where m is between 0 and 1 depending on the magnetic field geometry (Weber and Davis Jr, 1967; Mestel, 1984; Stȩpień, 1988). One further has to couple the average surface magnetic field strength, , with . This relation is essentially determined by the magnetic dynamo but can reasonably be parameterized as with p probably being 1 or 2 (Mestel, 1984). The approximately observed law (“Skumanich law”, Skumanich 1972, see below) is recovered for a thermal wind with p = 1 (Mestel, 1984), i.e., a linear dependence between average surface magnetic field strength and rotation rate. For another detailed study of this problem, see Stȩpień (1988).
Empirically, for solar analogs one finds
(Dorren et al., 1994), where t6 is the age in Myr after arrival on the ZAMS. Equivalently, for the rotational (equatorial) velocity and for the rotation rate (for constant R),
(Ayres, 1997) – see Figure 11. These equations imply a decrease in rotation period from ZAMS age to the end of the MS life of a solar analog by a factor of about 20.
At ages of approximately 100 Myr or younger, the stellar rotation period is not a function of age but of the PMS history such as the history of circumstellar-disk dispersal (e.g., Soderblom et al. 1993, see Figure 11). Once the inner disk disappears, the lack of magnetic locking via star-disk magnetic fields and the contraction of the star toward the MS will spin-up the star and thus determine the initial rotation period on the ZAMS. For example, the rotation periods of G-type stars in the Pleiades and the Per clusters still scatter considerably, ranging from less than a day (the so-called ultra-fast rotators) to many days (Soderblom et al., 1993; Stauffer et al., 1994; Randich et al., 1996), while they (and therefore the stellar X-ray luminosities, see Section 5.5) have converged to a nearly unique value at the age of the UMa Moving Group (300 Myr) or the Hyades (600 – 700 Myr; see Soderblom et al. 1993; Stern et al. 1995).
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