# White dwarfs identified in LAMOST Data Release 5

Jincheng Guo1,2,3,4 , Jingkun Zhao5,6, Huawei Zhang3,4, Jiajun Zhang5,6, Yu
Bai5, Nikolay Walters1, Yong Yang5,6, and Jifeng Liu5,6
1Department of Physics and Astronomy, University College London, London WC1E
6BT
2Beijing Planetarium, Xizhimenwai Road, Beijing 100044, China
3Department of Astronomy, Peking University, Beijing 100871, China
4Kavli Institute for Astronomy and Astrophysics, Peking University, Beijing
100871, P. R. China
5Key Laboratory of Optical Astronomy, National Astronomical Observatories,
Chinese Academy of Sciences, Beijing 100012, China
6University of Chinese Academy of Sciences, Beijing 100049, People’s Republic
of China E-mail: andrewbooksatnaoc<EMAIL_ADDRESS>fellow

###### Abstract

In this paper, we report white dwarfs identified in the 5th Data Release of
the Large Area Multi-Object fibre Spectroscopic Telescope, including spectral
types of DA, DB, DC, DZ, and so on. There are 2 625 DA spectra of 2 281 DA
stars, 182 DB spectra of 166 DB stars, 62 DC spectra of 58 DC stars, 36 DZ
spectra of 33 DZ stars and many other types identified, in addition to our
previous paper (Data Release 2). Among those sources, 393 DA stars and 46 DB
stars are new identifications after cross-matching with the literature. In
order to select DA candidates, we use the classification result from the
LAMOST pipeline, colour-colour cut method and a random forest machine learning
method. For DBs, since there is no template for DB in the pipeline model, a
random forest machine learning method is chosen to select candidates. All the
WD candidates have been visually checked individually. The parameters of
effective temperature, surface gravity, mass, and cooling age have been
estimated for relatively high signal-to-noise ratio DAs and DBs. The peaks of
the DA and DB mass distributions are found to be around 0.62 M⊙ and 0.65 M⊙,
respectively. Finally, the data and method we used to select white dwarf
candidates for the second phase of LAMOST survey are also addressed in this
paper.

###### keywords:

stars: white dwarfs; stars: fundamental parameters; Astronomical data bases:
surveys-catalogues

††pagerange: White dwarfs identified in LAMOST Data Release
5–LABEL:lastpage††pubyear: 2019

##  1 Introduction

The great majority of main-sequence stars are in the mass range of 0.07 M⊙ to
10 M⊙, which is also the mass range of white dwarf (WD) progenitors (Doherty
et al., 2015). According to the literature (Fontaine, Brassard, & Bergeron,
2001; Heger et al., 2003), up to 97% of all stars in our Galaxy will
eventually evolve to WDs. Based on spectroscopic features, WDs mainly consist
of DAs and DBs. They are the most explored types of single WDs, one reason is
that they account for 90% of WDs. The specific number of this fraction
recently was found vary with the effective temperature (Rolland, Bergeron, &
Fontaine, 2018; Cunningham et al., 2020), based on $Gaia$ spectroscopic
sample, after significant fraction of cool WDs were discovered (Gentile
Fusillo et al., 2019). Another reason is that they are objects of great
importance, providing crucial information in various fields. For instance, the
simple cooling mechanism of WDs makes it easier to obtain relatively accurate
ages. Therefore, for research on the age of Galactic stellar halo (Guo, Liu, &
Liu, 2016; Kilic et al., 2019; Guo et al., 2019), WDs are important age
estimation tools after their physics are well-understood. By studying mass
distribution (Kepler et al., 2007; Holberg et al., 2016; Hollands et al.,
2018) and luminosity functions (Harris et al., 2006; Munn et al., 2017; Lam et
al., 2019) of WDs, multiple astrophysical processes of scientific importance
can be learnt, in particular, the initial mass function and binary
interactions. Meanwhile, WDs can serve as accurate records of star formation
and reveal the evolution history of the Milky Way (Krzesinski et al., 2009;
Rowell, 2013). Additionally, for stars that will eventually evolve to WDs,
studies of their initial-final mass relation depend on both single WDs in
clusters (Catalán et al., 2008a; Kalirai et al., 2008, 2009) and WDs in
binaries (Catalán et al., 2008b; Zhao et al., 2012), These reseaches will help
to provide important information on the evolution of our Galaxy (Kilic et al.,
2017).

The goal to establish a large WD database has been pursued for more than three
decades. McCook & Sion (1987) spectroscopically identified 1 279 WDs that has
been updated to 2 249 entries by McCook & Sion (1999). The total number of WDs
has increased greatly, with the development of large surveys, e.g. Palomar-
Green (Green, Schmidt, & Liebert, 1986) and Sloan Digital Sky Survey (York et
al. 2000, SDSS) particularly (Kleinman et al., 2004; Eisenstein et al., 2006).
By using the data release (DR) 7 (Abazajian et al., 2009), Kleinman et al.
(2013) spectroscopically identified about 20 000 WDs. Recently, Kepler et al.
(2015) made $\sim$ 9 000 new identifications of WDs from SDSS DR10 (Ahn et
al., 2014). More recently, around 6 000 and 20 000 WDs were identified from
SDSS DR12 and DR14, respectively (Kepler et al., 2016, 2019).

