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Astron. Astrophys. 331, 581-595 (1998)

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4. Rotation versus activity

The relation between magnetic activity and rotation is observationally well established for G and K dwarfs (e.g. Soderblom et al. 1993 and Stauffer et al. 1994 for recent reviews of the connection with respectively chromospheric and coronal activity), and for M dwarfs in young clusters (e.g. Stauffer et al. 1997). Rotation drives the shell dynamos which are believed to excite stellar activity, and faster rotation excites stronger magnetic activity, up to a saturation threshold of [FORMULA] 10 [FORMULA]. We show here that similar relations hold for the field M dwarfs and observe no break in these relation at the spectral type where the stars become fully convective, and where shell dynamos must stop working.

4.1. Chromospheric activity

Fig. 5 shows the fractional luminosity in the first two Balmer lines as a function of v sin i , and indicates a saturation type relation between these chromospheric activity diagnostics and the rotational velocity. All stars with a significant v sin i have chromospheric activity as well, and the two flux ratios saturate for rather low velocities, of the order of our detection limit of 2  km.s -1. Most of the slowly rotating stars only have upper limits for both v sin i and the Balmer line luminosities, so that we are unable to document the chromospheric activity increase with rotation velocity, which presumably occurs at lower v sin i . The saturation levels ([FORMULA] / [FORMULA]) [FORMULA], and [FORMULA] / [FORMULA] [FORMULA]) are similar to those observed for earlier M dwarfs in the Hyades and Pleiades (Reid et al. 1995b; Stauffer et al. 1997).

[FIGURE] Fig. 5. Chromospheric and coronal activity diagnostics as a function of the projected equatorial velocity

The fraction of magnetically active stars amongst field M dwarfs has long been known to depend on both spectral type and age, as probed by the dynamical population (Stauffer & Hartmann 1986). Field M dwarfs with Balmer line emission become more frequent at later M types, and they represent a dynamically younger population than the non-active stars. The present data show that rotation is the underlying physical parameter and that the longer spin-down timescale at lower masses explain both behaviours.

4.2. Coronal activity

X-ray emission is the most convenient indicator of coronal activity, and for younger and more luminous stars is well known to correlate with stellar rotation (Bouvier 1990; Fleming et al. 1989). For the Pleiades G, K and M dwarfs for instance, Stauffer et al. (1994) find that [FORMULA] / [FORMULA] rises rapidly with rotational velocity until v sin i [FORMULA] 15  km.s -1, and then remains approximately flat at [FORMULA] / [FORMULA] [FORMULA] 10-3.

Fig. 5 displays the same diagram for the present sample of field M dwarfs, and indicates a qualitatively similar saturation behaviour. Saturation occurs at [FORMULA] [FORMULA] / [FORMULA] [FORMULA], the value found for M dwarfs in the Pleiades (Stauffer et al. 1994) and the Hyades (Reid et al. 1995b; Stauffer et al. 1997). The saturation velocity, on the other hand, is a factor of 3 lower than for the cluster M dwarfs, at v sin i [FORMULA] instead of v sin i [FORMULA]. The poorer spectral resolution of the cluster data and the smaller fraction of open cluster M dwarfs with x-ray data may contribute to a larger apparent saturation velocity: the rising part of the relation is not very well documented, and (in both cases) occurs close to the the minimum measurable rotational velocity. The most likely explanation for most of this difference is however the typically larger stellar radius in the cluster samples, since the rotation rate [FORMULA] (or more precisely the Rossby number) is expected to be the relevant parameter, rather than the equatorial velocity (e.g. Barnes & Sofia, 1996; or Krishnamurthi et al. 1997). The cluster samples are biased towards early M types, while the effective spectral type interval in Fig. 5 is [FORMULA] [M4,M6]: since no field star earlier than M3.5 has measurable rotation, the relation between coronal activity and rotation is only defined by cooler stars. Adopting representative spectral types of M2V for the cluster samples and M5V for the rotating nearby stars, typical radii are thus respectively [FORMULA] and [FORMULA] (Chabrier & Baraffe, 1995), and the two saturation velocities correspond to a similar rotational period of P [FORMULA]  day. Within our sample, there are possible indications for a spectral type dependence of the saturation velocity, though their significance is marginal. The apparent effect could still result from small number statistics, or be an artefact of our imperfect calibration of the instrumental correlation profile as a function of spectral type.

4.3. Activity in fully convective stars

The extreme M dwarf BRI 0021+0214 (M9.5+, v sin i = [FORMULA], Basri & Marcy 1995), on the other hand, has fast rotation and extremely faint H [FORMULA] emission (Basri & Marcy 1995), though it is detectable (Tinney et al. 1997). As this is clearly at odds with what is seen in young early M dwarfs (e.g. Stauffer et al. 1997; Stauffer et al. 1994; Patten & Simon 1996), and since the behaviour of mid-M dwarfs was then unknown, Basri & Marcy (1995) tentatively attributed this behaviour to a change in the dynamo processus at the mass (0.35 [FORMULA] (Chabrier & Baraffe 1997), corresponding to M2.5V (Baraffe & Chabrier 1996)) where stars become fully convective.

The present data show no obvious feature in the rotational velocity distribution at this spectral type, or elsewhere within the M0-M6 range. The activity/rotation relation for the fully convective M3-M6 dwarfs is also similar to that for young more massive stars that retain a radiative core. The change in this relation seen for M9.5V stars (0.08 [FORMULA]) must therefore happen at a spectral type later than M6V (0.1 [FORMULA]), and is thus not directly related to the transition to full convection. Since the radiative/convective boundary is essential to the operation of the standard [FORMULA] dynamo responsible for the large scale solar magnetic field, a different mechanism has to be invoked to explain the observed magnetic activity in low mass stars, as discussed by Durney et al. (1993). They show that a small scale, turbulent, magnetic field can be generated even in fully convective stars and is mildly enhanced by rotation. The source of stellar magnetic activity should therefore change from the large scale field in solar mass stars to a turbulent field in the fully convective low mass stars. The lack of a sharp boundary at the fully convective mass limit shows that the turbulent field already drives most of the magnetic activity in stars which retain a significant radiative core.

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© European Southern Observatory (ESO) 1998

Online publication: February 16, 1998
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