LAMOST SPECTROGRAPH RESPONSE CURVES: STABILITY AND APPLICATION TO FLUX CALIBRATION

Work by Xiang et al. (2015) shows that variations of the SRCs exist. This is done by using stars in highly dense fields; however, these suffer from high interstellar extinction. However, to study the variations of the SRCs, one should use stars with less extinction. Therefore, we selected stars at high Galactic latitude to analyze instrument response (Fitzpatrick & Edward 1999; Fitzpatrick & Massa 2007).

To obtain a good approximation of the ASPSRCs, we require as many flux standard stars possible. To ensure the quality of the sample, the stellar parameters of LASP (Wu et al. 2011a, 2011b) were used to select the F stars with the highest signal-to-noise ratios (S/Ns). We selected stars with 6000 K ≤ T_eff ≤ 7000 K, log g ≥ 3.5 dex, and Galactic latitude $| b| \geqslant 60^\circ$. This resulted in 29,526 targets with 37,931 pairs (blue and red arm) of single exposures. For the ASPSRC, we have enough stars in the temperature range 6000 K ≤ T_eff ≤ 7000 K, so we do not need to extend to 5750 K ≤ T_eff ≤ 7250 K as the 2D pipeline does. Metallicity mainly affects the blue-arm spectra at wavelengths less than 4500 Å. An error of 0.2 dex in [Fe/H] can change the spectral energy distribution (SED) shape between 3800 and 4500 Å by approximately 3%, while the effects at wavelengths greater than 4500 Å are only marginal (Xiang et al. 2015). The ASPSRCs are derived from a great number of standard stars instead of a group of several standards in the 2D pipeline, and 90% of the metallicities are in the range of [Fe/H] ≥ −1.0 dex, from which the averaged SRCs are generated. The accuracy of the parameters measured by LASP is good enough even for metal-poor stars and will not affect the averaged result. Thus, we did not use a metallicity cut in this sample selection.

With the benefit of the large sample of targets that satisfied the above parameter space, we find that there are sufficient and appropriate exposures across all fibers and spectrographs to allow us to use them as standards. Figure 1 shows the histogram of the number of standards per spectrograph from DR2, which indicates that there are at least seven standards per fiber (with 250 fibers in each spectrograph, this is equivalent to at least 1750 individual exposures, shown in Figure 1). Figure 2 shows the histogram of their effective temperatures, mostly located in the vicinity of 6100 K (i.e., F8-type stars).

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Let F_o(λ) and F_i(λ) denote the measured and intrinsic spectral flux density; thus,

$$\begin{eqnarray}&&{F}_{o}(\lambda )={d}_{s}(\lambda ){d}_{p}(\lambda ){F}_{i}(\lambda ),\end{eqnarray} \tag{ 3 }$$

where d_s(λ) is the combined atmospheric and interstellar extinction and d_p(λ) is the telescope and instrumental response. In this work, we adopted synthetic flux as F_i(λ), which is calculated using SPECTRUM based on the ATLAS9 stellar atmosphere model data released by Fiorella Castelli. The synthetic spectra of 1 Å dispersion from the library of KURUCZ were used, and then the spectra were degraded to the LAMOST spectral resolution by convolving with a Gaussian function. Only those with a constant microturbulent velocity of 2.0 km s⁻¹ and a zero rotation velocity were adopted, since these two parameters have little effect on the SED at a given temperature (Grupp 2004).

The interstellar extinction can be neglected owing to our selection of high-latitude standards; however, the atmospheric extinction cannot be separated from instrumental response. The SRCs in this paper include atmospheric extinction, and their variations are included in the uncertainty of the SRCs.

It is generally assumed that the SRCs are smooth functions of wavelength. In order to derive the SRCs, we applied a low-order piecewise polynomial fitting to the ratios of the observed and the synthetic spectra of the standard stars. Figure 3 shows examples of the SRC fitting for one fiber in both arms. For each standard star, the blue- and red-arm spectra were divided into five and six wavelength regions, respectively, and each region was fitted with a second- or third-order polynomial, which are represented by the thick colored lines in Figure 3. The piecewise polynomials were derived through minimizing ∣ synthetic×polynomial−observed ∣. We defined a series of clean spectral regions, avoiding the prominent stellar absorption features and the telluric absorption bands. The fitted polynomial values of data in these clean regions are indicated by asterisks in Figure 3, which were used for the final SRC fitting. The wavelengths of the join points were fixed to space between 200 Å for adjacent spectral regions, and the overlaps were median filtered to join together the adjacent regions. The final SRCs are represented by the black curves in the insets in Figure 3.