The Large Area Multi-Object fibre Spectroscopic Telescope (LAMOST) pilot
survey started in 2012, and the first phase was completed five years later.
After a transition from 2017 September to 2018 June, the survey began its
second phase. There has been medium resolution (resolving power $R\sim$ 7500)
spectroscopy carried out during bright nights in the second phase, together
with lower resolution observations during dark nights ($R\sim$ 1800). In the
five years of the first phase, several studies on LAMOST WDs have been
conducted. Zhao et al. (2013) identified 70 DAs from the LAMOST pilot survey.
Zhang et al. (2013) presented a catalog of 230 DAs by fitting Sersic profiles
to Balmer lines of spectra. Combining the spectral type results from LAMOST
pipeline, the Balmer line equivalent width measurements, and the colour-colour
cut method, Guo et al. (2015b) identified 1056 DAs, 34 DBs, 276 white dwarf
main sequence (WDMS) binaries and other spectral types of WDs in LAMOST DR2.
Gentile Fusillo et al. (2015) also reported the discovery of 253 new WDs in
LAMOST DR3. By exploiting a well characterised magnitude limited DA star
sample selected from LAMOST Galactic anticeter, space density, formation rate,
luminosity and mass functions of DA WDs were studied (Rebassa-Mansergas et
al., 2015). Recently, a catalog of 876 WDMS binaries identified in LAMOST DR5
are presented by Ren et al. (2018).

Apart from spectroscopic surveys, the studies of WDs has opened a new window
since the $Gaia$ data released (Gaia Collaboration, et al., 2016). Based on
$Gaia$ data, local complete WD samples have been built separately for 20 pc
(Hollands et al., 2018) and 40 pc (Tremblay et al., 2020). There are other
much larger but not volume complete WD sample discovered in $Gaia$ DR2 (Gaia
Collaboration, et al., 2018a). Jiménez-Esteban et al. (2018) presented a
catalogue of 73 221 WD candidates extracted from DR2. More recently, more than
260 000 high-confidence WD candidates were discovered in DR2, as well (Gentile
Fusillo et al., 2019). Evidence for merged WDs has also been revealed (Kilic
et al., 2018). By adopting accurate positions, proper motions and parallaxes,
detailed studies on WD kinematics have been conducted by several research
groups (Bovy, 2017; Gaia Collaboration, et al., 2018b; Rowell & Kilic, 2019;
Torres et al., 2019).

In this work, we present a catalogue of WDs discovered in LAMOST DR5111Spectra
available at http://dr5.lamost.org/, as well as their physical parameter
estimation. In Section 2, we present the selection methods of DAs and DBs. The
estimation of the parameters for DAs and DBs (effective temperature, surface
gravity, mass, and cooling age) is described in Section 3. We discuss our
white dwarf target selection for the second phase of LAMOST in Section 4.
Finally, we present our summary in Section 5.

##  2 Candidates selection

###  2.1 LAMOST observation

LAMOST is a 4-m reflecting Schmidt telescope, equipped with a multi-object
spectrograph that has a 20 deg2 field of view and 4 000 fibres. The LAMOST
project began its one-year pilot study in 2012, followed by a five-year first
phase survey. There is only low resolution spectroscopy in the first phase.
The spectral resolving power is $R\sim 1800$, covering a wavelength range
$3800-9000$ Å. With typical exposure times of 1.5 h, the limiting magnitude
can reach 20.5 mag (Cui et al., 2012). The first phase survey is composed of
two major parts (Zhao et al., 2012). The first part is the LAMOST Experiment
for Galactic Understanding and Exploration (LEGUE) survey, focused on
understanding the structure and evolution of the Milky Way (Deng et al.,
2012). The second part is the LAMOST Extra-Galactic Survey of galaxies
(LEGAS), whose purpose is to study the large-scale structure of the Universe.
The LEGUE survey consists of three smaller surveys, where each is selected for
distinct purposes (Chen et al., 2012; Carlin et al., 2012; Yuan et al., 2015).
The targets are mainly chosen from the Galactic disc, spheroid, and anti-
center. Although LAMOST is a spectroscopic survey only, there are also
photometric data provided by different astronomers from various photometric
catalogs, e.g. XSTPS-GAC (Liu et al., 2014; Guo et al., 2018, Xuyi Schmidt
Telescope Photometric Survey of the Galactic Anti-center), 2MASS, SDSS,
Kepler, NVSS etc. More than 50% of the input catalog entries at least have
$g$, $r$, $i$ magnitudes, mainly from XSTPS-GAC and SDSS. In LAMOST DR5, there
are almost 10 million spectra (details in Table 1). While the second phase of
LAMOST is ongoing, this work is based on the completed first phase of LAMOST,
in particular DR 3, 4, and 5.

Table 1: Updated spectral statistic of each data release for first phase.

