THE SLOAN DIGITAL SKY SURVEY DATA RELEASE 7 SPECTROSCOPIC M DWARF CATALOG. I. DATA

Previous large spectroscopic samples of M dwarfs have relied on automated spectral typing due to the quantity of time required to manually inspect tens of thousands of candidate spectra. Systematic discrepancies were recently identified in the spectral types from the W08 SDSS sample that were determined automatically by the "Hammer" spectral typing algorithm (Covey et al. 2007). The bias was detected as a systematic offset for late-type stars, whose automatic classification was often one subtype earlier than determined via visual inspection (see Figure 1). We thus decided that visual inspection would produce the most reliable and precise spectroscopic sample. We visually inspected all 116,161 M dwarf candidates and manually assigned spectral types. The sample was divided among 17 individuals¹⁴ who used the manual "eyecheck" mode of the Hammer (v. 1_2_5) to assign spectral types and remove non-M dwarf interlopers.

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Figure 1 shows the difference between the spectral types automatically determined by the Hammer and the mean visual inspection. For early-type M dwarfs (left panel), the Hammer and the spectral typers agree most of the time. However, for ∼38% of the late-type M dwarfs (right panel), the Hammer assigns spectral types one subtype earlier than the average human spectral typer. This confirms that while the Hammer generates automatic spectral types within the quoted ±1 subtype accuracy (Covey et al. 2007), there is a systematic offset of one subtype for the late-type stars, and justifies our effort to manually inspect more than 116,000 candidates.

Each spectral typer also examined a control sample of 1000 spectra, of which 638 were M dwarfs. We used this control sample to assess the quality and reliability of the visually inspected sample by quantifying the variations among the 17 individual typers, and by comparing the median visual type for each star to its automatic Hammer type. The results of the control sample show that there is excellent agreement between all of the spectral typers with a large fraction of the stars being assigned. Almost all of the visual classifications in the control sample agreed to within ±1 subtype of the median value; for most of the stars, the dispersion in visual classifications was <0.4 subtypes. To ensure that there were no major systematics in the spectral types assigned by any individual, we examined the mean difference between each typer's visual classifications of the control sample spectra and the median classifications of the entire group. We divided the sample into the early types (<M5) and late types (⩾M5) to investigate any spectral type dependence in typing quality: all of the spectral typers clustered near the median values with no individual displaying a systematic offset larger than 0.2 subtypes.

As part of our analysis we measured a number of spectral lines and molecular features in each M dwarf spectrum. All of the spectral measurements were made using the RV-corrected spectra. The TiO1, TiO2, TiO3, TiO4, TiO5, TiO8, CaOH, CaH1, CaH2, and CaH3 molecular band head indices and their formal uncertainties were measured using the Hammer with the molecular band heads as defined by Reid et al. (1995a) and Gizis (1997). We also measured the chromospheric hydrogen Balmer and Ca ii lines that are associated with magnetic activity. We expanded the Hα analysis of West et al. (2004, 2008) to include Hβ, Hγ, Hδ, and Ca ii K (H and Ca ii H are blended in SDSS data and were not included in our sample). All of the line measurements were made by integrating over the specific line region (8 Å wide centered on the line) and subtracting off the mean flux calculated from two adjacent continuum regions (Continuum A and Continuum B in Table 1). Equivalent widths (EWs) were computed for each line by dividing the integrated line flux by the mean continuum value (as in previous studies, we define the EW to be positive for emission lines; Hawley et al. 1996; West et al. 2004). The low resolution of SDSS spectra does not affect our ability to measure accurate line values, with the exception of Ca ii K. Due to the intrinsic Ca ii K absorption present in M dwarf photospheres, weak activity appears as an emission peak in the absorption line. This weak emission cannot be resolved in SDSS spectra. However, strong Ca ii K emission overwhelms the absorption and can be easily recovered from low-resolution spectra (Walkowicz & Hawley 2009). The lines and continuum regions (in vacuum wavelengths) can be found in Table 1. Formal uncertainties on the EWs for each line were also computed.

