A SPECTROSCOPIC CATALOG OF THE BRIGHTEST (J < 9) M DWARFS IN THE NORTHERN SKY^*,†

Targets for the follow-up spectroscopic program were selected from the catalog of 8,889 bright M dwarfs of Lépine & Gaidos (2011). All stars are selected from the SUPERBLINK catalog of stars with proper motions μ > 40 mas yr⁻¹. Stars are identified as probable M dwarfs based on various color and reduced proper motions cuts; all selected candidates have, e.g., optical-to-infrared colors V − J > 2.7. The low proper motion limit of the SUPERBLINK catalog excludes nearly all background red giants. The low proper motion limit however also results in a kinematic bias, whose effects are discussed in Section 2.3 below.

While some astrometric and photometric data have already been compiled for all the stars, most lack formal spectral classification. Spectral subtypes have been estimated in Lépine & Gaidos (2011) only based on a calibrated relationship between M subtype and V − J color. However, the V magnitudes of many SUPERBLINK catalog stars are based on photographic measurements (from POSS-II plates); the resulting V − J colors have relatively low accuracy and are sometimes unreliable. Besides from affecting spectral type estimates, unreliable colors can cause contamination of our sample of M dwarf candidates by bluer G and K dwarfs, which would have otherwise failed the color cut. These are strong arguments for performing systematic spectroscopic follow-up observations, to provide reliable spectral typing and filter out G/K dwarfs (or any remaining M giant contaminants).

A subsample of the brightest of the M dwarfs candidates, with apparent infrared magnitude J < 9 was assembled for the first phase of this survey. We also restricted the sample to stars north of the celestial equator. This initial list contains a total of 1,564 candidates. All stars were indiscriminately targeted for follow-up observations, whether or not they already had well-documented spectra. This would ensure completeness and uniformity, and allows comparison of our sample with previous surveys. In particular, our target list includes M dwarf classification standards from Kirkpatrick et al. (1991) which provide a solid reference for our spectral classification. The list includes 557 stars that were previously observed in the PMSU spectroscopic survey, and 161 that were observed and classified as part of the MCN spectroscopic program (including 82 stars observed in both the PMSU and MCN).

Of the 1,564 M dwarf candidates, we found that 286 had been observed at the MDM observatory by one of us (SL) prior to 2008 November, as part of a separate spectroscopic follow-up survey of very nearby (d < 20 pc) stars (Alpert & Lepine 2011). The remaining targets were distributed between our observing teams at the MDM Observatory (hereafter MDM) and University of Hawaii 2.2 m Telescope (hereafter UH), with the MDM team in charge of higher declination targets (δ > 30) and the UH team in charge of the lower declination range (0 < δ < 30). In the end we obtained spectra for all 1,564 stars from the initial target list.

To check for any possible systematic differences arising from using different telescopes and instruments, we observed 146 stars at both MDM and UH. We call this subset the "inter-observatory subset." Observations were obtained at different times at the two observatories. Data were processed in the same manner as the rest of the sample.

The full list of observed stars is presented in Table 1. We used the standard SUPERBLINK catalog name as primary designation; however, we also include the more widely used designations (GJ, Gl, and Wo numbers) for the 682 stars listed in the CNS3 (Gliese & Jahreiss 1991). The CNS3 stars are often well-studied objects, with abundant data from the literature; a majority of them (580) were classified as part of the PSMU survey or MCN spectroscopic program. Another 56 stars on our table which are not in the CNS3 were however classified as part of the PMSU survey or the MCN program. The remaining 821 stars are not in the CNS3, and were also not classified as part of the PMSU survey or MCN program; these are new identifications for the most part, and little data existed about them until now.

Table 1 lists coordinates and proper motion vectors for all the stars, along with astrometric parallaxes whenever available from the literature. The table also lists X-ray source counts from the ROSAT all-sky point source catalogs (Voges et al. 1999, 2000), far-UV (FUV) and near-UV (NUV) magnitudes from the GALEX fifth data release, optical V magnitude from the SUPERBLINK catalog (Lépine & Shara 2005), and infrared J, H, and K_s magnitudes from 2MASS (Cutri et al. 2003). More details on how those data were compiled can be found in Lépine & Gaidos (2011). The optical (V band) magnitudes listed in Table 1 come from two sources with different levels of accuracy and reliability. For 919 stars in Table 1, generally the brightest ones, the V magnitudes come from the Hipparcos and Tycho-2 catalogs. These are generally more reliable with typical errors smaller than ±0.1 magnitude; those stars are flagged "T" in Table 1. The other 645 objects have their V magnitudes estimated from POSS-I and/or POSS-II photographic magnitudes as prescribed in Lépine (2005). Photographic magnitudes of relatively bright stars often suffer from large errors at the ∼0.5 magnitude level or more, in part due to photographic saturation; those stars are labeled "P" in Table 1.

Spectra were collected at the MDM observatory in a series of 22 observing runs scheduled between 2002 June and 2012 April. Most of the spectra were collected at the McGraw-Hill 1.3 m telescope, but a number were obtained at the neighboring Hiltner 2.4 m telescope. Two different spectrographs were used: the MkIII spectrograph, and the CCDS spectrograph. Both are facility instruments which provide low- to medium-resolution spectroscopy in the optical regime. Their operation at either 1.3 m or 2.4 m telescopes is identical. Data were collected in slit spectroscopy mode, with an effective slit width of 10 to 15. The MkIII spectrograph was used with two different gratings: the 300 l mm⁻¹ grating blazed at 8000 Å, providing a spectral resolution R ≃ 2000, and the 600 l mm⁻¹ grating blazed at 5800 Å, which provides R ≃ 4000. The two gratings were used with either one of two thick-chip CCD cameras (Wilbur and Nellie) both having negligible fringing in the red. Internal flats were used to calibrate the CCD response. Arc lamp spectra of Ne, Ar, and Xe provided wavelength calibration, and were obtained for every pointing of the telescope to account for flexure in the system. The spectrophotometric standard stars Feige 110, Feige 66, and Feige 34 (Oke et al. 1991) were observed on a regular basis to provide spectrophotometric calibration. Integration times varied depending on seeing, telescope aperture, and target brightness, but were typically in the 30 s to 300 s range. Between 25 and 55 stars were observed on a typical night. Spectra for a total of 901 bright M dwarf targets were collected at MDM.

Additional spectra were obtained with the SuperNova Integral Field Spectrograph (SNIFS; Lantz et al. 2004) on the University of Hawaii 2.2 m telescope on Mauna Kea between 2009 February and 2012 November. SNIFS has separate but overlapping blue (3200–5600 Å) and red (5200–10000 Å) spectrograph channels, along with an imaging channel, mounted behind a common shutter. The spectral resolution is ∼1000 in the blue channel, and ∼1300 in the red channel; the spatial resolution of the 225-lenslet array is 04. SNIFS operates in a semi-automated mode, acquiring acquisition images to center the target on the lenslet array, and bias images and calibration lamp spectra before and after each target spectrum. Both twilight and dome flats were also obtained every night. Integration times depended on J magnitude but were 54 s for the faintest (J = 9) targets. Up to 75 target spectra were obtained in one night. Spectra for 655 bright M dwarf targets were collected at UH with SNIFS.

Spectroscopic data and results are summarized in Table 3. SUPERBLINK names are repeated in the first column and provide a means to match with the entries in Table 1. The second and third columns list the observatory and Julian date of the observations. The various spectroscopic measurements whose values are listed in the remaining columns are described in detail in the sections below.

2.3.1. MDM Data

Spectral reduction of the MDM spectra was performed using the CCDPROC and DOSLIT packages in IRAF. Reduction included bias and flat-field correction, removal of the sky background, aperture extraction, and wavelength calibration. The spectra were also extinction-corrected and flux-calibrated based on the measurements obtained from the spectrophotometric standards. We did not attempt to remove telluric absorption lines from the spectra. Many spectra were collected on humid nights or with light cirrus cover, which resulted in variable telluric features. However, telluric features generally do not affect standard spectral classification or the measurement of spectral band indices, since all the spectral indices and primary classification features avoid regions with telluric absorption.

A more common problem at the MDM observatory was slit loss from atmospheric differential refraction. Although this problem could have been avoided by the use of a wider slit, the concomitant loss of spectral resolution was deemed more detrimental to our science goals. Instead, stars were observed as close to the meridian as observational constraints allowed. In some cases, however, stars were observed up to ±2 hr from the meridian, resulting in noticeable slit losses. Fluctuations in the seeing, which often exceeded the slit width, played a role as well. As a result, the spectrophotometric calibration was not always reliable, since the standards were only observed once per night to maximize survey efficiency. Flux recalibration was therefore performed using the following procedure. Spectral indices were measured and the spectra were classified using the classification method outlined below (Section 3.1). The spectra were then compared to classification templates assembled from M dwarf spectra from the Sloan Digital Sky Survey (SDSS) spectroscopic database. Each spectrum was divided by the classification template of the same alleged spectral subtype. In many cases, the quotients yielded a flat function, indicating that the spectrophotometric calibration was acceptable. Other quotients yielded residuals consistent with first or second order polynomials spanning the entire wavelength range, and indicating problems in the spectrophotometric calibration. A second-order polynomial was fit through the quotient spectra, and the original spectrum was normalized by this fit, correcting for calibration errors. Spectral indices were then measured again, and the spectra reclassified; this yielded changes by 0.5 to 1.0 subtypes for ≈20% of the stars (no changes for the rest). The re-normalization was then performed again using the revised spectral subtypes, and the procedure repeated until convergence for all stars.

