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

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2. Observations and data processing

2.1. Sample selection

As we are interested in a fair sampling of M spectral subtypes, we decided to observe a volume-limited sample and initially selected all M dwarfs in the third edition of the nearby star catalog (Gliese and Jahreiss 1991) with a distance closer than 9 pc and a declination above -16 degrees. 136 stars fullfill these criteria. Of these, 7 (listed in Table 1) have apparent magnitudes fainter than V=15 and had to be dropped because they are beyond the sensitivity limit of the instrument we used. Gl 53B and Gl 451B are close companions to the much brighter Gl 53A (G5 VI) and Gl 451A (G8 VI) from which they cannot be separated by the spectrograph input fiber, and they were thus not observed. 7 very close pairs ([FORMULA] 1") have two separate entries in the Gliese catalog but had to be merged for this program, and two slightly wider binaries (GJ 1103AB and GJ 1116AB) could not be separated under the seeing conditions that prevailed when they were observed and only have a joint spectrum for the pair. We therefore have obtained spectra for 118 stars or systems.


Table 1. Stars with [FORMULA] and [FORMULA] too faint to be measured with ELODIE

2.2. Instrumental setup

All observations were obtained at Observatoire de Haute Provence with the ELODIE spectrograph (Baranne et al. 1996) on the 1.93m telescope, between September 1995 and March 1997. This fixed configuration dual-fiber-fed echelle spectrograph covers in a single exposure the 390-680 nm spectral range, at an average resolving power of 42000. Elaborate on-line processing is integrated with the spectrograph control software, and automatically produces optimally extracted and wavelength calibrated spectra, with algorithms described in Baranne et al. (1996). Brighter stars (V [FORMULA] 13) were observed with a thorium lamp illuminating the monitoring fiber, as needed for best (15  [FORMULA]) radial velocity accuracy (Baranne et al. 1996). Fainter stars always have insufficient S/N to reach such an accuracy, and they were instead observed with this fiber illuminated by the sky, allowing subtraction of the diffused solar light whose lines would otherwise bias the velocity profile. Integration times ranged between 10 minutes and 1 hour, and resulted in signal to noise ratios in the 47th order ([FORMULA] 555nm) ranging between 4 and 150, with a median of [FORMULA] 15.

2.3. Rotational velocity analysis

The extracted spectra were analysed for velocity by digital cross-correlation with a binary template (i.e. a spectrum where each pixel is set either to 1 or 0). This processing is standard for ELODIE spectra (Queloz 1995a, 1995b) and it closely mirrors the optical cross-correlation performed in the older CORAVEL spectrograph (Baranne et al. 1979). It effectively amounts to averaging with equal weights the few thousand lines included in the binary template. Given their random blending with weaker lines, and by virtue of the central limit theorem, this results in a very clean, nearly gaussian, instrumental velocity profile. This comes at a price in sensitivity, which could be improved in various ways, for instance by giving more weight to the deeper lines. Useful velocity information can nonetheless still be extracted from spectra with average S/N lower than 1.

The correlation template used for this program was generated by Baranne et al. (1996) from a Bell & Gustafsson (private communication) synthetic spectrum of a K0III star, and is part of the standard ELODIE reduction package. Though not an optimal match for the M stars discussed here, this mask was the reddest available when this program was started, and it generally produces a good correlation dip even for low signal to noise ratio spectra of the later M dwarfs in our sample. As discussed below, the width of this correlation profile for non rotating stars ([FORMULA]) is also nearly constant in the [K7V,M6V] interval. This advantageous feature (for the present purpose) is not shared by the redder masks which have now become available: the intrinsic full width to half maximum of their correlation profile varies by over 1  [FORMULA] over the [M0V,M6V] range (Delfosse et al. 1997). The calibration of the measured profile width to v sin i is then more difficult, and it would in particular require more accurate [FORMULA] colour indexes than are available for a number of stars. The K0 template was thus retained.

