On the radial velocity calibrations in the LAMOST Medium-Resolution Spectroscopic Survey of Nebulae

Nebulae are interstellar clouds consisting of dust, hydrogen, helium and other ionized gases. Among the various types of nebulae, emission nebulae are clouds of interstellar ionized gases and dust that emit light in various wavelengths. There are different kinds of emission nebulae, including H II regions, planetary nebulae (PNe), supernovae remnants (SNRs; Woltjer, 1972) and so on. Different types of emission nebulae have various different formation mechanisms, thus they can be used to study many aspects in the astronomical sciences from the star formation to the evolution of Milky Way. H II regions can be used as probes of the composition of the interstellar medium in galaxy, and their emission-line spectrum can be used to determine the gas-phase abundance of several elements (Shaver et al., 1983; Esteban et al., 2019). Due to the bright emission lines of PNe, they can be used as tracers of galaxy kinematics (Merrett et al., 2006), and as potential tracers of the chemical evolution of Milky Way and other galaxies (Cavichia et al., 2017; Kwitter et al., 2012). SNRs can provide insights into the mechanisms of supernova explosions, and probe the immediate surroundings of supernovae. SNRs are also fundamentally related to the star-forming process in a galaxy, and can also give us a picture of the on-going massive star formation rate (Kopsacheili et al., 2020).

Optical spectroscopic observations of emission nebulae can provide important information of nebulae, especially the ${\mathrm{H}\alpha}$, ${\mathrm{H}\beta}$, $[$N II$]$ $\lambda\lambda$ 6548, 6584, and $[$S II$]$ $\lambda\lambda$ 6717, 6731, $[$O II$]$ $\lambda\lambda$ 3726, 3729, $[$O III$]$ $\lambda\lambda$ 4959, 5007. These optical emission lines can be used to investigate the kinematics and dynamics properties of nebulae (Damiani et al., 2016). Furthermore, the optical line intensity ratio $[$S II$]$ $\lambda$ 6717/$[$S II$]$ $\lambda$ 6731 is electron density sensitive (Osterbrock & Ferland, 2006), ${\mathrm{H}\alpha}$/$[$S II$]$ $\lambda\lambda$ 6717,6731 ratio can be used to distinguish shocked nebulae from photoionized nebulae (Alvarez & Hoare, 2005), and the ${\mathrm{H}\alpha}$/$[$N II$]$ ratio is a widely used tool for investigating nitrogen-to-hydrogen abundance variations among SNRs (Fesen et al., 1985). The emission line ratios combining with the kinematics of ionized gas, can be used to characterize and identify the nature of the nebulae. Thus it is very important to obtain complete sampling of the optical line emissions in various nebulae. A lot of optical spectrophotometric observations have been carried out for emission nebulae. But most of them are only dedicated for some special nebulae (Fesen et al., 1985; Blair et al., 1991; Gerardy & Fesen, 2007; Chen et al., 2017), thus still lack of spectroscopic survey to sample a large sample of nebulae near the Galactic plane, especially for those with large spacial size.

The Large sky Area Multi-Object fiber Spectroscopic Telescope (LAMOST) is a quasi-meridian reflecting Schmidt telescope, which has a $\sim$4 meters effective aperture and a field of view of 5^∘ diameter (Wang et al., 1996; Su & Cui, 2004; Cui et al., 2012; Zhao et al., 2012). As a dedicated spectroscopic survey telescope, LAMOST can acquires optical spectra with 4000 fibers during one single exposure. Since September 2012, LAMOST has been carrying out the first five-years Regular Surveys, i.e. the first stage survey program of LAMOST (hereafter LAMOST I). The LAMOST I Regular Surveys mainly consist of two components (Zhao et al., 2012): the LAMOST Extra-Galactic Survey of Galaxies (LEGAS) that aims to study the large scale structure of the Universe; and the LAMOST Experiment for Galactic Understanding and Exploration (LEGUE; Deng et al., 2012) with the goal of obtaining millions of stellar spectra to study the structure and evolution of the Milky Way. The LAMOST I spectra cover the entire optical wavelength range ($\simeq$ 3700 – 9000 Å), with a resolving power R $\sim$ 1800 (Luo et al., 2012, 2015).

