Metallic-line Stars Identified from Low-resolution Spectra of LAMOST DR5

LAMOST is a reflecting Schmidt telescope with a 4 m effective aperture and 5° field of view. Four thousand fibers are mounted on the focal plane that enable it observe 4000 objects simultaneously. The telescope is dedicated to a spectral survey over the entire available northern sky and is located at the Xinglong Observatory of Beijing, China (Cui et al. 2012; Luo et al. 2012, 2015; Zhao et al. 2012). Compared with the Sloan Digital Sky Survey's spectroscopic observations, the LAMOST survey is more concentrated on the Galactic disk where more young stars exist and is very advantageous to search for Am stars.

By the end of the first five-year regular survey, LAMOST has obtained 9,017,844 spectra of stars, galaxies, and quiet stellar objects (QSOs) with spectral resolutions of R ≈ 1800, wavelength coverage ranging from 370 to 900 nm, and magnitude limitation that is about r ≈ 17.8 mag for stars. The total number of stellar spectra reaches 8,171,443, making it a gold mine waiting to be exploited. All the above numbers can be found in the LAMOST spectral archive.⁵

Before searching for Am stars, we limited the search scope to a certain range through the following conditions:

• 1.  
  Because spectral type of Am stars are generally A- and early F-type, we limited the search to only A-, F0-, F1-, and F2-type stars in LAMOST DR5, whose spectral types come from the LAMOST 1D pipeline.
• 2.  
  The spectral features of Am stars mainly appear in the blue wavelength band, and their metallic lines are relatively weak and susceptible to noise, thus we only retained spectra with the signal-to-noise ratio of the g band greater than 50 (a signal-to-noise ratio ≥ 50).
• 3.  
  To ensure the accuracy and stability of classification, we eliminated some spectra containing zero flux in the blue spectra.

More than 10% objects have been repeatedly observed multiple times by LAMOST. For such targets, we only retain the spectra with the highest signal-to-noise ratio. Finally, we obtain 193,345 stellar spectra as our searching data set. We need labeled data to form the training and testing data sets, and all the labeled data are also handled using the three operations above, except for Evaluation Set II.

In order to train and test the classifier, we collected known samples of Am stars and non-Am samples. We first selected Am samples with confidence greater than 0.5 and all non-Am stars from the work of Hou et al. (2015) and then removed those close to the experience separation curve to ensure the purity of the Am positive and the non-Am negative sample sets. This yielded 1805 Am stars as positive samples. For the non-Am stars, further screening was conducted using the MKCLASS software. We randomly chose the same number of non-Am stars as negative samples, and these positive and negative samples were distributed on average in the training and test sets. Finally, we obtained 1806 training samples and 1804 test samples.

In addition, we also chose some Am stars from Gray et al. (2016) and Renson & Manfroid (2009) as evaluation sets in order to evaluate the performance of a variety of methods. For 1067 Am stars presented by Gray et al. (2016), we applied the pretreatment process in Section 2.1. Then, according to K-line and metallic-line spectral subtypes, those samples were classified into classical Am stars and marginal Am stars. The former, the K-line type, is earlier than the metallic-line type for at least five spectral subtypes. For the latter, the difference between the two types is less than five spectral subtypes (Morgan et al. 1978; Gray & Corbally 2009). We obtained 357 classical Am stars and 76 marginal Am stars as Evaluation Set I. The 116 known Am stars from the catalog of Renson & Manfroid (2009) were crossmatched with LAMOST DR5, and only 4 counterparts were found, which were comprised in Evaluation Set II. All labeled data sets are summarized in Table 1.

According to the characteristics of the underabundance of Ca elements and the overabundance of Fe-group elements in the atmosphere of an Am star, Hou et al. (2015) classified Am stars using the ESC, which is derived from line indices of the K line and nine groups' Fe lines. We used Evaluation Set I to evaluate the classification ability of the ESC, as shown in Figure 1, in which there are 357 stars labeled as classical Am stars (green dots in the figure) and 76 stars labeled as marginal Am stars (blue dots). We found that only 345 classical and 52 marginal Ams were judged as Am stars by the ESC (red curve), i.e., the recall through the ESC is 0.966 for classical Am stars and 0.684 for marginal Am stars, respectively.