The three fastest rotators however produced shallow correlation dips with the K0 mask, since the same equivalent width is then spread over a wider velocity range. This didn't permit an accurate width determination, and they were thus recorrelated with a preliminary M0V mask generated from the observed spectrum of Gl 411 (Queloz, private communication). The resulting correlation dips are twice as deep and the linewidth accuracy correspondingly better. These fast rotators have broad enough lines that the correlation process doesn't measurably widen their correlation dips, and there is no need to calibrate out a contribution of the mask. An equivalent reprocessing was considered unnecessary for slower rotators, since the uncertainty on their v sin i is dominated by the intrinsic dispersion in their unbroadened profile (as discussed below), and improved S/N would not help much. The width of the correlation function was in all cases estimated by fitting a gaussian function. Accurate radial velocities were measured at the same time. They will be used in forthcoming papers to discuss the binary fraction in field M dwarfs and to obtain some accurate stellar masses.

[FIGURE] Fig. 1. 1/e half-width of the correlation profile as a function of the [FORMULA] color index for a and b all stars, and c the non-active stars (no [FORMULA] emission) only. Symbol codes are: open circles for the young disk, open squares for the young/old disk, filled triangles for the old disk, filled circles for the halo. Known or possible short period binaries (P [FORMULA] 30days) have been excluded in these plots.

The standard error on the profile width was calibrated as a function of spectral type and signal to noise ratio, through Montecarlo simulations along the lines of Baranne et al. (1996), adding controlled photon noise and CCD readout noise to high signal to noise ratio spectra. Their [FORMULA] constant (their equation (9)) is 0.085 for early M dwarfs ([M0,M2]) and 0.075 for M3V and cooler spectral types.

2.3.1. v sin i

The resulting profile 1/e half-widths are plotted in Fig. 1a, as a function of the R-I colour index. As can be seen, the plot has a well defined lower envelope, populated by slow rotators and/or nearly pole-on stars, which corresponds to the instrumental profile width [FORMULA] of the spectrograph+correlation combination. Fig. 1b zooms on this lower envelope and shows a small but significant colour dependence of this instrumental width, better seen in Fig. 1c which only shows the non-active (and thus non-rotating, Sect. 4) stars: [FORMULA] decreases from [FORMULA] 5.1 [FORMULA] to [FORMULA] 4.7 [FORMULA] between R-I=0.8 and R-I=1.5, and seems to saturate for redder stars. A somewhat larger variation is observed for earlier stars, with [FORMULA] increasing from 4.6  [FORMULA] to [FORMULA][FORMULA] over the G0V-K7V spectral range (R-I=[0.3,0.8]), (Queloz 1995a, and private communication). Part of this variation certainly results from the better spectral resolution in the red part of the ELODIE format, which carries increasing weight in the correlation profile for decreasing effective temperatures. Systematic changes in pressure broadening and microturbulent velocity with effective temperature probably contribute too.

At a given R-I colour there is also some significant intrinsic dispersion in [FORMULA], at a level of [FORMULA] (Fig. 1c). For G and K stars metallicity explains most of this intrinsic dispersion (Queloz, 1995a), with a larger fraction of the lines broadened by saturation in metal-rich stars. The same mechanism must also contribute in M dwarfs, but the Zeeman effect and different levels of microturbulent broadening in individual stars could play a role too.

Given the low level of the [FORMULA] variations, we have not attempted to calibrate them out. Instead, we have quadratically added a 200  [FORMULA] systematic uncertainty to the standard errors of all profile width measurements before we determined confidence intervals for v sin i . This currently sets the limit on the accuracy of the measured v sin i : even though ELODIE can measure the 1/e half-width of the correlation profile of bright stars to better than 20 [FORMULA] (i.e. to 1/200 pixel), we are unable to measure v sin i below [FORMULA][FORMULA].