Zoom In Zoom Out Reset image size

For the 250 fibers in each spectrograph, at least 1800 good SRCs (through multi-exposures) were derived (excluding the bad fibers). We chose the fitted SRCs rather than the direct ratios of observed and synthetic to estimate the ASPSRC because the direct ratios are susceptible to noise. We concentrate on the relative flux calibration rather than absolute flux calibration, such that, for a given spectrograph, SRCs yielded by the spectra of the individual standard stars were divided by the average of their SRCs (i.e., the SRCs were scaled to a mean value of unity). It is generally assumed that the differences in the sensitivity of the individual fibers are well corrected via flat-fielding and thus the 250 fibers of a given spectrograph share a single SRC. Accordingly, the SRCs of the fibers can be regarded as independent measurements of the SRC; thus, the ASPSRC and uncertainties can be derived by traditional statistical methods. The means and standard deviations of the Gaussian functions in Figure 4 give three examples of the spectral response and uncertainty estimation at wavelength point 4000, 4500, and 5000 Å of spectrograph no. 1. All wavelength points contribute to the final ASPSRC for a spectrograph, and the red curves in Figures 5–8 show the blue- and red-arm ASPSRCs of the 16 spectrographs.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

We expect that there is a unified response for a given spectrograph during exposures of different times and using different plates. The red curves in Figures 5–8 are more likely to be, at least, very close to the SRCs of the instrument including the atmospheric extinction, which means that the ASPSRCs derived can be used to calibrate the plates that lack standard stars. Some ASPSRCs drop deeply on the edges due to the very low sensitivities of the instrument, which is the most challenging problem for LAMOST flux calibration.

We calculated the mean values of absolute and relative uncertainties for g, r, and i bands, which are presented in Table 1. Table 1 shows that for all 16 spectrographs, the uncertainties are smaller than 8% for both g and i bands. The r band is located at the edge of both arms, and thus, due to the low sensitivities, the uncertainties for r band are much larger (e.g., spectrograph no. 5 can differ by up to 11.13%). This means that the fluxes and centroids of the lines located at the junction of the blue and red arms (such as Na D at 5892 Å) are sometimes not credible.

Generally, the LAMOST observational season spans 9 months from September to June. The DR2 collected the observed data from 2011 October to 2014 June, and there are nine quarters in total (about 3 consecutive months for a quarter). We calculated ASPSRCs for each quarter (hereafter called Quarter ASPSRC to distinguish from DR2 ASPSRC) and compared these nine Quarter ASPSRCs with the DR2 ASPSRC for each spectrograph. The distributions of residuals between the nine Quarter ASPSRCs and the DR2 ASPSRC are shown in Figures 9–12 (blue arm in left panel and red arm in right panel). The figures show that there are not obvious gradual and systematic errors along with time. Still, we can conclude that spectrographs no. 4, no. 11, no. 15, and no. 16 are more stable than others during the DR2 period.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

To improve the S/Ns and overcome the effect of cosmic rays, each field is designed to be exposed multiple times. The spectra of each single exposure may be on different scales due to the variation of observational conditions. The spectra on different scales cannot be co-added since they are divided by the same ASPSRC. Figure 13 shows the spectra of six exposures. Not only are the scales of exposures different, but also the scales of the two arms are discrepant. For the LAMOST 2D pipeline, the single-exposure spectra are scaled to the median of the multi-exposures. Here we try to scale the blue and red bands according to the photometry of the g and i bands, respectively.