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Obviously, the ESC based on the line index method is slightly inadequate for distinguishing marginal Am stars from normal early-type stars. This is mainly because the chemical peculiarity of the marginal Am stars is much weaker than the classical Am stars, and the difference between the marginal Am stars and the normal early-type stars is smaller than that of the classical Am stars. In addition, some spectral lines, such as Fe lines, are weaker, and the batch calculation of those line indices will lead to large errors, which will reduce the recall rate of marginal Am stars.

Based on the above reasons, we decided to use the fluxes of spectra as the input features of the classifier. Considering that the spectral line characteristics of Am stars are more densely concentrated in the blue wavelength range than the red, we choose the normalized fluxes in the wavelength range between 3800 and 5600 Å as the input values of the classifier model.

Before selecting a classification model, we must remove the influence of pseudocontinuum on the classifier. This is the key to successfully distinguish Am stars. We improved the fitting technology of pseudocontinuum (Lee et al. 2008) by applying the automatic identification operation of strong lines. The details of this procedure are as follows. Step 1: the wavelength of all spectra was truncated from 3800 to 5600 Å. Step 2: a ninth-order polynomial was used to fit each spectrum, and those points outside 3σ away from the fitted function were masked including the strong spectral lines, cosmic rays, and sky emission residual from data reduction. Step 3: a ninth-order polynomial was used to iteratively fit spectra, where points more than 3σ below the fitted function were rejected. The purpose is to find the approximate upper envelope of each spectrum as its pseudocontinuum. Step 4: the pseudocontinuum was removed from each spectrum by dividing the observed spectrum by the pseudocontinuum. The intensity of each spectrum was rectified using this method.

Figure 2 shows the results obtained with the improved method. One can see from Figure 2 that the pseudocontinuum is well removed from the spectrum.

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We selected six sophisticated classification algorithms from scikit-learn web: K-nearest neighbors (KNN), support vector classification (SVC), a Gaussian process (GP), a decision tree (DT), the RF, and Gaussian naive Bayes (GNB). According to the parameter values recommended by the website, we trained these classifiers on the training set separately and tested their performance on the test set. We then performed two external evaluations for the first three winning classifiers and compared them to the previous methods of searching for Am stars, such as the ESC and MKCLASS software, and finally chose the RF algorithm as the classifier in our work.

3.3.1. Classifier Evaluation Criteria

We used precision, accuracy, recall, and the F1 score as the criteria to evaluate the classifiers. The four evaluation criteria are defined as follows:

$$\begin{eqnarray*}\begin{array}{rcl}\mathrm{precision} & = & \displaystyle \frac{\mathrm{TP}}{\mathrm{TP}+\mathrm{FP}}\\ \mathrm{accuracy} & = & \displaystyle \frac{\mathrm{TP}+\mathrm{TN}}{\mathrm{TP}+\mathrm{FP}+\mathrm{TN}+\mathrm{FN}}\\ \mathrm{recall} & = & \displaystyle \frac{\mathrm{TP}}{\mathrm{TP}+\mathrm{FN}}\\ {\rm{F}}1 & = & 2\times \displaystyle \frac{\mathrm{precision}\times \mathrm{recall}}{\mathrm{precision}+\mathrm{recall}}.\end{array}\end{eqnarray*}$$

Since the test set is composed of labeled samples, it is easy to judge whether the classifier's classification results are correct on the test set. TP is the number of true positive samples that are correctly classified as Am stars by the classifier. FP is the number of false positive samples that are misclassified as Am stars by the classifier. Similarly, TN is the number of true negative samples that are correctly classified as non-Am stars by the classifier, and FN is the number of false negative samples that are misclassified as non-Am stars by the classifier. Precision is the fraction of true positive samples among the set of Am classified by the classifier. Accuracy measures the fraction of samples that are correctly classified in the entire set. Recall measures the fraction of Am that are correctly classified over the total amount of Am. F1 score is the harmonic mean of precision and recall.