Finally, all the spectra were wavelength-shifted to the rest frames of their emitting stars. This was done by cross-correlating each spectrum with the SDSS template of the corresponding spectral subtype. Spectral indices were again re-measured, and the stars re-classified. Any change in the spectral subtype prompted a repeat of the flux-recalibration procedure outlined above, and the cross-correlation procedure was repeated using the revised spectral template until convergence.

A sequence of MDM spectra is displayed in Figure 1, which illustrates the wavelength regime and typical quality. Note the telluric absorption features near 6850 Å, 7600 Å, and 8200 Å. Signal-to-noise ratio is generally in the 30 < S/N < 50 range near 7500 Å.

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2.3.2. SNIFS Data

SNIFS data processing was performed with the SNIFS data reduction pipeline, which is described in detail in Bacon et al. (2001) and Aldering et al. (2006). After standard CCD preprocessing (dark, bias, and flat-field corrections), data were assembled into red and blue 3D data cubes. The data cubes were cleaned for cosmic rays and bad pixels, wavelength-calibrated using arc lamp exposures acquired immediately after the science exposures, and spectrospatially flat-fielded, using continuum lamp exposures obtained during the same night. The data cubes were then sky-subtracted, and the 1D spectra were extracted using a semi-analytic PSF model. We applied corrections to the 1D spectra for instrument response, airmass, and telluric lines based on observations of the Feige 66, Feige 110, BD+284211, or BD+174708 standard stars (Oke et al. 1991). Because the SNIFS spectra are from an integral field spectrograph, operating without a slit, their spectrophotometry is significantly more reliable than the slit-spectra obtained at MDM. In fact, it is possible to perform synthetic photometry by convolving with the proper filter response.

As with the MDM data, SNIFS spectra were shifted to the rest frames of their emitting stars by cross-correlation to SDSS templates (Bochanski et al. 2007) of the corresponding spectral subtype. Spectral indices were re-measured and the stars re-classified. This process was repeated if there was a change in the spectral subtype determination.

A sequence of UH SNIFS spectra are displayed in Figure 2, which show the wavelength range and typical data quality. Signal-to-noise ratio is generally S/N ≈ 100 near 7500 Å.

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We first examined all the spectra by eye to confirm the presence of morphological features consistent with red dwarfs of spectral subtype K5 and later. The main diagnostic was the detection of broad CaH and TiO moleculars band near 7000 Å. Of the 1564 stars observed, 1408 were found to have clear evidence of CaH and TiO. The remaining 156 stars did not show those molecular features clearly, within the noise limit, and were therefore identified as probable contaminants in the target selection algorithm.

Most of these contaminants appeared to be early- to mid-type K dwarfs, with a few looking like G dwarfs affected by interstellar reddening. A number of stars also displayed carbon features consistent with low gravity objects, most probably K giants. We suspect that many of the G and K dwarfs have inaccurate V-band magnitudes, making them appear redder than they really are, which would explain their inclusion in our color-selected sample. Interstellar reddening would also explain the inclusion of more distant G dwarfs in our sample, due to their redder colors. An alternate explanation, however, might be that the targets were mis-acquired in the course of the survey, and that the spectra represent random field stars. Indeed the very large proper motion of the sources sometimes makes them difficult to identify at the telescope, as they often have moved significantly from their positions on finder charts. Stars in a crowded field are particularly susceptible to this effect. To verify this hypothesis, we compared the V − J color distribution of the contaminants to the distribution of the full survey sample (Figure 3, top panel); the fraction of contaminant stars in each color bin is also shown (bottom panel). The two distributions are significantly different, with the contaminants being dominated by relatively blue stars, and their fraction quickly drops as V − J increases. We can only conclude that the contaminants are not mis-acquired stars, otherwise one would expect the two distributions to be statistically equivalent. Rather, the majority of the contaminants must have been properly acquired and are simply moderately red FGK stars that slipped into the sample in the photometric/proper motion selection, as suggested first.

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We find an overall contamination rate of ≃10% in our survey, although most of the contamination occurs among stars with relatively blue colors. The contamination rate is ≃26% for red dwarf candidates in the 2.7 < V − J < 3.0 color range, but this rate drops to ≃8% for candidates with 3.0 < V − J < 3.3, and becomes negligible (<1%) in the redder

$$\begin{equation*} V-J>3.3 \end{equation*}$$

candidates. The 156 stars identified as contaminants are included in Tables 1 and 3 for completeness and future verification. Spectroscopic measurements for these stars, such as band indices, subtypes, and effective temperatures, are however left blank.

3.2.1. M Dwarf Classification from Molecular Bandstrengths

3.2.2. Definition and Measurement of Band Indices

The strength of the TiO, CaH, and VO molecular bands are measured using spectral band indices. These spectral indices measure the ratio between the flux in a section of the spectrum affected by molecular opacity to the flux in a neighboring section of the spectrum minimally affected by molecular opacity. The latter section defines a pseudo-continuum of sorts, although M dwarf spectra do not have a continuum in the classical sense, because their spectral energy distribution strongly deviates from that of a blackbody, and is essentially shaped by atomic and molecular line opacities.

We settle on a set of six spectral band indices: CaH2, CaH3, TiO5, TiO6, TiO7, VO1, and VO2. These band indices, which we previously used in Lépine et al. (2003a) to classify spectra collected at MDM, measure the strength of the most prominent bands of CaH, TiO, and VO in the 6000 Å < λ < 8500 Å regime. The spectral indices and are listed in Table 2 along with their definition. The CaH2, CaH3, and TiO5 indices are the same as those used in the Palomar-MSU survey, and were first defined in (Reid et al. 1995). The TiO6, VO1, and VO2 indices were introduced by Lépine et al. (2003a) to better classify late-type M dwarfs, whose CaH2 and TiO5 indices become saturated at cooler temperatures and are not as effective for accurate spectral classification of late-type M dwarfs. Each spectral band index is calculated as the ratio of the flux in the spectral region of interest (numerator) to the flux in the reference region (denominator), i.e.,

$$\begin{equation} {\rm IDX} = \frac{\int _{{\rm num}} I(\lambda) d\lambda }{\int _{{\rm denom}} I(\lambda) d\lambda }. \end{equation} \tag{ 1 }$$

Because the wavelength range for some indices is relatively narrow (especially the denominator for CaH2, CaH3, and TiO5) it is important that the spectra in which they are measured have their wavelengths calibrated in the rest frame of the star, which is why special care was made to correct all spectra for any significant redshift/blueshift (see above).

Table 2. Definition of Spectral Indices

Index	Numerator	Denominator	Reference
CaH2	6814–6846	7042–7046	Reid et al. (1995)
CaH3	6960–6990	7042–7046	Reid et al. (1995)
TiO5	7126–7135	7042–7046	Reid et al. (1995)
VO1	7430–7470	7550–7570	Hawley et al. (2002)
TiO6	7550–7570	7745–7765	Lépine et al. (2003a)
VO2	7920–7960	8130–8150	Lépine et al. (2003a)

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Because the measured molecular bandheads are relatively sharp, and because the spectral indices measuring them are defined over relatively narrow spectral ranges, the index values are potentially dependent on the spectroscopic resolution, and may thus depend on the specific instrumental setup used for the observations. In addition, the index values may be affected by systematic errors in the spectrophotometric flux calibration, which can also be dependent on the instrument and/or observatory where the measurements were made. One way to verify these effects is to compare spectral index measurements of the same stars obtained at different observatories. Because of the significant overlap with the Palomar-MSU survey, we can use those stars as reference sample, and recalibrate the spectral indices so that they are consistent to those reported in Reid et al. (1995).

Our census have 557 stars in common with the PMSU spectroscopic survey; these stars are all identified with a flag ("P") in the last column of Table 3. We identify 206 stars from the list observed at MDM and 281 stars from the list observed at UH which have spectral index measurements reported in the PMSU survey. The differences between our measured CaH2, CaH3, and TiO5 and those reported in the PSMU catalog are plotted in Figure 4. Trends and offsets confirm the existence of systematic errors, possibly due to differences in resolution and flux calibration. To verify the spectroscopic resolution hypothesis, we convolved the MDM spectra with a box kernel 5-pixel wide; we found that indeed the MDM indices for the smoothed spectra had their offsets reduced by 0.01–0.02 units, bringing them more in line with the PMSU indices. We also observe that the MDM measurements tend to have a larger scatter than the UH ones; we suggest that this may be due to spectrophotometric calibration issues with some of the MDM spectra, as discussed in Section 2.3.1.

