ROTATION AND ACTIVITY IN MID-M TO L FIELD DWARFS Subhanjoy Mohanty 1 and Gibor Basri 1

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1 The Astrophysical Journal, 583: , 2003 January 20 # The American Astronomical Society. All rights reserved. Printed in U.S.A. ROTATION AND ACTIVITY IN MID-M TO L FIELD DWARFS Subhanjoy Mohanty 1 and Gibor Basri 1 Received 2002 July 6; accepted 2002 September 26 ABSTRACT We analyze rotation velocities and chromospheric (H) activity, derived from high-resolution spectra, in a large sample of mid-m to L field dwarfs. The projected rotation velocity is found to increase from mid-m to L. This is consistent with a lengthening of spin-down timescale with later type, although in the L types the trend may also be a function of the observational bias toward younger objects. From M4 to M8.5 a saturation-type rotation-activity relation is seen, similar to that in earlier types, when activity is measured through either F H or L H /L bol. However, we find that activity saturates at a significantly higher velocity (10 km s 1 ) in the M5.5 M8.5 dwarfs than in the M4 M5 ones (d4kms 1 ). This may result from a change in the dynamo behavior with later type (see also below). We note that the saturation level in H emission appears to vary somewhat less with spectral type (from M4 to M8.5) when activity is measured through L H / L bol instead of F H. In M9 and later dwarfs, we observe a drastic drop in activity and a sharp break in the rotation-activity connection: H emission levels in these dwarfs are much lower than in earlier types, and often undetectable, in spite of very rapid rotation. This may be caused by the very high resistivities in the predominantly neutral atmospheres of these dwarfs, which would damp the magnetic energy available for supporting a chromosphere. It is also possible that the rapid formation of dust in these cool atmospheres exacerbates this effect, as charged particles are soaked up by (more massive) dust grains. Finally, we note that spectral type determination from low-resolution spectra may be affected by gravity effects: cooler, lower gravity objects may mimic hotter, higher gravity ones. Therefore, it is possible that the few unsaturated fast rotators from M5.5 to M8.5 (whose presence leads us to ascribe a higher saturation velocity to these spectral types, as noted above) may actually be very low mass objects, with lower T eff (and gravity) than their spectral types suggest. If so, their behavior (low activity, fast rotation) would be compatible with that of the cool M9 and later dwarfs (and no change in dynamo behavior would have to be postulated in the M5.5 M8.5 dwarfs). This interpretation is supported by a preliminary analysis of the high-resolution spectra of these anomolous objects. It is also bolstered by the fact that a saturation-type Rossby number activity relation is seen in the M5.5 M8.5 dwarfs when these anomalous objects are removed from the sample, while the relationship is much weaker when they are included. Subject headings: stars: activity stars: low-mass, brown dwarfs stars: rotation 1. INTRODUCTION A rotation-activity relation has long been noted in mainsequence and pre main-sequence solar-type stars (F5 and later) (Charbonneau, Schriver, & Macgregor 1995 and references therein). In recent years, the observations have been extended down to mid-m (Delfosse et al. 1998, hereafter D98). However, since high-resolution spectra provide the best means of investigating rotation and chromospheric activity, the intrinsically fainter late-m dwarfs have not been scrutinized in as much detail. The same is true of the new L-type objects, many of which are substellar. In this paper, we present high-resolution optical data for a large sample of mid-m to mid-l dwarfs in order to examine the trends in rotation, activity, and the connection between the two in very low mass stars and brown dwarfs. A preliminary version of this work was presented at the Cool Stars XI conference by Basri (2000). In the present paper, the previous sample has been extended to include more objects, and rotation velocity (v sin i), H flux, and effective temperature are determined more accurately. We also present a more detailed investigation of the trend in v sin i and of the rotation-activity connection. A summary of this work can be found in Mohanty & Basri Astronomy Department, University of California, Berkeley, CA 94720; subu@astron.berkeley.edu, basri@soleil.berkeley.edu. 451 To set this work in context, we briefly summarize here the trends in rotation and activity that have been observed in F5 M5 dwarfs and the salient issues that we wish to address in the later types. Rotation. Stars in this spectral range all spin down with age. However, the spin-down timescale appears to increase with later spectral type, with fast rotators occurring only at later and later types with increasing age. The following examples illustrate these points. In the Persei cluster (85 Myr), although half of all the stars are slow rotators (v sin id10 km s 1 ), very rapid rotators (v sin i 100 km s 1 ) are found at all spectral types (Prosser et al. 1996). By the age of the Pleiades (120 Myr), half the stars are still slow rotators, but rapid rotators (v sin i > 50 km s 1 ) are seen only among the K and M dwarfs and are nearly absent among the F and G dwarfs (Stauffer et al. 1994). In the Hyades (600 Myr), relatively rapid rotators (v sin i km s 1 ) are found only among the M dwarfs, and all F, G, and K dwarfs are slow rotators (Stauffer et al. 1997). In the field young-disk sample (d3 Gyr), only stars later than M3.5 are relatively rapid rotators (v sin ie5 km s 1 ) (D98). Finally, in the field old-disk and halo sample (e3 Gyr), only stars later than M5.5 appear to be relatively rapid rotators (v sin ie5kms 1 ) (D98), although this result is based on a very small sample. Activity. Activity, as measured through markers such as excess emission in X-rays (coronal activity) and H

