M DWARF CATALOG OF THE LAMOST PILOT SURVEY

The spectral subtype of an M dwarf, which is one of the most important fundamental parameters, is related to the temperature and the mass of the M dwarf. There are two primary approaches to classify an M dwarf by its spectrum. The first method uses the overall slope of the spectrum, which requires accurate spectrophotometric calibration over the full optical wavelength. The second approach matches the relative strength of atomic and molecular features in the spectrum, which has been normalized by being divided by an estimated local continuum. Considering the flux uncertainty of LAMOST M dwarf spectra, we choose the second method to derive the spectral types of the LAMOST M dwarfs.

The Hammer (Covey et al. 2007) is an IDL code that uses the relative strength of features. It has been widely used for classifying stellar spectra (Lee et al. 2008; West et al. 2011; Woolf & West 2012; Dhital et al. 2012), especially for M dwarf spectra. For classification of late-type stars, the Hammer computes 16 molecular band head indices of each spectrum, including the indices of Ca i, Mg i, CaH3, TiO5, VO, Na i, Cs, CrH, and Ca ii, and the wavelength of the indices covers 4000–9100 Å. The Hammer matches these indices with the indices computed from the templates, and the spectral type of the closest template is selected as the spectral type of the observed spectra. However, as described in the previous findings, the automatic Hammer tends to classify some spectra that are later than M5 as an earlier subtype (West et al. 2011).

In order to revise the late M classification problem of the Hammer code, we first tested the Hammer code with template spectra derived by Bochanski et al. (2007b, hereafter Bochanski2007b). We use the Hammer to automatically classify the Bochanski2007b templates and the results are shown in the second column of Table 2. In contrast to the first column of the table, M1, M5, M6, M7, and M9 templates are allocated with an earlier subtype.

We inspected each mismatch case and found that the spectral region between 6000 Å and 7000 Å and the one beyond 8000 Å are not well matched between the Bochanski2007b template and the Hammer template, which means that the original Hammer indices are not adequate to discriminate between all of the subtypes. We run an ensemble learning method Random Forest (RF; Breiman 2001) in search of the most important features for classifying M dwarf spectra.

RF is an ensemble classifier that consists of many decision trees and aggregates their results. The method injects randomness to guarantee that trees in the forest are different. This somewhat counterintuitive strategy turns out to perform very well compared to many other classifiers, including discriminant analysis, support vector machines, and neural networks (Liaw & Wiener 2002). RFs have become increasingly popular in many scientific fields (Strobl et al. 2008), and variable importance measures of RF have been receiving increased attention as a method of feature selection in many classification tasks in bioinformatics and related scientific fields (Díaz-Uriarte & Alvarez de Andrés 2006; Strobl et al. 2007).

Before we classified the Bochanski2007b M dwarf template using RF, we divided each spectrum from 6000 Å to 9000 Å into 600 regions, with each region covering 5 Å. The five adopted pseudo-continuum regions are 6130–6134 Å, 6545–6549 Å, 7042–7046 Å, 7560–7564 Å, and 8125–8129 Å. The mean flux of each region from 600 regions was computed and then was divided by the mean flux of each local pseudo-continuum. Finally, 3000 indices were obtained for each spectrum. These indices and corresponding subtypes were input to construct the forest. Knowledge or patterns were learned from the inputs during construction so that the constructed forest could classify a spectrum by what it had learned. Simultaneously, the variable importance measurements were provided by the forest.

The important features (the numerators of important indices) supplied by the RF method are shown in Figure 1. As a large number of LAMOST spectra are not of high quality in the blue part, and most of the obvious features of M dwarfs that can help distinguish between the spectral subtypes located in 6000–9000 Å, the spectral range we care about is limited to 6000–9000 Å. According to the importance list of the features, we adjusted the indices of the Hammer by adding three new indices and keeping the original Hammer indices that are in 6000–9000 Å. The three indices and their corresponding wavelength ranges are shown in Table 1. The features in the numerator range of CaH6385 and TiO8250 are sensitive to temperature. The numerator range of index 6545 is near Hα and is often used as a part of the continuum to compute the EW of Hα. So we take the index 6545 as a pseudo-continuum index, and name it Color6545. Table 1 shows the wavelength ranges of each index. The original Hammer indices Ca i, Mg i, and Color1 are removed because they are out of the wavelength of 6000–9000 Å. After adjusting the indices of the Hammer, there are still 16 indices. The 16 index values of the Hammer M dwarf template are calculated again. Figure 2 shows the values of the indices; points of the same color are index values in the same subtype. Lines from red to blue correspond to the subtypes of M0–M9. This figure indicates that the three new indices are good at identifying subtypes of M dwarf spectra.