Zoom In Zoom Out Reset image size

The monochromatic AB magnitude is defined as the logarithm of a spectral flux density with a zero point of 3631 Jy (Oke & Gunn 1983), where 1 Jy = 10⁻²⁶ W Hz⁻¹ m⁻² = 10⁻²³ erg s⁻¹ Hz⁻¹ cm⁻². If the spectral flux density is denoted f_ν, the monochromatic AB magnitude is

$$\begin{eqnarray}&&{m}_{\mathrm{AB}}(\nu )=-2.5\ {\mathrm{log}}_{10}{f}_{\nu }-48.60.\end{eqnarray} \tag{ 4 }$$

Actual measurements are always made across some continuous range of wavelengths. The bandpass AB magnitude is defined similarly, and the zero point corresponds to a bandpass-averaged spectral flux density of 3631 Jy:

$$\begin{eqnarray}&&{m}_{\mathrm{AB}}=-2.5\ {\mathrm{log}}_{10}\left(\displaystyle \frac{\int {f}_{\nu }{(h\nu )}^{-1}e(\nu )d\nu }{\int 3631\,\mathrm{Jy}{(h\nu )}^{-1}e(\nu )d\nu }\right)\end{eqnarray} \tag{ 5 }$$

where e(ν) is the equal-energy filter response function. The (hν)⁻¹ term assumes that the detector is a photon-counting device such as a CCD or photomultiplier. The synthetic magnitude can be obtained by convolving the flux spectra with the SDSS g- and i-band transmission curves (Hamuy et al. 1992, 1994). We adopted the g and i filter zero points from Pickles (Pickles 2010). The spectra are then scaled by comparing the synthetic magnitude with the photometry magnitude. The scale coefficients SC(g) and SC(i) are obtained as follows and are multiplied with observed spectra:

$$\begin{eqnarray}\mathrm{SC}(g) & = & {10}^{-0.4\times [\mathrm{mag}(g)-{\mathrm{mag}}_{\mathrm{synthetic}}(g)]};\\ \mathrm{SC}(i) & = & {10}^{-0.4\times [\mathrm{mag}(i)-{\mathrm{mag}}_{\mathrm{synthetic}}(i)]}.\end{eqnarray} \tag{ 6 }$$

The specta of Figure 13 were scaled using the method described above. The rescaled spectra can then be co-added and the final spectra derived, which is shown in Figure 13 (bottom panel). It should be noted that this method is subject to the S/N of the spectra, since the synthetic magnitudes depend on the quality of the spectra.

This method needs the g- and i-band photometry magnitudes for each target; thus, we cross-matched LAMOST targets with Pan-STARRS1 (Tonry et al. 2012) within 3 mas. The LAMOST sources are selected from multiple catalogs with multiband photometry. Consequently, not all the LAMOST targets overlap Pan-STARRS1. By cross-matching, we found that about 80% of the LAMOST targets are included in Pan-STARRS1. For those targets not in the Pan-STARRS1 catalog, SDSS PetroMag ugriz had been adopted. About 60% of the LAMOST targets have overlapping observations with SDSS. However, still about 10% of the LAMOST targets are included neither in Pan-STARRS1 nor in SDSS, and it is difficult to obtain their photometry in the optical band. For LAMOST, the efficiencies of the blue and red arms cannot be normalized by flat-fielding since the throughputs of the two arms for each spectrograph are different and vary when the telescope pointing changes. The flat fields of the two arms for each spectrograph are processed independently. Using photometry, we can avoid a big scale jump between the two arms, although there are some photometry errors. Without the reference of photometry, we can only use the overlap between the blue and red arms in a very small wavelength range to connect them, which might lead to a piecing discontinuity if the S/N is too low in the overlap.

For the final spectra, spline fitting with strict flux conservation is adopted to rebin the spectra to a common wavelength grid. Once the flux is co-added by this method, the blue and red arms are pieced together directly and the SEDs are consistent with their target colors. For the ones that do not have photometry in the optical band but have multiple exposures, we scaled the flux of multi-exposures to the flux of exposures with the highest S/N. After the multi-exposures have been co-added, the blue and red arms are pieced together, adjusting one of the scales (using the overlaps) to yield the final spectra.

Before discussing the accuracy of the ASPSRCs, we studied the SRCs of the DR2 plates, which are derived from the LAMOST 2D pipeline, to further confirm the stability of the LAMOST spectrograph response curves. Figures 5–8 show the distributions of the SRCs of the DR2 plates for high Galactic latitude (left panel) and for low Galactic latitude (right panel); the standard deviations of the SRCs, as a function of wavelength, are shown by the red dashed curves.

As described in Section 2.3, we used stars with high Galactic latitude and with high S/N to get the ASPSRCs. The red solid curves in Figures 5–8 represent the ASPSRCs, and it is consistent with the average SRC of the SRCs from the LAMOST 2D pipeline. Table 1 shows that the mean uncertainties of ASPSRCs are smaller than 10%, which are consistent with the 1σ uncertainties of the SRCs at high Galactic latitude from the 2D pipeline.