3.3.2. Internal Testing

3.3.3. External Evaluation I

3.3.4. External Evaluation II

Evaluation Set II was used to compare the RF algorithm with the MKCLASS software. The samples in Evaluation Set II come from the catalog of Renson & Manfroid (2009), in which only four counterparts can be found in LAMOST DR5. The RF algorithm and the MKCLASS package were used to classify the four well-studied Am stars, and the results are listed in Table 4. These stars were also recognized as Am in some literature based on analyzing the abundance of chemical elements, and these literature are also listed in Table 4 for reference. The RF algorithm classified these four stars as Am Stars, which is consistent with the results from the literature. However, the MKCLASS software can only classify the star HD 73818 out of the four stars as an Am star. Obviously, the RF classifier is a more suitable tool for searching for Am stars. After all, the MKCLASS software is not a specially developed software for Am stars.

Table 4.  The Results of the RF and the MKCLASS with the Evaluation Set II

HD Number	LAMOST FITS File Name	RF	MKCLASS	Spectral Type of References
HD 108486	spec-55959-B5595905_ sp01-168.fits	Am	A2 IV-V SrSi	Am(1, 7, 8)
HD 108642	spec-55959-B5595905_ sp05-141.fits	Am	A1 IV SrSi	Am(1, 7, 8)
HD 108651	spec-55959-B5595905_ sp01-134.fits	Am	A7 mA0 metal weak	Am(6, 7, 8)
HD 73818	spec-57392-KP083141N185915V01_ sp13-195.fits	Am	kA6hF1mF2 Eu	Am(2, 3, 4, 5)

Note. The first column indicates the identifiers of the stars in the HD catalog. The second column lists the names of FITS files of the LAMOST counterparts. The next two columns show the results of the RF algorithm and MKCLASS software, respectively. The last column gives the literature that identify the four stars as Am based on element abundance. Articles numbered 1, 2, 3, 4, 5, 6, 7, and 8 correspond to Gebran et al. (2008), Fossati et al. (2008a, 2008c, 2008b, 2007), Iliev et al. (2006), Monier & Richard (2004), and Burkhart & Coupry (2000), respectively.

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For visual inspection of the four Am stars, we plot their spectra and corresponding normal stellar templates with the same spectral types given by H lines in Figure 3. The best-matching Kurucz template (Castelli & Kurucz 2003) for each spectrum was obtained through cross correlation. The black one in each panel is the normalized Am spectrum, while the red one is the best-matching template. One can see that the Balmer lines of the four Am spectra fit well with their best templates, but the strength of the K lines are weaker than that of their templates; on the other hand, the metallic lines show just the opposite. This is in line with the characteristics of the first subgroup of Am stars with weak K lines and strong metallic lines.

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Compared with ESC, MKCLASS, GP, KNN, SVC, DT, and GNB methods, the RF algorithm is the best choice to search for Am stars. After obtaining Am candidates using the RF algorithm, an eyeball check was conducted comparing with the best-matching templates.

The RF algorithm a one-of-a-kind of bagging algorithm in ensemble learning. N training samples are randomly selected from the original sample set using the Bootstrapping method with replacement, and K training sets are obtained by K-round extraction. The K training sets are independent of each other, and elements can be duplicated. The K decision tree models are trained on the K training sets and vote to produce classification results.

The number of decision trees, K, is a key parameter in the RF algorithm: the larger the number of decision trees, the better the classification results and the longer time consumption. After multiple attempts, we used 1800 as the value of the number of decision trees as well as the number of input features. The remaining parameters were set to the default values.

One advantage of the RF algorithm is that it can be used to evaluate the importance of each feature. Figure 4 shows the importance and accumulative importance of all features. The importance decreases sharply with the number of features and is almost negligible after number 300. The first 300 features play important roles in classification, and their accumulated importance reaches 91.2%. Figure 5 shows the distribution of the first 300 features in a spectrum. Those features basically fall on the absorption lines of Ca ii K, H, and transition metal elements, which are considered to be very important elements for distinguishing Am stars.