Note: STAR, GALAXY, QSO and UNKNOWN are class assigned by LAMOST pipeline. Numbers may change as spectral reduction and classification pipelines update. Survey |  DATE | STAR | GALAXY | QSO | UNKNOWN | TOTAL
---|---|---|---|---|---|---
Pilot |  2011-10-24 2012-06-17 | 837,056 | 8,045 | 1,227 | 118,060 | 964,388
DR1 |  2012-09-28 2013-06-03 | 1,536,045 | 12,734 | 6,035 | 127,198 | 1,682,012
DR2 |  2013-09-10 2014-06-03 | 1,504,329 | 30,432 | 6,382 | 91,399 | 1,632,542
DR3 |  2014-09-10 2015-05-30 | 1,516,147 | 26,288 | 8,753 | 88,956 | 1,640,144
DR4 |  2015-09-12 2016-06-02 | 1,551,394 | 39,498 | 13,954 | 96,680 | 1,701,526
DR5 |  2016-09-09 2017-06-16 | 1,226,472 | 36,093 | 14,782 | 119,885 | 1,397,232
First phase |  2011-10-24 2017-06-16 | 8,171,443 | 153,090 | 51,133 | 642,178 | 9,017,844
Table 2: Classification for the 3522 spectra of 3069 sources.

Type | Spectra | Sources
---|---|---
DA/DA: | 2625 | 2281
DB/DB: | 182 | 166
DC/DC: | 62 | 58
DCA/DCQ | 2 | 2
DAH/DBH/DAP | 34 | 31
DZ/DZ: | 36 | 33
DZA/DZB | 6 | 4
DAZ/DAZe | 6 | 5
DBAZ/DBAZ: | 3 | 2
DBZ/DBZA | 7 | 4
DAB/DBA/DBA: | 76 | 64
DO/DAO/DOA/DBOAa | 23 | 20
DQ/DQ: | 19 | 19
CV/CV: | 130 | 106
(DA,DB,DC,DAH,DBA)+M/DA+(K,DQ)b | 311 | 274

  * •

Notes:
Spectral types listed in this paper followed the definitions in Section 2.2
from Kepler et al. (2019).
Especially, notation ":" means uncertainty mainly due to low S/N.
Notation "e" means emission line present in the spectrum.
aDBOA type means its a Helium dominated white dwarf with He II 4 686 Å line
and mild Balmer absorption lines.
bWhite dwarf binary. White dwarf with M, K type star or DQ white dwarf.

###  2.2 DA selection

The raw spectral data are processed with the LAMOST 2D pipeline (Luo et al.,
2015). The standard procedures of dark current subtraction, bias subtraction,
cosmic ray removal, 1D spectral extraction, sub-exposures combination are
performed in the process of 2D pipeline. Next, the 1D pipeline is used to
perform spectral classification, then calculate the radial velocity for each
spectrum. Spectral classification adopted by 1D pipeline is done by template
matching. The most important part is to construct a spectral classification
template library. The early version of this library for LAMOST is built
firstly by excluding outliers using local outlier probabilities, then
principal component analysis was used to reconstruct spectra. More description
can be found in Wei et al. (2014). The updated version of this library is
constructed through clustering algorithm (Kong & Luo, 2019). The pipeline
classification determines object class (STAR, QSO, GALAXY and UNKNOWN), and
subclass, e.g. (B2, G6, WD). With better pipeline development and more
information, there are more correctly classified spectra in DR5. We
successfully identify numerous false positives from our previous catalog,
mostly spectra with low signal to noise ratio, which we marked ":" for
uncertain about the classification (presented in Table 5).

Machine learning has drawn increasing attention in astronomy, where spectral
classification is an important potential application (Jiang et al., 2013; Liu
et al., 2014; Li et al., 2018). Thus we applied machine learning algorithm to
select DA candidates in this work, as another independent method besides
adopting pipeline subclass. There are various types of machine learning
algorithms, e.g. support vector machine, Bayesian networks, decision tree
learning. Based on our previous experience performing spectral classification
(Bai, Liu, & Wang, 2018; Bai et al., 2019), we choose an algorithm called
random forest (Breiman, 2001, RF). It performs better than other algorithms,
in terms of time cost and accuracy.