To verify the feasibility of applying the ASPSRCs to the flux calibration, we selected stars observed by both LAMOST and SDSS. We cross-matched the abandoned targets of LAMOST DR2 with SDSS DR12 and obtained 1746 spectra of 1702 stars with S/Ns higher than 6. We have calibrated the LAMOST spectra abandoned by the 2D pipeline and divided them by the spectra of the same sources from SDSS. The ratios of the two spectra were calculated and then scaled to their median values of unity, and the results are shown in Figure 14. The ratios yield an average that is almost constant around 1.0 for the whole spectral wavelength coverage except for the sky emission line region; oxygen and water vapor bands of Earth's atmosphere are attributed to the uncertainties of flat-fielding and sky subtraction. The standard deviation is less than 10% at wavelengths from 4500 to 8000 Å, but for both edges the standard deviation increases to 15% due to the rapid decline of the instrumental throughput. The results show that flux calibration using ASPSRCs has achieved a precision of ∼10% between 4100 and 8900 Å.

Zoom In Zoom Out Reset image size

For the bright and very bright plates, most can be calibrated successfully by the 2D pipeline. However, for LAMOST faint plates (F-plates) of DR2, the flux calibration failure rate of the 2D pipeline is around 9%, and for the medium plates (M-plates), the failure rate is around 8%. Figures 15–17 show the spectra of galaxies, QSOs, and stars rescued from the abandoned plates. We compared the rescued spectra with those of SDSS DR12 (the former are plotted with black curves, and the latter are represented with red curves). Most match with their corresponding SDSS spectra quite well, with differences of only a few percent for their continua. For LAMOST 20130208-GAC062N26B1-sp13-112, the spectra of the red arm have turbulent components for spectrograph no. 13; this is explained by the spectrograph having problems caused by the cooling system of the CCD. For LAMOST 20140306-HD134348N172427B01-sp10-014, the SED from the ASPSRC method is bluer than that of SDSS. We believe that this is due to the fact that we do not separate Earth's atmospheric extinction from the response of the spectrograph. Generally, the variations of the optical atmospheric extinction curve can be calculated by low-order polynomials (Patat et al. 2011). The atmospheric extinction curve included in the ASPSRC is an average one, and multiplication by a low-order polynomial is required to obtain the real atmospheric extinction curve when the target is observed. Therefore, some spectra calibrated using the ASPSRCs need low-order polynomials to match SDSS spectra. The atmospheric extinction of LAMOST will be deeply studied and integrated into this work.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Overall, the ASPSRC flux calibration has achieved a precision of ∼10% for the LAMOST wavelength range. The potential uncertainties and temporal variations of the atmospheric extinction generally do not have an impact on the final accuracy of spectral lines, although they do affect the shapes of SEDs deduced (low-order polynomials).

For the LAMOST DR2, there are 1095 spectrographs with 385 plates that have been abandoned by the 2D pipeline due to the failure of finding standard stars. We started with the 2D pipeline for fiber tracing, flux extraction, wavelength calibration, flat-fielding, and sky subtraction. The ASPSRCs were then adopted to calibrate the 195,694 spectra in 1095 spectrographs. After the flux calibration and the co-add, the LAMOST 1D pipeline was employed to classify the spectra and measure the radial velocity for stars and the redshift for galaxies and QSOs. Based on a cross-correlation method, the 1D pipeline recognizes the spectral classes and simultaneously determines the radial velocities or redshifts from the best-fit correlation function. The 1D pipeline produces four primary classifications, namely, STAR, GALAXY, QSO, and UNKNOWN.