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Table 3. Survey Stars: Spectroscopic Data

Star Name	Observatory	Julian Date	CaH2ca	CaH3c	TiO5c	VO1c	TiO6c	VO2c	Sp.Ty.b	Sp.Ty.	ζ	log gd	Teffd
		2,450,000+							Index	Adopted			(K)
PM I00006+1829	MDM	4791.75	...	...	...	...	...	...	...	G/K	...	...	...
PM I00012+1358S	UH22	5791.05	0.706	0.864	0.788	0.967	0.944	0.970	0.14	M0.0	1.08	5.0	3790
PM I00033+0441	UH22	5791.05	0.580	0.797	0.679	0.959	0.888	0.939	1.38	M1.5	0.93	4.5	3510
PM I00051+4547	MDM	5095.80	0.603	0.824	0.664	0.956	0.911	1.014	1.10	M1.0	1.10	4.5	3560
PM I00051+7406	MDM	5812.87	...	...	...	...	...	...	...	G/K	...	...	...
PM I00077+6022	MDM	5838.82	0.364	0.620	0.392	0.905	0.630	0.798	4.60	M4.5	0.90	5.0	3140
PM I00078+6736	MDM	5099.83	0.534	0.789	0.623	0.905	0.806	0.929	2.03	M2.0	0.96	5.0	3500
PM I00081+4757	MDM	5098.84	0.410	0.700	0.420	0.871	0.684	0.814	3.80	M4.0	1.01	5.0	3280
PM I00084+1725	UH22	5791.06	0.671	0.842	0.785	0.970	0.947	0.970	0.34	M0.5	0.91	4.5	3600
PM I00088+2050	MDM	4413.72	0.372	0.646	0.356	0.893	0.602	0.793	4.58	M4.5	0.99	5.0	3130
PM I00110+0512	UH22	5050.03	0.653	0.839	0.706	0.962	0.893	0.925	0.86	M1.0	1.16	4.5	3660
PM I00113+5837	MDM	5811.90	...	...	...	...	...	...	...	G/K	...	...	...
PM I00118+2259	UH22	5050.03	0.439	0.729	0.424	0.923	0.694	0.798	3.50	M3.5	1.10	4.5	3260
PM I00125+2142En	UH22	5791.06	0.721	0.865	0.851	0.973	0.967	0.988	−0.18	M0.0	0.80	4.5	3690
PM I00131+7023	MDM	5812.89	0.643	0.816	0.754	0.973	0.883	1.038	0.93	M1.0	0.88	4.5	3570

Notes. ^aAll spectral indices are corrected for instrumental effects, see Section 3.2. ^bNumerical spectral subtype M evaluated from the corrected spectral band indices (not-rounded). ^cHα spectral index, comparable to equivalent width. ^dGravity and effective temperature from PHOENIX model fits.

Only a portion of this table is shown here to demonstrate its form and content. Machine-readable and Virtual Observatory (VO) versions of the full table are available.

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To achieve consistency in the measurements obtained at different observatories, we adopt the values from the PMSU survey as a standard of reference, and calculate corrections to the measurements from MDM and UH by fitting linear relationships to the residuals. A corrections to a spectral band index is thus applied following the general function:

$$\begin{equation} {\rm IDX}_{c} = A_{{\rm IDX:OBS}}\ {\rm IDX}_{{\rm OBS}} + B_{{\rm IDX:OBS}}, \end{equation} \tag{ 2 }$$

where IDX_OBS represents the measured value of an index at the observatory OBS, and (A_{IDX: OBS},B_{IDX: OBS}) are the coefficients of the transformation from the observed value to the corrected one (IDX_c). Hence the corrected values of the indices CaH2, CaH3 and TiO5 for measurements done at MDM are defined as:

$$\begin{eqnarray} &&{\rm CaH2_{c} = {A}_{\rm CaH2:MDM}\ {\rm CaH2}_{\rm MDM} + {B}_{\rm CaH2:MDM} } \end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray} &&{\rm CaH3_{c} = {A}_{\rm CaH3:MDM}\ {\rm CaH3}_{\rm MDM} + {B}_{\rm CaH3:MDM} } \end{eqnarray} \tag{ 4 }$$

$$\begin{eqnarray} &&{\rm TiO5_{c} = {A}_{\rm TiO5:MDM}\ {\rm TiO5}_{\rm MDM} + {B}_{\rm TiO5:MDM}. } \end{eqnarray} \tag{ 5 }$$

The measurements from the PSMU survey are used as standards for these three indices, and we thus have by definition: A_{CaH2: PMSU} = A_{CaH3: PMSU} = A_{TiO5: PMSU} = 1.0, B_{CaH2: PMSU} = B_{CaH3: PMSU} = B_{TiO5: PMSU} = 0.0. For OBS = MDM and OBS = UH, the adopted correction coefficients are listed in Table 4. The corresponding linear relationships are shown as red segments in Figure 4.

Table 4. Coefficients of the Spectral Index Corrections, by Observatory

IDX	AIDX: PMSU	BIDX: PMSU	AIDX: MDM	BIDX: MDM	AIDX: UH	BIDX: UH
CaH2	1.00	0.00	0.95	0.011	0.92	0.004
CaH3	1.00	0.00	0.90	0.070	1.00	−0.028
TiO5	1.00	0.00	1.00	0.000	1.06	−0.063
VO1	...	...	1.00	0.040	1.00	0.000
TiO6	...	...	1.00	−0.021	1.00	0.000
VO2	...	...	1.00	0.005	1.00	0.000

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To verify the consistency of the corrected spectral band index values, we compare the corrected values for the stars observed at both MDM and UH (the inter-observatory subset). The differences are shown in Figure 5. We find the corrected values CaH2_c, CaH3_c, and TiO5_c to be in good agreement, with no significant offsets beyond what is expected from measurement errors. The corrected values of all three spectral indices are listed in Table 3.

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The TiO6, VO1, and VO2 spectral index measurements from MDM and UH are also compared in Figure 5. Those were not measured in the PMSU survey, since the indices were introduced later (Lépine et al. 2003a), and thus are displayed here without any correction. Small but significant offsets between the MDM and UH values again suggest systematic errors due to differences in spectral resolution and flux calibration. This time we adopt the UH measurements as fiducials, and determine corrections to be applied to the MDM data. The corrections are listed in Table 4 and the corresponding linear relationships are displayed in Figure 5 as red segments. The corrected values of the three spectral indices are also listed in Table 3.

The scatter between the MDM and UH values, after correction, as well as the scatter between the UH/MDM and PMSU values, provide an estimate of the measurement accuracy for these spectral indices. Excluding a few outliers, the mean scatter is ≈0.02 units (1σ) for the CaH2, CaH3, TiO5, TiO6, and VO1 indices, and ≈0.04 units for VO2. This assumes that M stars do not show any significant changes in their spectral morphology over time, and that the spectral indices should thus not be variable.

3.2.3. Spectral Subtype Assignments for K/M Dwarfs

Because of the correlation between spectral subtype and the depth of the molecular bands, it is possible to use the values of the spectral band indices to estimate spectral subtypes. This only requires a calibration of the relationship between spectral index values and the spectral subtypes, in a set of stars which were classified by other means, e.g., classification standards. The system adopted in this paper uses the spectral indices listed in Table 2, and follows the methodology outlined in (Gizis 1997) and (Lépine et al. 2003a). Relationships are calibrated for each spectral index, and spectral subtypes are calculated from the mean values obtained from all relevant/available spectral indices. The mean values are then be rounded to the nearest half integer, to provide formal subtyping with half-integer resolution. The system is extended to late-K dwarfs as well: an "M subtype" with a value <0.0 signifies that star is a late-K dwarf: the star is classified as K7 for an index value ≈ − 1.0 and as K5 for an index value ≈ − 2.0 (note: there is no K6 subtype for dwarf stars, and K7 is the subtype immediately preceding M0).

The original spectral-index classification method for M dwarfs/subdwarfs is based on a relationship between subtype and with the CaH2 index, which measures one of the most prominent band at all spectral subtypes, and notably displays the deepest bandhead in metal-poor M subdwarfs Gizis (1997), Lépine et al. (2003a). The original relationship is: [SpTy]_CaH2 = 10.71–20.63 CaH2 + 7.91 (CaH2)². To verify this relationship, we estimated spectral subtypes from our corrected indices CaH2_c for 16 spectroscopic calibration standards from Kirkpatrick et al. (1991), which were observed as part of our survey, and span a range of spectral subtypes from K7.0 to M6.0. We found small but significant differences in our estimated spectral subtypes and the values formally assigned by Kirkpatrick et al. (1991); subtypes estimated from the Gizis (1997) relationship tend to systematically underestimate the standard subtypes by ≈0.5 units for stars later than M3. To improve on the index classification method, we performed a χ² polynomial fit to recalibrate the relationship, obtaining:

$$\begin{equation} [ \rm SpTy]_{\rm CaH2} = 11.50\hbox{--}21.71 \ {\rm CaH2}_{c} + 7.99 \ ({\rm CaH2} )^2, \end{equation} \tag{ 6 }$$

which does correct for the observed offsets at later types. Using this relationship as a starting point, and guided by the formal spectral subtype from the classification standards, we performed additional χ² polynomial fits to calibrate an index-subtype relationships for CaH3:

$$\begin{equation} [ \rm SpTy]_{\rm CaH3} = 18.80\hbox{--}21.68 \ {\rm CaH3}_{c}, \end{equation} \tag{ 7 }$$

where the corrected values of the spectral bands indices (see Equations (2)–(5)) are used. The relationships are slightly different from those quoted in Gizis (1997) and Lépine et al. (2003a) but are internally consistent to each other, whereas an application of the older relationships to our corrected band index measurements would yield internal inconsistencies, with subtype difference up to one spectral subtype between the relationships.

The ratio of oxides (TiO, VO) to hydrides (CaH, CrH, FeH) in M dwarfs is known to vary significantly with metallicity (Gizis 1997; Lépine et al. 2007). In the metal-poor M subdwarfs, it is the oxides bands that appear to be weaker, while hydride bands remain relatively strong (in the most metal-poor ultrasubdwarfs, or usdM, the TiO bands are almost undetectable). Therefore it makes sense to rely more on the CaH band as the primary subtype/temperature calibrator. The same [SpTy]_CaH2 and [SpTy]_CaH3 relationships should be used to determine spectral subtypes at all metallicity classes (i.e., in M subdwarfs as well as in M dwarfs).