Similar to the West et al. (2004, 2008) samples, we defined magnetically active stars as those that had detectable emission lines in their spectra. Previously, this had been done solely for Hα. To be classified as active in a specific emission line, the following four criteria had to be satisfied: (1) the EW of the line was larger than some minimum value (see below), (2) the EW value must be three times the uncertainty, (3) the S/N in the continuum must be larger than 3, and (4) the height of the spectral line must be larger than three times the noise in the continuum. Stars were classified as inactive if they met criterion 3 and had no detectable emission. Criterion 3 preferentially selects brighter stars at any given color or spectral type. This selection bias should not have a large effect our results since we examine the properties of our sample in a Galactic context and both active and inactive stars with low S/N should be removed. However, if active stars are intrinsically more luminous than their inactive counterparts (at the same color; see Section 3.2 below), criterion 3 may serve to include slightly more active stars in our resulting analyses.

Because the strength of the stellar continuum changes dramatically from Ca ii K to Hα in M dwarfs, the EW thresholds used in criterion 1 are different for each line. We experimentally derived the EW thresholds by automatically measuring activity in a subsample of 300 M dwarfs (that spanned a range of S/N and spectral types) using 10 different EW activity thresholds. Additionally, each spectrum was visually inspected and the activity state for all five emission lines was determined. By comparing the results of our manual inspection with the 10 different automatic routines, we determined the EW thresholds that most accurately reproduced our visual activity classifications. The EW activity threshold for each of the five emission lines can be found in Table 1. We found that the previous Hα activity limit of 1 Å (West et al. 2004) was slightly too high and excluded a number of good detections. We have therefore reduced the Hα EW activity criterion to 0.75 Å.

Recently, Kruse et al. (2010, hereafter K10) investigated the time variability of SDSS M dwarfs and defined their Hα activity thresholds based on the median EW values that were detected at a 3σ confidence level as a function of spectral type. Although the K10 threshold EWs provide a robust way to select a clean sample, it unduly biases the sample toward the most active stars at later spectral types. For example, our DR7 catalog contains a large number of active M6 dwarfs (that have Hα emission lines with peak values that are more than five times larger than the noise) that have EWs below the 3 Å threshold used in the K10 study. In addition, the activity fractions presented in K10 (see their Figure 4) include these active stars (with EW < 3 Å) in the "inactive" component of the activity fraction denominator. This explains why the activity fractions reported by K10 are smaller than previous determinations (West et al. 2004, 2008) and indicates a serious selection bias in the K10 results.

For all of the active stars in the sample, we computed the ratio of luminosity in the emission line as compared to the bolometric luminosity (L_line/L_bol). We followed the methods of Hall (1996), Walkowicz et al. (2004), and West & Hawley (2008) who derived χ factors for the hydrogen Balmer and Ca ii chromospheric lines as a function of M dwarf spectral type. The χ factor uses empirical results for the bolometric luminosities of M dwarfs as a function of color and/or spectral type (Leggett et al. 1996, 2001) and relates the EW of a line to the fraction of the bolometric luminosity emitted by the line. The L_line/L_bol values were computed by multiplying the EW of each active star by the appropriate χ value. Formal uncertainties were computed for each L_line/L_bol value and are included in the final database.

We also computed the metal sensitive parameter ζ, defined by Lépine et al. (2007), which uses a combination of the TiO5, CaH2, and CaH3 molecular band indices to separate the sample into different metallicity classes (see Equations (1) and (2)). This is similar to the Gizis (1997) classification system but was re-calibrated using wide common proper motion pairs that were assumed to be at the same metallicity. Stars with solar metallicity ([Fe/H] = 0) have ζ values ∼1 and stars with [Fe/H] = −1 have ζ ∼ 0.4 (Woolf et al. 2009). Although there is considerable scatter in the [Fe/H] versus ζ relation at high metallicities, this parameter is very useful for finding and classifying low-metallicity stars that are likely members of the Galactic halo.