The RF algorithm operates by constructing a multitude of decision trees at
training and outputting the class that is the mode of the classification of
the individual trees (Breiman, 2001). Random decision forests correct for
decision trees’s habit of overfitting to their training set. The RF algorithm
implementation used in this work is a supervised algorithm, and adopts 100
trees (estimators). All flux values of a spectrum are used as parameters. The
largest weight is given to parameters in the Balmer line wings. For each
spectrum, a probability value will be produced by the RF algorithm. Then a
simple binary classification is used. If the probability of being a DA star is
greater than 50%, this object will be classified as a DA candidate. Otherwise,
it will be classified as non-DA. This algorithm implementation is from scikit-
learn python package (Pedregosa et al., 2011), and information of the specific
model can be found in their website 222https://scikit-
learn.org/stable/modules/generated/sklearn.ensemble.RandomForestClassifier.html.
Considering the fact that observed spectra, even for the same source, vary
from different surveys (i.e. for the same faint source, SDSS spectra are
likely to have higher signal-to-noise (S/N) than LAMOST spectra. And SDSS
spectra are better flux calibrated, compared to LAMOST spectra etc.), we first
built a DA training sample from LAMOST spectra. First of all, there are 379 DA
spectra of S/N greater than 10 in SDSS $g$ band selected from our previous
catalogue (Guo et al., 2015b). Secondly, we randomly selected 100 spectra with
the same S/N limit for each spectral type classified by LAMOST pipeline, which
is around 6k of non-DA spectra in total. Together, these 379 DA spectra and
$\sim$ 6k non-DA spectra are used to train the model, then the model is
applied to a randomly selected 50k spectra sample for initial test. Based on
our test result, most of the contaminants come from A stars. It is
understandable, because our RF algorithm mostly uses the broad and deep Balmer
line profile of DA stars to select candidates. Some A stars have similar
profiles in Balmer line regions. Thus, we added an additional training model
specific for separating DA and A stars. The main idea is to distinguish A
stars by using their multiple absorption line features in the near-infrared
region. Therefore, the largest weight is given to that region. This time, same
379 known DA stars and another 1 000 A type star spectra (classified by LAMOST
pipeline) with S/N above 10 are selected to train the model. Then this
additional model is applied to DA candidates identified by first model. It
produces a probability value as well. But this time, if the probability is
greater than 50%, this object is classified as A type star. Consequently, its
label is changed from DA to non-DA. At last, this code is applied to the whole
data set in LAMOST DR 3, 4, & 5\. In total, there are 6 662 unique spectra
candidates selected by our RF algorithm. Each spectrum is visually inspected
by eye, 1 710 DAs are identified.

In addition, we used a conventional colour-colour cut (Formula 1-4 in
Eisenstein et al. 2006, and Table 1 in Girven et al. 2011) as supplementary
methods to select DAs. Even though LAMOST is basically a spectroscopic survey,
there are imaging surveys like XSTPS-GAC and SDSS, providing $g$, $r$, $i$
magnitudes for more than 50% of the input catalogue entries. Around 1.46
million entries in LAMOST DR 3, 4 & 5 have $u$, $g$, $r$, $i$, and $z$
magnitudes, mostly from SDSS. Using method from Eisenstein et al. (2006), 43
461 white dwarf candidate spectra are selected, while 847 DA star candidate
spectra are selected adopting method from Girven et al. (2011). For pipeline
selection, we select spectra that are classified by the pipeline as WD,
WDMagnetic, DoubleStar, or CarbonWD as DA candidates. Spectral types of
WDMagnetic, DoubleStar, and CarbonWD are also included, because small number
of DA can be misclassified by the pipeline and identification of those types
of WD is a part of our goals as well. Those methods result in 6 662 unique
candidate spectra from RF algorithm, 43 461 candidate spectra from Eisenstein
et al. (2006), 847 DA candidate spectra from Girven et al. (2011), and 7 024
DA candidates from pipeline selection. In total 2 620 bona fide DA spectra and
many various types of WDs are identified after visual inspection (See Table.
2). After cross-matching with the literature, 393 DAs are new identifications
(Kleinman et al., 2004, 2013; Zhao et al., 2013; Zhang et al., 2013; Guo et
al., 2015b; Kepler et al., 2015, 2016, 2019).

One should note that our strategy in selecting DA stars is to include as many
DAs as possible with manageable candidate size. This may result in
considerable contamination rate, but rely on visual inspection, contaminants
are able to be removed and a relatively complete DA sample can be obtained.
Thus, we emphasis the importance of visual inspection of candidate spectra in
this work. According to our identification, the efficiency (defined as the
ratio of correctly identified DAs to the total number of objects identified as
DA candidates) of LAMOST pipeline is $2\,234/7\,024=31.8\%$. But more
accurately, there are 3869 spectra classified by LAMOST pipeline as DA (i.e.
subcalss WD). Spectra classified as subclass WDMagnetic and DoubleStar are
also included in pipeline method to ensure Magnetic WDs and WDMS binaries are
included in our main catalogue. Therefore, the actual efficiency of LAMOST
pipeline should be $2\,234/3\,869=57.7\%$. The main contaminants are low S/N
spectra. Of the 3 869 spectra classified as subclass WD, only 928 spectra have
S/N greater than 5 in $u$, $g$, $r$, $i$, and $z$ bands. Substantial type A
and F stars with very noisy spectra have been wrongly matched with DA
templates. The efficiency of RF algorithm is $1\,710/6\,662=25.7\%$.
Similarly, the main contaminants are still A stars (3 645 of 6 662), together
with some F stars and hot subdwarfs. Even though the efficiency of Eisenstein
colour cut is only $1\,172/43\,461=2.7\%$, majority of other WD types (except
DA and DB) are identified through this method. Contaminants are various, more
than half of the candidates selected by Eisenstein colour cut method are QSOs,
along with B, A, F stars and other types of WDs. The efficiency of Girven
colour cuts is $373/847=43.9\%$. The main contaminants are type G, A, B stars
and QSOs. There are 216 DAs missed by LAMOST pipeline and RF algorithm. After
a closer look at those DAs, about 100 DAs are found to be misclassified by
pipeline as A stars mostly, and B, F stars. Those DAs display relatively
narrow absorption lines, compared to the majority of DAs. But they are indeed
located in the WD region in the colour-colour plot and $Gaia$ colour-magnitude
diagram. This indicates the DA templates used by LAMOST pipeline lack low mass
DAs. Same problem exists in the RF method, since its training sample is based
on our previous catalogue, and identification of low mass DA is generally
difficult before $Gaia$. Apart from those 100 missed DAs, another 100 missed
DAs have very low S/N spectra (S/N<5 in all SDSS bands). It appears that broad
absorption line features in those very noisy spectra have not been picked up
by template matching and RF algorithm.