2 452 MOHANTY & BASRI (chromospheric activity), is strongly correlated with rotation velocity in the mid-f to mid-m dwarfs: it increases rapidly with increasing v sin i, then saturates above some threshold velocity (v sin i 10 km s 1 ). This is actually strictly true only down to the K types. In the M dwarfs, the fraction of emitters increases from early M to M6 (Hawley, Gizis, & Reid 1996), but the situation regarding the rotation-activity connection is less clear. The rising part of the rotation-activity curve has not been clearly resolved in the studies so far because of poor observational sensitivity to low v sin i. As a result, it can be confidently stated only that M dwarfs exhibit a saturation-type rotation-activity relation, wherein activity is saturated above a threshold velocity; it is unclear whether v sin i and activity are actually correlated in the unsaturated part of the curve in M dwarfs. There is also some evidence that it is rotation period, rather than rotation velocity, that is more germane to the level of activity for the mid-f to mid-m dwarfs. For example, in the Hyades M dwarfs, the threshold velocity above which X-ray activity saturates is 15 km s 1, while in the field M sample, saturation occurs at 5kms 1 ; both cases, however, correspond to a rotation period of 1.5 days (D98). The various physical processes that are thought to account for these trends are discussed in Mohanty et al. (2002), and other sources (see Charbonneau et al. 1995). Here we only outline the main points that are important to keep in mind for this paper. For mid-f to early-m dwarfs, rotation and activity are thought to be controlled by an dynamo, which operates at the interface between the radiative core and convective envelope. Its efficiency is strongly dependent on both rotation rate and convective timescales, i.e., on the Rossby number (Ro, where Ro ¼ P [rotation period]/ c [convective overturn timescale]); the field generation rate increases as Rossby number decreases. The reasons for saturation are not yet well understood; it may result when the dynamo is efficient enough to generate sufficient flux to cover the entire stellar surface. After about M3, stars are expected to be fully convective, so the dynamo can no longer operate. It is thought that a turbulent dynamo dominates at these late types (Durney, De Young, & Roxburgh 1993). The latter produces small-scale fields, which are not very efficient at driving angular momentum loss through winds, which may explain why these dwarfs are comparatively rapid rotators at late times (D98; Durney et al. 1993). However, the rotation-activity connection in these dwarfs is then puzzling, since the turbulent dynamo is expected to be only weakly dependent on rotation rate. Alternatively, a strongly rotation-dependent 2 dynamo may be operational in these fully convective objects (Rädler et al. 1990) and dominate over the turbulent mode. As noted above, D98 find only a saturation-type relation between rotation and activity in their mid-m sample. It may be that the 2 dynamo becomes dominant even before the onset of full convection and that it is sufficiently strong at these late types to produce saturation even at very low rotation rates. This can conceivably cause the saturation-type relationship observed in the mid-m dwarfs and explain the absence of a break in the relationship at the onset of full convection (at M3). We stress here that, even in the Sun, a substantial fraction of the field is noncyclical and on small spatial scales, indicative of the presence of a turbulent or 2 dynamo. It is plausible that the contribution of these dynamo modes strongly increases as convection begins to dominate the stellar interior. In this paper we wish to investigate how the observed trends in rotation and activity noted above change as one moves to still later spectral classes. Specifically, we wish to examine spectral classes M6 and later. The two main issues we address are (1) does the spin-down timescale continue to increase with later type and (2) is a rotation-activity connection still evident in these dwarfs. The latter issue is especially important, since there have been suggestions (Basri 2000; Basri & Marcy 1995, hereafter BM95; Gizis et al. 2000, hereafter G00) that activity levels decline in these very late types. In x 2 we detail our observational technique, data reduction methods, and sample selection. In x 3 we discuss the derivation of radial and rotational velocities and H parameters. Our results are given in x 4. In particular, we discuss radial velocity anomalies in x 4.1, rotational trends in x 4.2, and chromospheric activity and its connection to spectral type, rotation and Rossby number in x 4.3. Our conclusions are stated in x OBSERVATIONS AND DATA REDUCTION Observations were made with the W. M. Keck I 10 m Telescope on Mauna Kea using the HIRES echelle spectrometer (Vogt et al. 1994). The observation dates are listed in Table 1. All the targets were M5 or later, including several L types. The settings used were similar to those of BM95. The instrument yielded 15 spectral orders from 640 to 860 nm (with gaps between orders), detected with a Tektronix CCD. The CCD pixels are 24 lm in size and were binned 2 2; the bins are hereafter referred to as individual pixels. Each pixel covered 0.1 Å, and use of slit decker D1 gave a slit width of 1>15 projected on the sky, corresponding to 2 pixels on the CCD and a 2 pixel spectral resolution of R ¼ 31; 000. The slit length is 14>, allowing excellent sky subtraction. The CCD exhibited a dark count of 2 e hr 1 and a readout noise of 5 e pixel 1. The data were reduced in a standard fashion for echelle spectra, using IDL procedures. This includes flat-fielding with a quartz lamp, order definition, and extraction and sky subtraction. The stellar slit function is found in the redmost order and used to perform a weighted extraction in all orders. The wavelength scale is established using a ThAr spectrum taken without moving the grating; the solution is a two-dimensional polynomial fit good to 0.3 pixels or better everywhere. Cosmic-ray hits and other large noise spikes were removed using an upward median correction routine, wherein points more than 7 above the median (calculated in 9 pixel bins) were discarded. We have augmented our sample with a number of mid-m dwarfs (M4 M5.5) from D98, one late-m dwarf (ESO ) from Tinney & Reid (1998, hereafter TR98), and L dwarfs from Basri et al. (2000, hereafter B00). In all these cases, radial velocities and v sin i were adopted unchanged from the primary source. B00 did not undertake an analysis of H, and the equivalent widths and fluxes were calculated by us from their original spectra. We have also recalculated the H widths and fluxes from the original D98 spectra (which were kindly provided to us by Delfosse) to ensure a standardized sample. Only for ESO , for which we did not have access to the original spectrum, have the H values been adopted without change from the original source. For all other objects in our sample, we have calculated the radial velocities and v sin i as well as the H parameters.

