The First Data Release of LAMOST Low Resolution Single Epoch Spectra

LAMOST DR5 (http://dr5.lamost.org/) is the latest data release before the second stage of the LAMOST survey. The data, including the pilot survey (October 2011 to June 2012) and the first stage of sky survey (September 2012 to June 2017), covers $\sim$17000 deg² from $-10^{\circ}$ to $80^{\circ}$ in declination, as shown in Figure 2.

With its 4000 fibers, LAMOST is able to observe up to 4000 targets simultaneously. A LAMOST plate is a configuration of 4000 fibers consisting of target fibers, sky fibers and empty fibers. According to the brightness of the targets, LAMOST plates are grouped into V (very bright, $r\leq 14$), B (bright, $14<r<16.8$), M (medium, $16.8\leq{r}\leq{17.8}$) and F (faint, $r>17.8$). The typical single exposure durations for V, B, M, F plates are 600, 900, 1200 and 1800 seconds, respectively. Usually each plate is exposed consecutively 2-3 times in the same night to remove cosmic rays and other artifacts. Throughout this paper, these consecutive exposures of the same plate in the same night are defined as one observation. Thus, the same target in two plates is considered to be observed in two observations rather than one even if the two plates were observed in the same night.

Each spectrum released in DR5 is the combination of individual epoch spectra in one observation. Spectra of individual exposures and the corresponding RV and EW measurements were not released. Differing from the ongoing second stage survey, which is a hybrid of low and medium resolution for both regular and time domain survey, spectra in DR5 were observed in low resolution mode of R$\sim$1800 and mostly not designed for time domain survey. Most of the targets were repeated occasionally, usually less than 10 times, as can be appreciated from Figure 2. Figure 2 shows distribution of the number of individual exposures and the time intervals between exposures for repeated observations of a single target. Most of the targets had no more than three exposures in less than 2 hours, i.e., only one observation. 127 thousands targets have more than 10 exposures. Most of the exposures are repeated within 4 hours, and for about 10000 targets, the time lags are longer than 3 years.

There are 9 million flux and wavelength calibrated, sky-subtracted spectra in DR5, including 8 million stars. Stars were observed in all spectral type and the range of magnitude in $r$ band is $9\sim 20$ (Figure 3). For 5.3 million of them, mostly of which are A, F, G, K type stars within the temperature range of 3700 $\sim$ 8500 K, the basic stellar parameters such as effective temperature ($T_{\mathrm{eff}}$), surface gravity ($\mathrm{log}\textit{ g}$), metallicities ($[\mathrm{Fe/H}]$) and RVs are provided in the DR5 Parameter Catalog (hereafter DR5PC), while for the rest stars in DR5GC, the stellar parameters are not available. $T_{\mathrm{eff}}$, $\mathrm{log}\textit{ g}$ and $[\mathrm{Fe/H}]$ cover the range of 3700 $\sim$ 8500 K, 0 $\sim$ 5 dex and -2 $\sim$ 1 dex, respectively. Comparing with APOGEE data, the error of $T_{\mathrm{eff}}$, $\mathrm{log}\textit{ g}$ and $[\mathrm{Fe/H}]$ for the stars with SNR greater than 100 are 70 K, 0.14 dex and 0.06 dex, respectively, deteriorating to 107 K, 0.23 dex and 0.1 dex for stars with SNR in the range of 30 to 50 ³³3http://dr5.lamost.org/v3/doc/release-note-v3. Figure 4 shows the distribution of stars in the HR diagram ($T_{\mathrm{eff}}$ vs $\mathrm{log}\textit{ g}$) of DR5PC.

Lights from 4000 fibers are fed into 16 spectrographs, each holding 250 fibers. In the low resolution mode, the light beam is split into blue (3700-5900Å) and red (5700-9000Å) by a dichroic mirror in each spectrograph. Each segregated beam is then dispersed by a volume phased holographic grating and finally focused on a 4K$\times$4K CCD through a Schmidt camera respectively. Since the light path thus the instrument effect is different for the targets on different CCD, each CCD image is processed independently in the data reduction pipeline. The raw data are first processed by the LAMOST two-dimensional data reduction pipeline (2D pipeline), which is a part of LAMOST data pipeline. The basic data reduction steps and the relationship between different parts of the pipeline are laid out in the flow chart of Figure 5.