Since September 2017, the second stage survey program of LAMOST (hereafter LAMOST II) has been initiated. Except continuing the low-resolution spectroscopic observation, LAMOST II began the medium-resolution spectroscopic survey (MRS; Liu et al., 2020). In every lunar month, half of the nights (i.e. the dark/gray nights, from 23rd to 6th on lunar calendar) are used to continue the previous low-resolution spectroscopic surveys, while the remaining half of the nights (i.e. the bright/gray nights, from 7th to 22nd on lunar calendar) are assigned for the MRS. LAMOST II MRS spectra have a medium-resolution of R $\sim$ 7500, and cover the wavelength ranges of 4950 – 5350 Å in blue channel and 6300 – 6800 Å in red channel (Wu et al., 2020a). The main scientific aims of LAMOST II MRS include the time-domain (TD) and non-time-domain (NT) sciences. Hence the MRS survey can be broken down into a few different sub-surveys: the Kepler region survey (MRS-K), the TESS follow-up survey (MRS-T), the Star forming region survey (MRS-S), the Binary survey (MRS-B), the Galactic Nebulae survey (MRS-N), the Galactic archaeology survey (MRS-G), and Open cluster survey (MRS-O). Among them, MRS-K, MRS-T, MRS-B, and part fields of MRS-S are assigned as the TD survey, while the MRS-G, MRS-N, MRS-O, and part of the MRS-S are operated as NT survey (Liu et al., 2020).

The large field of view (5^∘), relatively higher resolution (7500), and dedicated wavelength coverage (6300 – 6800 Å, thus covering the emission lines ${\mathrm{H}\alpha}$, $[$N II$]$ $\lambda\lambda$ 6548, 6584, and $[$S II$]$ $\lambda\lambda$ 6717, 6731) make LAMOST II MRS an ideal spectroscopic survey to sample the optical emission lines of Galactic nebulae (Wu et al., 2020b) in unprecedented details. To better investigate the kinematics properties of nebulae, one of the most important things is to obtain better wavelength calibration thus improving the radial velocity determination of nebulae emission lines.

In this paper, we investigate the wavelength calibration and finally propose a method to improve the precision of the radial velocity determinations in the LAMOST II MRS nebulae survey. In Section 2, we describe the observation and data reduction of LAMOST II MRS nebulae survey. In Section 3 we present the method, and Section 4 presents the discussion. Finally Section 5 gives a summary.

Accurate Radial Velocity (RV) determinations of emission lines are very important for studying the kinematics and dynamics properties of nebulae. While for the MRS observations, the arcs (Th-Ar) used for wavelength calibration are obtained before or after the normal observations (i.e. not simultaneously). Thus the wavelength calibration from arcs may incorporate some uncertainties for RV determinations, due to direction change of the telescope or environment variation (such as temperature, pressure) in the spectrograph room. To obtain accurate RV measurements, it’s necessary to do a calibration. Unlike the RV calibrations of stars which can be obtained by using the RV standard stars (Liu et al., 2019; Wang et al., 2019), the main targets in MRS-N are nebulae features not stars. Thus new method should be developed to investigate the wavelength calibration precision and propose new RV calibration ways to improve the RV precision in MRS-N survey data.

For the LAMOST low-resolution spectra reduction, some strong sky emission lines were used during the wavelength calibration procedure. But for the MRS spectra, the sky emission lines were not used in the 2D data reduction pipeline. As we mentioned in Section 1, the MRS observations were carried out during the bright/gray nights (from 7th to 22nd on lunar calendar) every month. That means, the moonlight background is very bright during the MRS observations for most times, and the corresponding sky emission lines have very low S/N, thus are not available for the wavelength calibration. While for our MRS-N survey, the observations are scheduled only during the moonless bright/gray nights, thus the sky emission lines still have good quality, and can be used to help us to improve the MRS-N wavelength calibration.