3 TABLE 1 Observational Sample Name Other Spectral Type v rad (km s 1 ) Observation Date Reference a (K) T eff b Age c Gl 105B M OD GJ M OD Gl 169.1A M YO LHS M YO Gl M H G M YD GJ 2069B M YD Gl M YO Gl M YO G M YD Gl M YD Gl M HO G M YD Gl 860B M YO Gl M YD Gl M OD Gl 166C M OD Gl M YD Gl 234A M YD LHS M YO Gl M YD Gl M H GJ M OD Gl M YD GJ M YO LHS M YD GJ M OD Gl M YD Gl 896B M YD G M YD LP M YD GJ M OD GJ M OD GJ 1154A M YD GJ M YD GJ 1230B M YD GJ 1245AC M YO GJ 1245B M YO GJ M OD GJ M OD YZ CMi... GJ 285 M Nov YD Gl 65B... LHS 10 M Dec YD LP BRB M Sep GJ 1245A... LHS 3494 M Mar YO Gl 412B... LHS 39 M HO CTI M Sep GJ 3828B... LHS 2876 M May Gl LHS 36 M Nov OD Jun Dec GJ LHS 292 M Nov OD GJ LHS 1070 M Nov LP BRB M May CTI M Jun CTI M Dec GJ LHS 248 M Nov YD CTI M May GJ LHS 523 M Nov OD VB 8... Gl 644C M Mar OD GJ LHS 3003 M Mar LHS LP M Mar YO LHS LP M Nov OD Mar CTI M Mar

4 454 MOHANTY & BASRI Vol. 583 TABLE 1 Continued Name Other Spectral Type v rad (km s 1 ) Observation Date Reference a (K) T eff b Age c May 2MASS M May MASS M May LHS LP M Nov OD LP MASSW J M Nov OD RG RG M Nov YO VB Gl 752B M Nov OD Mar 2MASS M May ESO Ruiz M LHS 2397A... GJ 3655 M Mar OD TVLM M Mar YD LHS GJ 3849 M Mar OD CTI M Nov TVLM BRIB M Mar DENIS M LHS GJ 3517 M Nov YD LP BRIB M BRI M Mar YD DENIS M BRI M Nov Nov DENIS L0.0 3, DENIS L G196-3B... 2MASSW J L1.0 0, MASS L Kelu L DENIS L MASS L GD 165B... 2MASSW J L Mar LHS 102B L DENIS L4.5 4, DENIS L5.0 6:, MASS L6.0 5: DENIS L a These are the sources for the original spectra, v rad and v sin i. In all cases except ESO , H data is derived by us from the original spectra, even when the original authors derived H parameters themselves. (1) D98; (2) this paper; (3) TR98; (4) B00. b These are the T eff derived from the spectral type-t eff fit shown in Fig.1; the stars used to derive this fit are listed in Table 2. c OD ¼ old disk, YO ¼ intermediate young/old disk, H ¼ halo, YD ¼ young disk, HO ¼ halo/old disk. 3. ANALYSIS 3.1. Radial Velocity Barycentric and stellar radial velocity corrections were derived for each observed spectrum. We thank G. Marcy for the IDL routine, which calculates the barycentric correction. The radial velocities (v rad ) were derived by measuring the peak position for cross-correlation functions between each star and a radial velocity standard. We chose Gl 406 (M6), with a known radial velocity of 19 1kms 1 (Martín et al. 1997), as our standard for the M dwarfs. We have observed Gl 406 in 1997 June with two different setting and in 1997 December and 1993 November with two other settings. In all four cases, a calibration of its spectrum on an absolute wavelength scale indeed gives 19 1kms 1. A full description of our methods for calculating v rad by comparison to a template can be found in B00. The one important change in this paper is that we now calculate the cross-correlation function in multiple orders (instead of in just one) for a given star; this minimizes the effect of shift errors due to spectral mismatches in any one order. The final shift (in pixels) between the stellar and template spectrum is the average of the shifts in each order. Our velocity resolution varies from 4.2 to 4.4 km s 1 pixel 1, depending on the spectrograph setting. For a given setting, the resolution varies by 0.01 km s 1 pixel 1 from the bluest to the reddest order. This change affects our velocity determinations by at most 1 km s 1, and mostly by much less. We have chosen therefore to use the average of the bluest and reddest order resolutions for a given setting to convert the order-averaged pixel shift to a velocity. We conservatively estimate the errors in our velocities to be 2 kms 1. In all cases where we have more than one observation of a star (usually separated by a year or more and sometimes observed with different settings), our v rad agree to within better than 1 km s 1. The final derived v rad are given in Table 1, rounded to the nearest km s 1. Our 1993 November spectra were also used by BM95 to calculate radial velocities. Like us, they used Gl 406 as their v rad standard. However, they adopted a v rad ¼ 16:5 kms 1 for Gl 406, while we use a more recent and accurate determination of 19 km s 1 (Martín etal. 1997). Once this discrepancy is accounted for, our results agree very well in all cases. Radial velocitites for a number of our sample objects have also been determined by TR98.