Regarding the completeness ratio of our identified DA sample to all DAs
observed by LAMOST, we applied simple and rough ways to estimate, aiming to
evaluate the robustness of our DA identification methods. From four methods,
LAMOST pipeline identified 2 234 DA spectra, two colour cut methods identified
753 spectra, and RF algorithm identified 1 710 spectra. Most DA spectra are
discovered by two or more methods. Because there is no independent LAMOST
imaging survey, substantial LAMOST sources have no required colour to perform
the selection, DA spectra identified via colour cut method is highly
incomplete. Therefore, only pipeline and RF algorithm identified DAs are used
to estimate the completeness. There are 1 819, 1 523, and 2 106 DA spectra
with S/N no less than 5 in $g$ band identified by LAMOST pipeline, RF method
and four methods combined, respectively. The number of common spectra
identified by both pipeline and RF is 1 379. Thus, the percentage of pipeline
missed DA spectra is about $(2\,106-1\,819)/1\,819=18\%$. Since pipeline and
RF together identified 1 963 unique DA spectra, the percentage of pipeline and
RF missed spectra is about $(2\,106-1\,963)/1\,963=7\%$. Therefore, the total
missed DA spectra could be $2\,106\times 18\%+2\,106\times 7\%=527$, which
means a lower limit of completeness should be around
$2\,106/(2\,106+527)=80\%$. With the help of pipeline and RF method, we
managed to identify 1 963 DA spectra with S/N no less than 5 in $g$ band,
which means an upper limit of completeness of pipeline and RF combine is 1 963
/ 2 106=93%. In summary, the completeness ratio of identified DA sample to all
DAs observed by LAMOST is in the range of 80% to 93%. It shows the estimated
completeness is consistent, both indicate the number of DA spectra that are
not included in our catalogue is not significant.

Another separate test has been carried out by cross matching LAMOST DR 3, 4, &
5 spectra with most recently published SDSS DR 14 DA catalogue first (Kepler
et al., 2019), there are 272 DA common sources with S/N ratio no less than 5
in $u$, $g$, and $r$ band. Then those sources were cross matched with our DA
catalogue, five spectra were found to be missing in our DA catalogue.
Therefore, the completeness estimated this way is $5/272=98\%$, consistent
with our previous estimation. Note that those five missed sources were added
to our catalogue, making the total number of identified DA spectra 2 625.

To further illustrate the ability of different methods in identifying DA
spectra as a function of S/N, Fig. 3 is here to show the statistics of DA
spectra identified by LAMOST pipeline and RF versus S/N of LAMOST spectra in
SDSS $g$ band. DA spectra identified by colour cut methods are not considered
here as their sample are biased by lacking photometric data. All panels have
shown that pipeline method are better than our RF method in identifying more
DA spectra and yielding less contaminants, regardless of S/N. Bottom panel
indicates that pipeline method yields much more contaminants at low S/N than
at high S/N, while the contamination rate of RF method seems not much affected
by S/N of LAMOST spectra. Nonetheless, more than 60% of RF method selected
candidates are contaminants.

Figure 1: The colour-colour cut selection, based on SDSS $u$-$g$ and $g$-$r$,
de-reddened. The black dots are LAMOST sources with $u$, $g$, $r$ magnitudes,
while red dots are WD candidates selected following Eisenstein et al. (2006),
blue dots are DA stars selected following Girven et al. (2011). Magenta lines
have separated different regions defined by Eisenstein et al. (2006). Bottom
left is WD candidate region, while right region is main-sequence and blue
horizontal branch region. Black dots above the horizontal magenta line are
mostly quasars. Figure 2: Examples of various WD spectral types identified in
LAMOST. In order to focus on the relevant spectral features, this figure only
shows the wavelength range 3500–8000 Å. Classified types and their unique
LAMOST spectral IDs are also shown. Figure 3: The statistics of DA spectra
number identified by different methods as a function of S/N in SDSS $g$ band.
Top panel: Accumulated number histograms of LAMOST pipeline, RF algorithm, and
all methods identified DA spectra in blue, red and cyan colour, respectively.
Middle panel: Number percentage of LAMOST pipeline (blue line) and RF
algorithm (red line) identified DA spectra in all DA spectra identified as a
function of S/N. Bottom panel: Blue line represents number percentage of
LAMOST pipeline identified DA spectra in candidate spectra selected by
pipeline, while red line represents number percentage of RF algorithm
identified DA spectra in candidate spectra selected by RF method.

###  2.3 DB selection

Because there are no DB templates in the model database of LAMOST
classification pipeline, we only applied RF machine learning method to
identify DB stars.

