NEAR-INFRARED METALLICITIES, RADIAL VELOCITIES, AND SPECTRAL TYPES FOR 447 NEARBY M DWARFS

The MEarth project is photometrically monitoring 2000 of the nearest mid to late M dwarfs in the northern sky with the goal of finding transiting super Earths. Nutzman & Charbonneau (2008) described how the MEarth targets were selected from the Lépine-Shara Proper Motion catalog of northern stars (LSPM-North; Lépine & Shara 2005). For completeness, we summarize their method here. From the subset of stars believed to be within 33 pc (Lépine 2005), using spectroscopic or photometric distance estimates where parallaxes were unavailable, they selected those with V − J > 2.3, J − K_S > 0.7, and J − H > 0.15, resulting in a sample of probable nearby M dwarfs. The radius for each probable M dwarf was estimated by first using the absolute K_S magnitude/mass relation of Delfosse et al. (2000) and inputting this mass into the mass/radius relationship from Bayless & Orosz (2006). They subsequently selected all objects with estimated radii below 0.33 R_☉, driven by the desire to maintain sensitivity to planets with radii equal to twice Earth's.

MEarth is a targeted survey, visiting each object with a cadence of 20–30 minutes on each night over one or more observing seasons. A fraction of the sample has sufficient coverage and quality to estimate their rotation periods, with recovered periods ranging from 0.1 to 90 days. These will be discussed in a subsequent paper.

We targeted a subset of the MEarth M dwarfs for NIR spectroscopy. We re-observed 30 stars in common with R12, who focused their efforts on M dwarfs within 8 pc, in order to evaluate any systematic differences between our instruments and methods. The IRTF declination limit prevented us from observing stars above +70°. We divide our targets into four subsamples based on the reason for their selection.

• 1.  
  Rotation sample: 181 M dwarfs with preliminary rotation periods measured from MEarth photometry. These show periodic photometric modulation presumed to be due to star spots rotating in and out of view.
• 2.  
  Nearby sample: 257 M dwarfs drawn from the full MEarth sample, for which no clear periodic photometric modulation was detected at the time of selection. This included 131 M dwarfs selected because they have parallaxes available from the literature, 94 M dwarfs with photometric distance estimates, and 32 "photometrically quiet" M dwarfs. The photometrically quiet M dwarfs are those for which phase coverage and photometric noise were sufficient to achieve good sensitivity to rotationally induced photometric modulations, but for which no such modulations were observed.
• 3.  
  Metallicity calibrators: 46 M dwarfs in CPM pairs with an F, G, or K primary, where a metallicity measurement is available for the primary. These are discussed in Section 6. We used 36 M dwarfs in our final metallicity calibration.
• 4.  
  Potential calibrators: 10 potential calibrators are in CPM pairs with an F, G, or K star but do not have a metallicity measurement available for the primary. We did not include these stars in our metallicity calibration.

We present new observations of 447 nearby M dwarfs in Table 6 (the rotation and nearby samples and potential calibrators). Data for our 46 M dwarf metallicity calibrators are presented separately.

We first estimated the spectral type for each star using the relationship between H₂O–K2 index and spectral type that was presented in R12. We displayed the object spectrum and two spectral standards: the spectral standard with the estimated spectral type and the spectral standard with the spectral type one subtype later. We indicated the FeH bands identified in Cushing et al. (2005) with dashed lines, although the Wing-Ford FeH band at 0.99 μm is the only band head apparent across the entire M spectral sequence. FeH is known to be sensitive to spectral type (e.g., Schiavon et al. 1997; Cushing et al. 2005). Using a graphical user interface, we checked earlier and later spectral standards as desired, then selected a spectral type for the object. An example is shown in Figure 3.

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We did not consider half-spectral types. We found the difference between late K dwarfs and M0V stars, and similarly between M8V and M9V stars, to be marginal in the NIR. We used a combined M8V/M9V spectral standard in our program. While K7V and M0V spectral standards were included separately in our spectral typing code, in our later analysis we considered a joint K7/M0V spectral class. We took a holistic approach to spectral typing due to the metallicity dependence of many spectral features. We placed more weight on the redder orders and less weight on features known to be sensitive to metal content (such as the sodium line at 2.2 μm). Our NIR spectral types are included in Table 6.

We initially used the M dwarfs in the IRTF spectral library (Rayner et al. 2009) as spectral standards, using the KHM spectral standards except for our M0V (HD19305), M3V (AD Leo/Gl 388), and M6V (CN Leo/Gl 406) spectral standards. However, we noted several differences between the strengths of features in the standard spectra and the typical object spectra. In particular, the M4V spectral standard, Gl 213, is metal poor. This is to be expected: Cushing et al. (2005) identify Gl 213 as a probable low-metallicity object on the basis of its low Fe, Al, Na, and Ca EWs. By comparing with neighboring spectral standards and using our holistic approach to spectral typing, we were nevertheless able to accurately assess the NIR spectral types of solar metallicity stars.

To address the concern of spectral standards with extreme metallicities or other unique features, we created our own standard spectra. We assessed the spectral type of all stars observed through the 2012A semester by eye once, using the IRTF spectral library stars as standards. We then median combined stars of a single spectral type that were within 0.2 dex of solar metallicity or, for M5V-M7V stars, within 0.1 dex of solar metallicity (see Section 6 for a description of how we determine metallicities for our stars). There were two stars comprising the M1V spectral standard (with median $\overline{\rm{[Fe/H]}}=0.05$), 10 in M2V ($\overline{\rm{[Fe/H]}}=0.0$), 17 in M3V ($\overline{\rm{[Fe/H]}}=0.02$), 45 in M4V ($\overline{\rm{[Fe/H]}}=0.01$), 48 in M5V ($\overline{\rm{[Fe/H]}}=0.03$), 18 in M6V ($\overline{\rm{[Fe/H]}}=0.04$), and six in M7V ($\overline{\rm{[Fe/H]}}=0.04$). We included all five M8/9V stars observed through the 2012A semester in the M8/M9V spectral standard. We continued to use the IRTF spectral library standards for K dwarfs and M0V stars. We show our spectral sequence in four IRTF bands, from K7V to M8/9V, in Figures 4–7. We then re-classified each star by eye using our new standard spectra.

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We first compare our by-eye NIR spectral types with those measured with the H₂O–K2 index, using the relation in R12. These measures agree to within one spectral type; however, our by-eye spectral types are on average half a spectral type later than those measured using the H₂O–K2 index. We express M subtype numerically as Sp_NIR, where positive values are M subtypes (e.g., Sp_NIR = 4 corresponds to M4V) and negative values are K subtypes (e.g., Sp_NIR = −1 corresponds to K7V and Sp_NIR = −2 corresponds to K5V). We find:

$$\begin{equation} \rm{Sp}_\rm{NIR} = 25.4 - 24.2\left(\rm{H}_2\rm{O{--}K2}\right) \end{equation} \tag{ 2 }$$

Over 100 of our objects have optical spectral types from the Palomar/Michigan State University (PMSU) Survey (Reid et al. 1995; Hawley et al. 1996, included for comparison in Table 6). The PMSU survey used the depth of the strongest TiO feature in optical M dwarf spectra as the primary indicator of spectral type and calibrated their relation against nearly 100 spectral classifications on the KHM system. As in R12, we find a systematic difference between the PMSU spectral types and the NIR spectral types as a function of metallicity, shown in Figure 8 for stars earlier than M5V. For M5V stars, there appears to be no clear trend with metallicity.