5 No. 1, 2003 ROTATION AND ACTIVITY IN MID-M TO L FIELD DWARFS 455 In all but three cases, our v rad are in complete agreement. The three anomalous objects are discussed in x 4.1. Finally, we would like to correct a v rad error in B00. In that paper we found an anomalously high velocity, v rad 40 km s 1, for Gl 406 in 1997 June. However, we have found that there was a mistake in the barycentric velocity used for the 1997 June observation (resulting from a transcription error). This was entirely responsible for the high v rad derived. With this error now corrected, all our observations of Gl 406 are in agreement with each other, with no radial velocity anomalies; our observations are entirely commensurate with v rad ¼ 19 1kms 1 for this object Rotational Velocity Rotation velocities were calculated for our sample by cross-correlation of target spectra with Gl 406. Again, a detailed description of the methods used are given in B00, whose sample consisted mainly of comparatively fast rotating L dwarfs. For the M dwarfs, rotation velocities are usually low, so the following refinement was made to the B00 methods, to ensure accurate v sin i. The cross-correlation function between the target star and template was calculated separately in multiple orders containing molecular lines (TiO, VO, CrH, and FeH). These functions were coadded to yield an average cross-correlation function, and v sin i was obtained from the latter in the manner described in B00. This yields more precise values of v sin i: the average cross-correlation function is less noisy than the individual functions corresponding to separate orders, and as a result it is easier to distinguish between small v sin i. Ideally, a nonrotating template should be used. In our sample, Gl 406 has the lowest previously determined rotation velocity, with v sin i < 3kms 1 (Delfosse et al. 1998). Our instrumental profile broadening alone, on the other hand, is larger at 4 km s 1 (given our 1 pixel resolution of 0.1 Å in the optical). As a result, Gl 406 is close to being an ideal nonrotator in our observations and has been used as a template to determine v sin i for the rest of our sample. Instrumental broadening and rotation in the template are potential sources of error in our derived v sin i. A nonzero instrumental broadening (in both the target star and template), and a possible nonzero (but less than 3 km s 1 ) v sin i in our template star, may affect the cross-correlation function. This is especially a concern when the target v sin i values are not very high, and both the instrumental broadening and possibly the rotational broadening of the template are comparable to the rotational broadening of the target. To test the magnitude of the errors introduced, we have crosscorrelated model spectra that have been artificially broadened to simulate instrumental and rotational broadening. In these tests we have assumed that the template (artificially constructed from a model) has v sin i ¼ 3kms 1, the largest v sin i that Gl 406 can possibly have. We have found that the errors introduced are marginal. The instrumental broadening, combined with rotational broadening of the template, does limit the lowest v sin i to which we are sensitive, to 4 km s 1. For v sin ie11 km s 1, on the other hand, there is no discernible effect on the cross-correlation function (errors are <0.5 km s 1 ). For v sin i between 4 and 6 km s 1, instrumental broadening and rotational broadening in the template lead us to underestimate the v sin i by only 1 km s 1 ; for v sin i between 7 and 10 km s 1, we underestimate by only 0.5 km s 1. At the same time, we estimate from tests on Gl 406 and our other sample objects (which, unlike the idealized models, include noise and uncertainties in the slope of the cross-correlation functions) that our random errors are of order 1kms 1 for v sin i between 4 and 20 km s 1. That is, at low v sin i we can distinguish between stars that differ in v sin i by at least 1 km s 1. Consequently, the systematic errors discussed above are at most of order our random errors and less in all cases where the v sin i is found to be e 7kms 1. Therefore we do not correct our v sin i values for the systematic effects but instead adopt a (conservative) total error of 2 kms 1 in all cases. We note that our v sin i sensitivity of 1 km s 1 and the final adopted error of 2 km s 1 correspond to approximately 0.25 and 0.5 pixels, respectively. A subpixel velocity resolution is the whole point of using the cross-correlation function, which, by summing the contributions from a large number of molecular features, results in a much finer final accuracy than the actual spectral resolution. The same is true for radial velocity determinations. We note that the v sin i quoted here are slightly changed in some cases from those in Basri The values here are more accurate. Reid et al. (2002, hereafter R02) compared their v sin i to the Basri 2000 ones for the nine objects they had in common. In all but one case, the two sets of values agreed. The one glaring discrepancy was BRI , with v sin i 2kms 1 in Basri (2000) and 8 km s 1 in R02. We find in this paper, in agreement with the latter authors, that BRI indeed has a velocity of 8 km s 1 ; the Basri (2000) value is to be disregarded. In all other cases, the v sin i in this paper are in agreement with the R02 results, within the errors (2 kms 1 in both cases). For v sin i < 8 km s 1, we find that our values are systematically slightly higher (by 2 kms 1 ) than those in R02. We suspect this results from the latter authors use of v sin i calibrators that are appreciably faster rotators than ours. We use Gl 406, with v sin i < 3kms 1, while they use Gl 83.1, Gl 412B, and LHS 2632, with v sin i of 4, 7, and 5 km s 1, respectively. 2 As discussed above, a rotating template is expected to give lower than actual v sin i values, especially at low velocities (as the v sin i being determined approaches that of the template itself). In our case, this makes a difference of at most 1kms 1 ; for R02, with substantially faster rotating templates, the offset will be significantly larger. We suggest that this effect, for which R02 do not seem to have corrected, leads to their derived v sin i being systematically lower than ours at low rotation rates. Our derived v sin i are given in Table H Equivalent Width At a 2 pixel resolution of 31,000, we are sensitive to 0.2 Å in H equivalent width. The width for each object in our sample was measured as follows. A polynomial fit to the entire continuum was obtained in the H order, and the continuum divided by this fit to flatten it. Two different estimates of the continuum level at H were then obtained: the first by taking the average continuum value to the left of the H line, over the range [6545, 6559] Å, and the second 2 For LHS 2632, R02 find less than 4 km s 1 but do not give a reference for this value, while we find 5 km s 1 in this paper. At the very least, we find it to be a faster rotator than Gl 406 (<3 kms 1, from D98), which is compatible with the R02 value. For Gl 83.1 and Gl 412B, the values are from R02 itself, adopted from D98.

