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The Sun in Time: Activity and Environment 27
in particular for stars with small inclination angles. This model is preferred because correlations
involving the fractional variation in the rotation period show the same behavior for the two subclasses.
Support for the model comes from simulations of magnetic-field migration toward the
poles in very active stars, as performed by Schrijver and Title (2001) (Section 4.1.2). Specifically,
Messina and Guinan (2003) have found a power-law relation between the rotation-period variation,
∆P , and the average rotation period, P , of the form (see Figure 9a)
∆P ∝ P 1.42±0.5 . (2)
Further, a tight correlation is found between differential rotation, parameterized by ∆Ω/Ω, and
the activity cycle frequency, ωcycl,
ωcycl ∝ e (−0.055±0.004)∆Ω/Ω , (3)
suggesting that ∆Ω/Ω is a key parameter controlling the duration of the activity cycle (see
Figure 9b).
Differential rotation has also been measured on other very active stars (e.g., Donati et al.
2003a), among them a solar-like post-T Tauri star (Donati et al., 2000), in particular based on
Doppler imaging techniques (Section 4.1.1). Differential rotation was found to be solar-like in these
examples, although time-variable, which may hint at dynamo processes that periodically convert
magnetic into kinetic energy and vice versa (Donati et al., 2003a).
Figure 9: Left (a): Rotation period variation as a function of the mean rotation period, for a sample
of young solar analogs. The solid line is a power-law fit to the entire sample also containing early
K stars, while the dotted line is a fit to the G-star sample only. Key to the labels: A = BE Cet, B
= κ 1 Cet, C = π 1 UMa, D = EK Dra, E = HN Peg, F = DX Leo (K0 V), G = AB Dor (K0 V),
H = LQ Hya (K2 V), I = 107 Psc (K1 V), L = 61 UMa (G8 V), M = β Com, N = HD 160346
(K3 V), O = 15 Sge, S = Sun (from Messina and Guinan, 2003). Right (b): The activity cycle
frequency is shown as a function of the relative surface differential rotation amplitude, ∆Ω/Ω.
Vertical dotted lines connect multiple cycles. Three different branches are indicated by the solid
curves (from Messina and Guinan, 2003, reprinted with permission).
4.3.2 X-ray cycles of solar analogs
Given the much stronger variability in the outer, coronal layers of a stellar atmosphere, an activity
cycle may be more easily identified in the X-ray or radio domains. However, such cycles have eluded
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