In the MRS-N 1D wavelength calibrated spectra without sky subtraction, there are several sky emission lines as shown in Figure 3. There are 13 obvious sky emission lines in the red band (Osterbrock et al., 1996), of which 7 are single lines as listed in Table 2 and 6 are blended lines as presented in Table 3. Figure 4 presents an example MRS-N spectra showing these sky emission lines. Initially we hope to use all these sky emission lines (7 single + 6 blend lines) to calibrate RVs. By carefully investigating the blending situation and line profiles of the blended lines, we find it’s hard to differentiate the multi-peaks of the blended lines, thus it’s impossible to obtain accurate line centers even by multi-gaussian fitting under our relatively low resolution ($\sim$ 7500) spectra. Much higher resolution ($\sim$ 30 000) spectra are needed to well differentiate the multi-peaks of the blended lines (Osterbrock et al., 1996). If we apply single gaussian fitting to these blended lines, the fitted line centers may have relatively large uncertainties due to their blending features. Hence finally we exclude these 6 blended lines from our following analysis, and only use the 7 single lines. These sky emission lines cover the a relatively large wavelength range (6290 – 6560 Å) of the MRS-N red spectra (see Figure 4), and their intrinsic wavelengths are already well-known and fixed (see Table 2), thus they are ideal tools to investigate the precision of wavelength calibration of MRS in real time. Furthermore, the sky emission lines are obtained at the same time as the nebulae emission lines, so most importantly they can provide a simultaneous RV calibration and finally help us improve the precision of RV determinations of MRS-N.

Gaussian fitting method is widely used for measuring the stellar RVs based on SDSS (Rebassa-Mansergas et al., 2016) or LAMOST spectra (Ren et al., 2018a). Usually a a second-order polynomial plus a single-Gaussian line profile was used to fit a single line (such as H$\alpha$ emission line), while a second-order polynomial plus a double/triple-Gaussian line profile of fixed separation was used to fit the double/triple lines (like Na I $\lambda\lambda$ 8183.27, 8194.81 or Ca II absorption triplet at 8498.02, 8542.09, and 8662.14 Å), as described in Rebassa-Mansergas et al. (2007, 2017) and Ren et al. (2013, 2014). Here we adopt the similar method, i.e. a second-order polynomial plus a single-Gaussian line profile is used to fit the 7 single sky emission lines in Table 2. Figure 5 shows an example of the Gaussian fitting results of one nebula spectrum.

Table 4 lists the fitting results for every spectrum of the 15 MRS-N plates. For those strong sky emission lines like $\lambda$6300 and $\lambda$6363 (as shown in Figure 4 and 5), the fitting error is only $\lesssim$ 0.4 – 0.5 $\mathrm{km\,s^{-1}}$; for those not so strong lines like $\lambda$6498, $\lambda$6533 and $\lambda$6553, the fitting error is $\lesssim$ 0.7 – 1.0 $\mathrm{km\,s^{-1}}$; even for those relatively weak emission lines (i.e. $\lambda$6287 and $\lambda$6544), the fitting error is $\lesssim$ 1.6 – 2 $\mathrm{km\,s^{-1}}$mostly, all of which shows the good quality of sky emission lines, thus makes them the best tools to investigate and improve the precision of RV determinations of nebulae emission lines. From Figure 5, we can see that there is obvious systematic deviation around 4 $\mathrm{km\,s^{-1}}$ for the RV of this spectrum.