For warmer stars, the v sin i - [FORMULA] calibration is established (Queloz 1995a) by convolving the spectrum of a number of stars with known long rotational periods (hence negligible broadening) with a rotational broadening profile (e.g. Gray 1992, p 370), and measuring the resulting correlation width. We use the same method, but there are unfortunately very few rotation period measurements for late main sequence stars: no star later than M2 has a known long rotational period, and for the spectral type range of our sample, only Gl 411 (M2, old disk population, [FORMULA] days, v sin i [FORMULA]) and Gl 820B (K5, old disk population, [FORMULA] days, v sin i [FORMULA]) (Hempelmann et al. (1995)) have measured periods that imply v sin i   1.5 km.s -1. We have used those two stars for our calibration, and complemented them by Barnard's star (Gl 699, halo M4). Gl 699's rotational period is unknown, but it must be a very slow rotator given its old kinematic population and lack of magnetic activity, and the correlations discussed in Sect. 4. The v sin i difference between the three calibrations is less than 1  [FORMULA] below v sin i =8  [FORMULA], and only reaches 2 km.s -1 at large rotational velocities. The unknown sini factor is then always a more significant uncertainty source in the analysis. We have used the Gl 411 calibration, to which [FORMULA] is a good analytical fit. 68% confidence intervals for v sin i were obtained by applying the v sin i calibration to [FORMULA] 1 sigma intervals centered on the measured correlation profile width.

Because rotation and magnetic fields are linked, part or all of the broadening that we attribute to rotation could, in principle at least, be due to Zeeman splitting of individual lines, as first suggested by Benz and Mayor (1984). This would however require rather strong magnetic field, with 3  km.s -1 broadening already corresponding to [FORMULA] 5kG (Benz and Mayor, 1984). Such fields have only been found in the most active cool main sequence stars, and appear unlikely for the vast majority of the sample. Zeeman broadening in addition could not explain the faster rotators (v sin i [FORMULA]), since strong magnetic field would produce a resolved Zeeman pattern (e.g. Babel et al., 1995) which is quite distinct from the observed rotational profiles. We therefore believe that, with at most a few exceptions, the measured v sin i are indeed due to rotation.

Given the poorer v sin i sensitivity of Stauffer & Hartmann (1986), the most suitable comparison sample is Marcy & Chen (1992), who measured projected rotational velocities for 47 field late-K and M dwarfs, and found measurable rotation (v sin i [FORMULA]) in only 5. Contrary to them, we find that one quarter of the field M dwarfs have measurable rotation (up to v sin i [FORMULA]). This apparent discrepancy may be partly due to our slightly lower detection threshold of 2  [FORMULA], but it mostly reflects a better sampling of the late M subtypes. As discussed below, the late M dwarfs have a much larger fast rotator fraction. For the 19 stars in common with Marcy & Chen (1992), the two measurements are fully consistent. For Gl 285 and Gl 388 they respectively measure [FORMULA] and [FORMULA], where we obtain [FORMULA] and [FORMULA]. For the 17 other stars their upper limits of [FORMULA] are consistent with our measurements of at most [FORMULA]. GJ 1111 was measured by Basri & Marcy (1995) and there is also good agreement: they measure [FORMULA] where we obtain [FORMULA].


A significant fraction of the sample shows emission in the hydrogen Balmer lines, sometimes extending to [FORMULA]. We have then used the spectra to determine their [FORMULA] and [FORMULA] fluxes. We didn't on the other hand attempt measuring the (weaker) Balmer absorption seen in most of the early M spectra.

Since line spectrophotometry wasn't an initial objective of the program, the observations have no matching spectrophotometric calibration. Comparison of two observations of the OV spectro-photometric standard HD93512 separated by [FORMULA] one year (D.Queloz, private communication) however shows that the relative efficiency of ELODIE (+telescope+atmosphere) is stable to within [FORMULA] 10% over the [460 nm,680 nm] range, even though variations at bluer wavelength are considerably larger. This interval contains [FORMULA], [FORMULA], and the V filter passband. The average of these two spectra was thus used to convert all observations to relative flux density.

