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

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3. Rotational velocities

3.1. Sample pruning

A total of 19 binary stars had to be ignored in the study of the rotational velocity distribution (Table 3). Eight are double-lined spectroscopic binaries with measured or possible short periods: Gl 268 (P=10 days, Tomkin & Pettersen 1986), GJ 1230A (Gizis & Reid 1996), G 203-47, LP 476-207, GJ 2069A (P = 3 days), Gl 896A, LHS 6158 (P = 7.5 days) and LHS 2887 (Delfosse et al. 1997). At short orbital periods (P10 days), rotation is tidally locked to the orbit, and it no longer reflects the processes at play in an isolated star. Conservatively, we have thus eliminated all binaries whose measured or probable period is less than 30 days.

We have also eliminated 11 multiple systems for which we could not simply disentangle the velocity signatures of the components. Gl 381 is a marginally separated double-lined spectroscopic binary and Gl 487 is a triple-lined system with one long period (Delfosse et al. 1997). The other 9 are known visual or speckle binaries where both stars contribute significant light to the joint spectrum (([FORMULA]): Gl 473 (Perrier et al. 1991; Henry et al. 1992) Gl 644 (Pettersen et al. 1984), Gl 661 (Henry & McCarthy 1993; Hartkopf et al. 1996)), Gl 695BC (Al-Shukri et al. 1996), Gl 747 (Blazit et al. 1987), Gl 831 (Henry & McCarthy 1993), Gl 866 (Leinert et al. (1990)), GJ 1103AB and GJ 1116AB. Our sample includes a few other speckle binaries (GJ 1245AC, Gl 623, Henry & McCarthy 1993; Gl 234AB, Coppenbarger et al. 1994), but their secondaries are faint enought that they don't affect the rotational velocity measurement of the bright component. Some additional marginally resolved double lined spectroscopic binaries could still remain unrecognised. Over 90% of the sample however now has multiple measurements, separated by typically one year. Since only one such object (Gl 381) has been identified with those data, at most a few should remain in the sample.

Gl 829 and Gl 268.3 are both well separated long period double lined spectroscopic binaries, and each enter as two data points in Table 2. 101 individual measurements therefore contribute to the rotation velocity distribution.


[TABLE]

Table 2. Basic parameters of the sample stars, which have been selected from the CNS3 (Gliese & Jahreiss 1991) as having d [FORMULA] 9pc and [FORMULA]. Spectral type are from Reid et al (1995a), except a from Henry et al. (1994). [FORMULA] is from Leggett's (1992) compilation, except: b from the CNS3 catalog (Gliese and Jahreiss, 1991; the Kron R-I in the CNS3 were transformed to the Cousins system using the Bessel (1983) relation, [FORMULA]); c from Bessel (1990); d estimated from spectral type, using Leggett's (1992) relation for the Young Disk. Parallax and proper motion are from e the Yale General Catalogue of Trigonometric Stellar Parallaxes (Van Altena et al. 1991), or f the Hipparcos input catalogue (Turon et al 1993).



[TABLE]

Table 2. (continued)




[TABLE]

Table 3. Binary stars not considered for the rotation study




[TABLE]

Table 4. Rotational, activity and kinematic parameters of the program stars. [FORMULA]: width of correlation profile with the K0 template, except a with the M0 template. The quoted uncertainty on [FORMULA] is that due to photon and readout noise, while the standard error on v sin i also includes a 200 [FORMULA] dispersion on [FORMULA], the width of the correlation profile of a non rotating star. b: space velocities were computed using an inaccurate radial velocity ([FORMULA]), because we have not yet covered a full orbital period. c space velocities use the barycentric radial velocity from Marcy & Chen (1992).



[TABLE]

Table 4. (continued)


3.2. Distribution of rotational velocities

Fig. 3 shows the distribution of v sin i as a function of the R-I colour index, separately for stars with young and old kinematic characteristics. It is immediately apparent that rotational velocity has a strong dependence on both spectral type (as measured by the R-I color) and dynamic population (used as an ersatz for age). Below [FORMULA] =1.4 (M3V), there is no star with measurable rotation in either plot. Above this value, an increasingly large fraction of the dynamically young stars has large rotational velocities, and beyond [FORMULA] =1.9 (M5.5) essentially all of them rotate. The plot for the older population on the other hand only includes two stars with significant rotation, the M4.5 ([FORMULA] =1.6) dwarf Gl 166C with v sin i  = 5.2  [FORMULA] and the M6 dwarf ([FORMULA] =2.1) Gl 412B with v sin i  = 9.4  [FORMULA]. For the size of the two subsamples ([FORMULA] 65 dynamically younger objects and [FORMULA] 33 older ones) this difference is statistically significant (Fig. 4).