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We identified the spectral lines where the first 50 feature points are located by consulting the line table (Moore et al. 1966) and other early-type stars literature (Smith 1973; Coupry et al. 1986; Adelman 1994; Przybilla et al. 2017). The details are listed in Table 5. We only listed the main elements contained in spectral lines since metal lines in low-resolution spectra are mostly blended lines. Note that feature numbers and importance are not absolute. Different RF algorithm classifiers will produce different results because the data used by RFs in constructing each decision tree are randomly selected from the training set. Fortunately, their ranking and importance do not change much for most of the important features. It should also be noted that the wavelengths of the features are all in a vacuum because the spectra of LAMOST are all converted to a vacuum wavelength, and you can find the relevant keyword "VACUUM" in the FITS header of the spectra.

Three reasons require manual inspections of the Am candidates obtained using the RF method. First, the intensities of metal lines in Am spectra are very weak and are easily masked by noise, which would lead to errors in the results. Second, although the spectra were rectified, the residual continua still could affect the classification. Third, the precision of the RF algorithm is 0.991, which means there is still a small fraction of stars that might be wrongly recognized.

The specific process of manually inspection is to compare the spectral lines of those candidates with their best-matching synthetic template. A set of quantitative standards is as follows:

$$\begin{eqnarray*}&&\begin{array}{l}\left\{\begin{array}{l}\mathrm{EW}({K}_{\mathrm{spe}})\lt \mathrm{EW}({K}_{\mathrm{mod}})\\ \displaystyle \sum \mathrm{EW}({M}_{\mathrm{spe}})=\displaystyle \sum \mathrm{EW}({M}_{\mathrm{mod}})\\ \end{array}\right.\\ \ \ \ \ \mathrm{or}\\ \left\{\begin{array}{l}\mathrm{EW}({K}_{\mathrm{spe}})=\mathrm{EW}({K}_{\mathrm{mod}})\\ \displaystyle \sum \mathrm{EW}({M}_{\mathrm{spe}})\gt \displaystyle \sum \mathrm{EW}({M}_{\mathrm{mod}})\\ \end{array}\right.\\ \ \ \ \ \mathrm{or}\\ \left\{\begin{array}{l}\mathrm{EW}({K}_{\mathrm{spe}})\lt \mathrm{EW}({K}_{\mathrm{mod}})\\ \displaystyle \sum \mathrm{EW}({M}_{\mathrm{spe}})\gt \displaystyle \sum \mathrm{EW}({M}_{\mathrm{mod}})\\ \end{array}\right.,\end{array}\end{eqnarray*}$$

where K_spe and K_mod are the Ca ii K lines of a spectrum and its matching template, respectively. M_spe and M_mod are metallic lines of a spectrum and its matching template, respectively. EW(·) is the equivalent width of a spectral line.

In this work, we adopted the same EW definition of the Ca ii K line as Liu et al. (2015), the line is in the window of [3927.7–3939.7 Å], and the blue and red sidebands are in [3903–3923 Å] and [4000–4020 Å], respectively. For metallic lines, conventional EW calculation is not suitable because the Fe absorption in A-type stars is generally weak and too narrow to give wavelength bands that EW needs. So we had to use the method proposed by Hou et al. (2015) to calculate their equivalent width. We selected part of the Fe i lines listed in Table 5 by eliminating several Fe i lines that blended with ionized elements. We merged adjacent Fe lines into 15 Fe-group lines and listed the left ends and the right ends of these groups in Table 6. To calculate the EW, sidebands for blue and red are defined in [Left_End-5 Å, Left_End] and [Right_End, Right_End+5 Å], respectively. We limited the sidebands to 5 Å to get the best local pseudocontinuum for each of the 15 Fe-group lines, avoiding affection by other lines. Figure 6 shows an example of a local pseudocontinuum of 15 Fe-group lines.

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Although there are some uncertainties in calculating the equivalent width in batches, such as noise interference in Fe lines or mixing of other metal lines in the Ca ii K line wing, the line ratio of the Ca ii K to Hε or Hδ can be verified as important criteria during manual inspection.