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We then classified the Bochanski2007b template using the modified Hammer. The results are shown in the third column of Table 2. The classification result of each template is correct now. In order to verify the performance of Hammer after adjusting the indices, we further tested the code with 70,841 spectra from the SDSS DR7 M dwarf catalog (West et al. 2011). The results are shown in Figure 3. The top panel of the figure is the difference distribution of all spectral subtypes for the 70,841 total spectra. It shows a number of spectra that were misclassified as a later subtype by the original Hammer, and now are partially corrected by the modified Hammer. The accuracy of the modified Hammer is greater than the original Hammer. The bottom panel shows the difference distributions of subtypes for spectra later than M5 and indicates that the original Hammer classifies a larger fraction of late-type M dwarfs as an earlier subtype (as indicated by West et al. 2011). This is greatly remedied by the improved Hammer. According to the statistical results of all the data, the mean subtype difference is 1 subtype before adjusting the indices, while the mean subtype difference is 0.6 subtypes for the modified Hammer.

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The radial velocity of each M dwarf is measured by the cross-correlation method. Each observed spectrum is cross-correlated with the Bochanski2007b M dwarf template of the best matched subtype. In order to decrease the impact of inaccurate flux calibration, we use a cubic polynomial to rectify the observed spectra to the best fitted template spectra. We constrain the range of RVs to ±500 km s⁻¹, then move the observed spectra from −500 km s⁻¹ to 500 km s⁻¹ in 2 km s⁻¹ steps. After each move, the observed spectra are multiplied by an optimal cubic polynomial to cross-correlate the observed spectrum, with the corresponding template fitting all correlation values to produce a Gaussian peak. The corresponding RV of the Gaussian peak is chosen as our final RV. A bootstrap estimate is conducted to access the internal error of the RV estimation.

We use spectra from the SDSS DR7 M dwarf catalog to test our RV measurement method. Figure 4 shows the results. The left panel shows the comparison of our measured RV values to the values of West2011. The right panel shows the distribution of RV differences, in which 67,843 RV differences between −100 km s⁻¹ and +100 km s⁻¹ are shown. Figure 4 indicates that the RVs we measured generally agree with the RVs West2011 measured. The mean of two RV differences is 0.17 km s⁻¹, while the standard deviation is 6.4 km s⁻¹, which is less than the reported uncertainties of West2011. The larger scatter of RVs around the center of the figure is due to the low S/N of the spectra, which can be seen in Figure 5. It is intrinsically difficult to derive accurate RVs from these spectra with low S/N. We further select a subsample consisting of 479 spectra to examine the performance of our method by checking the Na doublet at 8183 Å and 8195 Å. In this subsample, the S/Ns are between 10 and 20 and the differences between the two RVs are between 50 and 200. We correct each spectrum of this subsample with its corresponding two RVs, respectively. The result is that for some spectra, our RVs are more accurate and for others, West's are better. Both measurements have their own advantages and their accuracies are close. We also inspect the points in the bottom of the left panel of Figure 4, and we find for this subsample our RVs are more accurate. Our comparisons indicate that our RV measurements of M dwarf spectra are generally accurate.