[FIGURE] Fig. 3. Projected rotational velocity as a function of the [FORMULA] color index for a stars with young disk kinematics, and b stars with kinematics typical of older populations. Known short period binaries or binaries with blended correlation profile have been excluded in both plots. The symbol coding is the same as in Fig. 1, except that stars in b) are old disk stars from Basri et al. 1996.
[FIGURE] Fig. 4. Fraction of stars with large rotational velocity (v sin i [FORMULA][FORMULA]) as a function of their spectral type.

Given the overlap of the velocity distributions of the various galactic populations, Fig. 3b by necessity contains some younger stars, so that it would in principle be possible that no old star actually has significant rotation. There is indeed good evidence that Gl 166C is a young disk star on the tail of the velocity distribution of its population, since Eggen (1996) deduce an age of only 1.6 Gyr from the [FORMULA] chromospheric flux of Gl 166A, the K1Ve brightest member of the Gl 166 system (Gl 166B is the prototypical white dwarf 40 Eri B). Based on the same argument for Gl 412A, the Gl 412 system on the other hand is 9 Gyr old (Eggen 1996), and Gl 412B is thus probably a true member of the old disk, with significant rotation. At spectral type M6V it is also one of the latest star in the sample, consistent with a general increase of spin-down timescale with decreasing mass, which we advocate for below. This is in line with recent measurements by Basri et al. (1996) who find significant rotation (v sin i [FORMULA] 5 [FORMULA]) for 13 out of 18 very late M dwarfs ([FORMULA] M6.5V). Some of them have no published radial velocities, but there are at least 7 which kinematically belong to the old disk population.

Adopting the calibration of Kirkpatrick & McCarthy (1994), the mass at the M3-M4 spectral type of the break in the rotational velocity distribution of the young population is 0.18 to 0.25 [FORMULA]. This break could thus possibly correspond to the mass (0.35 [FORMULA] 0.05 [FORMULA], Chabrier & Baraffe 1997) below which main sequence stars become fully convective. The radiative/convective boundary is essential to the operation of the shell dynamo which is invoked to explain the large scale solar magnetic field (e.g. Spiegel & Weiss 1980; Spruit & van Ballegooijen 1982), and a change at about this spectral type could thus be expected for both magnetic properties and rotational braking. This approximate agreement must however be coincidental, since a similar feature should otherwise be present at this spectral type in the rotational velocity distribution of the old stellar population, and none is seen. In addition, the recent mass to spectral type calibration of Baraffe & Chabrier (1996) pushes the full convection limit to earlier than M2.5, inconsistent with the position of the break. We therefore believe that, instead of a break at 0.35 [FORMULA], we observe the continuation to lower masses of the increase in spin-down timescale with decreasing mass, seen in young clusters for the more massive star. This implies that the spin-down timescale is a significant fraction of the age of the young disk ([FORMULA] 3 Gyr: Mayor 1974; Meusinger et al. 1991) at spectral type M4 ([FORMULA] 0.15 [FORMULA], Baraffe & Chabrier 1996), and a significant fraction of the age of the old disk ([FORMULA] 10 Gyr) at spectral type M6 ([FORMULA] 0.1 [FORMULA]).

3.3. Fast rotators

In our sample seven stars have v sin i [FORMULA] km.s -1 and three are fast rotators, with v sin i [FORMULA] km.s -1: the M4 dwarfs G165-08 (v sin i [FORMULA]), and G188-38 (v sin i [FORMULA]) and the M4.5 dwarf Gl 791.2 (v sin i [FORMULA]). Adopting radii of respectively [FORMULA] and [FORMULA] for M4V and M4.5V (Chabrier & Baraffe 1995), the maximum rotational periods P/sini for these three stars are respectively 7.2, 12.7 and 8 hours. For a more massive G dwarf, the same periods would correspond to rotational velocities of v sin i of 170-100  km.s -1, similar to those of the fastest rotators in young open clusters. With a large telescope, these three stars would be good candidates for a doppler imaging program, and could provide extremely important constraints on the magnetic field geometry in fully convective stars.

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© European Southern Observatory (ESO) 1998

Online publication: February 16, 1998
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