To investigate the situation of the whole plate, we obtain the mean and standard deviation of the fitted sky RVs for every MRS-N plate (see Table 5), by gaussian-fitting of the histogram distribution of sky RVs. Figure 6 shows the histogram distribution of the fitted RVs for the 7 single sky emission lines for plate “20180305-HD474690801”. For those relatively strong sky emission lines (i.e. $\lambda$6300, $\lambda$6363, $\lambda$6498, $\lambda$6533, $\lambda$6553), the standard deviation is lower ($\sim$ 1.2 – 2.0 $\mathrm{km\,s^{-1}}$); while for those relatively weak lines (such as $\lambda$6287, $\lambda$6544), the standard deviation is a little large ($\sim$ 2.4 – 3.4 $\mathrm{km\,s^{-1}}$), which can be easily explained as the weak lines have low spectral quality thus can transfer relatively large fitted uncertainties. From Figure 6 and Table 5, we can clearly see the systematic deviation of wavelength calibration for almost the whole plate, thus it’s very necessary to calibration these systematic deviations to obtain accurate RVs of nebulae emission lines.

Then by using the fitted line center of these 7 single sky emission lines (as shown in Figure 6 and Table 5), a second-order polynomial was used to do the fit. We also try the third- and fourth-order polynomial fit, but they show obvious over-fitting, thus we suggest that the second-order polynomial fitting is the best choice. Furthermore, as we mentioned before, the 7 single sky emission lines we used cover the wavelength range: 6290 – 6560 Å, which should be enough to calibrate the RVs of ${\mathrm{H}\alpha}$ and $[$N II$]$ $\lambda\lambda$ 6548, 6584 emission lines of nebulae. While another important emission line, i.e. $[$S II$]$ $\lambda\lambda$ 6717, 6731 locates far from this range. We then extrapolate the RVs calibration to 6731 Å by applying a constraint that the RVs calibration at 6731 Å and 6548 Å are similar. Thus at least we can correct the systematic deviations at $\sim$ 6731 Å. Finally the RVs calibration function is fitted by using the 7 single sky emission lines and the value extrapolated at 6731 Å. Figure 7 shows an example of the fitted RVs calibration function (the red curve).

After the calibration, the sky RVs can go to as accurate as 0 $\mathrm{km\,s^{-1}}$(which is the true RVs of sky emission lines) with a standard deviation 0.5770 $\mathrm{km\,s^{-1}}$, while before the calibration, the sky RVs have a systemic uncertainty as large as $-$3.9192 $\mathrm{km\,s^{-1}}$ with a standard deviation 0.7500 $\mathrm{km\,s^{-1}}$, for plate“20180305-HD474690801” as shown in Figure 7. Furthermore, when fitting the RVs calibration function, we suggest to do a RV error cut 3 $\mathrm{km\,s^{-1}}$ of the sky emission lines. We also try a RV error cut 1.5 $\mathrm{km\,s^{-1}}$, the fitted RVs calibration function did not show large difference, thus the RV error cut of 3 $\mathrm{km\,s^{-1}}$ is suggested to be used.

We applied the method described in the previous section for all the 15 MRS-N plates. Table 6 lists the fitted parameters of the RVs calibration function (f($x$) = a $x^{2}$ + b$x$ +c, where $x$ is the wavelength in unit of $\mu$m). We need to note that for the 10 plates observed in 2018 March/December and 2019 January, the 7 single sky emission lines (the black points shown in Figure 7) are already very good to provide accurate RVs calibration.