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The Hα emission line is the best indicator of chromospheric magnetic activity in M dwarfs due to their red colors. Thus, we estimate the magnetic activity of M dwarfs following the methods of West et al. (2004, 2011). We use a 14 Å wavelength region to calculate the EW of Hα. The central wavelength is 6564.66 Å in vacuum with 7 Å on either side. The continuum regions are 6555.0–6560.0 Å and 6570.0–6575.0 Å. Our magnetic activity criteria are similar to the West2011 criteria. As our sample contained all M dwarf spectra from the LAMOST pivot survey irrespective of S/N, we add an additional S/N (marked up with HASN2 in our catalog) constraint to obtain a more clean sample. The S/N constraint is that the average S/N of the spectral regions 6500–6550 Å and 6575–6625 Å should be larger than 10. From this clean sample, if a star is classified as active, its spectrum needs to satisfy the four criteria listed below.

• 1.  
  The S/N of the continuum near Hα is larger than 3.
• 2.  
  The EW of Hα must be larger than 1.
• 3.  
  The EW of Hα is larger than three times its error.
• 4.  
  The height of the Hα emission line is larger than three times the noise in the adjacent continuum.

The only difference between our criteria and West's is criterion 2. we carefully inspect our sample and find that it is more reasonable to use 1 as the boundary of the Hα EW. When a star from our clean sample is classified as inactive, its spectra should meet criterion 1, and the spectrum should have no detectable emission.

We have also measured the important molecular band features TiO1–TiO5, CaH1–CaH3, and CaOH following the wavelength ranges defined by Reid et al. (1995a, Table 2). The errors of these indices are given as well.

A rough indicator of metallicity ζ is computed, which was initially defined by Lépine et al. (2007). The definition of ζ is based on the strength of the TiO5, CaH2, and CaH3 molecular bands. This indicator was designed to divide main-sequence M into different metallicity classes: dwarf, subdwarf, extreme dwarf, and ultra subdwarf (Lépine et al. 2007). Dhital et al. (2012) refined the index ζ, which can better fit their observed M sample consisting of more M0–M3 dwarf spectra. Mann et al. (2013) found that the ζ parameter is correlated with [Fe/H] for super-solar metallicities and it does not always correctly identify metal-poor M dwarfs. Lépine et al. (2013) found that the metallicity mentioned in Lépine et al. (2007) overestimated the metallicity at earlier subtypes, while the Dhital et al. (2012) calibration tends to underestimate metallicity, so they recalibrated ζ. We measure the parameter ζ and its error following the latest definition of ζ by Lépine et al. (2013).

Spectral types of M dwarfs in our catalog are derived using the modified Hammer method and then confirmed by a visual check. As the LAMOST pilot survey is a test run of the telescope system, all celestial spectra, not just M dwarf spectra, have been visually inspected to ensure the instruments and processing pipeline work well. During visual inspection, roughly one-fifth of the automatic classification results are modified, and this classification bias is caused primarily by spectral noise and part-flux absence in the wavelength range of the adopted indices. The average difference between the automatic classification and the visually inspected classification is 0.26 spectral types. Figure 8 shows the spectral type distribution of LAMOST M dwarfs, in which early-type M dwarfs account for a large proportion and the peak spectral subtype is around M1–M2. Late-type M dwarfs from M6 to M9 are few (only 599), of which only 157 meet the S/N constraint of being larger than 10. This is likely due to target selection effects and the magnitude limitation of the LAMOST telescope.

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We have measured RVs and errors for all spectra of our catalog with our tested method described in Section 3.2. Although many factors may cause RV uncertainties, we try to reduce the unfavorable effects on the RV. We use the best matched spectral type template and cross-correlate it with the observed spectra, which minimizes the error introduced by spectral type mismatch. In order to reduce the effect of inaccuracy of the spectral flux, we use an optimal cubic polynomial to calibrate the observed spectra. The mean internal error of our RVs is 11.5 km s⁻¹, estimated by a Monte Carlo method. Because we specifically consider M dwarf spectra instead of all stellar spectra, our measurement results are more accurate than the LAMOST 1D pipeline. Using our measured RVs, we correct all spectra of this catalog to zero RV for measurements of the Hα emission line and molecular band indices.