Our catalog containing all of the measured quantities is publicly available on the VizieR¹⁵ site or can be obtained by contacting the corresponding author. The individual spectra are available from the SDSS DR7 Web site.¹⁶ As with previous SDSS spectroscopic catalogs of low-mass stars, we remind the community that these data do not represent a complete sample and that the complicated SDSS spectral targeting (see Section 3.1) introduces a variety of selection effects. However, our new sample covers a large range of values for many of the physical attributes of the M dwarfs, including parameters that are sensitive to activity, metallicity, and Galactic motion, making accurate activity, kinematic, and chemical analyses possible. In addition, because some of the derived quantities are computed by automatic routines, values for a small percentage (∼4%; West et al. 2004) of individual stars may be incorrect; this should not affect large statistical results. Users are nevertheless cautioned to understand the origin of specific data products before using them indiscriminately.

All of the magnitudes included in our DR7 catalog and used to compute the median colors were extinction corrected using the Schlegel et al. (1998) line-of-sight dust maps (and the dust model of Cardelli et al. 1989, and R_V = 3.1). We provide extinction corrections for each band in the catalog so that observed magnitudes can be easily reproduced. Because of the close proximity of many of the M dwarfs in the sample, the entire Schlegel et al. (1998) extinction is likely an overestimate for many lines of sight. The uncertainty in the extinction correction introduces a small uncertainty in the derived distances. However, given the small amount of extinction toward objects in the SDSS footprint, the added uncertainties to the distances are typically less than 5%. We are currently determining the amount of extinction needed to reproduce an unreddened spectrum for each object in our DR7 sample and will report on that analysis in a future paper (Jones et al. 2011).

We computed median colors for each subtype of the DR7 sample, applying stringent cuts to include only those stars with the highest quality photometry. To be included in the median color calculation, SDSS stars had to have GOODPHOT = 1, r-band extinction <0.05 mag, and r-, i-, and z-band magnitude uncertainties <0.05 mag. Median colors incorporating 2MASS magnitudes were calculated from the subset of stars with J, H, and K_S uncertainties <0.05. The median colors and standard deviations (in parentheses) are shown in Table 2. Due to the systematic offset in the Hammer automatic spectral types for late-type M dwarfs, our average colors are bluer than previously reported (W08; Kowalski et al. 2009). We include the g − r colors but warn that they are likely metallicity dependent (West et al. 2004; Bochanski et al. 2007b; see also Section 3.3 below).

Figure 3 shows the r versus r − z Hess diagram for the M dwarfs in the SDSS DR7 sample. The gaps in color space reflect the non-uniform sampling due to the spectral-targeting algorithm. To quantify the effect of SDSS spectroscopic-targeting algorithms on the median colors, we conducted the following test. We began with the straw man assumption that the median r − i, i − z, and r − z color–spectral-type relations reported in Table 2 are representative of the underlying stellar population. We then used these quantities, along with the observed color spread in each spectral type bin, to construct a synthetic stellar population with a uniform distribution in both magnitude and spectral type. We then applied photometric cuts to the smooth underlying distribution, replicating the SDSS spectroscopic selection and producing a synthetic "observed" sample that is highly structured in color–magnitude space. The median colors and spreads were then calculated as a function of spectral type from this synthetic sample and compared to the measured colors in Table 2. In general, the colors of the synthetic stars agree to within 0.02 mag of the observed sample (an agreement that would not be expected if the underlying population were different from the observed SDSS stars) and we conclude that the colors presented in Table 2 are not severely affected by the spectroscopic selection.

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Figure 4 shows the Hα activity fraction as a function of M dwarf spectral type for stars with data quality sufficient to measure Hα emission (and GOODPHOT = 1 and WDM = 0). Our results are in good agreement with previous studies (West et al. 2004; W08), but with much lower uncertainties due to the ∼59,000 M dwarfs used to generate Figure 4 (7952 are Hα active and 51,034 are Hα inactive). There are a few small differences between Figure 4 and the Hα activity fractions reported by W08 that are likely due to the changes in some of the spectral types (see above) and the different Galactic sightlines included in the DR7 sample. Because of the lower S/N in the blue portion of M dwarfs, fewer stars were available to measure activity for the higher order Balmer and Ca ii K emission lines. Table 3 gives the number of active and inactive stars for each emission line indicator that had the necessary quality for our activity analysis.