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For early and mid M dwarfs, the NIR spectral type is typically half a spectral type later than the PMSU spectral type, with more metal poor stars being prone to the largest differences between the PMSU and NIR spectral types. We see the same trend with metallicity as in R12: stars that are metal poor were assigned PMSU spectral types that are earlier than the NIR spectral type we assigned.

We calibrated a metallicity-sensitive function relating NIR spectral type to PMSU spectral type to facilitate the joint use of our data. We found that a linear combination of NIR spectral type and metallicity is sufficient only between NIR spectral types M1V and M3V, while a non-linear combination qualitatively explains the trends seen in our data. Our best fitting non-linear relation is given by

$$\begin{eqnarray} \rm{Sp}_\rm{PMSU} &=& 0.82 \, (\rm{Sp}_\rm{NIR}) + 4.5 \, (\rm{[Fe/H]}) \nonumber\\ &&- 0.89 \, (\rm{Sp}_\rm{NIR}) \, (\rm{[Fe/H]}) + 0.47 \end{eqnarray} \tag{ 3 }$$

where spectral types are expressed numerically, as described above, and [Fe/H] is given in  dex. It is valid over NIR spectral types from M1V-M4V and has a scatter of half a subtype.

We used NIR spectral type and the H₂O–K2 index to calibrate a relation with absolute K_S magnitude, using 187 M dwarfs with parallaxes and K_S magnitudes (Figure 9). We calculated errors on absolute K_S magnitude from the parallax errors, imposing a lower limit of 0.01 mag (this limit was applied to three stars). We performed a linear least squares fit, using the average of the positive and negative errors on the distance to calculate the K_S magnitude measurement error. The fit is valid for NIR spectral types M0V-M8V or 0.7 < H₂O–K2 < 1.06. Expressing the M subtype numerically, our best fits are:

$$\begin{eqnarray} M_K &= 4.72+0.64\;(\rm{Sp}_\rm{NIR})\qquad\ \ \end{eqnarray} \tag{ 4 }$$

$$\begin{eqnarray} &= 20.78-15.26\left(\rm{H}_2\rm{O{--}K2}\right) \end{eqnarray} \tag{ 5 }$$

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To estimate the error on the inferred magnitudes and distances, we remove 5σ outliers and calculate the standard deviation between the measured and inferred absolute magnitudes. Outlier rejection removes four objects for the spectral type relation and three for the H₂O–K2 relation. The standard deviation is 0.30 mag for the NIR spectral type relation and 0.27 mag for the H₂O–K2 relation, indicating that most of the scatter is intrinsic, rather than due to binning by spectral type. Using standard Gaussian error propagation, we estimated that the uncertainty in the distances inferred using Equation (4) is approximately 14%. Spectroscopic distance estimates based on the H₂O–K2 index are included for stars in our sample in Table 6. For binaries where only the total magnitude of two components is available, we assume that they contribute equally to the luminosity.

For our potential primary stars, we used FGK stars with metallicities measured by Valenti & Fischer (2005, hereafter VF05), Santos et al. (2004, 2005, 2011, hereafter Santos+), Sousa et al. (2006, 2008, 2011, hereafter Sousa+), and Bonfils et al. (2005). We use VF05 metallicities where available. We also considered those stars with metallicities measured from Sozzetti et al. (2009). VF05 and Sozzetti et al. (2009) fit an observed spectrum to a grid of model spectra (Kurucz 1992). They reported errors of 0.03 dex on [Fe/H] for measurements of a single spectrum. Work by Santos+, Sousa+, and Bonfils et al. (2005) used the EWs of iron lines in conjunction with model spectra to measure [Fe/H].

We verified that [Fe/H] measurements for FGK stars from different sources are not subject to systematic differences. In Figure 10, we compare the [Fe/H] values measured by Sousa+, Santos+, and Sozzetti et al. (2009) with the VF05 measurements for single FGK stars, finding that the majority of the measurements are within 0.1 dex. The differences between the metallicities from these sources and VF05 are 0.00 ± 0.05 for Sousa+, 0.00 ± 0.06 for Santos+, and −0.05 ± 0.13 for Sozzetti et al. (2009). Our findings are consistent with those from Sousa et al. (2011) and Sozzetti et al. (2009). We did not have a large sample with which to compare [Fe/H] measurements from Bonfils et al. (2005) and VF05. However, Bonfils et al. (2005) followed the methods of Santos et al. (2004) to measure [Fe/H] and found that their work is in agreement.

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Out of the 46 M dwarfs in FGK-M CPM pairs with metallicity measurements, there are four M dwarfs for which only a metallicity measurement from Sozzetti et al. (2009) was available: LSPM J0315+0103, LSPM J1208+2147N, LSPM J1311+0936, and PM I16277-0104. These M dwarfs are useful in extending the calibration regime to lower metallicities, but the scatter in their measured metallicities was large enough to be of concern, so we did not use these M dwarfs as part of our final calibration sample. However, we did use these four stars to validate the extrapolation of our calibration to [Fe/H] = −1.0 dex.

We used 0.03 dex divided by the square root of the number of spectra analyzed as the error for VF05 metallicity measurements, as described by the authors (typically 1–2 spectra were analyzed in VF05). Errors for metallicities from Santos+, Sousa+, and Bonfils et al. (2005) were reported individually in the literature. Since the errors were consistent with the scatter we find between VF05 and these measurements, we did not further inflate the error bars.

We used calibrators from previous works (Bonfils et al. 2005; Johnson & Apps 2009; Schlaufman & Laughlin 2010; Terrien et al. 2012), but also identified new calibrators. To locate new FGK-M CPM pairs, we cross-matched the LSPM-North and LSPM-South (S. Lépine 2010, private communication) catalogs with themselves and with those stars with measured metallicities from VF05, Sousa+, Santos+, or Sozzetti et al. (2009). Our search was subject to the following requirements: the secondary must be within 5', have colors consistent with an M dwarf (V − J > 2, J − K_S > 0.6 and H − K_S > 0.1), and have proper motions within 6σ of the primary, where the uncertainties were assumed to be those stated in the LSPM catalogs.

We used a χ² statistic to identify CPM pairs. The statistic was constructed from the angular separation (a), the difference in proper motions (ΔPM = |PM₁ − PM₂|), and the difference in distance modulii (ΔDM = DM₁ − DM₂). For the distance, we used parallaxes where available and otherwise used the M_J versus V − J relation (Lépine 2005) using the V − J estimates from Lépine & Shara (2005):

$$\begin{equation} \chi ^2=\left(\frac{a}{2{^\prime }}\right)^2+\left(\frac{\Delta \rm{PM}}{\sigma _{\Delta \rm{PM}}}\right)^2+\left(\frac{\Delta \rm{DM}}{\sigma _{\Delta \rm{DM}}}\right)^2. \end{equation} \tag{ 6 }$$

We required χ² < 15 for selection of an object as a candidate binary.

We note that the M_J values estimated from Lépine & Shara (2005) V − J measure were often highly uncertain, because many were derived from photographic estimates of the V magnitude. Thus, the constraints from requiring a common distance modulus are weak in these cases. Additionally, the LSPM catalogs gave the same proper motion value for many very close systems where separate values could not be measured; our analysis assumed that the proper motions were independently measured.

