6.5. Is the rotation limit linked to the fully convective boundary? . . 67
6.1. Comparison to field stars
Our new data of the Hyades suggest that the fraction of fast rotators seen in the field is low in the mid-M range when compared to the younger Hyades stars. For the 625 Myr population, we find 30% of the M3 stars to be rapidly rotating, whereas this ratio is down to 15% for the field M3 stars. Fig. 6.1illustrates our findings and compares the fractional rotation as seen in the field, and in our catalog. We plot as open squares data for the field stars adapted from Reiners et al.(2012, M0–M4) andReiners & Basri(2010, M7–M9), and include 1σ statistical error bars drawn from the number of stars considered per spectral type bin. For the M5 and M6 bins, data is very limited (West & Basri 2009b; Browning et al. 2010) and statistically not firm, so we do not plot these two bins (eg. in the sample by West & Basri 2009b, there are only two stars of type M6, both fast rotators). It is important to realize that the field star distribution shows the ratio of stars rotating faster than vsini >3 km/s, whereas this fixed threshold is not suitable for the Hyades. Other than in the field, a good fraction of Hyades in any spectral type bin, also among the “slow” early K-types, shows detectable rotation (ie. vsini >3 km/s in most cases; cf. Fig. 5.10), but clearly a change towards higher vsini is observed for the later-type stars. An additional inconvenience is caused by the quickly dimishing stellar radius R with respect to effective temperature among the M-dwarfs. R decreases by a factor of 1.4 over the K-type range, but it does so by more than a factor of 5 across the M-types, hence the stellar surface velocities are vastly higher among the M stars and a direct comparison ofvsiniacross the K–M range is difficult. Consequently, the matter of moment for the present discussion is the change from a slow level of rotation to an increased level of rapid rotation, with respect to the behaviour in field stars. To account for the radius effect, we derive rotation periodsP/sini= 2πR/vsinibased on radii inferred from the BCAH models. These periods are still bound to the siniambiguity (a mean inclination of i= 90◦ is assumed), so that P is actually a lower limit. Rapid rotation in period space is considered forP <3 days, and the resulting distribution of rapid rotators is shown in Fig.6.1 as starred symbols. Note that the distribution in case of the field stars in Fig. 6.1 does not significantly change when based on periods, as no K-types are covered.
It is striking that not only is the frequency of enhanced rotation lower in the field, but also we see a rise of rotation at earlier spectral types in the Hyades than in the field stars. No significant fraction of the old field stars (few Gyr) hotter than M3 are detected with rotation,
Figure 6.1.: Fraction of stars with detected rotation for the Hyades (this catalog, starred) and for field stars (squares). Data for the field stars adapted fromReiners et al.
(2012, M0–M4) andReiners & Basri(2010, M7–M9). Error bars show statistical 1σuncertainties. For the Hyades, the fractions are expressed in rotational periods to eliminate the bias introduced by the stellar radius R, as R quickly drops in this spectral type range.
whereas in the intermediate age Hyades (625 Myr) already more than 10% of the M0 stars are rapidly rotating, and 30% do so by M3. On the contrary, the field stars only begin to speed up notably at M3, and probably half of the field stars are rapid at M6, when already all of the cluster stars are observed rotating at high levels. Although no star in the M1 bin qualifies as rapid, we believe this is due to the low number of stars in that bin (three), and does not reflect a real paucity of increased rotation rate. An onset of rotation in the Hyades cluster thus starts as early-type as K7–M0. 12% of the M0 stars show fast rotation periods; or in terms ofvsini, between 37% and 50% of M0 dwarfs rotate at a rate higher than 6 km/s—this is not observed at higher temperatures,1 —so the onset clearly occurs at higher massses than in the field.
At the same time, Fig. 6.2makes clear, that when compared to the Gyr-aged field popu-lation, the 625 Myr Hyades start to become also magnetically active at earlier spectral type.