6 456 MOHANTY & BASRI Vol. 583 by taking the average value to the right of the line, over [6567, 6580] Å. This was done to account for any residual slope remaining in the continuum after flattening. H equivalent widths using each of the two continuum estimates were obtained, and the final width adopted was the average of the two. The difference in the two continuum estimates is a source of measurement error. However, we found that in most cases the difference is d0.2 Å, and in all cases it is less than 10% of the final equivalent width. Another possible source of error is the fact that the blue wing of the H line appears to sit on a small spectral feature. Whether this is an emission feature or a bump in the continuum formed by two adjacent molecular absorption features is impossible to say. The final equivalent widths used were measured after excluding this feature by eye; our measurements are in error insofar as this exclusion was inaccurately performed. We estimated this error by finding the width with the feature included in a selected subsample. Once again, in most cases the width changed by d0.2 Å, and in all cases by less than 10% of the final width. The main source of error, of course, is the continuum estimate itself. That is to say, the large number of molecular absorption lines destroys any possibility of estimating the true continuum. There is no true continuum observable in these objects, only a pseudocontinuum, which we have attempted to measure as described. The fact that our two continuum estimates usually agree within 0.2 Å of each other does not preclude the fact that both may be systematically off from the true continuum value by a much larger amount. This would systematically change our derived H widths. However, without a knowledge of the true continuum, it is not possible to quantify this error. Therefore we ignore this effect from now on, with the caveat that our H equivalent widths should be regarded only as pseudowidths. The final equivalent widths derived are noted in Table T eff Determination When discussing excess H emission as an indicator of chromospheric activity, it is usual to consider the H surface flux (F H ) or the ratio of H luminosity to bolometric luminosity (L H /L bol ). To translate equivalent width into surface flux one needs to know the underlying continuum flux against which the H is observed, which in turn requires a knowledge of the star s effective temperature. The same is true for calculating L bol. Furthermore, the rotation activity connection at earlier types is often understood in terms of Rossby number. To calculate the latter, convective overturn timescales are needed, which are again a function of T eff. For these reasons, we need an effective temperature scale for our mid-m to L dwarfs, to enable conversion to T eff from the observed spectral type. In the L dwarfs, much progress has been made in constructing such a scale (Schweitzer et al. 2001; B00; Kirkpatrick et al. 1999), but some uncertainty persists. Indeed, the spectral classification itself of L dwarfs is still an ongoing process, although the community appears to be converging onto a robust scheme (see Geballe et al and references therein). For the M dwarfs, the spectral classification scheme is on firmer footing (Kirkpatrick, Henry, & McCarthy 1991, hereafter KHM; Kirkpatrick, Henry, & Simons 1995, hereafter KHS), but the conversion scale to T eff is still uncertain. Preliminary scales have been devised on the basis of model fitting to observed spectra, but more detailed modeling is required. Specifically, dust in the atmosphere is very important in the late-m dwarfs and perhaps in the early L dwarfs. Grains are expected to begin forming at T eff 2000 K (late-m) and gravitationally settle out of the atmosphere by early to mid- L. The appearance and subsequent settling of dust therefore needs careful consideration in the late-m dwarfs. In the L types, the situation is still unclear. B00, using high-resolution optical spectra and model spectra (Allard et al. 2000), showed that dust appears to have already settled out of the atmosphere by early L. However, using more recent atmospheric models (Allard et al. 2001), Schweitzer et al. (2001) find that dust remains suspended in the atmosphere in these dwarfs and begins to gravitationally settle out only around mid-l. Spectral energy distribution (SED) fitting to lowresolution data appears to agree with this conclusion (Leggett et al. 2001). The presence of grains, as well as their settling behavior, strongly affects the spectral characteristics at both high and low resolution and thus the T eff determination. We are currently engaged in a detailed analysis of atmospheric dust in the mid-m to mid-l dwarfs (S. Mohanty et al. 2002, in preparation, hereafter MBAH). For the purposes of this paper, however, we adopt the following tactic. For the mid- and late-m dwarfs, we have compiled the spectral classification and effective temperatures quoted in Jones et al. (1996), Leggett et al. (1996), and B00 for objects ranging from M3 to M9.5 and interpolated between them to construct a spectral type to T eff conversion. For the L dwarfs we use the same technique, using the spectral types and T eff given in B00. All objects in this analysis are the spectral type to T eff conversion are listed in Table 2. Our fits correspond to T eff ¼ 3775:5 (152:5 spectral type) for mid to late dwarfs and T eff ¼ 2214 ð89 spectral typeþ for L dwarfs. The conversion is plotted in Figure 1, and the values of T eff derived from it for our sample objects are listed in Table 1. The empirical scatter in T eff over any 0.5 spectral subtype range is relatively small, d100 K, as shown in Figure 1. The scatter is likely to arise from both spectral typing and T eff determination errors (as shown by the different spectral type and T eff determined, in some cases, by different authors for the same objects; see Table 2), as well as from real differ- Fig. 1. Effective temperature scale for our sample. Squares mark a sample of M dwarfs with T eff from various sources, and crosses mark L dwarfs from B00. The dashed line is a linear least-squares fit to the M dwarfs, and the dotted line the fit to the L dwarfs.