There is some contamination by Ap stars when obtaining Am candidates because of similar spectral features. Most of the Ap stars are actually B-type stars, while a small portion of Ap stars are also found in A- and F-type stars. Among those cooler Ap stars, some also exhibit the characteristics of the overabundance of Fe elements and the underabundance of Ca elements. Therefore, a small amount of Ap stars will be mixed with Am stars.

According to the definition of an Ap star, we thought of objects whose Sr, Cr, Eu, or Si element are extremely abundant as Ap candidates. In general, the abundance of Sr, Cr, Eu, and Si in Am stars rarely exceeds 2.0 relative to the abundance of the Sun (Lane & Lester 1987; Smith 1996; Catanzaro & Ripepi 2014; Catanzaro et al. 2015). Therefore, stars with Sr, Cr, Eu, or Si element abundance exceeding 2.0 are likely to be Ap stars. The detailed method of finding Ap candidates is as follows. First, according to the prominent spectral lines in the blue-violet spectra of Ap stars (Gray & Corbally 2009), and excluding some lines with nearby Fe i lines or other line interference, we selected the 4077 Å line as a reference line, which is a blending line of Sr ii, Cr ii, and Si ii in LAMOST spectra. Second, we generated corresponding synthetic templates by setting the values of [Sr/H], [Cr/H], [Eu/H], and [Si/H] as 2.0 in the spectrum generator SPECTRUM. Stellar parameters that Kurucz model required, such as T_eff, $\mathrm{log}\,g$, and [Fe/H], were taken from the corresponding Am models that have a normal abundance of the above-mentioned heavy elements. Finally, we use the method of Hou et al. (2015) to calculate the EW(tem) and EW(obs) of the 4077 Å blend line for both the templates and observed Am spectra and marked those objects as Ap candidates if their EW(obs) > EW(tem).

For 193,345 spectra of the searching data set described in Section 2.1, we simply fitted with Kurucz templates in the wavelength range of [3900 Å, 5600 Å] to obtain T_eff and $\mathrm{log}\,g$. With the stellar parameters, we can further constrain the searching data set with 6500 K < T_eff ≤ 11,000 K and $\mathrm{log}g\,\geqslant \,4.0$ dex, since the Am phenomenon often occurs in A- and early F-type main-sequence stars. By this constraint, 98,202 spectra were retained, and then the RF classifier was applied to identify 15,269 Am candidates, for which we carried out manual inspections. After these inspections, we discarded 4766 spectra, among which 1338 candidates (28%) do not meet the reference criteria of Section 3.5; 2585 spectra (54%) cannot be recognized by human eyes because of their small peculiarity; and 843 spectra (18%) are of bad spectral quality and are insufficient to identify the Fe line. In addition, using the method described in Section 3.6, we found 1131 objects with an extreme overabundance of Sr, Cr, or Si elements and labeled them as Ap candidates in the catalog. Whether or not they have the nature of Ap needs to be identified by a subsequent analysis of their magnetic field strength. In total, the catalog has 10,503 entries, including 9372 Am stars and 1131 Ap candidates. In the statistical analysis section below, we excluded them from Am stars.

For each Am star in the catalog, we also determined three different spectral subtypes of its K line, H lines, and metallic lines using the template-matching method. The band used to match the spectral subtype of metallic lines is the combined band of [4140 Å, 4300 Å], [4410 Å, 4600 Å], and [4900 Å, 5400 Å]. The matching band for H lines is a combination of the Hβ, Hγ, and Hδ bands. It is worth noting that the spectral subtype obtained by matching with templates in the specific wavelength ranges alone are not completely accurate, and the spectral subtypes of some Am stars do not conform to the common characteristics of Am stars, i.e., the K-line spectral subtype is earlier than the metallic-line spectral subtype. This is why we cannot use this criterion for Am search directly.

The complete catalog of identified Am stars can be downloaded in the online journal and from  http://paperdata.china-vo.org/Qinli/2018/dr5_Am.csv; the example catalog is presented in the Appendix.