There are 1 842 objects in SIMBAD that are listed as DB stars. Those known DBs
in SIMBAD were cross-matched with all spectra from LAMOST DR5, resulting in
178 matches, where 150 of these are classified as UNKNOWN by LAMOST pipeline.
A large portion of those 150 spectra have very low S/N ratio that are not able
to be identified by eyes. Thus, 58 of 178 known DBs are not recovered by our
DB selection. Because we can not identify them based on their unrecognisable
noisy LAMOST spectra alone, and these noisy spectra have no use for any
analysis, those are not included as DBs in this paper. In order to select a
high quality sample to best represent DB features, we only chose those LAMOST
spectra with S/N $>10$ in the SDSS $g$ band. There are 45 spectra that meet
this criterion and form the training sample. Next, after removal of the 178
known SIMBAD DB spectra, roughly 1 000 spectra with S/N>10 were randomly
selected from LAMOST DR5. Most of those 1 000 spectra are different types of
star, together with galaxies and QSOs. DB spectra are ensured to be excluded
by careful spectral inspections. Similar to RF method applied to identify DAs,
we used all unsmoothed 45 DB and $\sim$1 000 non-DB spectra to construct the
supervised DB classifier for the RF algorithm. All flux values of a spectrum
are adopted as parameters. The largest weight is given to parameters in the
region of Helium absorption line wings. A simple DB or non-DB classification
is used. An object is classified as a DB candidate, when its probability of
being DB star is greater than 50%. Or this object will be classified as non-
DB. In the final step, all spectra in DR 3, 4 & 5 are fed to the classifier,
DB candidates are obtained.

There are 12 572 DB candidates selected by the RF algorithm. After visual
inspection, 182 spectra of 166 sources were found to be bona fide DBs. After
cross-matching with previous published catalogs, 46 DBs are new
identifications (Kleinman et al., 2004, 2013; Kepler et al., 2015, 2016; Guo
et al., 2015b). We believe that higher contamination rate in DB selection is
caused by smaller training sample size relative to DA training sample. In
addition, a second training is applied to distinguish DA and A star in DA
machine learning selection.

Figure 4: Balmer line fitting examples for J041010.37+180222.8 (upper panel,
S/N=107) and J071004.93+292403.2 (lower panel, S/N=28). For both cases, the
black solid lines are observed and normalised DA spectra, while red dashed
lines are the best fit model. From bottom to top of each panel, fitted
absorption lines are H$\beta$, H$\gamma$, H$\delta$, and H$\epsilon$,
respectively.

###  2.4 Other WD spectral types

Besides DA and DB stars, other spectral types of WD are identified as well, as
a result of our effort in searching for DA stars. They are from the colour-
colour cut selection method from Eisenstein et al. (2006), Girven et al.
(2011) and visual inspection of spectra that are classified as WDMagnetic,
DoubleStar and CarbonWD. Colour-colour cut from Eisenstein et al. (2006)
yielded more types of WD than any other methods. But not all LAMOST sources
have SDSS photometry, so WD types except DA and DB are highly incomplete.

There are 5 DAZs, 4 DBZs and 2 DBAZs identified in this work. Two of five DAZs
are classified as WD by LAMOST pipeline, Three of four DBZs and one of two
DBAZs are selected as DB candidates by RF algorithm. The rest $3+1+1=5$ are
discovered by Eisenstein’s colour cut method. Based on a rough estimation, the
fraction of those special metal polluted WDs in Eisenstein’s colour cuts
selected WD candidates is about $5/43\,461=0.011\%$, and the fraction of this
colour cuts selected candidates in LAMOST DR3, 4 & 5 that have SDSS photometry
is $43\,461/1\,455\,566=2.98\%$. Therefore, the number of those special WDs
that have been missed in LAMOST because they do not have SDSS photometry is
$(4\,740\,458-1\,455\,566)\times(0.011\%\times 2.98\%)\approx 11$. Besides
those three types of WDs, magnetic WDs (DAH, DBH, and DAP) mainly come from
pipeline classified WDMagnetic, while pipeline classified DoubleStar
identified most WDMS binaries and CVs. And all the spectral types identified
in this work with their corresponding numbers are listed in Table. 2. A small
part of basic parameters of all WDs identified in LAMOST DR 3, 4 & 5,
including designation, ra, dec, observation date, unique spectral ID, and WD
subtype, has shown in Table. 3.

##  3 Parameter determination

###  3.1 $T_{\rm eff}$ and log $g$ for DA stars

In order to ensure the accuracy of the derived parameters for DAs, only
spectra with S/N $>15$ in SDSS $g$ band are fitted. For sources with multiple
observations, those with highest $g$ band S/N are used. To estimate the
effective temperature and surface gravity of DA stars, absorption line
profiles from H$\beta$ to H$\epsilon$ were fitted to theoretical spectral
models. Before performing the spectral fitting, both the observed and model
absorption line profiles were trimmed and normalised following standard
procedures (Liebert, Bergeron, & Holberg, 2005). The next step is to use a
minimisation technique to fit the line profile. The technique adopted here is
the well known non-linear least-squares method of Levenberg-Marquardt, that is
based on a steepest descent method. To fit the best model template, the open
source idl package mpfit was used (Markwardt, 2009). The DA atmosphere models
used here are provided by D. Koester (2015, private communication) and are
based on those described in Koester (2010). The errors for $T_{\rm eff}$ and
log $g$ were determined by stepping the parameters about the minimum
$\upchi^{2}$. The difference, which is calculated between each current minimum
$\upchi^{2}$ and the previous true minimum $\upchi^{2}$, corresponds to
1$\sigma$ for a given number of free model parameters is regarded as the
error.