It is difficult to recognize galaxy and QSO spectra and determine their redshift, and as such the LAMOST 1D pipeline does not work as well as for stellar classification due to the S/Ns of galaxy and QSO spectra being relatively lower. An additional independent pipeline, the Galaxy Recognition Module (GM for short), has been designed for galaxy recognition and redshift measurement. After the 1D pipeline was run, it automatically identifies galaxies and measures the redshifts by recognizing lines. The redshifts of galaxies are determined through line centers. Before line centers are measured, a Gaussian function with sigma of 1.5 times the wavelength step is applied to the spectra to eliminate noises. The continua, which were smoothed by a median filter, are divided to complete normalization. Those data points that exceed 2σ of a normalized spectrum are selected as candidates of emission lines, and then a set of Gaussian functions is used to fit the lines. All the line centers are compared with line lists, which are spaced by steps of 0.0005 in redshift (z). If most of the lines are matched successfully with heavily weighted lines such as Na D, Mg b, Ca ii H, or Ca ii K for absorption galaxies, or Hα, O ii, Hβ, O iii, or N ii for emission galaxies, the spectrum is classified as a galaxy, and the corresponding z is the raw redshift of the spectrum. However, for QSOs, the classifications and measurements highly depend on visual inspection. We combined the classification of GM, the 1D pipeline, and expert inspection, and the final classifications of the spectra of the 1095 spectrographs are presented in Table 2. In total, 52,181 additional spectra have been recognized in DR2 and will be officially released in the Third Data Release (DR3) of the LAMOST Regular Survey. The fraction of objects rescued is about 52,000/2,000,000 (∼2.5%).

For the rescued 52,181 targets, we evaluated the quality by plotting the magnitude against S/N relationships for galaxies, QSOs, and stars. For galaxies and QSOs, most of the magnitudes are spread between 17.0 and 19.0, which is shown in Figure 18. This is close to the limit of LAMOST observation; consequently, the majority of their S/Ns are so low that they do not reach an S/N of 10. To reduce the differences of S/Ns due to differences in exposure times, all of the S/Ns in this paper were scaled to 5400 s. For stars, there are two peaks in the distribution of magnitudes, as shown in Figure 19. The magnitudes of A-, F-, G-, and K-type stars range from 13.0 to 17.0, and M-type stars range from 15.0 to 18.0 mag. The S/Ns of the stars are higher than those of galaxies and QSOs; however, most are below 30, which is comparatively low for stars. With the exception of M-type stars, we selected the stars with S/Ns in the r band larger than 2.0 for the release. Therefore, an obvious cut is seen in the bimodal point distributions of early- and late-type stars in Figure 19. For F-, G-, and K-type stars, by running LASP, we parameterized those with S/Ns in the g band larger than 6.0 for nights with a dark moon and 15.0 for nights with a bright moon. The final stellar parameter coverage is presented in Figure 20.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

The variation of vignette and fiber efficiency caused by telescope pointing has not been modeled, which will lead to the problem of flat-fielding, since the flat that LAMOST used is twilight, which is observed once a day. The flat-fielding using twilight can partly correct the efficiency differences of fibers. To minimize potential errors introduced by poor sky subtraction, the current LAMOST 2D pipeline (v2.7) scales the sky spectrum to obtain the same flux intensities of sky emission lines as those of the target spectra, from which it will be subtracted. It is assumed that the emission lines are homogeneous across the FOV of individual spectrographs (about 1°). However, for the bright nights, the spatial distribution of the sky background is not uniform (Bai et al. 2007). Consequently, scaling the sky spectra by the measured fluxes of sky emission lines risks subtracting an incorrect level of sky background. Comparing the ASPSRCs with the SRCs from the LAMOST 2D pipeline, we found that 6 out of 28,866 spectrographs from DR2 are abnormal. And all of those 6 plates were observed in the nights with a very bright moon. For these 6 spectrographs, the standard stars' telluric bands are extremely undersubtracted, and thus it turns out that the SRCs of the standards are overfitted (see Figure 21). The oxygen band is undersubtracted for the spectra of the standards. This leads to the overfitted SRC also containing the oxygen band and introduces artificial spectral lines to all the spectra of the spectrograph, making the classification of spectra by the 1D pipeline difficult.

Zoom In Zoom Out Reset image size

Figure 22 shows one example of artificial spectra calibrated by the overfitted SRC (from Figure 21 using the 2D pipeline), which is plotted with black curves. We recalibrated the spectra using the ASPSRCs, which is presented with red curves in Figure 22. After recalibration, the spectra were classified as F0 by the 1D pipeline (an improvement over the "Unknown" classification by the 1D pipeline previously). The ASPSRC method has been used to correct this problem, and the spectra of these six spectrographs will be released in LAMOST DR3, and are flagged to warn users that the residues of sky background might still exist in these spectra.

Zoom In Zoom Out Reset image size