Each CCD image is first bias subtracted, then cosmic rays are rejected by a two-dimensional profile fitting method ([Bai et al., 2017a]). For each row in the spatial direction, the scatter light is sampled in the pixels of dead fibers and those between the fiber trace then interpolated to all the pixels. The final scatter light is filtered by a 5 by 5 median boxcar and subtracted from the 2D image. This step is applied to both the flat field and object images. The fiber traces are first derived from the flat field image taken at twilight in the zenith direction. Then for each individual exposure image, the fiber trace is adjusted in the spatial direction to better match the profile center in the object image. Spectrum for each fiber is then extracted by integrating a weighted aperture of 15 pixels along the corrected fiber trace. Arc lamps (Hg/Cd for blue and Ne/Ar for red) taken at the beginning, middle and the end of the observation night are used to calibrate the wavelength. Wavelength solutions are interpolated to derive the wavelength of the spectra taken between the arc lamps. The wavelength is further tweaked by the sky emission lines in both red and blue spectra. The overall wavelength calibration accuracy is less than 5 km s^-1 ([Bai et al., 2017b]). The final output wavelength is corrected to the heliocentric frame in vacuum. The fiber-to-fiber relative throughput are corrected by the flat field and further adjusted by sky emission lines. The sky background spectrum built from sky fibers is subtracted from object spectra after careful wavelength and throughput correction. The detail of wavelength calibration, throughput correction and sky subtraction algorithm could be found in [Bai et al., 2017b].

In DR5, the flux calibration curve is obtained through the selected F-type flux standard stars and their corresponding templates. The blue and red sky-subtracted spectra are divided by their respective curves, and then stitched together. The results of the 2D pipeline, i.e., the co-added spectra, are then analyzed by the LAMOST one-dimensional data pipeline (1D pipeline) and the LAMOST Stellar Parameter pipeline (LASP, [Wu et al., 2011]) to derive their spectral type and basic parameters. The single epoch spectra released in this work are the intermediate produce of the 2D pipeline. The spectra in blue and red are released separately and not flux calibrated. We attached the flux calibration curve in the data product (see section 5), so the flux could be relatively corrected if necessary. The measurements of RV and EW are discussed in the following sections.

As many as 60 elemental lines are measured, whose wavelengths and sources are listed in Table 1. Some blended lines are not measured because they cannot be independently separated at the low resolution mode ($\Delta\lambda$=2.8Å @ 5000Å  and $\Delta\lambda$=4.4Å @ 8000Å), such as Mg lines ($\lambda 5167,5172,5183$), Na doublets ($\lambda 5890,5896$ and $\lambda 8183,8194$). The blended lines will be measured with an alternative method in the future work. To be mentioned, He $\lambda 3888$/H $\lambda 3889$ and Fe $\lambda 4920$/He $\lambda 4921$ have the close wavelength values that we treat them as single lines. We do not judge which elements they come from or decompose them.

Given a spectrum from LAMOST single epoch data, it is first normalized to remove the continuum. A certain range around each line is fitted by a symmetric function to measure the line center and calculate the full width at half maxima (FWHM). Then the spectrum within a certain width is added up to obtain EW. The details are as follows.

Normalization. Blue and red branches are normalized separately. For each branch, the whole spectrum is first median-filtered by a 9-pixel window to remove the outliers. Then a 15-order polynomial, iteratively fitted with both absorption and emission lines rejected, is taken as the continuum and divided.