After gathering our observations, we checked that the RV of the primary was in agreement with our measurement of the RV of the secondary and that the distance to the primary was in agreement with our spectroscopic distance estimate for the secondary. We compared the RV and distance measurements for each calibrator and three stars were immediately obvious as outliers. Two have RVs differing by more than 10σ: Gl 806.1B and CE 226. One has a distance differing by 7.5σ: HD 46375B. (This star is noted on SIMBAD as not being a CPM pair, although in MEarth imaging they do appear to move in tandem). LP 731-76, a mid M dwarf, has the same K_S magnitude as its primary, an early K dwarf, clearly indicating that these are not associated. We did not include these four stars in our final sample of calibrators. While some of these systems may be physically associated, unresolved hierarchical triples, we consider the purity of our sample to be more important than its completeness.

Two of the remaining calibrators are concerning, but we do not have sufficient cause to exclude them from our sample. LSPM J0045+0015N has a distance estimate of 22 pc (compared with 41 pc for the primary) and an RV of 16 km s⁻¹ (compared with 32 km s⁻¹). 2MASS J03480588+4032226 has a distance estimate of 30 pc (compared with 50 pc for the primary) and an RV of 0 km s⁻¹ (compared with −10 km s⁻¹); the low proper motion of this object means that the evidence for the physical association of the pair from proper motion alone is weakened.

We identified 2MASS J17195815-0553043 as a visual double and a comparison between the National Geographic Society-Palomar Observatory Sky Survey and Two Micron All Sky Survey (2MASS) indicates that the pair likely has a CPM. The distance estimates and RVs of the components also support the pair being physical associated. To estimate the distance to 2MASS J17195815-0553043, we assumed that the two components had equal magnitudes such that the sum of their fluxes matches the published value. PM I14574-2124W (Gl 570BC) is a known spectroscopic binary, comprised of 0.6 M_☉ and 0.4 M_☉ components (Forveille et al. 1999). As we demonstrate below, the Na line we use to measure metallicity appears to be only weakly sensitive to temperature over the spectral type range of our calibration and therefore the EWs should not be strongly influenced by the presence of a binary companion; this object was not removed from the calibration sample. To be consistent with our treatment of known and unknown spectroscopic binaries, we use the total magnitude of PM I14574-2124W when estimating its distance.

The M dwarf calibrators and our observations are presented in Tables 2 and 3. Forty-six FGK-M CPM pairs appear in these tables. As previously stated, four of these objects were removed from our final calibration sample because they may not be physically associated. An additional four M dwarfs with measurements of the primary star's metallicity from Sozzetti et al. (2009) were not included in the calibration sample, although we used them to validate our calibration to lower metallicities. Two M0V dwarfs were also not included in our final metallicity calibration, as discussed in subsequent sections. Our final calibration sample therefore consisted of 36 M dwarfs with NIR spectral types ranging from M1V to M5V, with one M7 dwarf, and metallicities between −0.7 and +0.45 dex. The typical calibrator is an M4 or M5 dwarf and has a metallicity within 0.2 dex of solar.

Table 2. Observational Properties of M Dwarf Common Proper Motion Pairs

Secondary	R.A.a	Decl.a	PMR.A.	$\rm{PM}_\rm{Dec {\rm l.}}$	Astrometryb	KSc	dSpd	Primary	PMR.A.e	$\rm{PM}_\rm{Dec{\rm l.}}$e	Diste
	(hh:mm:ss)	(dd:mm:ss)	(arcsec yr−1)	(arcsec yr−1)	(Ref.)	(mag)	(pc)		(arcsec yr−1)	(arcsec yr−1)	(pc)
M dwarfs used to calibrate metallicity relation
LSPM J0045+0015N	00:45:13.58	+00:15:51.0	0.207	−0.041	LS05	9.260	22	HD 4271	0.265	−0.051	41
Gl 53.1B	01:07:38.53	+22:57:20.8	0.102	−0.492	LS05	8.673	20	HD 6660	0.099	−0.492	20
G 272-119	01:54:20.96	−15:43:48.2	0.295	−0.137	S06/SG03	9.434	38	HD 11683	0.299	−0.137	36
LSPM J0236+0652	02:36:15.26	+06:52:18.0	1.813	1.447	LS05	6.570	6	HD 16160	1.810	1.449	7
LSPM J0255+2652W	02:55:35.78	+26:52:20.5	0.270	−0.191	LS05	8.660	20	HD 18143	0.274	−0.185	22
GJ 3195B	03:04:43.45	+61:44:09.0	0.717	−0.697	LS05	8.103	19	HD 18757	0.721	−0.693	22
2MASS J03480588+4032226	03:48:05.8	+40:32:22.6	0.049	0.022	LG11	8.450	28	HD 23596	0.054	0.021	50
Gl 166C	04:15:21.56	−07:39:21.2	−2.239	−3.419	S06/SG03	5.962	3	HD 26965	−2.239	−3.420	5
LSPM J0455+0440W	04:55:54.46	+04:40:16.4	0.136	−0.185	LS05	7.620	21	HD 31412	0.136	−0.185	30
LSPM J0528+1231	05:28:56.50	+12:31:53.6	0.093	−0.211	LS05	8.790	18	HD 35956	0.087	−0.216	28
LSPM J0546+0112	05:46:19.38	+01:12:47.2	−0.066	−0.148	LS05	8.800	39	HD 38529	−0.079	−0.141	42
LSPM J0617+0507	06:17:10.65	+05:07:02.3	−0.198	0.164	LS05	8.270	16	HD 43587	−0.195	0.165	19
PM I06523-0511	06:52:18.05	−05:11:24.2	−0.576	−0.011	LG11	5.723	7	HD 50281	−0.544	−0.003	8
Gl 297.2B	08:10:34.26	−13:48:51.4	−0.250	0.050	S06/SG03	7.418	17	HD 68146	−0.251	0.058	22
LSPM J0849+0329W	08:49:02.26	+03:29:47.1	−0.149	0.056	LS05	9.910	29	HD 75302	−0.148	0.060	29
LSPM J0852+2818	08:52:40.86	+28:18:59.0	−0.467	−0.238	LS05	7.670	11	HD 75732	−0.485	−0.234	12
Gl 376B	10:00:50.23	+31:55:45.2	−0.529f	−0.429f	2MASS	9.275	11	HD 86728	−0.529	−0.429	14
LSPM J1248+1204	12:48:53.45	+12:04:32.7	0.225	−0.128	LS05	10.570	36	HD 111398	0.234	−0.141	36
Gl 505B	13:16:51.54	+17:00:59.9	0.632	−0.261	LS05	5.749	10	HD 115404	0.631	−0.261	11
Gl 544B	14:19:35.83	−05:09:08.1	−0.633	−0.122	S06/SG03	9.592	23	HD 125455	−0.632	−0.122	20
PM I14574-2124W	14:57:26.51	−21:24:40.6	0.987	−1.667	LG11	3.802	3:	HD 131977	1.034	−1.726	5
LSPM J1535+6005E	15:35:25.69	+60:05:00.6	0.166	−0.160	LS05	8.410	15	HD 139477	0.171	−0.163	19
LSPM J1604+3909W	16:04:50.85	+39:09:36.1	−0.547	0.055	LS05	9.160	18	HD 144579	−0.572	0.052	14
PM I17052-0505	17:05:13.81	−05:05:38.7	−0.921	−1.128	LG11	5.975	8	HD 154363	−0.917	−1.138	10
2MASS J17195815-0553043Ag	17:19:58.15J	−05:53:04.5J	0.049J	−0.182J	LS05	10.385J	55:	HD 156826	0.045	−0.194	53
2MASS J17195815-0553043Bg	17:19:58.15J	−05:53:04.5J	0.049J	−0.182J	LS05	10.385J	41:	HD 156826	0.045	−0.194	53
LSPM J1800+2933NS	18:00:45.43	+29:33:56.8	−0.128	0.169	LS05	8.230	24	HD 164595	−0.139	0.173	28
PM I19321-1119	19:32:08.11	−11:19:57.3	0.237	0.026	LG11	8.706	18	HD 183870	0.235	0.018	18
Gl 768.1B	19:51:00.67	+10:24:40.1	0.240	−0.135	2MASS	8.012	15	HD 187691	0.240	−0.135	19
LSPM J2003+2951	20:03:26.58	+29:51:59.4	0.689	−0.515	LS05	8.710	14	HD 190360	0.684	−0.524	17
LSPM J2011+1611E	20:11:13.26	+16:11:08.0	−0.432	0.399	LS05	8.880	16	HD 191785	−0.413	0.398	20
LSPM J2040+1954	20:40:44.52	+19:54:03.2	0.107	0.312	LS05	7.420	12	HD 197076A	0.118	0.310	19
LSPM J2231+4509	22:31:06.51	+45:09:44.0	−0.167	0.027	LS05	9.500	37	HD 213519	−0.174	0.038	43
Gl 872B	22:46:42.34	+12:10:20.9	0.234	−0.492	LS05	7.300	14	HD 215648	0.233	−0.492	16
LSPM J2335+3100E	23:35:29.47	+31:00:58.5	0.548	0.256	LS05	8.850	24	HD 221830	0.539	0.254	32
HD 222582B	23:41:45.14	−05:58:14.8	−0.148	−0.117	S06/SG03	9.583	30	HD 222582	−0.145	−0.111	41
M0 dwarfs in a CPM pair not used in our metallicity calibration
Gl 282B	07:40:02.90	−03:36:13.3	0.067	−0.286	H00	5.568	13	HD 61606	0.070	−0.278	14
LSPM J1030+5559	10:30:25.31	+55:59:56.8	−0.181	−0.034	LS05	5.360	13	HD 90839	−0.178	−0.033	12
M dwarfs in a CPM pair where the primary has a metallicity measurement from Sozzetti et al. (2009)
LSPM J0315+0103	03:15:00.922	+01:03:08.2	0.362	0.118	LS05	10.85	77	G 77-35	0.362	0.118	79
LSPM J1208+2147N	12:08:55.378	+21:47:31.6	−0.439	0.037	LS05	10.38	83	G 59-1	−0.397	0.036	113:
LSPM J1311+0936	13:11:22.445	+09:36:13.1	−0.517	0.269	LS05	8.86	55	G 63-5	−0.521	0.269	61
PM I16277-0104	16:27:46.699	−01:04:15.4	−0.340	−0.106	LS05	10.57	54	G 17-16	−0.347	−0.102	62:
M dwarfs in a CPM pair that may not to be physically associated
HD 46375B	06:33:12.10	+05:27:53.1	0.114	−0.097	2MASS	7.843	11	HD 46375	0.114	−0.097	33
CE 226	10:46:33.27	−24:35:11.2	−0.141f	−0.109f	2MASS	9.447	31	HD 93380	−0.141	−0.109	20
LP 731-76	10:58:27.99	−10:46:30.5	−0.201	−0.094	S06/SG03	8.640	14	BD-103166	−0.186	−0.005	25:h
Gl 806.1B	20:46:06.42	+33:58:06.2	0.356	0.330	MEarth	8.7:i	19:	HD 197989	0.356	0.330	22