Using our magnetic activity criteria, 1971 of 58,360 M dwarfs are Hα active while 22,987 are Hα inactive. The Hα activity fractions of M0–M5 are listed in Table 3. We confirm that later subtypes have higher active fractions. The fraction values are not very consistent with those from West2011; however, the trend of the active fraction from M0 to M5 is in good agreement with West2011, as shown in Figure 9. The number of late-type M dwarfs is too small (as mentioned in Section 4.1) to produce a reasonable activity fraction when using the same magnetic activity criteria. Therefore, the activity fraction of M6–M9 was not provided here.

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The important molecular band indices and their errors (as mentioned in Section 3.3) are measured and included in our catalog. In this section, we assess the accuracy of these quantities and discuss the impact of spectral flux uncertainties and noise on the accuracy of these quantities.

We compare the nine molecular band indices with those from the SDSS DR7 M dwarf catalog (West et al. 2011), as shown in Figure 10, where indices of each molecular band are averaged after grouping by spectral subtypes. The error bars in blue and red in Figure 10 represent the standard deviation of LAMOST indices and SDSS indices, respectively, at each spectral type. The spectral indices with spectral types later than M5 are not presented here because the spectral number is not enough for completeness. In general, for all nine indices in this figure, the LAMOST average indices at each spectral subtype match well with those of SDSS. This good consistency confirms that the LAMOST M dwarf spectral sample and the SDSS M dwarf spectral sample are similar and allow us to be confident in the correctness of these quantities. Furthermore, the error bars of LAMOST and SDSS display a similar trend, that is, with an increase in spectral type, error bars get larger. It should be known that the intrinsic differences of M dwarf spectra also play a role in the size of error bars. However, the CaH1 and CaOH indices of LAMOST have larger error bars than those of SDSS, which can be due to noise effect and spectral flux uncertainties.

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In order to find the influence of spectral noise on the measured indices in our catalog, we examine the TiO5 index distribution at each spectral type with different S/Ns. Figures 11–14 show the changes in TiO5 by S/N. In each figure, we show the TiO5 index distribution at each spectral type with S/Ns (HASN2) below 5, 5–10, 10–20, and 20 and above, respectively. Given a spectral type, the difference "diff" gradually declines with increasing S/N. Specifically, at SPT (spectral type) = 0 the "diff" are 0.064, 0.031, and 0.016 for S/N < 5, 5 < S/N < 10, and 10 < S/N < 20, respectively, and at other spectral types the trends are the same. The standard deviations of TiO5 indices also decline with increasing S/N. At SPT = 0, the standard deviations are 0.12, 0.09, 0.06, and 0.05 for S/N < 5, 5 < S/N < 10, 10 < S/N < 20, and S/N > 20, respectively. These indicate that spectral noise does affect index accuracy and that the lower the S/N, the less reliable the indices are. For S/N < 5, standard deviations of TiO5 indices are around 0.14, while for S/N > 5, they are almost below 0.1; for this S/N most "diff" are below 0.03, which means the average index offset to the corresponding ones of SDSS is not more than 5%. However, the S/N should be larger than 10 for more reliable indices.

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We exclude low S/N spectra to estimate the influence from LAMOST spectral flux uncertainties. Using S/N > 15 spectra of LAMOST and SDSS, we compare the nine molecular indices again, as shown in Figure 15. For TiO indices, the LAMOST indices are generally in agreement with SDSS. However, for other indices at later spectral types, the consistency between LAMOST and SDSS indices does not appear to be as good, which is caused by flux uncertainties. We estimate that the index bias of the LAMOST pilot survey may be introduced by flux uncertainties by comparing the index differences. In this figure, the largest difference between LAMOST and SDSS appears in CaH1 indices at SPT = 5; the index difference between LAMOST and SDSS is 0.07, about 10% of that of SDSS. Currently, LAMOST uses a relative flux calibration method (Song et al. 2012) due to the lack of a high-precision companion photometric survey telescope to aid in absolute flux calibration, which may lead to flux uncertainty, as well as the effects of skylight and telluric lines. However, these factors have been taken into full account and in the LAMOST regular survey the spectral quality is improving gradually.

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In summary, the molecular band indices in our catalog have been measured correctly and these quantities are generally accurate. We have discussed the impact of the spectral noise and flux uncertainties on the accuracy of these indices. We suggest a S/N > 10 cutoff for more accurate indices.