Because the TiO and VO bands are also strong in the metal-rich M dwarfs, it is still useful to include these bands as secondary indicators, to refine the spectral classification. In the late-type M dwarfs, in fact, the CaH bandheads are saturating, and one has to rely on the TiO and VO bands. In fact, the VO bands were originally used to diagnose and calibrate ultracool M dwarfs of subtypes M7–M9 (Kirkpatrick et al. 1995). The main caveat in using the oxide bands for spectral classification is that this can potentially introduce a metallicity dependence on the estimated spectral subtype, with more metal-rich stars being assigned later subtypes than what they would have based on the strength of their CaH bands alone. In any case, because our sample appears to be dominated by near-solar metallicity stars, we calibrate additional relationships between subtype and the TiO5 and TiO6 bands indices. We first recalculate the subtypes by averaging the values of [SpTy]_CaH2 and [SpTy]_CaH2, and perform a χ² fit of the TiO5 and TiO6 indices to the mean subtypes calculated from CaH2 and CaH3, finding:

$$\begin{equation} [ \rm SpTy]_{\rm TiO5} = 7.83\hbox{--}9.55 \ {\rm TiO5}_{c} \end{equation} \tag{ 8 }$$

$$\begin{eqnarray} [ \rm SpTy]_{\rm TiO6} &=& 9.92\hbox{--}15.68 \ {\rm TiO6}_{c} +21.23 \ ({\rm TiO6}_{c} )^2\nonumber\\ &&- 16.65 \ ({\rm TiO6}_{c} )^3, \end{eqnarray} \tag{ 9 }$$

where again the corrected band indices are used. The relatively sharp non-linear deviation in the TiO6 distribution around M3 forces the use of a third order polynomial in the fit.

We also determine the relationships for the VO1 and VO2 band indices. This after recalculating the subtypes from the average of [SpTy]_CaH2 and [SpTy]_CaH2, [SpTy]_TiO5, and [SpTy]_TiO6, a χ² fit again yields:

$$\begin{equation} [ \rm SpTy ]_{\rm VO1} = 69.8\hbox{--}71.4 \ {\rm [\rm VO1]_{c}} \end{equation} \tag{ 10 }$$

$$\begin{eqnarray} [ \rm SpTy ]_{\rm VO2} &=& 9.56\hbox{--}12.47 \ {\rm [\rm VO2]_{c}} + 22.33 \ ({\rm [\rm VO2]_{c}} )^2\nonumber\\ &&- 19.59 \ ({\rm [\rm VO2]_{c}} )^3. \end{eqnarray} \tag{ 11 }$$

The VO indices, however, make relatively poor estimators of spectral subtypes for our sample, mainly because the shallow slope at earlier subtypes provides little leverage. The VO2 index also shows unexpectedly large scatter in the MDM spectra, including in the classification standard stars, which we suspect is due the fact that the index is defined very close to the red edge of the MDM spectral range and is thus more subject to statistical noise and flux calibration errors. We therefore do not include [SpTy]_VO12 and [SpTy]_VO2 in the final determination of the spectral subtypes.

Figure 6 plots all the corrected spectral band indices as a function of the adopted spectral subtype. The relatively small scatter (≈0.02) in the distribution of [CaH2]_c, [CaH3]_c, [TiO5]_c and [TiO6]_c demonstrate the internal consistency of the spectral type calibration for the four indices. All four relationships have an average slope ≈10, which means that since those indices have an estimated measurement accuracy of ≈0.02 units, the spectral subtypes calculated by combining the four indices should be accurate to about ±0.10 subtype assuming that the measurement errors in the four indices are uncorrelated. While this would make it possible to classify the stars to within a tenth of a subtype, we prefer to follow the general convention and assign spectral subtypes to the nearest half-integer.

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To verify the consistency of the spectral classification, we compare the spectral types evaluated independently for the list of 141 stars observed at both MDM and UH. We find that 82% of the stars end up with the same spectral type assignments from both observatories, i.e., they have spectra assigned to the same half-subtype. All the other stars have classifications within 0.5 subtypes. This is statistically consistent with a 1σ error of ±0.18 on the spectral type determination, slightly larger than the assumed 0.1 subtype precision estimated above. This suggests a 3σ error of about ±0.5, which justifies the more conservative use of half-subtypes as the smallest unit for our classification.

The resulting classifications based on the CaH and TiO band index measurements are listed in Table 3. The numerical spectral subtype measured from the average of the band indices is listed to two decimal figures. These values are rounded to the nearest half integers to provide our more formal spectral classifications to a half-subtype precision. The non-rounded values are however useful for comparison with other physical parameters as they provide a continuous range of fractional values; these fractional subtype values are used in the analysis throughout the paper

A histogram of the distribution of spectral subtypes is shown in Figure 7, with the final tally compiled in Table 5. Most of the stars in our survey have subtypes in the M0.0–M3.0 range. The sharp drop for stars of subtypes K7.5 and K7.0 is explained by the color selection used in the Lépine & Gaidos (2011) catalog (V − J > 2.7) which was originally intended to select only M dwarfs; note that stars with subtypes earlier than K7.0 are also excluded from the graph, and are probably contaminants of the color selection in any case. Our deficit of K7.0 and K7.5 star spectra however demonstrates that the adopted selection criterion is efficient in excluding K dwarfs from the catalog. The distribution of spectral subtypes also shows a marked drop in numbers for subtypes M4 and later. This is a consequence of the relatively bright magnitude limit (J < 9) of our subsample, combined with the low absolute magnitudes of late-type M dwarfs, which excludes most late-type stars from our survey, since these tend to be fainter than our magnitude limit, even relatively nearby ones.

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Table 5. Distribution by Spectral Subtype of the 1564 Survey Stars

Spectral Subtype	N
G/Ka	160
K7.0	27
K7.5	101
M0.0	177
M0.5	160
M1.0	152
M1.5	147
M2.0	141
M2.5	119
M3.0	125
M3.5	125
M4.0	72
M4.5	36
M5.0	13
M5.5	4
M6.0	2
M6.5	2
M7.0	1

Note. ^aStars identified as earlier than K7.0 and/or with no detected molecular bands.

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To verify the accuracy and consistency of spectral typing based the spectral-index method described above, we performed independent spectral classification using the Hammer code (Covey et al. 2007). The Hammer was designed to classify stars in the Sloan Digital Sky Survey Spectroscopic database, including M dwarfs (West et al. 2011). The code works by calculating a variety of spectral-type sensitive band indices, and uses a best-fit algorithm to identify the spectral subtype providing the best match to those band indices. For late-K and M dwarfs, spectral subtypes are determined to within integer value (K5, K7, M0, M1, ..., M9).

However, to ensure that the automatically determined spectral types were accurate we used the manual "eye check" mode of the Hammer (version 1.2.5). This mode is typically used to verify that there are no incorrectly typed interlopers. The Hammer allows the user to compare spectra to a suite of template spectra to determine the best match. West et al. (2011) have found that for late-type M dwarfs, the automatic classifications were systematically one subtype earlier than those determined visually. Our analysis confirms this offset, and we therefore disregarded the automatically determined Hammer values to adopt the visually determined subtypes.

The resulting subtypes are listed in Table 3. Some 170 stars were not found to be good fits to any of the K5, K7, or M type templates, and thus identified as early-K or G dwarfs. This subset includes all of the 156 stars that were visually identified as non-M dwarfs on first inspection (see Section 3.1). The remaining 14 stars were initially found to be consistent with late-K stars, and classified as K7.0 and K7.5 objects using the spectral index method described in Section 3.2 above; we investigated further to determine why the stars were classified as early K using the Hammer. On closer inspection, we found that three of the stars are indeed more consistent with mid-K dwarfs that K7.0 or K7.5, and we thus overran the spectral index classification and reclassified them as "G/K" in Table 3. For the other 11 stars flagged as mid-K type with the Hammer, we determined that the stars do show significant evidence for TiO absorption, which warrants that the stars retain their spectral-index classification of K7.0/K7.5.

In the end Table 3 lists 159 stars from our initial sample that are identified and early-type G and K dwarf contaminants, and most likely made our target list due to inaccurate or unreliable V − J colors. The remaining 1405 stars are formally classified as late-K and M dwarfs.

A comparison of spectral subtypes determined from the spectral-index and Hammer methods is shown in Figure 8. Because the Hammer yields only integer subtypes, we have added random values in the −0.4, 0.4 range to facilitate the comparison. Slanted lines in Figure 8 show the range expected if the two classification methods (spectral index, Hammer) agree to within 1.0 subtypes. There is, however, a mean offset of 0.26 subtypes between the spectral index and Hammer classifications, with the Hammer subtypes being on average slightly later.

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Figure 8 also reveals a number of outliers with large differences in spectral subtypes between the two methods. We found 48 stars with differences in spectral subtyping larger than ±1.5. The spectra from these stars were examined by eye: except for one star, we found the band-index classifications to agree much better with the observed spectra than the Hammer-determined subtypes. The one exception is the star PM I11055+4331 (Gl 412B) which the band index measurements classify as M6.5; in this case the Hammer determined subtype of M 5.0 appears to be more accurate. This exception likely occurs because of the saturation of the CaH2 and CaH3 subtypes in the late-type star, which make the band-index classification less reliable.

After the PMSU survey, the largest spectroscopic survey of M dwarfs in the northern sky was the one presented in the "Meet the Cool Neighbors" (MCN) paper series (Cruz & Reid 2002; Cruz et al. 2003, 2007; Reid et al. 2003, 2004, 2007). In this section we compared the spectral classification from the MCN survey with our own spectral type assignments.