We analyzed the effective temperature distribution for these Am stellar samples. Figure 7 shows that the distribution of Am stars and the incidence of Am stars in different effective temperature bins. As can be seen from Figure 7, the results are consistent with the conclusion presented by Smalley et al. (2017)—namely that the temperature of Am stars is mostly distributed between 7250 K (F0) and 8250 K (A4), peaking near 7750 K. Due to our strict screening, the fraction of Am stars to the total A- and early F-type stars is smaller than the values reported in previous studies (Smith 1971; Abt 1981; Gray et al. 2016). The incidence of Am stars we give can be used as the lower limit.

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The spatial distribution of Am stars in the Galactic coordinate plane is plotted in Figure 8. The blue points indicate all A- and early F-type stars, and the red points are for Am stars. As shown in Figure 8, the number of Am stars on the Galactic disk is significantly higher than that in other regions because most of the observations of LAMOST are concentrated on the Galactic disk, especially in the anti-center direction. The LAMOST Spectroscopic Survey of the Galactic Anti-center (LSS-GAC), which covers Galactic longitudes of $150^\circ \,\leqslant {\ell }\leqslant 210$ and latitudes of $| b| \leqslant 30^\circ$, is a unique component of LAMOST Experiment for Galactic Understanding and Exploration spectroscopic survey (Luo et al. 2015).

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In order to further understand the spatial distribution of Am stars, we analyze the frequency of occurrence of Am stars as a function of the vertical distance from the Galactic plane (Z). We obtained the parallax (ω) of most spectra by crossmatching with Gaia DR2. For spectra with a parallax ≥0, we then crossmatched with the catalog in Bailer-Jones et al. (2018) and got their estimated distances. Eventually, we obtained the distances of 92,870 early-type stars and 8951 Am stars. The vertical distance Z for each star can be calculated with the following formula:

$$\begin{eqnarray*}&&Z\,=\,r\times \sin (b),\end{eqnarray*}$$

where b is the Galactic latitude, and r is the estimated distance. In Figure 9, the blue and green histograms show the distribution of early-type stars and Am stars along the vertical distance, $| Z|$, respectively. In each bin, we calculated the incidence of Am stars and represented them as red points. Figure 9 suggests that the incidence of Am stars increases as $| Z|$ decreases.

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We also performed an infrared photometric analysis on these Am stars. First, we crossmatched them with Two Micron All-Sky Survey (2MASS) and Wide-field Infrared Survey Explorer (WISE) catalogs with a matching radius of 3.0 arcsec and obtained the corresponding magnitudes of the J, H, K, W1, W2, W3, and W4 bands. Because the WISE satellite has low angular resolutions of 6.1, 6.4, 6.5, and 12.0 arcsec in the W1, W2, W3, and W4 bands, we often found that one 2MASS counterpart is a different object to the WISE counterpart. In order to avoid this, multiple WISE sources within a search radius of 10.0 arcsec were eliminated. In order to improve the accuracy of the result, the photometric errors were limited to less than 0.1 mag in all three 2MASS bands (Skrutskie et al. 2006) and 0.05 mag in the W1 and W2 bands (Wright et al. 2010). Then, the color excess of all data in the color (a − b) are estimated using the formula: E(a − b) = R(a − b) × E(B − V), where E(B − V) values are given in Schlafly & Finkbeiner (2011), and the R(a − b) values are reddening coefficients of the color (a − b) from Yuan et al. (2013). We calculated color excess and dust reddening of 7799 Am stars for the ($J-H$), ($H-K$), and (W1 – W2) colors. Finally, our conclusions are shown in Table 7. One can see a very clear downward trend in the incidence of infrared excess from the near-infrared to mid-infrared, and the incidence reduces to 0.15% in the W1 – W2 region.

This is in contradiction with the conclusion about Am stars from Chen et al. (2017). They found that over half of Am stars have clear infrared excess ($(W1-W2)\gt 0.1$) in the W1 – W2 region and have little to no infrared excess in the remaining regions, including J, H, K, and IRAS regions. We checked the data set from Chen et al. (2017) and found that they do not restrict the photometric precision to $W{1}_{\mathrm{error}}\,\lt$ 0.05 mag and $W{2}_{\mathrm{error}}\lt 0.05$ mag. When we add this constraint, there are only three sources in Chen's Am data set with infrared excess. Thus, we statistically conclude that Am stars have no infrared excess in the W1 – W2 region.