7 No. 1, 2003 ROTATION AND ACTIVITY IN MID-M TO L FIELD DWARFS 457 TABLE 2 Stars used for Spectral Type T eff Conversion Name Spectral Type T eff (K) Reference a Gl M M Gl 299 b... M M Gl 896A... M Gl 699 c... M M Gl M Gl M LHS M Gl 65AB d... M Gl M M GJ M M VB M Gl 569B... M LHS M M LP M DENIS-P J M DENIS-P J L DENIS-P J L G196 3B... L MASSW J L Kelu-1... L DENIS-P J L MASSW J L LHS102B... L DENIS-P J L DENIS-P J L MASSW J L DENIS-P J L a Sources for spectral type and T eff. (1) Jones et al. 1996; (2) Leggett et al. 1996; (3) B00. b M subdwarf. The different spectral types, M3 and M4, given by references 1 and 2, respectively, for Gl299 have been retained, since the difference appears larger than usual spectral typing errors. c M subdwarf. The slightly different spectral types, M3.5 and M4, given by 1 and 2, respectively, for Gl699 have been averaged, since 0.5 subtype is consistent with spectral typing errors. d We quote the mean of the spectral type range, M5.5 M6, given by Leggett et al for Gl 65AB. ences in T eff between identically classified objects. The point, however, is that this observed scatter is relatively small. We note that Gl 699 and Gl 299 appear to be M subdwarfs (Jones et al. 1996), so their inclusion in objects used to derive an M dwarf T eff scale may not be completely justified. However, we find that the T eff scale derived when these two stars are excluded differs only negligibly (specifically, it is hotter by d50 K from M4 to M4.5, and by d25 K at later M types) from the one we adopt here. We expect a systematic uncertainty of 200 K in the derived temperature scale, i.e., it is possible that Figure 1 may need to be vertically translated by this amount. Adjustments to the relative change in temperature, in going from one spectral class to the next, may also be expected as the T eff scale is refined (i.e., the exact slope of Fig. 1 may not be quite correct). However, it is important to bear in mind that, even though there is some uncertainty about the precise fashion in which T eff declines as one moves down the spectral sequence, there is no question that later types do generally correspond to lower temperatures. It is also fairly certain that, in going from mid-m to mid-l, one drops roughly by e1000 K. One other point needs to be mentioned here, and that is the influence of gravity on spectral typing and T eff determination. In the late-m and L dwarfs, the wings of the strong resonance lines of K i and Na i contribute significantly to the continuum opacity in the optical, as does dust (Allard et al. 2001). However, the broadening of the resonance lines and the formation of dust are strongly affected by surface gravity; lower gravity leads to narrower lines with weaker wings and less efficient grain formation. As a result, we find that spectral typing using the slope of the optical SED (see, for example, KHM and KHS) may be somewhat prone to confusion between objects with different gravities (MBAH). The low-resolution spectrum of a cooler, lower gravity object may mimic that of a hotter, higher gravity one, at least in the overall spectral slope. Consequently, cool lowmass objects may be classified as spectral types that are too early for their real T eff. For now, we will ignore this effect, but we will return to it in x 4.3 in order to try and resolve apparent discrepancies in the data H Activity Calibration Using the spectral type to T eff conversion shown in Figure 1, we find F ch, the appropriate continuum flux per unit wavelength at H. This is used to derive the H surface flux (F H ) from the observed equivalent width (EW H ). The F ch are obtained from the atmospheric models of Allard & Hauschildt (see also Allard et al. 2001). The models currently come in three flavors: no dust, dusty, and cond (standing for condensed dust ). In the first case, no dust grains are allowed to form; observations of late M and L dwarfs appear to rule out this scenario at these spectral types (e.g., Jones & Tsuji 1997; Basri et al. 2000; Leggett et al. 2001). In the second case, dust is accounted for in both the depletion of grain-forming molecules and in the opacity calculations. This simulates the situation where dust forms and remains suspended in the photosphere. In the third case, the depletion of grain-forming molecules is accounted for, but dust does not contribute to the opacity. This corresponds to the formation of grains and their subsequent settling below the photosphere. In this work, we adopt the cond models (the latest, 2000 version) for 1500 K T eff 2500 K, reflecting the B00 result that dust condenses out of the photosphere at these temperatures. If dust remains in the atmosphere at T eff < 2500 K, we should use dusty instead of cond models there. However, as we will see, such a procedure would only strengthen our results. For now, we will stick with the cond models at low T eff. For 2500 K < T eff 3200 K, we use the dusty models (slightly older, 1999 version 3 ). Actually, this procedure is equivalent to using cond models throughout, since, for T eff above 2500 K, all three models currently predict almost identical F ch in the H region. In other words, the models predict minimal grain formation at higher tempera- 3 F ch is almost identical in the dusty 1999 and 2000 versions. Detailed dusty 2000 model grids have not been constructed for T eff > 2500 K, since the effect of dust at these temperatures is found to be minimal.