To identify the stars in common between the two surveys, we first performed a cross-correlation of the celestial coordinates of the stars listed in the MCN tables, to the coordinates listed in the SUPERBLINK catalog. This was performed for the 1077 stars in MCN which are north of the celestial equator. We found counterparts in the SUPERBLINK catalog to within 1'' for 860 of the MCN stars. Of the 217 MCN stars with no obvious SUPERBLINK counterparts, 148 are classified as ultracool M dwarfs (M7–M9) or L dwarfs (L0-L7.5) which means they are very likely missing from the SUPERBLINK catalog because they are fainter than the V = 19 completeness limit of the catalog. Of the 71 remaining stars, close examination of Digitized Sky Survey scans failed to identify the stars at the locations quoted in MCN. A closer examination of the fields around those stars identified 49 cases where a high proper motion stars could be found within 3' of the quoted MCN positions. These nearby high proper motion stars are all listed in SUPERBLINK, and have colors consistent with M dwarfs; we therefore assumed that the quoted MCN positions are in error, and matched those 49 MCN entries with the close by high proper motions stars from SUPERBLINK. Of the remaining 22 stars we found 6 that have proper motions below the SUPERBLINK limit of μ > 40 mas yr⁻¹ and another 5 stars with proper motions within the SUPERBLINK limit but that appear to have been missed by the SUPERBLINK survey. Finally, there were 11 MCN stars that we could not identify at all on the Digitized Sky Survey images, and we can only assume that the positions quoted in MCN are too large for proper identification, and that the stars should be considered "lost."

Of the 909 stars in the MCN program with SUPERBLINK counterparts, we found only 219 which satisfy the magnitude limit (J < 9) of our present sample of very bright M dwarfs. Of those, 52 stars have colors bluer (V − J < 2.7) than our sample limit; 48 of them are classified as F and G stars in MCN, consistent with their bluer colors. The other four stars are classified as M dwarfs, although they have V − J < 2.7 according to Lépine & Gaidos (2011). We infer that our V − J colors for those stars are probably underestimated, which suggests that our color selection may be overlooking a small fraction of nearby M dwarfs. In addition, we found another six stars which have V magnitudes and V − J colors within our survey range, but were rejected by the additional infrared (J − H, H − K) color-color cuts used in Lépine & Gaidos (2011) to filter out red giants. All six stars are very bright in the infrared, and it appears that at least one of the H or K magnitudes listed in the 2MASS catalog may be in error, making the stars appear to have J − H and/or H − K colors more consistent with giants. Four of the stars are classified as M dwarfs in MCN, the other two are late-K dwarfs. Overall, this makes a total of eight M dwarfs from the MCN census that were overlooked in our selection out of the MCN subset of ≈150 nearby M dwarfs. This suggests that our color cuts, combined with magnitude measurement errors, might be missing ∼5% of the very bright, nearby M dwarfs.

In the end, this leaves only 161 stars in common between the MCN program and our own spectroscopic survey. The stars are all classified as late-K and M dwarfs by MCN, with subtypes ranging from K5 to M5.5. All 159 stars are identified with a flag ("M") in the last column of Table 3; we note that 82 of these stars were also observed as part of the PMSU survey. We compare the spectral type assignments from both surveys in Figure 9, where the M dwarf subtypes from MCN are plotted against the (non-rounded) subtypes calculated from the spectral-band indices. To ease the comparison, random values of ±0.2 are added to the MCN subtypes. Overall, our classifications agree to within ±0.5 subtypes with the MCN values. The MCN subtypes, however, tend to be marginally earlier on average, by 0.28 subtypes; this is in contrast with the Hammer classifications (see above) which tend to be slightly later than our own. For the MCN subtypes, the effect is more pronounced for the earlier M dwarfs (<M2.5), where the mean offset is 0.43 subtypes, whereas the mean offset is only 0.09 for the later stars.

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To investigate the difference in spectral subtype assignments, we compare the recorded values of the CaH2, CaH3, and TiO5 indices between the MCN program and our own survey. After a search of the various tables published in the MCN series of papers, we identified 54 stars in common between the two programs, and for which values of CaH2, CaH3, and TiO5 were also recorded in both. The differences between the spectral index values are shown in Figure 10. For our own survey, the corrected values of these indices are used, i.e., CaH2_c, CaH3_c, and TiO5_c as defined in Section 3.2.2. We find that the CaH2 and TiO5 are estimated marginally higher in the MCN program than they are in our survey, and this very likely explains the difference in spectral typing: the higher index values yield marginally earlier spectral subtypes. This again emphasizes the variation in the spectral index measurements due to spectral resolution and other instrumental setups, and the need to apply systematic corrections between observatories to obtain a uniform classification system.

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We note that smaller subsets of stars in our census may also have spectroscopic data published in the literature, from various other sources. This is especially the case for the 102 stars from the CNS3 and stars with very large proper motions mu > 02 yr⁻¹ which have been more routinely targeted for follow-up spectroscopic observations. Additional spectroscopic surveys of selected bright M dwarfs include, Scholz et al. (2002, 2005), Reyle et al. (2006), and (Riaz et al. 2005), which all have a few stars in common with our catalog. Other surveys of nearby M dwarfs have mainly been targeting fainter stars (Bochanski et al. 2005, 2010; West et al. 2011), and do not overlap with our present census.

Spectral subtypes were initially estimated in Lépine & Gaidos (2011) based on V − J colors alone. Here we verify this assumption and re-evaluate the color–magnitude relationship for bright M dwarfs. The V − J color index combines estimated optical (V) magnitudes from the SUPERBLINK catalog to the infrared J magnitudes of their 2MASS counterparts. The SUPERBLINK V magnitudes are estimated either from the Tycho-2 catalog V_T magnitudes, or from a combination of the Palomar photographic B_J (IIIaJ), R_F (IIIaF), and I_N (IVn) magnitudes, as described in Lépine & Shara (2005). Values of V are more accurate for the former (≈0.1 mag) than for the latter (≳0.5 mag); Table 1 indicates the source of the V magnitude.

Mean values and dispersion about the mean of the V − J colors are listed in Table 6, for each bin of half-integer subtype; the table also lists how many stars of each type are in each bin. The V − J colors of our stars are also plotted as a function of spectral subtype in Figure 11 (top panel). The adopted color–subtype relationship from Lépine & Gaidos (2011) is shown as a thick dashed line in Figure 11. Stars with the presumably more reliable Tycho-2 magnitudes are shown in blue, while stars with photographic V magnitudes are shown in red. Stars with Tycho-2 V magnitudes appear to have marginally bluer colors at a given subtype; this however is an effect of the visual magnitude limit of the Tycho-2 catalog, which includes only the brightest stars in the V band and is thus more likely to list bluer objects. The Lépine & Gaidos (2011) relationship generally follows the distribution at all subtypes, but with mean offsets up to ±0.4 mag in V − J, especially at earlier and later subtypes. We perform a χ² fit to determine the following, improved relationship:

$$\begin{eqnarray} [ \rm SpTy]_{V-J} &=& { -32.79 + 20.75(V - J) - 4.04(V - J)^2}\nonumber\\ && + 0.275(V - J)^3 \end{eqnarray} \tag{ 12 }$$

after exclusion of 3σ outliers. The relationship is shown in Figure 11 (solid line). There is a scatter of 0.7 subtype between [SpTy]_{V − J} and the subtype determined from spectral band indices. While the spectroscopic classification is more accurate and reliable, photometrically determined spectral subtypes using the equation above should still be accurate to ±0.5 subtype about 80% of the time, and to ±1.0 subtype 95% of the time, which may be useful for a quick assessment of subtype when spectroscopic data is unavailable.

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Table 6. Colors and T_eff for Red Dwarfs in our Survey as a Function of Spectral Subtype

Subtype	nNUV − Va	$\overline{{\rm NUV}-V}$a	σNUV − Va	nV − J	$\overline{V-J}$	σV − J	$\overline{T_{{\rm eff}}}$	$\sigma _{T_{{\rm eff}}}$
K 7.0	11	8.17	0.21	25	2.90	0.31	4073	98
K 7.5	47	8.60	0.31	97	2.89	0.16	3883	82
M 0.0	87	8.66	0.36	175	2.94	0.21	3762	71
M 0.5	79	8.74	0.30	159	3.11	0.34	3646	48
M 1.0	76	8.89	0.39	151	3.19	0.18	3565	44
M 1.5	57	9.07	0.38	147	3.36	0.23	3564	39
M 2.0	57	9.25	0.47	139	3.52	0.34	3518	57
M 2.5	48	9.45	0.50	118	3.69	0.28	3500	61
M 3.0	34	9.61	0.38	125	3.91	0.28	3423	62
M 3.5	28	9.69	0.33	124	4.17	0.33	3320	66
M 4.0	5	9.72	0.35	71	4.45	0.41	3204	76
M 4.5	1	...	...	36	4.81	0.46	3119	43
M 5.0	0	...	...	12	5.23	0.50	3014	61

Note. ^aNon-active ("quiescent") red dwarfs only.

Only a portion of this table is shown here to demonstrate its form and content. Machine-readable and Virtual Observatory (VO) versions of the full table are available.

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We also compare the near-UV to optical magnitude color NUV − V for the 714 stars in our sample which have counterparts in GALEX; the distribution is shown in Figure 11 (bottom panel). We find that stars become progressively redder as spectral subtype increases, from NUV − V = 8 at M0 to NUV − V = 10 at M4. There is however a significant fraction of M dwarfs which display much bluer NUV − V colors at any given subtype. The excess in NUV flux is strongly suggestive of chromospheric activity (see Section 6 below for a more detailed analysis). We separate the active stars from the more quiescent objects with the following condition:

$$\begin{equation} [ {\rm {NUV}} - V ] > 7.7 + 0.35 [\rm Spty], \ \end{equation} \tag{ 13 }$$

where [Spty] is the mean spectral subtype calculated from Equations (8)–(11). After excluding active stars, we calculate the mean values and scatter about the mean of NUV − V for each half-integer spectral subtype. Again those are listed in Table 6 for reference; the table also lists the number of non-active stars used to calculate the mean. There is not a sufficient number of stars to calculate mean values and scatter at M4.5 (1 star) and M5.0 (0 star).