Notes. ^aPositions are given in the International Celestial Reference System (ICRS), and have been corrected to epoch 2000.0 where necessary assuming the proper motions given in the table. ^bAstrometry references. If one reference is provided, it applies to both position and proper motion; if two are provided, the first is for position and the second for proper motion. ^cApparent K_S magnitudes are from S06. ^dErrors on the distance estimates are 14%. ^eProper motions and distances for primary stars are from Hipparcos (van Leeuwen 2007) except when otherwise noted. ^fFor CE 226 and Gl 376B, the Hipparcos proper motion for the primary was found to be a better match to the observed motion of the secondary from 2MASS to recent epoch MEarth imaging than the proper motion given in Ruiz et al. (2001, for CE 226) or in LSPM-North (for Gl 376B). In these cases, the Hipparcos value has been adopted in the table. ^gS. Lépine 2010, private communication. We resolved this object as a binary. An appended "J" indicates a measurement that was derived for the components jointly. We assume the two components contribute equally to the luminosity in order to estimate their spectroscopic distances. ^hNo parallax was available for the primary. Its distance was estimated assuming an absolute K_S magnitude of 6, typical for an early K dwarf. ⁱNo K_S magnitude could be found for Gl 806.1B. We estimated a rough magnitude from 2MASS Atlas images using a 4 pixel aperture radius (this value was chosen to reduce contamination from nearby stars), and applied an aperture correction of 0.04 mag, derived from stars of similar K magnitude elsewhere in the field. References. Høg et al. (2000, H00); Salim & Gould (2003, SG03); Lépine & Shara (2005, LS05); Skrutskie et al. (2006, S06); Lépine & Gaidos (2011, LG11).

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We looked for combinations of spectral features that are good tracers of [Fe/H]. Based on the lines listed in Cushing et al. (2005) and Covey et al. (2010), we identified 27 spectral lines prominent across most of our sample for which relatively uncontaminated continuum regions could be defined. These features and the continuum regions, one on either side of each feature, are listed in Table 4. To measure the EW of a feature, we first mitigated the effect of finite pixel sizes by linearly interpolating each spectrum onto a 10-times oversampled wavelength grid with uniform spacing in wavelength. The continuum was estimated by linear interpolation between the median fluxes of the two continuum regions. We then applied the trapezoidal rule to numerically integrate the flux within the feature. We also measured 10 spectral indices. We considered three indices quantifying the deformation in the continuum due to water absorption: the H₂O–K2 index, introduced in Section 4 (R12), the H₂O–H index (Terrien et al. 2012), and the H₂O–J index (Mann et al. 2013). We also measured the flux ratios defined by McLean et al. (2003) and used by Cushing et al. (2005). These ratios quantify absorption in several water, FeH, and CO bands. The indices we measured are summarized in Table 5. We also considered three non-linear combinations. The combinations we considered were motivated by previous work: Luhman & Rieke (1999) suggested that $\rm{\rm{EW}_\rm{Na}/\rm{EW}_\rm{CO}}$ is temperature-sensitive and R12 used the ratios $\rm{\rm{EW}_\rm{Na}}/(\rm{H}_2\rm{O{--}K2})$ and $\rm{\rm{EW}_\rm{Ca}}/(\rm{H}_2\rm{O{--}K2})$ to fit their metallicity relation.