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As discussed in W08, the activity fraction is highly dependent on the location of the samples in the Galaxy. Because M dwarfs have finite activity lifetimes and are dynamically heated in the Galactic disk as they age, their activity state is correlated with position in the Galaxy. One of the reasons that the M dwarfs in our sample have much smaller activity fractions than those studied nearby (e.g., Hawley et al. 1996; Gizis et al. 2000) is that the SDSS volume is much larger than those used in previous catalogs and is concentrated on the north galactic cap, yielding a much older stellar population. This is particularly clear for the early-type M dwarfs, which have median distances greater than 500 pc, and therefore ages that are considerably older than their short activity lifetimes (∼1–2 Gyr). We reiterate the warning from W08 that activity fractions in M dwarfs must be discussed in the proper Galactic context.

The various emission lines measured in our spectra are formed at slightly different locations in the chromosphere, suggesting that the strength of one emission line may not necessarily predict the strength of another. We therefore examined how the various activity induced emission lines trace each other as a function of spectral type and absolute distance from the Galactic plane (a proxy for age). Figure 5 shows the Hα (diamonds) and Hβ (asterisks) activity fractions for M2–M7 dwarfs as a function of Galactic height. Only the Hα activity fractions for stars that could have detected Hβ emission are included. This limits the sample to the brighter stars at each spectral type that meet the S/N criterion and does not include all of the M dwarfs that are sensitive to Hα emission. Spectral types earlier than M2 and later than M7 were not included due to an insufficient sample size of active stars. As seen in previous studies, the magnetic activity fractions decrease as a function of Galactic height, confirming an age–activity relationship; stars closer to the Plane are statistically younger and more likely to be active. Figure 5 also demonstrates that Hα and Hβ trace each other extremely well for the entire DR7 sample, implying that the Hβ activity lifetimes are essentially the same as those for Hα.

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The other activity tracers also appear to correlate with Hα emission. Figure 6 shows the activity fractions for all five emission lines in M4 dwarfs as a function of vertical distance from the Galactic plane. Each panel plots the activity fractions for stars where the data are good enough to measure (i.e., sensitive to) Hβ (top left), Hγ (top right), Hδ (bottom left), and Ca ii K (bottom right) activity as well as the emission lines redder than that specific tracer. The activity fractions for all of the lines are in excellent agreement with each other and indicate that all five emission lines are produced for the same amount of time during the lifetime of an M dwarf. This new result is complementary to previous studies that found strong correlations among different emission line strengths in M dwarfs (Rauscher & Marcy 2006; Walkowicz & Hawley 2009). Although the relative emission line strengths for individual stars may fluctuate over time (see Cincunegui et al. 2007), the mean values of the emission lines are well correlated in the large DR7 sample. The unprecedented size and Galactic distribution of our spectroscopic sample confirms that not only the strength, but the duration of activity appears to be similar for all of the Balmer and Ca ii activity indicators.

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Figure 6 also demonstrates a possible (and important) selection effect present in magnitude-limited or activity-selected samples. A close examination of Figure 6 (and Figure 5) reveals that the activity fractions are larger for the stars that are sensitive to the bluer emission lines. This trend was not expected since the stars used to compute the activity fraction were drawn from the same volumes in each of the four panels. The only difference was that the stars selected for the bluer emission line analyses were required to have higher S/N. With this in mind, we can explain the different activity fractions as follows.

The actual spread in absolute magnitude (or luminosity) at a given spectral type can be quite significant.¹⁷ Some of this spread may be due to differences in the physical properties of the stars. Hawley et al. (1996) showed that magnetically active stars are brighter in M_V than their inactive counterparts. Recently, Bochanski et al. (2011, hereafter Paper II) found that both active and higher metallicity M dwarfs (many stars are both) appear to be brighter in M_r at a given color or spectral type. Because the bluer emission lines that we are examining in Figure 6 require higher S/N spectra to accurately measure activity, the M4 dwarfs at a given distance that meet the S/N criterion are preferentially more luminous than other stars in the same distance bin. If activity is correlated with luminosity, our S/N selection will bias our sample toward containing a higher fraction of active stars.