Fitting range. We use a symmetry function to fit each line. Before that, we need to determine the range of fitting. Since the width of the lines varies between stars by temperature, gravity and rotation, etc, there is no universally applicable range to measure all the lines in different types of stars. To avoid the complexity of measuring any single line with a set of fixed window size, we develop a method to measure the EW of lines with an adaptive window size. To determine the proper fitting range, the normalized spectrum is temporarily smoothed by a median-filter with the width of 5 pixels. For a line with the wavelength of $\lambda$, the range from $\lambda-1.5\lambda_{r}$ to $\lambda+1.5\lambda_{r}$ is initially selected, where $\lambda_{r}$ is the resolution of the spectrum. For LAMOST, the resolution is $R\sim$1800, so we adopt 3.0Å and 4.5Å for blue and red branches, respectively. The boundaries of the initial range continue to grow until the flux begins to significantly cease to increase for an absorption line or decrease for an emission line, and the final range is determined.

Fitting. The segment of the normalized spectrum within the fitting range is then fitted with a Sérsic profile ([Sérsic, 1968]) added by 1, as described in Eq. 1, where $a$, $\lambda_{0}$ is the intensity and center of the line, $\sigma$ and $\delta$ are two parameters. The Pearson correlation coefficient (CC) between the spectrum and the fitted profile is calculated when the fit is successful. Generally, CC greater than 0.9 indicates that the fit is reliable while lower CC means worse fitting. Since the calculation of EW is based on the fitted profile (see below), EW is not calculated if the fit fails or the Pearson CC is less than 0.7.

Calculation. Once the line is successfully fitted, FWHM is calculated. EW is defined as the integration of the normalized spectrum subtracted by 1 over the wavelength region $|\lambda-\lambda_{0}|<2\lambda_{\mathrm{FWHM}}$. The line wing beyond this region is not used due to its much less contribution and larger uncertainty. The integration is consist of two parts. For the line core ($|\lambda-\lambda_{0}|<\lambda_{\mathrm{FWHM}}$), the integration is performed on the actual spectrum to account for the possible second component (e.g. emission core). While for the outer part of the line ($\lambda_{\mathrm{FWHM}}\leq|\lambda-\lambda_{0}|<2\lambda_{\mathrm{FWHM}}$), the fitted profile is used instead to calculate the integration to avoid the influence of weaker lines of other elements. If the line is an emission, the EW is set to be negative. The error of the EW is calculated based on the error cumulation formula.

Considering the huge difference of line width of different elements due to different broadening effect (e.g. thermal, pressure and rotation), it is not possible to use a uniform width to measure EWs for different elements lines in various stellar types. There are two ways to meet this challenge: using an adaptive width like in this work, or using a series of fixed wavelength width, as used in the SSPP (the SUGUE Stellar Parameter Pipeline, [Lee et al., 2008]). Figure 6 gives two examples, for a K7 star and an A5 star, respectively. For the late type stars, since the Balmer lines are relatively weak, the wings contribute much less than the core to the EW, so the adaptive method could exquisitely choose the width neither too wide to contain nearby lines nor too narrow to miss any core region. The same is true for the early type stars, where the Balmer lines are much stronger and there are less metal lines in the wing. The wavelength region to calculate EW ($|\lambda-\lambda_{0}|<2\lambda_{\mathrm{FWHM}}$) looks narrow for early type stars, leading the EWs to be underestimated but with a certain fraction to the real EW. We did not try to include more wings for the Balmer lines, since the wings may be affected by both other lines and the uncertainty in the continuum determination especially when the resolution is low.

In Figure 7 and Figure 8, the comparison between EW from adaptive width (hereafter EWaw) and EW of four fixed widths, i.e., 12Å, 24Å, 48Å and 70Å (same as the width selected in [Lee et al., 2008], hereafter EW12, EW24, EW48 and EW70, respectively), of H$\alpha$ lines from A and F star are present. From the figures, we can see that scatter increases with the increasing of the width, caused by the pollution of metallic lines and the uncertainty in the continuum determination of the line wings. For A-type stars, EWaw agrees well with EW12 and EW24 where EW is less than 4Å and where EW is larger than 7Å, respectively. EW48 and EW70 show linear correlation with EWaw, but systematically higher, indicating that EWaw could cover most of the width range, but with slightly underestimate. For the case of F-type stars, EW12 agrees well width EWaw where EW is less than 4Å and begin to be underestimated as EW grows. Since H$\alpha$ is weaker but the metallic line in the wings are stronger than A type stars, EW24, EW48 and EW70 obviously could not properly measure the real EW and the EW grows larger when more line wings are included. From the figures, we can see that neither of the four fixed width could properly measure the EW considering the various width of the H$\alpha$ line. By using adaptive width we could measure the line EW in different width with higher accuracy and smaller uncertainty.