The ζ_TiO/CaH parameter (denoted ζ for short) is a combination of the TiO5, CaH2, and CaH3 spectral indices, which was shown to be correlated with metallicity in metal-poor M subdwarfs (Woolf et al. 2009). The index was first described in Lépine et al. (2007), and a revised calibration has recently been proposed by Dhital et al. (2012). The index measures the relative strength of the TiO molecular band around 7,000 Å with respect to the nearby CaH molecular band. In cool stars, in fact, the ratio between TiO and CaH is a function of both gravity and metallicity. The CaH band is noticeably stronger in giants (Mann et al. 2012), and this effect can be used as affective means to separate out M giants from M dwarfs using optical spectroscopy. In the higher gravity M dwarfs/subwarfs however, the TiO to CaH ratio is however believed to be mostly affected by metallicity, although young stars may show gravity effects as well.

The ζ parameter was originally introduced to rank metal-poor, main-sequence M stars into three metallicity classes (Lépine et al. 2007); stars with 0.5 < ζ < 0.825 are formally classified as subdwarfs (sdM), 0.2 < ζ < 0.5 defines extreme subdwarfs (esdM), while a ζ < 0.2 identifies the star as an ultrasubdwarf (usdM). However, it is conjectured that ζ could be used to measure metallicity differences in disk M dwarfs, i.e., at the metal-rich end. Disk M dwarfs are generally found to have 0.9 < ζ < 1.1, though it is unclear if variations in ζ correlate with metallicity for values within that range. Measurement of Fe lines in a subset of M dwarfs and subdwarfs does confirm that the ζ parameter is correlated with metallicity (Woolf et al. 2009), with ζ ≃ 1.05 presumably corresponding to solar abundances. However there is a significant scatter in the relationship, which raises doubts about the accuracy of ζ as a metallicity diagnostic tool.

A important caveat is that the TiO/CaH ratio is not sensitive to the classical iron-to-hydrogen ratio Fe/H, but rather depends on the relative abundance of α-elements to hydrogen (α/H) because O, Ca, and Ti are all α-elements. Variations in α/Fe would thus weaken the correlation between ζ and Fe/H. The α/Fe abundance ratio is however relatively small in metal-rich stars of the thin disk (±0.05 dex) disk stars, and are found to be significant (±0.2 dex) mostly in more metal-poor stars associated with the thick disk and halo (Navarro et al. 2011). It is thus unclear whether typical α/Fe variations would affect the ζ parameter significantly in our subset, which is dominated by relatively metal-rich stars.

On the other hand, it is clear that the index has significantly more leverage at later subtypes. This is because the strengths of both the TiO and CaH bands are generally greater, and their ratio can thus be measured with higher accuracy. The index is much less reliable at earlier M subtypes, however, and is notably inefficient for late-K stars.

A more important issue is the specific calibration adopted for the ζ parameter, which is a complicated function of the TiO5, CaH2, and CaH3 indices. The ζ parameter itself is defined as

$$\begin{equation} \zeta = \frac{1-{\rm TiO5}}{1-[{\rm TiO5}]_{Z_{\odot }}}, \end{equation} \tag{ 14 }$$

which in turns depend on $[{\rm TiO5}]_{Z_{\odot }}$, itself a function of CaH2+CaH3. The function $[{\rm TiO5}]_{Z_{\odot }}$ represents the expected value of the TiO5 index in stars of solar metallicity, for a given value of CaH2+CaH3. In (Lépine et al. 2007), ${\rm TiO5}]_{Z_{\odot }}$ was defined as

$$\begin{equation} [{\rm TiO5}]_{Z_{\odot }} = -0.050\hbox{--}0.118 \ {\rm CaH} + 0.670 \ {\rm CaH}^2 - 0.164 \ {\rm CaH}^3, \end{equation} \tag{ 15 }$$

where CaH = CaH2 + CaH3. The more recent calibration of Dhital et al. (2012), on the other hand, uses

$$\begin{eqnarray} [{\rm TiO5}]_{Z_{\odot }} &=& -0.047\hbox{--}0.127 \ {\rm CaH} + 0.694 \ {\rm CaH}^2 \nonumber\\ &&- 0.183 \ {\rm CaH}^3 - 0.005 \ {\rm CaH}^4. \end{eqnarray} \tag{ 16 }$$

The difference between the two calibrations is mainly in the treatment of late-K and early-type M dwarfs, as illustrated in Figure 14. When overlaid on the distribution of CaH2+CaH3 and TiO5 values from our current survey, however, the two calibrations fail to properly fit the distribution of data points at the earliest subtypes (high values of CaH2+CaH3 and TiO5). This results in the Lépine et al. (2007) overestimating the metallicity at earlier subtypes, while the Dhital et al. (2012) calibration tends to underestimate metallicity.

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In any case, the evidence presented in Sections 3.3 and 3.4, which shows that differences in spectral resolution and flux calibration can yield differences in the TiO5, CaH2, and CaH3 spectral indices of the same stars, also suggests that a calibration of the ζ parameter may only be valid for data from a particular observatory/instrument. A general calibration of ζ may only be adopted after corrections have been applied as described in Section 3.2. Because we do not have any star in common with the Dhital et al. (2012) subsample, we cannot verify the consistency of their ζ calibration to our data at this time. In addition, because we have now applied a correction to our MDM spectral index measurements, the Lépine et al. (2007) calibration of ζ may now be off, and should not be used for our sample.

Instead, we recalibrate the ζ parameter again, using our corrected spectral index values. Our fit of [TiO5]_c as a function of [CaH]_c = [CaH2]_c + [CaH3]_c yields:

$$\begin{eqnarray} [{\rm TiO5}]_{Z_{\odot }} &=& 0.622\hbox{--}1.906 \ ([{\rm CaH}]_{c}) - 2.211 \ ([{\rm CaH}]_{c})^2 \nonumber\\ &&- 0.588 \ ([{\rm CaH}]_{c})^3. \end{eqnarray} \tag{ 17 }$$

We calculate the new ζ values using the corrected values of the TiO5 index, i.e.,

$$\begin{equation} \zeta = \frac{1-{\rm [TiO5]_{c}}}{1-[{\rm TiO5}]_{Z_{\odot }}}. \end{equation} \tag{ 18 }$$

All our values of ζ are listed in Table 3.

In order to evaluate the accuracy of the ζ measurements, we compared the values of ζ independently measured at both MDM and UH for the 146 stars in our inter-observatory subset. Values are compared in Figure 15 (top panel) which shows Δζ = ζ_MDM − ζ_UH as a function of spectral subtype. We find a mean offset $\bar{\Delta \zeta }=-0.01$ and a dispersion σ_Δζ = 0.10. The small offset indicates that the ζ measurements are generally consistent between the two observatories. The dispersion σ_Δζ, on the other hand, provides an estimate of the measurement accuracy. Splitting the stars in three groups, we find the mean offsets and dispersions $(\bar{\Delta \zeta },\sigma _{\Delta \zeta })$ to be (−0.086, 0.244) for subtypes K7.0–M0.5, (−0.011, 0.103) for subtypes M1.0–M2.5, and (0.008,0.036) for subtypes M3.0–M5.5. Assuming that stars do not show significant variability in those bands, we adopt the dispersions as estimates of the measurement errors on ζ for that particular subtype range. It is clear from Figure 14 that early-type stars should have larger uncertainties in ζ because of the convergence of the iso-ζ lines. The best leverage for estimating metallicities from the TiO and CaH bandheads is at later types when the molecular bands and well developed.

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The overall distribution of ζ values as a function of spectral subtype also shows a decrease in the dispersion as a function of spectral type (Figure 15, bottom panel). In early-type dwarfs (K7.0–M0.5), the scatter in the ζ values is relatively large, with σ_ζ ≃ 0.174. It then drops to σ_ζ ≃ 0.100 for subtypes M1.0–M2.5, and to σ_ζ ≃ 0.059 for subtypes M3.0–M5.5. Note that the scatter in the M3.0–M5.5 bin is a factor of two larger than the estimated accuracy of the ζ for that range, as estimated above. We suggests this to be evidence of an intrinsic scatter in the ζ values for the stars in our sample, which we allege to be the signature of a metallicity scatter. If we subtract in quadrature the 0.035 measurement error on ζ, we estimate the intrinsic scatter to be ≈0.05 units in ζ. This intrinsic scatter, which presumably affects all subtypes equally, is unfortunately drowned in the measurement error at earlier subtypes (<M3).

To test our ζ as a tracer of metallicity for dM stars from M3 to M6, we compared the values to two recent [Fe/H] calibration techniques for M dwarfs with solar metallicities. First, we used the photometric calibration of Neves et al. (2012), which is based on optical-to-infrared V − K color and absolute magnitude M_K. The method is sensitive to small variations in V − K/M_K and thus requires an accurate, geometric parallax. A total of 143 stars in our sample have parallaxes, and thus can have their metallicities estimated with the method. Figure 16 (top panel) plots the estimated [Fe/H] as a function of ζ for those 143 stars. The distribution shows significant scatter, but we find a weak correlation of [Fe/H] with ζ, which we fit with the relationship

$$\begin{equation} [{\rm Fe/H}]_{\rm N12} = 0.750 \zeta - 0.743. \end{equation} \tag{ 19 }$$

Stars are scattered about this relationship with a 1σ dispersion of 0.383 dex. One drawback of the photometric metallicity determination is that it assumes the star to be single. Unresolved double stars appear overluminous at a given color, and will thus be determined to be metal-rich. Also, young and active stars often appear overluminous in the color–magnitude diagram (Hawley et al. 2002), and their metallicities based on V − K/M_K would also be overestimated. Multiplicity and activity could therefore contribute in the observed scatter. Stars with [Fe/H]_N12 > 0.4, in particular, could be overluminous in the V − K/M_K diagram, as their ζ does not suggest them to be metal-rich.