In addition to activity fractions, we also investigated the median luminosity in each emission line as a function of spectral type. Previous studies have investigated how the Hα luminosity changes as a function of spectral type (Hawley et al. 1996; Gizis et al. 2000; Burgasser et al. 2002; West et al. 2004). These studies found that the fraction of luminosity emitted in Hα is constant over the range M0–M5 and decreases by almost an order of magnitude for late-type M dwarfs. However, most of the previous studies concentrated on Hα and did not include similar analyses for the other Balmer or Ca ii lines, and those that did were based on a small sample of stars (Hawley & Pettersen 1991; West & Hawley 2008).

Each panel of Figure 7 shows the median luminosity of a specific activity tracer (as compared to the bolometric luminosity of the stars) for active stars sensitive to that particular emission line. All of the activity tracers exhibit similar behavior, with the relative luminosity staying constant for the early-type M dwarfs and then falling to lower values at or around a spectral type of M5. The median values and the upper and lower quartiles that are plotted in Figure 7 are also given in Table 4. The bluer emission lines produce smaller fractional luminosities as expected and are consistent with previous Balmer decrement studies (Hawley & Pettersen 1991; Bochanski et al. 2007b; West & Hawley 2008). W08 found evidence for a slight decrease in L_Hα/L_bol as a function of Galactic height, but the effect is small and not included in our analysis.

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Table 4. Luminosity in Activity Tracer Emission Lines

Spectral	LHα/Lbol	LHβ/Lbol	LHγ/Lbol	LHδ/Lbol	$L_{{\rm Ca\,{\mathsc{ii}}\ \rm K}}$/Lbol
Type	(×10−4)	(×10−4)	(×10−4)	(×10−4)	(×10−4)
M0	1.27+0.39−0.21	0.85+0.29−0.17	0.50+0.13−0.08	0.76+0.19−0.46	0.33+0.07−0.11
M1	1.51+0.49−0.35	0.81+0.28−0.15	0.50+0.20−0.13	0.39+0.09−0.06	0.45+0.21−0.14
M2	1.42+0.45−0.35	0.77+0.26−0.24	0.44+0.15−0.15	0.32+0.08−0.09	0.34+0.18−0.08
M3	1.36+0.42−0.42	0.67+0.22−0.19	0.35+0.12−0.11	0.26+0.10−0.05	0.30+0.14−0.15
M4	1.44+0.63−0.47	0.61+0.29−0.22	0.35+0.14−0.13	0.29+0.09−0.10	0.28+0.11−0.11
M5	0.81+0.25−0.22	0.33+0.11−0.08	0.37+0.10−0.11	0.26+0.07−0.07	0.37+0.09−0.15
M6	0.57+0.20−0.13	0.22+0.07−0.06	0.13+0.02−0.02	0.08+0.02−0.02	0.17+0.04−0.05
M7	0.19+0.08−0.05	0.06+0.03−0.01	0.07+0.00−0.03	0.06+0.02−0.03	0.05+0.03−0.03
M8	0.27+0.12−0.07	0.14+0.06−0.05	...	...	...
M9	0.20+0.05−0.06	0.12+0.14−0.07	...	...	...

Notes. Bolometrically scaled luminosities were derived using stars that show activity in each emission line. Reported uncertainties are the 25th and 75th quartile values.