8 458 MOHANTY & BASRI Vol. 583 tures, which appears to be compatible with the observations (Jones & Tsuji 1997). At lower T eff, the models diverge, with the dusty models predicting lower F ch than the cond ones. The adopted F ch is the average, in the models, from 6554 to 6572 Å; this region brackets the H line at 6563 Å. The continuum in this region drops very rapidly with temperature in these cool dwarfs (H now occurs in the Wien part of the Planck function). It declines by roughly a factor of 1.5 for each 100 K drop in T eff, or by almost a factor of 1000, from 3200 to 1500 K. Notice that this is a much steeper falloff than that in the bolometric flux; the latter, proportional to Teff 4, falls by a comparatively small factor of 20 over the same range in effective temperature (or by a factor of 1.2 for every 100 K decrease in T eff ). Using the derived T eff, we calculate F bol ¼ Teff 4 and F H ¼ EW H F ch. The ratio of H luminosity to bolometric luminosity is then obtained using the fact that L H =L bol ¼ F H =F bol. Notice that, as a result of the latter relationship, no theoretical determination of the stellar radius is required to calculate the ratio of the luminosities. Since our method for finding flux (or luminosity) ratios is anchored in theoretical models, how certain can we be of our final values? To address this, we compare the luminosity ratios we find for the D98 objects to those quoted by D98 for the same stars. The comparison is tabulated in Table 3. In both cases, the same spectra have been used to calculate the H equivalent widths, using very similar methods. Any difference between the results, therefore, is primarily due to differences in the derived bolometric fluxes and underlying continuum fluxes at H. We calculate the first via our spectral type to-t eff conversion and the second from theoretical models at the appropriate T eff. D98, on the other hand, calculate bolometric flux through a spectral type-dependent bolometric correction applied to the observed (R I ) C colors, and continuum flux at H directly from flux-calibrated spectra. Of the 41 D98 stars we have used (40 in the M4 M5.5 range and one at M6), there are minor discrepancies between our results in four. In two of these stars, we did not detect any H, while D98 did using the same spectra. In two others, the reverse occurred. These four stars have the lowest inferred luminosity ratios in the M4 M5.5 range, i.e., the H emission (if any) is extremely small, so the discrepancies are not surprising. Moreover, they reveal the difficulty in detecting H at very low emission values, not problems in flux ratio derivation per se. In 16 out of the remaining 37 stars, no H is detected by either us or D98 (with similar upper limits). In all the remaining 21 stars with detected H, our luminosity ratios are in excellent agreement with those of D98: the two values agree with each other, on average, to within 20% (0.08 dex on a log scale), and always to within a factor of 1.5 (0.2 dex). No systematic offset is evident between our and D98 values for these 21 stars. Given the uncertainties in both our method and that of D98 and the very different methods used to calculate the luminosity ratios (mainly theoretical vs. primarily empirical), this level of consistency is remarkable. The differences are negligible, particular since both we and D98 find that mid- to late-m dwarfs cover a range of almost 2 dex in L H /L bol (with the envelope of saturated stars alone covering 0.75 dex) (see Fig. 9). Of course, we have tested the validity of our method over only 1.5 spectral subclasses at mid-m, while we will apply Name TABLE 3 Rotation and Activity Spectral Type v sin i (km s 1 ) EW H (Å) L H =L bol This Paper (D98) a Gl 105B... M4.0 <2.4 <0.2 < 5.16 (none) GJ M4.0 < (none) Gl 169.1A... M4.0 <1.9 <0.2 < 5.16 (none) LHS M4.0 < (none) Gl M4.0 <2.9 <0.2 < 5.16 (none) G M ( 3.92) GJ 2069B... M ( 3.89) Gl M4.0 <2.3 <0.2 < 5.16 (none) Gl M4.0 <2.0 <0.2 < 5.16 (none) G M ( 3.61) Gl M <0.2 < 5.16 (none) Gl M4.0 <2.8 <0.2 < 5.16 (none) G M ( 3.73) Gl 860B... M ( 4.11) Gl M4.0 <2.0 <0.2 < 5.16 (none) Gl M ( 4.35) Gl 166C... M ( 3.95) Gl M4.5 <3.1 <0.2 < 5.21 (none) Gl 234A... M ( 4.05) LHS M4.5 < ( 4.18) Gl M ( 3.66) Gl M <0.2 < 5.21 (none) GJ M4.5 <4.1 <0.2 < 5.21 (none) Gl M ( 3.96) GJ M4.5 < ( 4.03) LHS M ( 4.08) GJ M4.5 <2.3 <0.2 < 5.21 (none) Gl M ( 4.01) Gl 896B... M ( 3.84) G M ( 3.99) LP M ( 3.90) GJ M5.0 <2.2 <0.2 < 5.26 (none) GJ M5.0 <2.8 <0.2 < 5.26 ( 4.85) GJ 1154A... M ( 3.86) GJ M ( 3.98) GJ 1230B... M5.0 <7.1 <0.2 < 5.26 (none) GJ 1245AC... M ( 4.27) GJ 1245B... M ( 4.25) GJ M5.5 <5.7 <0.2 < 5.34 ( 4.96) GJ M5.5 <3.0 <0.2 < 5.34 (none) YZCMi... M Gl 65B... M LP M GJ 1245A... M Gl 412B... M CTI M GJ 3828B... M Gl M6.0 < GJ M GJ M LP M CT I M CT I M GJ M CTI M GJ M VB 8... M GJ M LHS M LHS M CTI M MASS M MASS M