Notably, we introduced Gaia $G\rm_{BP}$-$G\rm_{RP}$ colour into the spectral
fitting process. First, a sample of SDSS identified DAs with relatively high
precision $T_{\rm eff}$ is constructed. Next, an empirical relation is
established between $T_{\rm eff}$ and their corresponding Gaia colour. Then
for a new DA spectrum to be fitted, an initial effective temperature value was
given by the empirical relation, based on its Gaia colour. The initial value
was then used as one input parameter in mpfit code to start model fitting
iterations (More details in Zhang et al. in prep). After this preparation,
it’s the same pure conventional spectral fitting to theoretical model spectra
to obtain the final $T_{\rm eff}$ and log $g$. By using Gaia data in this way,
the final effective temperature will be determined more robustly and
accurately than our previous study (Guo et al., 2015b). Two examples of Balmer
line fitting are shown in Fig.4. For comparison purposes, we chose one
spectrum with high S/N (J041010.37+180222.8), and another spectrum with low
S/N (J071004.93+292403.2). Figure 5 shows a $\upchi^{2}$ contour plot of
$T_{\rm eff}$ and log $g$ for the source J041010.37+180222.8. The best-fitted
values for $T_{\rm eff}$ and log $g$, together with their uncertainties are
estimated from the minimum converged residual $\upchi^{2}$. The median error
of $T_{\rm eff}$ and log $g$ in our DA sample is roughly 8% and 4%,
respectively.

Figure 5: $\upchi^{2}$ contour plot of $T_{\rm eff}$ and log $g$ determination
for DA J041010.37+180222.8. Red cross represents final result with its
uncertainties.

###  3.2 $T_{\rm eff}$ and log $g$ for DB stars

To ensure the number of DB stars with parameters that can be compared with the
literature, we adopt a S/N limit of 10. The DB spectrum with highest S/N was
chosen for model fitting in the case that a source has multiple spectra. Also,
because there can be a large number of helium absorption lines, the fitting
process is complicated by their normalisation. Therefore, the parameter
determination for DB spectrum is usually done by fitting the entire spectrum
to the theoretical model. But in this case, flux calibration errors may affect
the accuracy of parameter estimation. Flux calibration is difficult for LAMOST
spectra, owing to e.g. flat-fielding over large fields of view, use of pseudo-
standard stars, and possible unknown reddening (Du et al., 2016). To evaluate
which is more suitable for LAMOST DB spectral fitting, by fitting only Helium
absorption lines after continuum normalisation (similar to DA spectral
fitting) or fitting the entire flux calibrated spectrum directly, a sample of
a few tens of known DB stars from Koester & Kepler (2015) is selected to
perform a less formal test. Those DB stars are common sources of our LAMOST DB
sample and DB catalogue from Koester & Kepler (2015) with relatively small
errors of derived $T_{\rm eff}$ and log $g$. Two sets of parameters are
derived from these two different methods, who performed on LAMOST spectra.
Next, both results were compared with SDSS catalogue values, and we found that
fitting the entire flux calibrated spectrum yielded more consistent results.
Therefore, we chose this method despite flux calibration concerns. The DB
models used in the fits were pure He models, kindly provided by Koester
(2010). Fig. 6 shows two examples of DB stars where the entire spectra were
fitted by models. One is DB spectrum with high S/N (J164718.38+322832.8,
S/N=57), while the other has lower S/N (J012148.23-001053.0, S/N=29). The
best-fitted $T_{\rm eff}$ and log $g$, as well as their uncertainties are also
obtained from the minimum converged residual $\upchi^{2}$. It is noted that
the effective temperature and surface gravity for DB training sample we
adopted ranges from 11 722 K to 33 894 K and 7.6 to 8.7 dex, respectively,
according to SIMBAD records. Therefore, even though these ranges should cover
most of DB stars, it is still possible that a small number of DBs with $T_{\rm
eff}$ and log $g$ outside these ranges are missing in our DB catalogue.

Figure 6: DB Helium absorption lines model fit comparison between
J164718.38+322832.8 (upper panel, S/N=57) and J012148.23-001053.0 (lower
panel, S/N=29). The black solid lines are observed DB spectra, while red
dashed lines are best fit model spectra.

###  3.3 Mass and cooling age

Once the $T_{\rm eff}$ and log $g$ are obtained from the model fitting, their
mass and cooling age can be estimated based on evolutionary models (Fontaine,
Brassard, & Bergeron, 2001) 333The cooling model can be downloaded from the
Web site: http://www.astro.umountreal.ca/~bergeron/CoolingModels/.. For DAs,
the cooling models in Wood (1995) was used for the carbon-core with thick
($q_{\rm H}=M_{\rm H}/M_{\star}=10^{-4}$) hydrogen layers with $T_{\rm eff}$
greater than 30,000 K. For models with effective temperature less than 30,000
K, the cooling models for carbon-oxygen cores in Fontaine, Brassard, &
Bergeron (2001) with thick ($q_{\rm H}=10^{-4}$) hydrogen layers are used. For
DBs, the cooling models in Wood (1990) was adopted for the carbon-core with
thick ($q_{\rm He}=M_{\rm He}/M_{\star}=10^{-4}$) helium layers (Bergeron,
Leggett, & Ruiz, 2001).