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Metallicity continues to be one of the most elusive physical quantities to measure in M dwarfs. Recent work using infrared spectroscopy and improved photometry for M dwarfs in wide binaries may soon lead to accurate metallicity determinations for large samples of M dwarfs (Woolf et al. 2009; Johnson & Apps 2009; Rojas-Ayala et al. 2010). However, the Lépine et al. (2007) ζ parameter is currently the best indicator of metallicity in optical M dwarf spectra. Using the DR7 M dwarf sample, we examined how ζ changes as a function of Galactic height. Figure 8 shows median ζ values for M1 and M2 dwarfs as a function of absolute height above the Galactic plane. These specific spectral types were chosen because they span a large range of distance and contain a significant number of stars with ζ uncertainty <0.1. Figure 8 shows a clear decrease in ζ for both spectral types with increasing Galactic height. The discrepancies in the nearby bins reflect the scatter in the high-metallicity end of the ζ versus metallicity relation (Woolf et al. 2009). The results shown in Figure 8 suggest a significant change in the median metallicity of M dwarfs (and by extension the Galaxy) as a function of age, with the oldest stars (that are farther from the Plane) having the lowest metallicity. Similar trends have been seen in both the radial and vertical directions from previous spectroscopic samples of higher-mass stars (Nordström et al. 2004; Ivezić et al. 2008). However, the higher density and longer main-sequence lifetimes of M dwarfs may provide a better probe of the metal content (and evolution) of the local Galactic disk. The ζ values of ∼0.6 in the most distant bins of Figure 8 have metallicities of [Fe/H] ∼ −0.7 according to the wide binary analysis of Woolf et al. (2009).¹⁸ We note that the photometric distances derived in our sample are likely affected by metallicity and that the farthest bins in Figure 8 (that have lower metallicities) are closer than shown due to fainter M_r magnitudes (Paper II). Regardless, this strong trend in metallicity demonstrates the utility of large spectroscopic samples of M dwarfs (such as the one presented in this paper) for understanding the chemical evolution of the Milky Way. However, additional calibration is required to convert quantities such as ζ into precise metallicities.

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Previous SDSS studies have shown that the g − r color of M dwarfs appears to correlate with metallicity (West et al. 2004; Lépine & Scholz 2008). Future large photometric surveys such as LSST (Ivezic et al. 2008) will rely heavily on the ability to classify objects based on their broadband colors alone. A large spectroscopic sample of M dwarfs, like the one presented here, can help correlate photometric properties of M dwarfs to spectroscopically derived physical parameters. Figure 9 shows the g − r colors of M dwarfs as a function of ζ for M1–M4 dwarfs. Although there is a trend of decreasing ζ with redder g − r color, the change in g − r is different across spectral types. Therefore, g − r color alone is not a good tracer of M dwarf metallicity across the range of M dwarf spectral types. However, when we examined the ζ values as a function of both g − r and r − z (a proxy for spectral type; see Table 2), we found a strong trend of decreasing ζ diagonal to the g − r, r − z axis and perpendicular to the stellar locus (Covey et al. 2007). Figure 10 highlights a region of color space that can be used to probe the metallicity content of M dwarfs and obtain low-metallicity members of the Galactic halo from solely broadband photometry. Using a Levenberg–Marquardt minimization technique, we derived a two-dimensional fit that relates ζ to the g − r and r − z colors:

$$\begin{eqnarray} \zeta = & 1.04-0.98(g-r)^2-0.07(r-z)^2+1.07(g-r)\nonumber \\ & -0.53(r-z)+0.63(g-r)(r-z). \end{eqnarray} \tag{ 3 }$$

Equation (3) is valid over the ranges shown in Figure 10 and has typical uncertainties of 10%–20%.

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Prompted by the discovery of new low-mass stars in the solar vicinity from other SDSS studies (e.g., Schmidt et al. 2010a), we inspected our catalog for M dwarfs that are possibly within 25 pc of the Sun. We found 21 nearby M dwarf candidates (8 of which were previously unidentified) based on the distances derived using the M_r, r − z photometric parallax relation of Bochanski et al. (2010). Three of the stars were in the W08 SDSS DR5 sample but were not identified there as potential solar neighbors. Table 5 gives the positions, spectral types, and distance estimates for all 21 of the nearby candidates. The closest candidate is SDSS1410+1846, which has an estimated distance of 14.8 pc. Since roughly one out of every 1000 M dwarfs in SDSS has a spectrum, there is a strong possibility that many more nearby stars await discovery and will be cataloged in future studies.