A uniformly defined EW is more convenient to do comparison between different elements and stellar types. As shown in Figure 9, there is a clear correlation between EW of H$\alpha$ and effective temperature of all LAMOST single epoch spectra in DR5PC. When $T_{\mathrm{eff}}$ is lower than 4300 K, giants and dwarfs could be clearly separated by their EWs.

For stars hotter than F, Balmer lines are more important in RV measurements than in cooler stars, because they are the dominating lines and the metal lines are weak. The pure emission lines are masked out during measuring the RV of a star. Abnormal Balmer lines, such as emission line embedded in an absorption line or double absorption lines of double-line spectroscopic binaries (SB2), can lead to errors in RV determination. The cases of stellar absorption line mixed with emission line, which originates mainly in (1) stellar envelopes or outer stellar atmospheres, (2) stellar activities and (3) binary interaction, are more popular in abnormal Balmer lines than SB2s. In the case of SB2, only when the brightness of the two components is similar and the RV difference is greater than the resolution, can it be observed, which requires that the mass ratio of the two components is close to 1 and they are in special phases in their orbit. These conditions make the probability to observe SB2 very small.

For the cooler stars, the Balmer lines are weak and the line cores are usually narrower than 100/kms ([Moss & Smith, 1981]), and the line wings are polluted by metal lines. They look narrow and appear in either pure emission or absorption in the low resolution mode, thus it is hard to separate the emission from the absorption line. Also the abnormal Balmer lines will not lead to errors in the RV measurement, since there are enough metal lines even when the hydrogen lines are masked. Due to these reasons, we do not try to identify the second component of Balmer lines for stars later than F-type.

We use the following procedure to identify the abnormal H$\alpha$, H$\beta$, H$\gamma$ and H$\delta$ for the stars earlier than or equal to the F-type. First of all, an initial line range is defined depending on the stellar type. Because A-type stars have the strongest Balmer lines among all types, a wider range is applied to A star than others. The range for O, B, A, and F types is set to be 60, 60, 100, 60Å, respectively. Given a spectrum, the local pseudo-continuum of the Balmer line is derived by fitting a fourth-order polynomial to the segments about 200Å beyond the initial range. The local pseudo-continuum is then divided to obtain the normalized spectrum $f$.

As indicated in Figure 10, a spectral line could be detected by searching the segments of ascending and descending pairs. Both emission and absorption contain a pair of an ascending segment and a descending segment. For spectrum $f$, we define $\Delta{f}$ as follows,

where $e$ is the error of corresponding $f$. A successful detection of an(a) ascending(descending) segment requires at least 5 consecutive pixels (2.5Å) of $\Delta{f}=1(-1)$. If segments length is less than 5 pixels, $f$ is smoothed with a median filter of 3-5 pixels and $\Delta{f}$ is recalculated to see if the 5-pixels-length condition could be met. If more than one pairs of segments are detected within the wavelength range, the line is very likely to be abnormal. Segments are combined into pairs according to Table 2. Each pair is first fitted by a Sérsic profile $\hat{f}$, then subtracted from $f$. The residual $r=f-\hat{f}$ is then fitted by a new Sérsic profile, $\hat{r}$, so the fitted profile is $f-\hat{f}-\hat{r}$. The goodness of the fit is evaluated by the reduced $\chi^{2}$. Among all combination of pairs, the one with the smallest reduced $\chi^{2}$ is considered as the best fit.