Table 5. Spectral Indices Searched as Part of Metallicity Calibration

Name	Absorption Band	Definition	Source
H2O–J	J-band water deformation	$\frac{\langle 1.210{--}1.230\rangle /\langle 1.313{--}1.333\rangle }{\langle 1.313{--}1.333\rangle /\langle 1.331{--}1.351\rangle }$	Mann et al. (2013)
H2O–H	H-band water deformation	$\frac{\langle 1.595{--}1.615\rangle /\langle 1.680{--}1.700\rangle }{\langle 1.680{--}1.700\rangle /\langle 1.760{--}1.780\rangle }$	Terrien et al. (2012)
H2O–K2	K-band water deformation	$\frac{\langle 2.070{--}2.090\rangle /\langle 2.235{--}2.255\rangle }{\langle 2.235{--}2.255\rangle /\langle 2.360{--}2.380\rangle }$	Rojas-Ayala et al. (2012)
H2OA	1.35 μm H2O band	〈1.341–1.345〉/〈1.311–1.315〉	McLean et al. (2003)
H2OB	1.4 μm H2O band	〈1.454–1.458〉/〈1.568–1.472〉	McLean et al. (2003)
H2OC	1.7 μm H2O band	〈1.786–1.790〉/〈1.720–1.724〉	McLean et al. (2003)
H2OD	2.0 μm H2O band	〈1.962–1.966〉/〈2.073–2.077〉	McLean et al. (2003)
CO	2.29 μm 12CO 2–0 band	〈2.298–2.302〉/〈2.283–2.287〉	McLean et al. (2003)
J-FeH	1.17 μm FeH 0–1 band	〈1.198–1.202〉/〈1.183–1.187〉	McLean et al. (2003)
Y-FeH	0.99 μm FeH 0–0 band	〈0.990–0.994〉/〈0.984–0.988〉	McLean et al. (2003)

Note. Angle brackets denote the median of the wavelength range indicated. All wavelengths are in microns.

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We searched for the combination of three parameters that provide the best fit to metallicity, using the forms:

$$\begin{eqnarray} \rm{[Fe/H]}&=A (\rm{F}_1) + B\, (\rm{F}_2) + C \,(\rm{F}_3) + D \end{eqnarray} \tag{ 7 }$$

$$\begin{eqnarray} &=A(\rm{F}_1)+B\,(\rm{F}_1)^2+C\,(\rm{F}_2)+D \end{eqnarray} \tag{ 8 }$$

$$\begin{eqnarray} &=A(\rm{F}_1)+B\,(\rm{F}_1)^2+C\,(\rm{F}_1)^3+D \end{eqnarray} \tag{ 9 }$$

where F_n is the EW of one of the 27 spectral features in Table 4, one of the 10 indices in Table 5, or one of three non-linear combinations of parameters described above. We used the RMSE as a diagnostic to identify the best potential metallicity relations.

There were a multitude of relations with RMSE < 0.14 dex, of which the majority included the EW of the Na line at 2.2 μm as the primary indicator of metallicity (sometimes appearing as $\rm{\rm{EW}_\rm{Na}/\rm{EW}_\rm{CO}}$ or $\rm{\rm{EW}_\rm{Na}}/(\rm{H}_2\rm{O{--}K2})$) and included a quadratic term. However, we preferred the two-parameter fit [Fe/H] = A(EW_Na) + B(EW_Na)² + C because it uses one fewer parameter. Motivated by the clear trend with metallicity seen in EW_Na, we also considered functional forms other than a quadratic, including a spline. No other forms tested resulted in a statistically superior fit. We show our result in Figure 11.

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In performing our final fit, we did not include the two K7/M0V stars. In Figure 11 these are evident as having an EW_Na lower than other calibrators of similar metallicity. As discussed in Section 6.4, we attempted to find a metallicity relation that was valid through these early spectral types, but did not converge on a suitable result. Our final calibration sample therefore includes 36 M dwarfs with spectral types M1V and later. We address this choice in detail in the following section.

Our best fit is given by

$$\begin{eqnarray} \rm{[Fe/H]} &=& - 1.96\rm{\ dex}+ 0.596 \rm{\ dex}\, (\rm{EW}_\rm{Na}/\rm{\rm \mathring{\rm{A}}}) \nonumber\\ &&- 0.0392 \rm{\ dex}\, (\rm{EW}_\rm{Na}/\rm{\rm \mathring{\rm{A}}})^2 \end{eqnarray} \tag{ 10 }$$

It is calibrated for EW_Na between 3 and 7.5 Å, corresponding to metallicities of −0.6 dex < [Fe/H] < 0.3 dex, and for NIR spectral types from M1V to M5V. There are indications that EW_Na begins to saturate for [Fe/H] > 0.3 dex and that our best fit becomes multivalued for EW_Na > 7.5 Å, so the calibration cannot be extrapolated past this point. The four M dwarfs for which the primary star has a metallicity measured by Sozzetti et al. (2009) indicate that our relation appears to be valid when extrapolated to EW_Na = 2 Å, corresponding to [Fe/H] = −1.0 dex. In Section 6.5, we confirm the validity of the relation for later NIR spectral types by comparing metallicities estimated for members of CPM M dwarf multiples with a range of spectral types. While there is only one calibrator later than M5, this object also indicates that the relation can be extrapolated as late as M7.

We estimated the error introduced by our limited number of calibrators by bootstrapping. We randomly selected 36 of our calibrators, allowing repeats, and re-fit our metallicity relation. The standard deviation of the difference between the best fitting metallicities of the M dwarf secondaries and the metallicities of the primaries, averaged over 100 bootstrap samples, was 0.12 ± 0.01 dex. The correlation coefficient, $R_{{\rm ap}}^2$ is often used to evaluate the goodness of fit. The correlation coefficient indicates how well the fit explains the variance present in the data and is given by

$$\begin{equation} R_{{\rm ap}}^2=1-\frac{(n-1)\sum (y_{i,{\rm model}}-y_i)^2}{(n-p)\sum (y_i-\bar{y})^2} \end{equation} \tag{ 11 }$$

where n is the number of data points and p is the number of parameters. The $R_{{\rm ap}}^2$ value for our fit is 0.78 ± 0.07.

The best-fitting metallicities for our calibrators are included in Table 3. The errors on metallicity include the errors on EW_Na, bootstrap errors, and the scatter in our best fit, added in quadrature. We took the bootstrap errors to be the 1σ confidence interval on the resulting metallicities when considering the best fits from 100 bootstrap samples. The intrinsic scatter in the relation (0.12 dex) dominates for all but the lowest metallicity stars.

The scatter in our metallicity relation is similar to those reported by R10, R12, Terrien et al. (2012), and Mann et al. (2013) despite differences in sample size, lending support to the idea that the scatter is astrophysical in origin. We consider potential temperature and surface gravity effects in Section 6.4. One possibility is variations between the Na abundance and [Fe/H] of the primary solar-type star. We considered whether an M dwarf's EW_Na is a better tracer of its primary star's Na abundance than its Fe abundance. 32 of our calibrators have measured abundances for Na from VF05. We related the spectral features and indices in Tables 4 and 5 to the Na abundance of the primary star. We found several suitable tracers; however, none reduced the scatter.

In Table 6, we include the EWs of the Na line at 2.20 μm and the Ca line at 2.26 μm, the H₂O–K2 index, our inferred [Fe/H], and their associated errors for each of our targets. The corresponding values for the FGK-M CPM pairs can be found in Table 3.