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Next, we retrieve metallicity measurements from Rojas-Ayala et al. (2012), who estimated [Fe/H] based on the spectroscopic calibration from infrared K-band atomic features. Their list has 37 stars in common with our survey. The [Fe/H] values are plotted as a function of our ζ values in the bottom panel of Figure 16. Again there is significant scatter, but we also find a weak correlation which we fit with the relationship

$$\begin{equation} [{\rm Fe/H}]_{\rm RA12} = 1.071 \zeta - 1.096, \end{equation} \tag{ 20 }$$

about which there is a dispersion of 0.654 dex. The statistics are relatively poor at this time, and more metallicity measurements in the infrared bands would be useful.

The weak correlation found in both distribution is interesting in itself. Using a sample of stars spanning a wide range of metallicities and ζ values, including metal-poor M subdwarfs, extreme subdwarfs (esdM), and extremely metal-poor ultrasubdwarfs (usdM), Woolf et al. (2009) determined a relationship of the form [Fe/H] = −1.685 + 1.632ζ, over the range 0.05 < ζ < 1.10. All the stars in the two distributions from the present survey have ζ values between ∼0.9 and ∼1.2, and thus represent the metal-rich end of the distribution. The weaker slopes we find in our correlations (0.75 and 1.07) may indicate that the relationship levels off at high metallicity end, which would make ζ much less useful as a metallicity diagnostic tool in solar-metallicity and metal-rich M dwarfs. The correlations are however weak, and more accurate measurement of ζ and Fe/H would be needed to verify this conjecture.

The primary purpose of the ζ parameter is the identification of metal-poor M subdwarfs, for which it has already proved effective. By definition, M subdwarfs are stars with ζ < 0.82 (Lépine et al. 2007). Though we have a few stars with values of ζ just marginally under 0.82, only one star clearly stands out as a definite M subdwarf: the star PM I20050+5426 (= Gl 781) which boasts a ζ = 0.58 well within the M subdwarf regime. The star also clearly stands out in Figure 14 where it lies noticeably below the main locus at TiO5_c ≃ 0.75.

PM I20050+5426 is also known as V1513 Cyg, a star previously identified as an M subdwarf by Gizis (1997), and one clearly associated with the Galactic halo (Fuchs & Jahreiss 1998). The star is also notorious for being a flare star, with chromospheric activity due not to young age but to the presence of a low-mass companion on a close orbit (Gizis 1998). Our own spectrum indeed shows a relatively strong line of Hα in emission, which is extremely unusual for an M subdwarf. It is an interesting coincidence that the brightest M subdwarf in the northern sky should turn out to be a peculiar object.

In any case, because the TiO molecular bands are weaker in M subdwarfs than they are in M dwarfs, the use of TiO spectral indices for spectral classification leads to underestimates of their spectral subtype. The convention for M subdwarfs is rather to base the classification on the strengths of the CaH bandheads (Gizis 1997; Lépine et al. 2003a, 2007). We adopt the same convention here, and recalculate the subtype from the mean of Equations (6) and (7) only (CaH2 and CaH3 indices). We thus classify PM I20050+5426 as an sdM2.0, which is one half-subtype later than the sdM1.5 classification suggested by (Gizis 1997).

A prediction of current atmospheric models is that metallicity variations in M dwarfs yield significant variations in optical broadband colors (Allard et al. 2000). The metal-poor M subdwarfs have in fact long been known to have bluer V − I colors than the more metal-rich field M dwarfs of the same luminosity (Monet et al. 1992; Lépine et al. 2003a). The bluer colors are due to reduced TiO opacities in the optical, which make the spectral energy distribution of M subdwarfs closer to that of a blackbody, while it makes the metal-rich M dwarfs display extreme red colors.

Interestingly, the SDSS g − r color index shows the opposite trend, and is bluer in the more metal-poor stars. This is because the TiO bands very strongly depress the flux in the 6000 Å–7000 Å (r-band) range, an effect which in fact makes the metal-rich M dwarfs degenerate in g − r, as the increased TiO opacities in cooler stars balance out the reduced flux in g from lower T_eff. This effect is much weaker in metal-poor stars due to the reduced TiO opacity, which makes metal-poor stars go redder as they are cooler, as one would normally expect. This has been observed in late-type M subdwarfs, which have significantly redder color than field M dwarfs (Lepine & Scholz 2008). The color dependence of M dwarfs/subdwarfs on metallicity is also predicted by atmospheric models. Figure 17 (bottom right panel) shows the predicted g − r and r − z colors from the PHOENIX/BT-SETTL model of Allard et al. (2000). The models corroborate observations and predict redder g − r colors in metal-poor stars.

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Although ugriz photometry is not available for our stars (all of them are too bright and saturated in the Sloan Digital Sky Survey), it is possible to use the well-calibrated SNIFS spectrophotometry to calculate synthetic broadband riz magnitudes for the subset of stars observed at UH. We first examine any possible correlation between the optical to infrared r − K_S color (taken as a proxy for V − I) and the ζ index. Figure 17 plots r − K_s as a function of spectral subtype, with the dots color-coded for the ζ values of their associated M dwarf (top left panel). We find a tight relationship between r − K_s and spectral subtype, which we fit using a running median. The residuals are plotted in the top right panel, and show no evidence of a correlation with ζ. There are a significant number of outliers with redder r − K_s colors than the bulk of the M dwarfs: these likely indicate systematic errors in estimating the synthetic r band magnitudes. The absence of any clear correlation suggests that an optical-to-infrared color such as r − K_S is not sensitive enough to detect small metallicity variations, at least at the metal-rich end.

The synthetic g − r and r − z colors are plotted in Figure 17 (lower-left panel). The redder stars (r − z > 1.2) show a wide scatter in g − r, on the order of what is predicted for stars with a range of metallicities −0.5 < [Fe/H] < 0.5. Though we do not find a clear trend between the synthetic g − r colors and the ζ values measured in the same stars, the high-ζ stars (red and orange dots on the plot) do seem to have lower values of g − r on average than the low-ζ ones (green dots). The trend is suggestive of a metallicity link to both the g − r colors and the ζ values, and should be investigated further with data of higher precision.

Astrometric parallaxes are available for 631 of the stars in our sample, spanning the full range of colors and spectral subtypes. We combine these data with our spectroscopic measurements to re-evaluate photometric and spectroscopic distances calibrations for M dwarfs in our census. Absolute visual magnitudes M_V are calculated and are plotted against both V − J color and spectral subtype in Figure 21. M dwarfs with signs of activity (Hα, UV, X-ray) are plotted in green; other stars are plotted in black. The solid red lines are the best-fit second-order polynomials, when both active and inactive stars are used, and after elimination of 3σ outliers. The equations for the fits, where spT is the spectral type (K7 is −1 and M0 = 0, etc.) are

$$\begin{eqnarray} &&M_J = 1.194 + 1.823 (V-J) - 0.079 (V-J)^2 \end{eqnarray} \tag{ 22 }$$

$$\begin{eqnarray} &&M_J = 5.680 + 0.393 ({\rm SpT}) + 0.040 ({\rm SpT})^2, \quad\ \ \ \end{eqnarray} \tag{ 23 }$$

where SpT are the spectral types, and with the least-squares fit performed after exclusion of 3σ outliers. The 1σ dispersion about these relationships are ±0.61 mag for (M_J, V − J), and ±0.52 mag for (M_J, SpT). The smaller scatter in the spectroscopic relationship suggests that spectroscopic distances may be marginally more accurate than the photometric ones. We suspect that the larger uncertainty on the photographic V magnitudes may be the cause.

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The most notable feature in the diagrams is that active stars appear to be systematically more luminous than non-active stars. This corroborates the observation made previously by Hawley et al. (2002), as part of the PMSU survey. Hawley et al. (2002) found that active stars were more luminous by 0.48 mag in a diagram of M_K against TiO5 index, used as proxy for spectral subtype. For stars in our census, we find that among stars of spectral subtype M2 and earlier, active stars are on average 0.46 mag more luminous at a given subtype than non-active stars; in the color–magnitude diagram, bluer stars of colors V − J < 4.0 which are active are on average 0.47 mag more luminous than non-active stars of the same color. Both values agree well with the values quoted by Hawley et al. (2002). The systematic overluminosity of active stars is also responsible for some of the scatter in the color–magnitude and spectral-type–magnitude relationships. If we exclude active stars, the scatter about the color–magnitude relationship falls marginally to ±0.58, and the scatter in the spectral-type–magnitude relationship falls to ±0.49.

