Travis Metcalfe¹, Jennifer van Saders², Ricky Egeland^3
1 Space Science Institute, Boulder CO 80301 USA
² Carnegie Observatories, Pasadena CA 91101 USA
³ High Altitude Observatory/NCAR, Boulder CO 80307 USA

Astronomers have known for a long time that the Sun is a typical star near the middle of its main-sequence lifetime. What we didn’t appreciate until recently is that all Sun-like stars experience a fundamental shift in their rotation and magnetism around middle-age. We have now identified the manifestation of this unexpected transition in the best available data on stellar cycles¹. The observations suggest that the solar cycle will grow longer over a few billion years before the global dynamo shuts down.

More than four decades ago, Skumanich suggested that both the rotation rate and the magnetic activity of stars decay with a power-law dependence on stellar age². Although stars are formed with a range of initial rotation rates, the stellar winds entrained in their magnetic fields lead to angular momentum loss from magnetic braking. The effect is stronger in more rapidly rotating stars, which forces convergence to a single rotation rate at a given mass after roughly 500 Myr in Sun-like stars. The evidence for this scenario relies on studies of rotation in young star clusters at various ages, and until recently the only calibration point for ages beyond 2.5 Gyr was from the Sun.

Recent observations from the Kepler space telescope provided the first opportunity to measure rotation rates for a variety of field stars with ages determined from asteroseismology. The younger stars appeared to obey the Skumanich relation, but the older stars were rotating more quickly than expected. This anomalous rotation became significant near the solar age for G-type stars, but it appeared at 2-3 Gyr for hotter F-type stars and at 6-7 Gyr for cooler K-type stars. This dependence on spectral type suggested a connection to the Rossby number, because cooler stars have deeper convection zones with longer turnover times. The observations were reproduced with rotational evolution models that eliminated angular momentum loss beyond a critical Rossby number³. In other words, the Skumanich relation no longer applies to stars beyond middle-age.

Ground-based observations of chromospheric activity for the Kepler sample quickly revealed a magnetic counterpart to the newly discovered rotational transition⁴. The critical Rossby number was equivalent to a specific level of chromospheric activity, and stars of various spectral types would take different amounts of time to reach this threshold. The shutdown of magnetic braking near the solar activity level appeared to lock the stellar rotation rate while the chromospheric activity level continued to decrease with age. The disruption of magnetic braking was a natural consequence of concentrating the global field into smaller spatial scales, possibly due to a change in the character of differential rotation from a diminishing imprint of Coriolis forces on the turbulent convection.

The new picture of rotational and magnetic evolution provides a framework for understanding some observational features of stellar activity cycles that have until now been mysterious. Figure 1 shows an updated version of a diagram originally published by Böhm-Vitense more than a decade ago⁵. Using the best observations of stellar activity cycles and rotation from the Mount Wilson Survey, Böhm-Vitense noted that there were two distinct relationships between the rotation rate and the length of the cycle. She interpreted this dual pattern as evidence for two stellar dynamos operating in different shear layers, possibly at the bottom of the convection zone and in the near-surface regions. Most significantly, she found that the Sun appeared to fall between the two stellar sequences.

Figure 1|Updated version of a diagram originally published in [5], showing two distinct relationships between rotation rate and activity cycle period (solid lines). Points are colored by spectral type, indicating F-type (blue), G-type (yellow), and K-type stars (red). Schematic evolutionary tracks are shown with dashed lines, leading to stars that appear to have completed the magnetic transition.

When we color coded the points in Figure 1 by spectral type and marked the rotation periods of non-cycling stars along the top, it immediately became clear that cycles were no longer observed in stars beyond the critical Rossby number where magnetic braking shuts down. Cycling stars that were outliers, including the Sun and α Cen A as well as 219834A, could then be understood as transitional dynamos. Considering the evolutionary sequence defined by 18 Sco (4.1 Gyr), α Cen A (5.4 Gyr) and 16 Cyg (7.0 Gyr), the data suggest that a normal cycle on the lower sequence may grow longer across the transition (yellow dashed line) before disappearing entirely. The Sun falls to the right of this evolutionary sequence because it is slightly less massive than the other stars.

Future tests of this new scenario for magnetic evolution will come from ground-based chromospheric activity measurements of Kepler targets that span the magnetic transition, and from asteroseismology with the TESS mission to determine the precise masses and ages of bright Mount Wilson stars with known cycles.

References

[1] Metcalfe, T.S., & van Saders, J., 2017, SoPh, in press (https://arxiv.org/abs/1705.09668)
[2] Skumanich, A., 1972, ApJ, 171, 565
[3] van Saders, J., Ceillier, T., Metcalfe, T.S., et al., 2016, Nature, 529, 181
[4] Metcalfe, T.S., Egeland, R., & van Saders, J., 2016, ApJL, 826, L2
[5] Böhm-Vitense, E., 2007, ApJ, 657, 486