It turns out that the combination of an emission and an absorption line always give a better fitting than double absorptions. This agrees with that in the low resolution mode most binaries are single-lined spectra. But caution must be taken that some real double-lined binaries might be misidentified as an embedded emission and an absorption. This is because two absorption solution usually includes a pair of unsymmetrical segments, leading to larger residual than using combination of symmetric emission and absorption profile. So for these relative rare cases, current fitting might be wrong. We leave the disentangling of double-lined binary for the future work. The outer wing of the fitted profile and the central part of the actual spectrum are used to calculate the EW, similar to Section 3.2. The RV of the emission and the absorption are measured respectively. Figure 11 shows several examples of the absorption and emission combo, in which the first sample is the fit of Figure 10.

Balmer emission line can have complex structure, such as Smak profile of a disk ([Smak, 1969]) or P Cygni profile of strong stellar wind, although most of these profiles will not show too much difference with a single emission line added on an absorption in the low resolution mode. We did not try to decompose the different components of these complex Balmer lines. The primary purpose of the detection is to measure EW correctly and remove the abnormal Balmer bands in the following calculation of RV.

The wavelength bands to calculate the cross-correlation function (CCF) for stars hotter than G stars are 4000-5300Å and 6350-7000Å, for those cooler than K are 4550-5300Å and 6350-9000Å. To remove the pixels with low SNR, only the segments that have more than 40 consecutive pixels with SNR greater than 5 are retained. The obvious DiB bands (4431Å, 5782Å, 5798Å, 6285Å, 6616Å), telluric bands (A band at 7560$\sim$7720Å, B band at 6850$\sim$6960Å, as well as 7150$\sim$7350Åand 8105$\sim$8240Å), strong sky emission lines, nebular lines and the detected emission lines (described in Section 3.2 and 3.4) are masked in the calculation. Note that caution should be taken when using data earlier than 2012 Jan 14. Due to a problem with Ne/Ar lamp, only the wavelength calibration in the blue part is reliable. For these data, only 4000-5300Å  band is used to measure RVs for all type of stars. The RVs might have large uncertainty for late type stars or spectra with low SNR in that wavelength range.

The overall template selection scheme is summarized in Figure 12. For each star, an appropriate template is chosen according to the spectral classification of 1D pipeline. For the stars in DR5PC, since the basic stellar atmosphere parameters are provided, the templates are constructed from the corresponding Kurucz model with resolution degraded to R$\sim$1800. For other stars in DR5GC, the stellar parameters are not available. Since the CCF method is not sensitive to $\mathrm{log}\textit{ g}$ and $[\mathrm{Fe/H}]$ in the low resolution mode, their $\mathrm{log}\textit{ g}$ and $[\mathrm{Fe/H}]$ are fixed to 4 and 0, respectively, and $T_{\mathrm{eff}}$ is determined by their stellar sub-class ([Gray & Corbally 2009]), as in Table 3. For seven special types listed in DR5GC, including Carbon, CarbonWD, CV, DoubleStar, WD, WDMagnetic and Non, due to lack of corresponding template, the RVs are not released, only the single epoch spectra are available. For the remaining stars, various stellar atmosphere template are used according to their typical $T_{\mathrm{eff}}$. For stars with typical $T_{\mathrm{eff}}$ higher than 15000 K, the templates are generated by TLUSTY model of hot stars ([Lanz & Hubeny, 2007]) with a set of $v\mathrm{sin}i$ from 100 km s^-1 to 200 km s^-1 in a step of 20 km s^-1. The same $v\mathrm{sin}i$ grids are constructed for templates of stars with $T_{\mathrm{eff}}$ in the range of 7500K to 15000K, but with the Kurucz model. For $T_{\mathrm{eff}}$ between 5000K and 7500K, we use Kurucz templates with no rotation. For stars cooler than 5000K, the dwarf model from BOSS ([Kesseli et al., 2017]) is adopted.