But for the 5 plates observed in 2018 November, we need to remove two sky lines $\lambda$6287 and $\lambda$6300 in the blue end (for the one plate in 2018 October, only remove one sky line $\lambda$6287), as the histogram distribution of the line center of $\lambda$6287 and $\lambda$6300 are not single Gaussian symmetric or even multi-peaks (which is the situation shown in Figure 8). In order to investigate the multi-peaks features of these sky RVs of the plates on 2018 November, we present the coordinate distribution of 7 sky RVs for plate “20181118-NT070341S003325N01” in Figure 9. For reference, the rightmost panel shows the spacial distribution of the 16 spectrographs. We can see that for the sky RVs from $\lambda$6287 and $\lambda$6300, almost half of the spectrographs focused around another peak (see the red dots in the left two panels). By carefully checking the spectra obtained in the “green” and “red” spectrographs (the blue and red dots in the left two panels), we can see exact and clear large shift of the emission line $\lambda$6287 and $\lambda$6300. That means, for these five MRS-N plates observed in 2018 November, there are large systematic deviations near 6300Å for almost half of the spectrographs, which should be due to the bad wavelength calibration in this region. As we can see in the bottom panel of Figure 2, there are only two very week arc lines near 6300 Å  which thus may lead to bad wavelength calibration near this region when these two lines are too weak and have bad quality.

In December 2018, the systematic deviation near 6300 Å has disappeared. Figure 10 shows the coordinate distribution of sky RVs for one plate observed in December 2018, i.e. “20181216-NT065450N031415N01”. Although the multi-peaks problem has disappeared near 6300 Å, there is another obvious problem: one of the spectrograph, i.e spectrograph 15 has large ($\gtrsim$ 5 $\mathrm{km\,s^{-1}}$) systematic difference from other spectrographs. Then by checking the 5 plates observed in 2019 January, we find this effect still exists. Figure 11 shows the situation of one plate obtained in 2019 January, i.e. plate “20190125-NT041453N482433N01”, from which we can see that the systematic difference of spectrograph becomes minus by comparing with Figure 10, and another spectrograph (ID: 5) has the same situation. This can be explained due to the spectrograph drift for these two spectrographs (i.e. 15 and 5).

While for the two plates observed in March 2018, the situation is very different from the above plates (see Figure 12), which is totally dominated by the systematic deviation ($\sim$ 4 $\mathrm{km\,s^{-1}}$, which can also be seen from Table 6) of the whole spectra for the whole plate. And those bluer than 6363 Å are even worse that those redder than 6363 Å, which can also be seen from Figure 7 and 6. This can be easily explained, as in March 2018, the arc lamp MRS used is Sc lamp, which only has very limited number of arc lines (as shown in the top panel of Figure 2), thus affected the wavelength calibration and finally resulted in the large systematic deviations of the two MRS-N plates in March 2018.

From Table 5 – 6 and above discussions, we can see that for the two MRS-N plates in 2018 March and one plate in October, there are large systematic deviations around 2 $\sim$ 4 $\mathrm{km\,s^{-1}}$ for the whole plate, which can be roughly eliminated after our calibration presented in Table 6. While for the five plates observed in 2018 November, two plates in 2018 December, and five plates in 2019 January, the systematic deviations of the whole plates are around 0.2 $\sim$ 0.5 $\mathrm{km\,s^{-1}}$, which can also be roughly calibrated after applying our calibrations in Table 6. The decreasing of the systematic deviations of the whole plates from early 2018 to late 2018 indicates that the wavelength calibration has been improved at least since 2018 November. The improvement of MRS wavelength calibration from early 2018 to 2019 was mainly due to the updates of arc lamps: (1) At early 2018, the arc lamp used by MRS was Sc which only had a very limited number of available arc lines as we mentioned before, and the Sc lamp had serious systematic deviation about 4 $\sim$ 5 $\mathrm{km\,s^{-1}}$; (2) From May 2018, MRS began to use Th-Ar lamp, but only 10 Th-Ar lamps were used initially. Due to the long optical path and large focal plane of LAMOST, only using 10 Th-Ar lamps were not enough to get high enough brightness and uniform distribution of illumination, thus may affect the wavelength calibration. (3) At the end of 2018 and beginning of 2019, the number of Th-Ar lamps has been increased from 10 to 20, which enhanced the brightness and uniformity of illumination, thus improved the wavelength calibration of MRS in 2019.