9 No. 1, 2003 ROTATION AND ACTIVITY IN MID-M TO L FIELD DWARFS 459 Name TABLE 3 Continued Spectral Type v sin i (km s 1 ) EW H (Å) L H =L bol This Paper (D98) a LHS M LP M RG M VB M MASS M ESO M LHS 2397A... M TVLM M LHS M CTI M TVLM M DENIS M LHS M LP M BRI M DENIS M BRI M <0.2 < 6.01 DENIS L <0.2 < 6.05 DENIS L <0.2 < 6.05 G196 3B... L <0.2 < MASS L <0.2 < 6.08 Kelu 1... L DENIS L <0.2 < MASS L <0.2 < 6.11 GD 165B... L LHS 102B... L DENIS L DENIS L <0.2 < MASS L <0.2 < 6.23 DENIS L <0.2 < 6.23 a For the stars taken from D98, we quote both the L H =L bol value we find (by directly measuring EW H from their spectra and applying our methods as described in x 3.5), and, in parantheses, the value quoted by D98. None indicates no H detected by D98, translating to an upper limit of 10 5 for L H /L bol in the D98 scheme. The agreement between D98 and our values is excellent in almost all cases (see text). our method to objects ranging from mid-m to mid-l. The reliability of the luminosity ratios we derive over this entire range will have to be tested through future analyses similar to the foregoing one, as well as through detailed comparisons of synthetic spectra to observations. We are currently working on such comparisons for mid- to late-m dwarfs (MBAH). However, our agreement with D98 for M4 M5.5 stars is at least very encouraging and implies we are on the right track. Furthermore, as we shall see, one of the main results of this paper is that chromospheric H emission in M9 and later objects is much lower than that in earlier types. This result depends primarily on the indisputable fact that both T eff and continuum flux at H do decrease as one moves to later types, and it is largely insensitive to the details of how this decrease occurs (i.e., is independent of the exact luminosity ratios derived). 4. RESULTS 4.1. Radial Velocity Anomalies In three stars GJ 111, TVLM , and BRI we find radial velocities at odds with those determined by other authors. For GJ 1111, TR98 find 47:3 3:2 kms 1, while we see 10:1 2kms 1. However, our measurement is in good agreement with that of D98 (9 1kms 1 ). BM95 also find a velocity similar to ours (11:2 3 km s 1 after correcting for differences in the adopted v rad of Gl 406; see x 3.1), using the same 1993 November spectrum we have used. In the case of TVLM , we find 35:7 2 km s 1, while TR98 get 47:3 5kms 1. This difference is not too large, but it is still beyond the measurement errors. We have been unable to find any other references to the radial velocity of this object, so it is impossible to judge whether this discrepancy is real or whether it results from some undiscovered error in one of the v rad values. BRI presents a puzzle. From the 1994 November spectrum, we determine 24:5 2kms 1 and, by combining two spectra from 1993 November, 16:0 2 km s 1. Using the latter two spectra, BM95 found 12:9 3km s 1. However, this becomes 15.4 km s 1 after amending their adopted v rad for Gl 406 (16.5 km s 1 ) to our more accurate value (19 km s 1 ); their result is thus in excellent agreement with ours for the 1993 November observations. A v rad of 16 km s 1 also agrees with the Reid, Tinney, & Mould (1994) measurement of km s 1, based on a 1992 observation. TR98, however, measure 2.6 and 12.8 km s 1 on consecutive nights in 1992, and 1.1 and 0.4 km s 1 on consecutive nights in 1993; their errors are of the order 5 km s 1. For all other objects that are common to their study and ours (except the three discussed here), our v rad are in very good agreement with theirs. In other words, there are no obvious indications of errors in either their study or ours. To summarize, none of the v rad for BRI using different spectra are in agreement: TR98 combine their 1992 and 1993 observations to find a weighted average v rad of 4:3 2:2 kms 1, BM95 and we find approximately 16 2 km s 1 in 1993 (using common spectra), and we find 24 2 km s 1 in The errors in the Reid et al observations are large enough to encompass all these different values. If v rad in BRI is actually constant, then at least two of these determinations, by different researchers using different techniques and standards, have to be in error. On the other hand, BRI is a very rapid rotator (we find v sin i 34 2kms 1 in both 1993 and 1994, TR98 find 42 8kms 1, and BM95 find 40 7km s 1 ), with significant broadening of its molecular features. Consequently, there is an outside chance that the discrepant v rad result from errors in identifying the centroid of a broad peak, during cross-correlation. We note that, by comparing the two 1993 November spectra, BM95 rule out v rad variations at the 3 km s 1 level over a 90 minute period. Longterm monitoring of this object is necessary to discover whether the changes in v rad are indeed real and perhaps due to an as yet undiscovered companion Rotation Velocity In Figure 2 we show the v sin i derived for our sample. We see that rotational velocity distinctly continues to increase with later spectral type. For convenience, let us (arbitrarily) define rapid rotators as those with v sin i 10 km s 1, moderate rotators as those with 5 km s 1 v sin i < 10 km s 1, and slow ones as those with v sin i < 5kms 1. Then, of 47 stars in the range M4 M5.5 (defined in this paper as mid- M), roughly half are slow (with most of these being only upper limits in v sin i) and a quarter are fast. In the M6 M9.5 range (defined here as late M), the situation is