RV is calculated by minimization of $\chi^{2}$ between the normalized spectra and the RV-shifted normalized template. To reduce the computing time, the calculation is performed in two rounds. In the first round, the RV grid added to the template is -1500 km s^-1$\sim$1500 km s^-1 with a step of $\Delta{\log\lambda}=0.0001$ ($\Delta{v}=69$ km s^-1). Then $v_{b}$, the RV with the minimum $\chi^{2}$, is selected as the peak of the first round. In the second round, in the range of $v_{b}-138$ km s^-1$\sim{}v_{b}+138$ km s^-1, we use a grid of $\Delta{\log\lambda}=0.00002$ ($\Delta{v}=13.8$ km s^-1), as shown in Figure 13. The bottom of the $\chi^{2}$ curve is fitted by a Gaussian function to find the minimum and the fitting error. The minimum is regarded as the final RV. The error of the final RV is the square root of the sum of the squares of two factors. One is the fitting error of the profile center of the Gaussian function and the other is the formal error where $\Delta\chi^{2}=1$.

We first compare our single epoch RVs with those released in DR5PC, for which the co-added spectral SNR of the $g$ band is required to be greater than 20. The results is shown in Figure 14. The RV of this work is 0.5 km s^-1 larger than the RV in DR5PC, with a standard deviation of 2.2 km s^-1. Considering the resolution unit is about 170 km s^-1, there is no system difference between the DR5PC RV and the RV in this work.

The RV differences between different exposures of the same star are used to estimate the RV measurement error. The RV uncertainty depends on the number and width of the absorption lines in the spectrum, so the most important factor affecting the RV accuracy is the spectrum type, although $\mathrm{log}\textit{ g}$ and $[\mathrm{Fe/H}]$ also play a smaller role. Due to the relatively small size of the hot star samples, only stars of A, F, G, K and M types are included in the statistics. For different exposures on the same day, the typical time span between different exposures is less than 2 hours, as shown in Figure 2. The same object is usually observed in the same fiber and the instruments are stable within the short period. While for exposures in different days, the situation is more complex. Many reasons can result in the difference in RV measurement. For example, the temperature difference could cause the shift of the spectrograph and a slow decay of the image quality. The profile difference between different fibers in different date leads to a wavelength calibration error of a few km s^-1. To better represent the actual RV error, we distinguish the RV differences on the same day from those in different days.

We make statistics of the RV difference depending on the spectral types under different SNR ranges. For a certain range, only the two spectra whose SNR are both in this range can participate in the statistics. No systematic difference is found between exposures for all type of stars, indicating that the wavelength calibration is stable over the first stage of the LAMOST survey. The standard deviations are shown in Figure 15 and Table 4. As can be seen in Figure 15, hotter stars have larger scatter since there are fewer absorption lines and the lines are broader as the temperature increases. It also could be noticed that the RV accuracy increases with the SNR of the spectrum. For the spectra with SNR greater than 10, the deviations from different days are less than 10 km s^-1 for all types but A stars, for which the scatter is 14.41 km s^-1 when the SNR is between 10 and 20. For G, K and M stars, the RV accuracy is higher than 10 km s^-1 when SNR is higher than 5. Figure 15 and Table 4 could be used as a standard to select RV variation stars. Because SNR of both the two spectra are in the same range, their RV uncertainties are in the same level, so that the RV difference is approximately $\sqrt{2}$ times the RV uncertainty.

There are a few issues needed to be aware of when using the data. First, the pollution from the bright adjacent fibers could affect the RV measurement. The spectra polluted by their bright neighbor usually have obvious irregular features, such as abnormal continuum, large residual of the telluric bands, or wrong spectral lines. One can use the ratio of the flux to the stronger neighbor (included in RV data) to see if the fiber is possibly affected. Second, early type stars which have strong Balmer emission lines may have bad RV measurements since hot stars are lack of other absorption lines. Once the emission component is detected in H$\alpha$, other Balmer absorption lines could also be polluted even if no emission component is detectable, leaving the RV measurement to be biased. Third, the RV may be wrong due to the strong sky background if the exposures are taken in the condition that is not good for astronomical observation, e.g. in nearly full moon nights, too close to the Moon, or beyond astronomical twilight. Information about the observation, including the position of the Sun, the Moon as well as the Moon phase, can be browsed online.