Table 6. All Stars from Our Rotation and Nearby Samples

LSPM Name	Comp	R.A.a	Decl.a	PMR.A.a	$\rm{PM}_\rm{Dec {\rm l.}}$a	KSb	Spectral Type		EWNa	EWCa	H2O–K2	[Fe/H]	RV	RVPMd	dSpe	Parallax	Plx	Julian Date	Note
		(hh:mm:ss)	(dd:mm:ss)	(as yr−1)	(as yr−1)	(mag)	NIRc	PMSUd	(Å)	(Å)		(dex)	(km s−1)	(km s−1)	(pc)	(marcsec)	Ref
LSPM J0001+0659		00:01:15.82	+06:59:35.6	−0.447	−0.081	10.418	M5V	...	5.35 ± 0.18	2.09 ± 0.25	0.830 ± 0.005	+0.10 ± 0.12	−1 ± 4	...	28	...	...	2456167.0	Rotator
LSPM J0007+0800		00:07:59.11	+08:00:19.4	−0.349	−0.413	8.652	M4V	M3V	2.32 ± 0.18	1.51 ± 0.20	0.890 ± 0.005	−0.79 ± 0.18	−20 ± 5	−51.3	20	44.0 ± 6.3	vA95	2455787.0	Nearby
LSPM J0008+2050		00:08:53.92	+20:50:25.4	−0.061	−0.255	8.010	M5V	M4.5V	5.59 ± 0.14	2.93 ± 0.17	0.841 ± 0.005	+0.14 ± 0.12	9 ± 4	−31.8	10	...	...	2455841.9	Nearby
LSPM J0015+4344		00:15:18.83	+43:44:34.8	0.232	0.038	10.396	M5V	...	6.40 ± 0.16	3.95 ± 0.18	0.856 ± 0.005	+0.25 ± 0.12	4 ± 4	...	34	...	...	2456167.0	Rotator
LSPM J0015+1333		00:15:49.25	+13:33:22.3	0.621	0.333	7.807	M4V	M3V	4.13 ± 0.19	2.57 ± 0.15	0.886 ± 0.005	−0.17 ± 0.13	50 ± 6	33.5	12	85.8 ± 2.6	R10	2455841.9	Rotator

Notes. For binaries that were not resolved in the LSPM catalogs but which we resolve, we use the appropriate LSPM name in the first column and identify the components in the second column. We append a "J" to indicate measurements that apply to two resolved components jointly. ^aAstrometry is from LS05 and LSPM-South. Positions are given in the ICRS and have been corrected to epoch 2000.0 where necessary assuming the proper motions given in the table. ^bApparent K_S magnitudes are from S06. A "Q" appended to the magnitude indicates that the 2MASS qual_flag was not "AAA." ^cNIR spectral types were assigned by eye as described in Section 5. ^dReferences for PMSU spectral types and RVs are Reid et al. (1995); Hawley et al. (1996). ^eSpectroscopic distances were estimated using Section 4, relating the H₂O–K2 index to absolute K_S magnitude. For binaries where individual magnitudes are not available, we assume the two components have equal luminosities. Errors on estimated distances are 14%. ^fParallax was assumed to be that of the CPM primary. References. Monet et al. (1992, M92); Harrington et al. (1993, H93); van Altena et al. (1995, vA95); Ducourant et al. (1998, D98); Benedict et al. (2000, B00); Henry et al. (2006, H06); Smart et al. (2007, S07); van Leeuwen (2007, vL07); Gatewood (2008, G08); Gatewood & Coban (2009, G09); Lépine et al. (2009, L09); Smart et al. (2010, S10); Riedel et al. (2010, R10); Khrutskaya et al. (2010, K10); Shkolnik et al. (2012, S12); Anglada-Escudé et al. (2013, A13).

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We examine the potential influence of differences in the effective temperature and surface gravity on the metallicity calibration presented in Section 6.3 by computing EW_Na for a grid of BT-Settl theoretical spectra for spectral types K5V-M7V, shown in Figure 12 (Allard et al. 2011, the behavior of NIR lines in theoretical spectra are discussed in some detail in R12). The spectral type range corresponds to approximately K5V-M6.5V, depending on the adopted temperature scale (we quote the temperature scale from E. Mamajek, which is available online.⁵). The BT-Settl theoretical spectra show EW_Na varying by 1 Å between M0V and M8V stars (Figure 12). We also note that in our K-band SpeX spectral sequence (Figure 4) the Na line at 2.2 μm is broader for the latest spectral types.

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We plot in Figure 13 the median EW_Na for each NIR spectral type as a function of H₂O–K2, for two subsamples. Our "nearby sample" (Section 2.2) formed the first and kinematically young stars (V_tot < 50 km s⁻¹) formed the second. We selected the nearby sample to approximate a volume-limited sample, which is unlikely to be influenced by selection effects that may exist in the rotation sample. We selected the kinematically young sample in order to isolate stars that are expected to be of similar age and metallicity. We found a similar increase in the median EW_Na of mid to late M dwarfs, as we noted in the theoretical spectra. This could introduce a systematic error of 0.1 dex in the metallicities of early M dwarfs relative to mid M dwarfs. However, we are uncertain of the origin of this effect, given the differing behavior of our two subsamples and the relative differences in the number of early and late type stars (there are 23 stars with NIR spectral types M0V-M2V and 231 with spectral types M4V-M5V across the two subsamples).

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We considered whether an alternative parameterization could account for this potential bias. We show the residuals for our chosen parameterization and three alternatives, including the parameterization from R12, in Figure 14. In Figure 15, we show the effect that the alternative calibrations have on the metallicities of the sample as a whole. With the R12 parameterization, the inferred metallicities of the latest stars decreased by 0.1 dex and metallicities were consistent across spectral types. However, the metallicities of M5 were lowered relative to those of M4 dwarfs, the spectral range across which our relation is best calibrated. Furthermore, the fit is unconstrained at the latest spectral types where the choice of the R12 parameterization makes the most difference. Including the EW of magnesium or the H₂O–K2 as a third parameter in the metallicity calibration improves the fit for the two K7/M0V calibrators and has only a marginal effect at other spectral types. However, only scatter above the best fit plotted in Figure 11 was reduced in this case, while the scatter below the best fit remained.

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When the M0V calibrators were not included in the fit, the addition of these extra parameters makes little difference. Therefore, rather than including an additional parameter to fit these two points at the far end of our spectral type range, we simply limit our calibration to a range of spectral types that appear to be well fit by a relation depending solely on Na.

The insensitivity of NIR spectral types to late K dwarfs may be partially responsible for the behavior seen in our two M0V calibrators. The optical spectral type of PM I07400−0336 places it as a K6.5V dwarf (Poveda et al. 2009) and LSPM J1030+5559 has been identified previously as a K7V dwarf (Garcia 1989). However, theoretical models indicate that the EW_Na should remain constant between late M and mid K dwarfs (with slight dependence on surface gravity) and Mann et al. (2013) reported a metallicity calibration that is valid from K5V-M5V.