The calibrated spectra were integrated over the V filter passband and the width of the two Balmer lines to produce relative fluxes in these three bands. Those for the lines were continuum subtracted, using the average flux density of two nearby bandpasses (655.0-655.9 nm and 656.8-657.7 nm for the [FORMULA] line; 484.8-485.7 nm and 486.6-487.5 nm for the [FORMULA] line) as an estimate of the continuum level at the line wavelength. Continuum definition is difficult for these very cold stars, whose spectra are made up of a forest of overlapping blended lines. For weak chromospheric lines, its uncertainties are the dominant error source on the relative line flux, and they prevent us from measuring equivalent widths smaller than [FORMULA] 0.4 Å (typically [FORMULA] [FORMULA] [FORMULA]   [FORMULA]   [FORMULA] for an M5 dwarf). Their contribution to the eventual error bars on [FORMULA] [FORMULA] [FORMULA] and [FORMULA] [FORMULA] [FORMULA] was estimated from the difference between the continuum computed at the right and at the left of the line, probably giving slightly overestimated errors. The fluxes were then converted to relative luminosities, [FORMULA] and [FORMULA]. To convert those to fractional luminosities in the lines, [FORMULA] and [FORMULA], a V band bolometric correction is needed. We have compiled the bolometric correction measurements from Tinney et al. (1993), Berriman & Reid (1987), Reid & Gilmore (1984), and Greenstein (1989), and determined a fit as a function of the [FORMULA] colour: [FORMULA] (Fig. 2) [FORMULA] was taken from Leggett (1992) whenever possible, or the Kron R-I listed in the CNS3 catalog (Gliese & Jahreiss 1991) were converted to the Cousin system using the transformation given in Bessel (1983). The resulting Balmer lines luminosities are listed in Table 4.

[FIGURE] Fig. 2. Bolometric correction curve. The fit is [FORMULA]

Standard errors for the fractional luminosities in the two chromospheric lines were estimated from the quadratic sum of the pseudo-continuum definition uncertainty with a 10% uncertainty for the relative spectrophotometric calibration. They are usually much lower than the typical intrinsic variability of the Balmer lines in these active stars: multiple observations of the same star often differ by more than a factor of two.


Schmidt et al. (1995) list the X-ray luminosity of all K and M stars within 7 pc. They have obtained deep ROSAT pointed observations for all their stars which were not detected in the ROSAT all-sky survey (RASS), so the nearer half of our sample has nearly complete X-ray information. Between 7 and 9 pc we have used the RASS catalog data (Voges et al. 1997), with the count-rate to flux calibration (Fleming et al. 1995) used by Schmitt et al. (1995). Use of the RASS data results in a limiting sensitivity of about [FORMULA] (Schmidt et al. 1995), and 34 non detections.

2.6. UVW space motion and kinematic population

The UVW space motion in Table 4 is calculated from our measurements of radial velocity, trigonometric parallaxes and proper motions taken from either the Yale General Catalogue of Trigonometric Stellar Parallaxes (Van Altena et al. 1991) or the Hipparcos input catalogue (Turon et al. 1993). U, V and W are heliocentric, with U positive toward the Galactic anticenter. The proper motion standard errors typically translate into [FORMULA][FORMULA] uncertainties on the space motion, while the parallax typically contribute a [FORMULA] 5% proportional uncertainty. The accurate radial velocities do not contribute appreciably to the overall UVW errors, except perhaps for an occasional unrecognised spectroscopic binary. The space velocities were then used to distribute the stars into young disk, old disk, and Population II, with two intermediate groups young/old disk and old disk/Population II, adopting the criteria of Leggett (1992). Our classification agrees with hers for stars in common, except where our improved radial velocities significantly change the space velocity. It must of course be remembered that these population assignments are only statistically valid, as there is significant overlap between the velocity distributions of the different galactic populations (e.g. Carney et al. 1990). Given the low relative local density of the halo, the older kinematic group is most likely dominated by the thick disk rather than the true halo.

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Online publication: February 16, 1998