Although the wavelength calibration of MRS has been improved at the end of 2018 and beginning of 2019, there still some problems such as the spectrograph drift effect as mentioned previously (see Figure 10 – 11. Thus, we also investigate the distribution of sky RVs for different spectrographs of the same plate. Figure A1 and A2 in the appendix shows the histogram distribution of sky RVs and the fitted calibration function for two different spectrograph (i.e. spectrograph ID 04 and 08 of plate “20180305-HD474690801”) of one plate. We can see clear difference between the systematic deviation (around 0.5 $\mathrm{km\,s^{-1}}$) of the these two spectrographs. Figure 13 plots the RVs calibration function of all the 16 spectrographs of plate “20180305-HD474690801”. There is a systematic deviation about 3 $\sim$ 4 $\mathrm{km\,s^{-1}}$ between these 16 spectrographs, which implies the RVs calibration should be different for different spectrographs even in a same plate. Even for those plates in January 2019, the systematic deviations between different spectrographs still exist, as shown in Figure 14 and Figure 11. Table 7 list the fitted calibration function for the 16 spectrographs of the 15 MRS-N plates.

Although most of the sky RVs from one plate or spectrograph are focused near a peak (as shown in Figure 6, A1 and A2), there are still some fibers with sky RVs a little far from the peak value. To obtain higher precision of RV determinations, it’s also necessary to provide a RV calibration function for every nebula spectrum, not only the whole plate or spectrograph. Figure 15 shows an example of the fitted RVs calibration functions of all the spectra in one spectrograph of one plate. We can see that even in one spectrograph, the fitted calibration function of each spectrum is still a little different. Thus it should be better to do the calibration for each spectrum. Table 8 lists the parameters of the fitted RVs calibration function for every spectrum. For those without sky RVs available due to their low spectral quality or shortage of data, the RV calibration function of very nearby spectra can be applied instead. Figure 16 shows an example (for plate “20180305-HD474690801”) of the histogram distribution of sky RVs after applying the RVs calibration function provided in Table 8. We can see that the systematic deviation as large as 4 $\mathrm{km\,s^{-1}}$ has disappeared, especially for those sky lines near 6550Å which harboring the important nebulae emission features (i.e. ${\mathrm{H}\alpha}$, $[$N II$]$ $\lambda\lambda$ 6548, 6584).

The future MRS-N pipeline (Wu et al., 2020c, in preparation) will adopt the method developed here to investigate the precision of wavelength calibration of MRS-N nebulae spectra in real time, and fit a RVs calibration function for every nebula spectrum by using sky emission lines to finally improve the precision of nebulae RVs. Furthermore, this method is also valuable for other sub-surveys of MRS if they have some plates fortunately with available strong sky emission lines.

LAMOST II MRS survey has initiated a sub-survey of nebulae, i.e. MRS-N survey since 2017 September. MRS-N survey will monitor a large sample of nebulae emission line features, mainly including $[$N II$]$ $\lambda\lambda$ 6548, 6584, ${\mathrm{H}\alpha}$, and $[$S II$]$ $\lambda\lambda$ 6717, 6731. Before studying the kinematics and dynamics properties of nebulae, it’s important to investigating the precision of the wavelength calibration of nebulae spectra, and finally calibrate RVs of nebulae emission lines.

We propose a method to investigate the precision of wavelength calibration of MRS-N, by using the sky emission lines in the red spectra of MRS. We find that the RVs of the 15 observed MRS-N plates have systematic deviations from $\sim$ 0.2 to 4 $\mathrm{km\,s^{-1}}$for different plates obtained at different times. A RVs calibration function is fitted by using the fitted centers of the sky emission lines, which can successfully calibrate the RVs deviations of nebulae in real time. The future released value-added catalogue of MRS-N will apply this RVs calibration function to provide accurate RVs of nebulae emission lines. We suggest other MRS-N users to use our method to investigate and improve the RVs precision of nebulae spectra in the future too.