Surface gravity remains one possible explanation for the K7/M0V discrepancy and has yet to be explored in the context of empirical calibrations. Luhman et al. (1998) demonstrated that in the low surface gravity environments of very young stars, Na may appear abnormally weak. It is therefore possible that an M dwarf with an age of several Myr could be masquerading as a metal-poor object. The CO band head is sensitive to gravity in the opposite manner and is therefore a useful indicator of youth (Luhman et al. 1998). In Figure 16, we plot EW_Na against EW_CO for all stars in our sample. We found a general positive correlation and spectral dependence, but no object stood apart as having low EW_Na but high EW_CO. This is not surprising as it is unlikely that we would find a new, bright young star within 25 pc.

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We considered the potential for other systematics by comparing the difference between our best fitting metallicities and the metallicities of the primaries to the EWs of all other indices. In all cases, we found no significant systematic effects.

As a test of our metallicity calibration, we compared the metallicities we estimated for the components of M dwarf–M dwarf CPM pairs. We have observed 22 such pairs. Eleven were placed on the slit together and so share observing conditions, while 11 were observed separately but close in time. In both cases, the two stars were reduced with the same telluric standard. In Figure 17, we show the results of this comparison. The mean metallicity difference between the primary and secondary components is −0.01 dex with a standard deviation of 0.05 dex. This is less than the uncertainty of our metallicity measurement by a significant amount, lending support to the idea that most of the scatter in the metallicity relation is astrophysical in origin, as mentioned in Section 6.3.

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We also compared EW_Na measurements for stars that were observed on more than one occasion in Figure 1 (see Section 4). We found that our EW_Na measurements were consistent even for observations taken in very different conditions and separated in time by months or more. The mean EW_Na difference between the observation we elected to keep and the observation we discarded was −0.01 dex with a standard deviation of 0.04 dex.

R12 published their measurements of EW_Na, EW_Ca, and [Fe/H] for 133 M dwarfs using the TripleSpec instrument on Palomar (Herter et al. 2008). To facilitate the joint use of our observations and those from R12, we determined the relationship between TripleSpec and SpeX EWs. We compare our EW_Na measurements directly in Figure 18. We used the following relation to convert from TripleSpec to IRTF EW_Na:

$$\begin{equation} \rm{EW}_\rm{Na,N13}=0.036+0.90\, (\rm{EW}_\rm{Na, R12}). \end{equation} \tag{ 12 }$$

Similarly for the Ca line at 2.26 μm:

$$\begin{equation} \rm{EW}_\rm{Ca,N13}=0.22+0.88\, (\rm{EW}_\rm{Ca,R12}). \end{equation} \tag{ 13 }$$

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We also directly compared our metallicity estimates for the 28 stars in common (excluding metallicity calibrators). As seen in Figure 18, the metallicity measurements agreed well for sub-solar metallicities, but for metallicities above solar, the relation in this work gives higher metallicities for late M dwarfs (M5V-M7V). The difference between our inferred metallicities and those from R12 is 0.0 ± 0.07 dex for M1V-M4V stars and 0.08 ± 0.05 for M5V-M7V stars. This difference is consistent with the effects discussed in Section 6.4, but we note that our relation is most strongly constrained for M4 and M5 dwarfs.

The objects observed by R12 are listed in Table 7. We have included EWs updated using Equations (12) and (13). After applying our EW_Na relationship, we can directly compute the metallicities for stars published in R12 using our metallicity calibration. We also present these updated metallicities in Table 7.

Table 7. M Dwarfs Observed by R12

LSPM Name	R12 Name	R.A.	Decl.	PMR.A.	$\rm{PM}_\rm{Dec {\rm l.}}$	Astron.a	KSb	Spectral Type		EWNad	EWCad	H2O–K2d	[Fe/H]d	RVPMe	dSpf	dPlx	Plx	Note
		(hh:mm:ss)	(dd:mm:ss)	(arcs yr−1)	(arcs yr−1)	Ref.	(mag)	NIRc	PMSUe	(Å)	(Å)		(dex)	(km s−1)	(pc)	(pc)	Ref.
LSPM J0011+5908	LSPM J0011+5908	00:11:31.81	+59:08:39.9	−0.915	−1.166	L05	9.093	M6V	...	4.66 ± 0.19	1.26 ± 0.16	0.805 ± 0.003	−0.04 ± 0.12	...	13	11.7	R97	LSPM
LSPM J0023+7711E	LHS 1066	00:23:31.83	+77:11:26.7	−0.799	0.042	S06	9.110	M5V	M4V	4.98 ± 0.19	3.06 ± 0.16	0.851 ± 0.002	+0.03 ± 0.12	−60.7	18	16.6	R97	LSPM
LSPM J0027+4941	LHS 6007	00:27:06.79	+49:41:52.8	0.397	−0.264	S06	8.852	M4V	M4.5V	5.97 ± 0.19	3.70 ± 0.16	0.891 ± 0.002	+0.20 ± 0.12	−74.3	21	21.3	vA95	LSPM
LSPM J0032+6714N	V* V547 Cas	00:32:29.43	+67:14:08.4	1.741	−0.247	vL07	6.037	M3V	M2V	3.28 ± 0.19	3.06 ± 0.16	0.945 ± 0.003	−0.43 ± 0.13	6.5	8	10.1	vL07	LSPM
LSPM J0032+6714S	LHS 115	00:32:29.59	+67:14:03.6	1.741	−0.247	vL07	6.377	M3V	M3V	3.74 ± 0.19	2.54 ± 0.16	0.905 ± 0.004	−0.28 ± 0.13	9.7	7	10.2	R97	LSPM

Notes. ^aPositions are given in the International Celestial Reference System (ICRS) and have been corrected to epoch 2000.0 where necessary assuming the proper motions given in the table. ^bApparent K magnitudes are from S06. ^cNIR spectral types were calculated from the H₂O–K2 index using Equation (2). ^dEW and [Fe/H] measurements have been converted to their equivalent IRTF values, as described in Section 6.6. ^eReferences for PMSU spectral types and RVs are Reid et al. (1995) and Hawley et al. (1996). ^fSpectroscopic distances were estimated using Section 4, relating the H₂O–K2 index to absolute K magnitude. Errors are 14%. References. Bessel (1990, B90); Leggett (1992, L92); Gliese & Jahreiß (1991, GJ91); Reid et al. (1995); Hawley et al. (1996, PMSU); van Altena et al. (1995, vA95); Gould & Chaname (2004, GC04); Lépine (2005, L05); Skrutskie et al. (2006, S06); van Leeuwen (2007, vL07); Koen et al. (2010, K10); Lépine & Gaidos (2011, LG11).

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Atmospheric absorption features present in our data provided a natural replacement to arc spectra. By correlating the telluric lines in our spectra with a theoretical atmospheric transmission spectrum (hereafter called simply the "transmission spectrum"), we determined the absolute wavelength calibration. The SpeXtool package includes a transmission spectrum created using ATRANS (Lord 1992). This spectrum was created using environmental parameters typical of Mauna Kea and an airmass of 1.2 and has a resolution five times that of SpeX. We used the wavelength calibration determined by SpeX using ThAr arc spectra as our initial wavelength guess for the non-telluric corrected science spectrum. From this wavelength solution, we created a wavelength vector that was oversampled by a factor of six and linearly spaced in wavelength.

