Comments:Sun's mood swings not so strange after all, say scientists
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A few comments on this article (as a contributor) since it is now locked and can't be edited except for minor edits.
First, for a star, the "Stellar Rossby Number" is defined as the rotation period of the star divided by the thermal convection turnover time (in the star's surface). This doesn't have anything to do with the plasma and magnetic activity on the face of it, but in a 1984 paper Noyes et al found a correlation between the Rossby number and the activity of a star. The more active a star is, in terms of magnetic and plasma activity, the lower its Rossby number.
So anyway, astronomers had already hypothesized a connection between the Rossby number and the length of the stellar cycle. To try to tease out what was going on, they drew graphs of the length of the cycle against the rotation period of the star and they thought they had spotted a correlation. Stars that rotated more slowly, so with a longer rotation period, seemed to reverse their magnetic field over longer cycle times.
That's explained at the start of the paper. So the old hypothesis was that the cycle period correlated to the rotation period - more slowly rotating stars would have longer cycles. Though they did have the idea already for some unusually slow rotators that they were anti correlated.
But there seemed to be two separate "branches" - parallel lines of stars, with our sun rather uncomfortably situated between the two. The rotation period is easy to observe, through precise measurements of variation in brightness and of doppler broadening of spectral bands. However, the Rossby number depends on the convection turnover time as well, not just the rotation period, but that's something we can't observe directly, even for the sun.
Stars that rotate more slowly have lower Rossby numbers, so it would seem that lower Rossby numbers correlate with longer cycle times.
The authors of this paper tried a new tack. They did seven simulations of stars (Table S1 of the article) differing in rotation period and a parameter that describes how they convect heat.
They found that the cycle got shorter, in their models, as the star spins more slowly, so the opposite of what the astronomers thought they had observed with the real stars. However they found a new correlation from their luminosity calculations, that the cycle is also shorter for slightly brighter stars — these were stars that were brighter only because of increased convection.
So, they then tried using a luminosity correction for the real stars. To do this they need very exact measurements of the luminosity. They did this for 27 sun like stars. After doing this they then found that their modeled stars lined up nicely with the longest cycles of observed stars, which suggested they were onto something.
They then worked out the Rossby numbers for their model stars (they didn't attempt to calculate any empirical Rossby numbers for the real stars). When they did this they found that the lower the Rossby number, the longer the cycle period. S
We can't measure the Rossby number, even of our sun, directly. But based on their models, then it seems that the more active stars, so the ones with a lower Rossby number, have longer magnetic cycles. In particular, if a star is identical in other respects (same convective turnover time) and rotates more quickly, then it actually has a longer magnetic cycle, even though its rotation period is shorter. So, their conclusion is that the length of the magnetic cycle is anti-correlated with the period of the star.
If you want to take a look at the paper, the key figures are Figure 2D which shows their modeled stars as dark blue dots, and the other stars, and you can see how the graph slopes down to the right, so that stars with longer rotation periods have shorter magnetic cycles. The other graph to look at is graph 3A which shows that in their models then the stars with higher Rossby numbers have shorter periods.