The offset in absolute magnitude between active and non-active stars suggests that spectroscopic and photometric distances would be more accurate for active stars in our census if their estimated absolute magnitudes were made 0.46 mag brighter that suggested by Equation (23). We therefore adopt the following relationships to be applied only on active stars of subtype M2.5 and earlier:

$$\begin{eqnarray} &&{[M_J]}_{{\rm early-active}} = 0.734 + 1.823 (V-J) - 0.079 (V-J)^2\nonumber\\ \end{eqnarray} \tag{ 24 }$$

$$\begin{eqnarray} &&{[M_J]}_{{\rm early-active}} = 5.220 + 0.393 ({\rm SpT}) + 0.040 ({\rm SpT})^2.\quad\ \ \ \end{eqnarray} \tag{ 25 }$$

Again we define as "active" any star which qualifies as such based on any one of our criteria (Hα, UV, X-ray). There are several reasons that would explain why active, early-type stars are more luminous at a given subtype. Activity in an early-type M dwarf could mean that the star is younger (Delfosse et al. 1998); early-type M dwarfs with ages <100 Myr are known to be overluminous at a given color, due to lower surface gravity (Shkolnik et al. 2012). Older stars could remain active due to interaction with a close companion (Morgan et al. 2012), in which case the active stars would also appear overluminous due to this unresolved companion. Late-type M dwarfs, however, can remain active for long periods of time, and would thus not require the star to be young or have a close companion.

Splitting the active and inactive stars results in lowering the scatter of non-active stars in the subtype–magnitude relationship (to ±0.5 mag). Overall, our spectroscopic distances for non-active M dwarfs provide a 1σ uncertainty of ±26% on the distance. For active stars, we find a scatter of ±0.6 mag, which suggests distance uncertainties of ±32%. Our photometric distances estimated from (V, V − J) have similar though perhaps slightly larger uncertainties. Photometric and spectroscopic parallaxes, estimated from the above relationships for active and non-active stars, are listed in Table 7.

We estimated the effect of two relevant sampling biases on the calibration between M_J and V − J color. In Eddington bias, photometric errors scatter more numerous, bluer, and intrinsically brighter stars to redder apparent colors than redder stars are scattered to bluer apparent colors (Eddington 1913). The net effect is to make stars at a given apparent color appear more luminous than they are. In Lutz–Kelker (LK) bias, a form of Malmquist bias, errors in trigonometric parallax will scatter more numerous and more distant stars with lower parallax to higher apparent parallax values, making them appear less luminous than they are (Lutz & Kelker 1973). By taking the derivative of M_J with respect V − J color, multiplying by the derivative of the number of stars in our J-magnitude-limited catalog with respect to M_J, assuming that the errors in V − J are Gaussian-distributed with standard deviation σ_{V − J}, and integrating over the distribution, we find the Eddington bias in M_J to be;

$$\begin{equation} \Delta _E = -\ln 10\, [1.918 = 0.178\,(V-J)]^2 \,(0.6 - 0.4\gamma ) \sigma _{V-J}^2, \end{equation} \tag{ 26 }$$

where γ is the power-law index of a luminosity function for M stars which we take to be 0.325. Performing a similar derivation for the effect of LK bias on M_J, we find:

$$\begin{equation} \Delta _{{\rm LK}} = \frac{15}{\ln 10} \sigma _{\pi }^2, \end{equation} \tag{ 27 }$$

where σ_π is the fractional error in parallax. Using published parallax errors for our Hipparcos stars and adopting a conservative σ_{V − J} = 0.05, we find that LK bias usually dominates over Eddington bias and that 74% of our stars have a total bias of less than +0.2 magnitudes. A running median (N = 100) versus V − J color is highest (∼0.15) for the bluest (V − J = 2.7) stars and falling to less than +0.05 magnitudes for V − J > 3.3. An analogous analysis can be performed for the bias in M_J versus spectral type, with a similar result. To debias values of M_J, these values should be subtracted from our calibration but we do not perform that operation here because of the small magnitude of the effect, which would overestimate distances by about 2% on average. The correction would also seem negligible compared with the intrinsic scatter in our color–magnitude and subtype–magnitude relationships are of the order of ±0.5–0.6, much larger than the LK correction.

Figure 22 shows the distribution of photometric distances for our complete sample using Equation (23) and the M_J = M_J(V − J) color–magnitude relationship. The spectral subtypes are plotted in separate colors and demonstrates that the earlier-type stars, which are intrinsically brighter, are sampled to significantly larger distances compared with the later-type stars. In the 20 pc volume, the M3–M4 stars still appear to dominate. We also plot the Galactic height of the stars in our sample, adopting a Galactic height of 15 pc for the Sun (Cohen 1995; Ng et al. 1997; Binney et al. 1997). It is clear that our survey is largely contained within the Galactic thin disk, and barely extends south of the midplane. This is consistent with the relative absence of metal-poor stars associated with the thick disk and halo.

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Accurate radial velocities are not available for most of the stars in our sample, which prevents us from calculating the full (U, V, W) components of motion for each individual star. However, it is possible to use the distance measurements (for stars with parallaxes) or estimates (for stars with no parallax), and combine them to the proper motions to evaluate with some accuracy at least two of these components for each star. More specifically, we calculate the (U, V, W) components by assuming that the radial velocities R_V = 0. We then consider the (X, Y, Z) positions of the stars in the Galactic reference frame, from the distances and sky coordinates. For stars with the largest component of position in +X or −X, the radial velocity mostly contribute to U, and has minimal influence on the values of V and W. Likewise stars with the largest component of position in +Y or −Y (+Z or −Z) make good tracers of the velocity distribution in U and W (U and V). We use this to assign any one of (U, V) or (U, W) or (V, W) velocity component doublet to every M dwarf in our catalog. Estimated values of the components of velocity are listed in Table 7. For each star, one of the components is missing, which is the component that would most depend on the radial velocity component based on the coordinates of the star. Again, the other two components are estimated only from proper motion and distance. For the distance, we use the trigonometric parallaxes whenever available; otherwise the spectroscopic distances as are used, based on the relationships described in the previous section.

The resulting velocity distributions are displayed in Figure 23. We measure mean values of the velocity components using all allowable values and find:

$$\begin{equation*} \langle U\rangle = -8.1 \ {\rm km\ s^{-1}}, \quad\sigma _U = 32.8 \ {\rm km\ s^{-1}},\ \, \end{equation*}$$

$$\begin{equation*} \langle V\rangle = -17.0 \ {\rm km\ s^{-1}}, \quad\sigma _V = 22.8 \ {\rm km\ s^{-1}}, \end{equation*}$$

$$\begin{equation*} \langle W\rangle = -6.9 \ {\rm km\ s^{-1}},\quad \sigma _W = 19.3 \ {\rm km\ s^{-1}}.\ \ \end{equation*}$$

The values are also largely consistent with those found from the PMSU survey and described in (Hawley et al. 1996). They are also remarkably similar to the moments of the velocity components calculated by Fuchs et al. (2009) for SDSS stars of the Galactic thin disk, and which are 〈U〉 = −8.6, σ_U = 32.4, 〈V〉 = −20.0, σ_V = 23.0, and 〈W〉 = −7.1, σ_W = 18.1. The agreement suggests that our distance estimates are reasonably accurate, and it corroborates earlier results about the kinematics of the local M dwarf population which indicate a larger scatter of velocities in U. The mean values of 〈U〉 and 〈V〉 are consistent with the offsets from the local standard of rest as described in Dehnen & Binney (1998).

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Active stars are found to have significantly smaller dispersions in velocity space. All 252 stars with at least one activity flags (i.e., stars found to be active either from Hα, X-ray flux, or UV excess) are plotted in red in Figure 23. Those active stars have first and second moments:

$$\begin{equation*} \langle U\rangle = -9.3 \ {\rm km\ s^{-1}}, \quad\sigma _U = 25.2 \ {\rm km\ s^{-1}},\ \ \end{equation*}$$

$$\begin{equation*} \langle V\rangle = -13.4 \ {\rm km\ s^{-1}},\quad \sigma _V = 16.8 \ {\rm km\ s^{-1}}, \end{equation*}$$

$$\begin{equation*} \langle W\rangle = -6.6 \ {\rm km\ s^{-1}},\quad \sigma _W = 15.3 \ {\rm km\ s^{-1}}.\ \ \end{equation*}$$

The values are consistent with (Hawley et al. 1996), who also reported that active M dwarfs tend to have a smaller scatter compared with inactive M dwarfs. The smaller dispersion values suggest that these active stars may be significantly younger than the average star in the solar neighborhood.

In any case, we also note that the velocity–space distribution is non-uniform and shows evidence for substructure. Our M dwarf data shows velocity-space substructure as that observed and described in Nordstrom et al. (2004), Holberg et al. (2008) for solar-type stars in the vicinity of the Sun. This substructure is sometimes referred to as "streams" or "moving groups," although an analysis by Bovy & Hog (2010) shows that these groups do not represent coeval populations arising from star-formation episodes. The velocity-space substructure is more likely transient and associated with gravitational perturbations which are the signature of the Galactic spiral arms (Quillen & Minchev 2005) and the Galactic bar (Minchev et al. 2012). A simple description of the velocity-space distribution in terms of mean values and dispersions, or as a velocity ellipsoid, is therefore only a crude approximation of a more complex and structured distribution.

Finally, we note that the stars of our catalog that were previously part of the CNS3 and stars with measured trigonometric parallaxes (e.g., from the Hipparcos catalog) tend to have larger velocity dispersions, with (σ_U, σ_V, σ_W) = (38.4, 25.9, 23.1), while the newer stars have (σ_U, σ_V, σ_W) = (26.2, 19.4, 15.3). The difference could be due to systematic underestimation of the photometric/spectroscopic distances, but a more likely explanation is that the CNS3 and parallax subsample suffers from proper motion selection. This is because most of the CNS3 stars and M dwarfs monitored with Hipparcos were selected from historic catalogs of high proper motion stars, which have a higher limit than the SUPERBLINK proper motion catalog used in the LG2011 selection. This kinematic bias means that the current subset of M dwarfs monitored for exoplanet programs suffers from the same kinematic bias, which could possibly introduce age and metallicity selection effects.