We found that excellent continuum removal was required for the wavelength calibration to be determined through direct cross correlation of the science spectrum and the transmission spectrum. However, the large atmospheric features made this difficult. Instead of attempting to remove the continuum from the M dwarf and subsequently finding the offset between the stellar spectrum and the atmospheric spectrum, we tackled these problems simultaneously. We did this by finding the modifications to the transmission spectra that provided the best match to the telluric features observed in the science spectrum. There were three differences between the theoretical transmission spectrum and the telluric features as observed in the science spectrum: the continuum, the strength of the telluric features, and the pixel offset between the spectra.

The first parameter of our model was a Legendre polynomial as a function of pixel; the transmission spectrum was multiplied by this quantity in order to replicate the shape of the spectrum. The curvature of the spectrum was affected by both instrumental effects and the M dwarf SED. We used a third or fourth degree Legendre polynomial and fit for the coefficients. We selected the degree of the polynomial by eye for each order, using the lowest degree polynomial required to model several representative M dwarf spectra.

The second parameter was an exponential scaling of the flux, to account for the effects of airmass and atmospheric water vapor on the depths of telluric features. The transmission spectrum represents typical conditions on Mauna Kea, while we observed at airmasses from 1.0 to 1.7 with humidity from 85% to less than 15%.

As discussed in Blake et al. (2010), differences in airmass scale the depths of the telluric features (T) as $T=T_{0}^\tau$, where the optical depth τ scales linearly with airmass. Blake et al. (2010) were able to find a single linear scaling between airmass and τ using a large sample of A0V stars. We attempted to use the same approach, but found substantial scatter and systematic differences in the scaling of different telluric features with airmass. This is likely due to the water absorption features in our spectral region, which are time variable, and cannot be modeled by a simple function of airmass alone. We therefore chose to take an empirical approach and included the exponential scaling τ as a model parameter.

The third and final parameter was the offset in pixels between the transmission and science spectrum. We modeled the offset as being linear in wavelength. To apply the shift, we created a new wavelength vector that was linearly shifted from the original and interpolated the transmission spectrum onto the new wavelength vector. We constrained the allowable range for the offset because atmospheric features appear at regular spacing and we found that if unconstrained, our fitting program could too often land in a local minimum. We used 0.0008 μm as the limit, which is larger than any offset we expected. In our full sample, no shifts beyond 0.0006 μm were found and very few beyond 0.0004 μm were found.

We modeled each order of the non-telluric-corrected science spectrum independently, minimizing the difference between our model and the science spectrum using a nonlinear least squares approach, implemented through mpfit (Markwardt 2009). We determined by trial and error the region of each order to use. Regions with high S/N and strong telluric features but uncontaminated by strong stellar features were required for optimal performance. Because of these constraints, this method worked better in the J-, H-, and K-bands than it did in the Y- or Z-bands.

Once we determined the absolute wavelength solutions of science target and an RV standard, we interpolated the telluric-corrected spectra onto a common wavelength vector that was oversampled and uniform in the log of the wavelength (such that a RV introduces a constant offset in pixels). The continuum is different in the telluric-corrected spectrum because telluric correction removed instrumental effects, so we used a spline to remove the continuum. We used xcorl to cross-correlate the two spectra and determine the offset. We used the same standard star (Luyten's star, also known as Gl 273 or LSPM J0727+0513) throughout because it had an accurately measured absolute RV from Chubak et al. (2012) and an NIR spectral type in the middle of our range (M4V).

We took the final RV for each target to be the median of the RVs measured in the J-, H-, and K-bands and applied the heliocentric correction, implemented through the IDL routine baryvel (Stumpff 1980). Our final estimate of the error is the 1σ confidence limit on the RV after 50 trials added in quadrature to 4.4 km s⁻¹ (our internal measurement error; see Section 8.3). These values are reported in Table 6.

This method of measuring RVs is applicable to other moderate-resolution NIR spectrographs, including TripleSpec, and uses observations of the target star to refine the wavelength calibration. Our method is therefore likely to be useful for instruments where obtaining lamp spectra is expensive.

Chubak et al. (2012) presented absolute, barycentric-corrected RVs for 2046 dwarf stars with spectral types ranging from F to M. M dwarf RVs were measured by comparing with an M3.5V RV standard, offset to agree with the measurements from Nidever et al. (2002). No corrections were made for convective or gravitational effects for M dwarfs and Chubak et al. (2012) report a systematic error of 0.3 km s⁻¹ (random errors are at this level or lower in nearly all cases). Ten of their M dwarfs are in our sample. We chose one of these, LSPM J0727+0513, as our standard star. For the other nine stars, we compare our measurements with those from Chubak et al. (2012) in Figure 22. Considering the RV measured in each order separately, we found that the bluest two bands (Z and Y) systematically underestimate (Z-band) or overestimate (Y-band) the RV. The wavelength calibration is also subject to failure in those bands. We suggest that this is because in these two orders, the strongest stellar features overlap with the strongest telluric features, compromising the wavelength calibration and therefore the velocity measurement. They were also the orders with the lowest S/N. The RVs reported in this paper are the median of the J-, H-, and K-band measurements.

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We measured RVs for all our targets using each of the 10 RV standards from Chubak et al. (2012) in order to determine our internal error and systematic RV offset. The typical standard deviation of RVs measured against an alternative standard relative to those measured against LSPM J0727+0513 was 4.2 km s⁻¹. We used this value as our internal random error. RVs measured using LSPM J0727+0513 were systematically higher than those measured using other RV standards. Considering M3V-M5V standards, the median offset was 2.6 km s⁻¹ with a standard deviation of 1.5 km s⁻¹. The values reported in this paper include a −2.6 km s⁻¹ systematic RV correction. Our total internal measurement error is 4.4 km s⁻¹, which is our internal random error (4.2 km s⁻¹) added in quadrature to our internal systematic error (1.5 km s⁻¹).

Our choice of a single, mid-M RV standard does not appear to systematically affect the RV measurements or errors of early and late M dwarfs at this level of precision. We investigated the effect of the standard spectral type by comparing the results using LSPM J0727+0513 with using an M2V star, PM I06523-0511 (Gl 250), to measure the RVs of early M dwarfs, and an M7V star, J1056+0700 (Gl 406), to measure the RVs of late M dwarfs, finding that these choices did not appear to systematically affect the measured RVs, and that the scatter remained consistent with our estimated uncertainties.

To determine the precision of our wavelength calibration method, we used the transmission spectrum to create simulated data in each order, which we then calibrated. We simulated stellar absorption lines of random widths, depths, and locations on top of the transmission spectrum and multiplied by a polynomial (drawn from a random distribution) to curve the data. We then offset the spectrum and monitored how well we could recover that offset. The accuracy declined as more stellar absorption lines were added to the spectrum. With 50 added lines, the accuracy was better than 5 km s⁻¹ in all orders and better than 1 km s⁻¹ in the H-band.

We have multiple observations for 26 stars at different epochs. The time between observations ranges from days to months to years. We compared our RVs for these stars (Figure 23). The mean difference between the observation we elected to keep and the observation we chose to discard was 0.08 km s⁻¹ with a standard deviation of 4 km s⁻¹, consistent with our calculation of the error.

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Finally, we compared the RVs of CPM pairs (Figure 24). Eleven of these stars are separated and were observed independently and 11 were observed together on the slit. These observations were taken close in time, at near-identical conditions and were reduced using the same wavelength calibration and telluric standard. The mean RV difference between the primary and secondary components is 0.2 km s⁻¹ with a standard deviation of 2 km s⁻¹.

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