This activity dependence on stellar age has been first suspected by Stauffer et al. (1991) and further developed by Hawley & Reid(1994) andHawley et al.(1999), but the sampling remained sparse, and the locus of the Hα-limit dilute. The new data in our catalog enables to refine this picture, providing further evidence for an Hα-limit shifted to higher masses than in older stars (Fig. 6.2), and constraining its locus to spectral type K7/M0 (Fig. 5.6).
1Given the low number of stars in some K-type bins, particularly K6 and M1, the rotation onset in terms of spectral type has some uncertainty. However, rotation is clearly detected in stars typed M0 (see above).
We also notice an increasedvsini(ie. below-average periods) in one K2 and one K4 star (cf. Fig.5.10), though with low statistical significance (the rapid K4 rotator, vA 677, is discussed above, see Sec.5.3).
6.1. Comparison to field stars 63
Figure 6.2.: Comparison of the fraction of stars with detected chromospheric activity in the Hyades and in field stars. Data from this catalog is shown as circles, field star data is taken from Reiners et al. (2012, M0 through M4) and West et al.(2008, M5 through M9), plotted as squares. Error bars show statistical 1σuncertainties.
The observed X-ray activity distribution (Fig. 5.7) shows virtually the same distribution, supporting the locus seen in Hα.
Fig.6.1now provides a direct link to rotation, and supports the coexistence of an activity-limit and a rotation-activity-limit, so that the locus of both prevalent activity and rapid rotation coincide. Thus, at the younger age of the Hyades, both rapid rotation and activity become predominant at higher masses than at older ages, and remain connected in the transition region. Hence, the rotation-activity correlation seems to be valid (in terms of mass) above, at, and below the Hα-limit, though with different implications.
Our results in the Hyades cluster corroborate the idea that the highest mass at which Hα activity (or rapid rotation) is still predominant is a well defined function of stellar age. This is equivalent to a mass and age-dependent magnetic braking process, and the underlying braking efficiency function at a given age steepens at what is observed as the limiting Hα (or limiting rotation) mass. For other cluster ages, several determinations of the limiting Hα locus exist, eg.Hawley et al. (1999), and a few studies have reported indications of an onset also in rotation for younger clusters (eg. Stauffer et al. 1997b; Jackson & Jeffries 2010b), or have noticed a possible drop-off in rotational periods (Lamm et al. 2005; Irwin et al. 2009;
Delorme et al. 2011). The caveat at young ages of less than hundred Myr, however, is the high intrinsic spread of rotation rates. In these young clusters, the distribution of rotation has not yet converged onto an envelope of slow, effectively braked rotators. This is because the spin-up process emerging from the pre-MS contraction phase has not yet finished, leaving too little time for braking to take effect (even in the higher mass stars). Consequently, no mass-regime of converged, slow rotators (and thus inactive stars) yet exists, rendering a transition
(activity-limit) difficult or impossible to discern.
The derived distribution of rotational velocities in the Hyades low-mass stars is controlled by considerable scatter in the levels ofvsini. As the inclination angle siniremains unknown, the projected rotation rates pose individual lower limits to the true velocities. To lift the degeneracy, photometric periods are needed (see below)—but mostly not available for low-mass Hyades. However, there is no reason to assume that the inclination angle is not randomly oriented in a cluster like the Hyades (Jackson & Jeffries 2010a), so that a systematic bias resulting from restrictions on sini is not expected. Thus, individual stars may be off from their true value of rotational velocity, but this is not the case for the distribution ofvover the entire sample with random inclinations (cf. estimates in Reiners et al. 2012). The scatter in observed rotation rates should therefore map the real distribution, so that a range of volocities exists especially among the M-dwarfs, where most stars are seen rapid (Fig. 5.12). In turn, it also means that the majority of stars in which no or little rotation is observed, still rotate slightly above the detection limit (cf. light grey distribution in Fig. 5.12). This basal level of rotation in the Hyades K-dwarfs is consistent with an age-effect: Magnetic braking over the age of the cluster has not yet brought these stars to the same slow level of rotation that is observed in old field K-dwarfs. The spin-down time span for this spectral type thus must be of order, but slightly longer than the 625 Myr of the Hyades cluster.