion of the results and to the manuscript.

### Corresponding author

Correspondence to Jyri J. Lehtinen.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature Astronomy thanks Gopal Hazra 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 Chromospheric Ca II H&K emission ratio, $${R}_{{\rm{HK}}}^{\prime}$$ against the stellar rotation period Prot.

The diagram shows giant stars as a distinct population with comparable activity levels but notably longer rotation periods than main sequence stars, in contrast to the common rotation-activity sequence seen using the Rossby number. The colour scale indicates surface gravity, log g, as in Fig. 2a and the position of the Sun is indicated by the circled dot symbol.

### Extended Data Fig. 2 Gaussian clustering for the rotation-activity relation.

a, Chromospheric Ca II H&K emission ratio, $${R}_{{\rm{HK}}}^{\prime}$$, vs. Rossby number, Ro. b, Chromospheric Ca II H&K emission ratio, $${R}_{{\rm{HK}}}^{\prime}$$, vs. combined rotation period and stellar radius, $${P}_{{\rm{rot}}}^{-2}{R}^{-4}$$. c, Chromospheric Ca II H&K luminosity LHK vs. rotation period, Prot. Optimal clustering of the data is indicated by the blue and red ellipses, reflecting the corresponding 95% confidence regions, and individual stars are coloured according to their inferred cluster membership.

### Extended Data Fig. 3 Rotation-activity relations using the chromospheric Ca II H&K surface flux $${F}_{{\rm{HK}}}^{\prime}$$.

a, Chromospheric surface emission flux, $${F}_{{\rm{HK}}}^{\prime}$$, vs. stellar rotation period, Prot. b, Chromospheric surface emission flux, $${F}_{{\rm{HK}}}^{\prime}$$, vs. Rossby number, Ro. The colour scale indicates surface gravity, log g, as in Fig. 2a and the position of the Sun is indicated by the circled dot symbol.

### Extended Data Fig. 4 Metallicity distribution of the sample stars.

One low metallicity giant, HD 122563, with [Fe/H] = − 2.42 is left outside the shown metallicity range since it lacks both a determined Prot and τc value and so does not enter our analysis.

### Extended Data Fig. 5 Selected stellar evolution tracks with the time evolution of convective turnover time, τc.

a, Evolution in the Hertzsprung-Russell (HR) diagram from the zero age main sequence (ZAMS) to the termination age main sequence (TAMS). b, Evolution in the HR diagram from TAMS to the red giant branch (RGB) tip. c, Evolution of τc from ZAMS to TAMS. d, Evolution of τc from TAMS to RGB tip. All ages are normalised to TAMS or RGB tip age.

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Lehtinen, J.J., Spada, F., Käpylä, M.J. et al. Common dynamo scaling in slowly rotating young and evolved stars. Nat Astron 4, 658–662 (2020). https://doi.org/10.1038/s41550-020-1039-x

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• DOI: https://doi.org/10.1038/s41550-020-1039-x