An example of mass and cooling age determination is demonstrated in Figure 7.
The resulting distributions of mass and cooling age are shown in Figure 8 and
Figure 11, respectively. There are 1316 DAs and 70 DBs with good quality
spectra that can be used to construct these distributions.

Figure 7: One example of mass and cooling age determination, based on
effective temperature and surface gravity. Black cross represents the location
of this example with uncertainties in the effective temperature vs. surface
gravity space. Different lines represent theoretical models with correspondent
mass. Determined mass and cooling age are shown in the upper left with their
errors.

Looking at Fig. 8, the DA mass range is from 0.3 M⊙ to 1.2 M⊙, with a peak
near 0.62 M⊙. This is in agreement with the mean mass of 0.613 M⊙ from
Tremblay, Bergeron, & Gianninas (2011) and our previous research (Guo et al.,
2015b). But our peak mass is slightly less massive than the mean mass of 0.649
M⊙ from Kepler et al. (2015). As is well established in the literature
(Rebassa-Mansergas et al., 2015, and references therein) as well as in Guo et
al. (2015b), two obvious, non-single Gaussian distribution features present
near 0.4 M⊙ and 1.0 M⊙. However, these features are not evident in our
combined DA mass distribution of DR 1-5.

Figure 8: Distributions of derived DA parameters, including DAs with updated
parameters from LAMOST DR2. From top to bottom: mass, effective temperature,
surface gravity, cooling age and inverted parallax from Gaia DR2.

Of all the fitted LAMOST DAs, 506 stars are found to have fitted parameters in
the SDSS DR14 white dwarf catalogue (Kepler et al., 2019). In Fig. 9, we
compare our results with Kepler et al. (2019). In general, both sets of
results are in good agreement. Sources common to both studies with higher S/N
LAMOST spectra exhibit higher consistency between the studies. Also, the
derived surface gravities and thus corresponding masses are more discrepant at
the high and low ends. Our study systematically underestimates masses at the
high end, and overestimates mass at the low end, relative to the SDSS WD
study. In terms of S/N, the difference is displayed clearly in the bottom
panel of Fig. 9. Regarding DAs with LAMOST spectra S/N of less than $\sim$50,
the SDSS spectra quality are obviously better than LAMOST spectra. However, as
for DAs with LAMOST spectra S/N of greater than 50, the LAMOST spectra quality
are clearly better. We suggest our derived parameters are reliable for S/N
above 30. Similarly, there are 1059 stars found to have fitted parameters in
the Gaia DR2 WD catalogue (Gentile Fusillo et al., 2019). In Fig. 10, our
parameters and results from Gentile Fusillo et al. (2019) are compared.
Results from both catalogues are generally agree with each other. However, the
derived surface gravity and mass data are clearly more disperse than the data
from comparisons between LAMOST and SDSS, despite S/N of LAMOST spectra. It is
understandable that parameters like surface gravity and mass derived from
spectral fitting are generally more accurate and reliable. Moreover, derived
$T_{\rm eff}$ from $Gaia$ are much more consistent with LAMOST $T_{\rm eff}$
when they are low. This implies derived $T_{\rm eff}$ from $Gaia$ for
relatively cool WDs are generally reliable, while for hotter WDs, derived
$T_{\rm eff}$ should be used cautiously.

Figure 9: Comparisons between LAMOST DA parameters (DAs with updated
parameters from LAMOST DR2 are also included) and SDSS parameters from Kepler
et al. (2019). From top to bottom: mass, effective temperature, surface
gravity and S/N. Black circles represent DAs with S/N of LAMOST spectra
between 10 and 30, while blue crosses are DAs with S/N of LAMOST spectra
greater than 30. The red solid lines are unit slope relation. Figure 10:
Comparisons between LAMOST DA parameters (DAs with updated parameters from
LAMOST DR2 are also included) and Gaia DR2 WD parameters from Gentile Fusillo
et al. (2019). From top to bottom: mass, effective temperature and surface
gravity. Black circles represent DAs with S/N of LAMOST spectra between 10 and
30, while blue crosses are DAs with S/N of LAMOST spectra greater than 30. The
red solid lines are unit slope relation.

With respect to the parameter distributions of the 70 relatively high S/N DBs,
the peak in mass is located near 0.65 M⊙, and the peak in log $g$ distribution
is around 8.0. These distributions are consistent with the literature
(Eisenstein et al., 2006; Kleinman et al., 2013). It is difficult to draw any
further conclusions from these distributions, because there are so few
sources.

Figure 11: Distributions of derived DB parameters. From top to bottom: mass,
effective temperature, surface gravity, cooling age and inverted parallax from
Gaia DR2.

Among the 70 DBs with derived parameters, 42 have parameters in Kleinman et
al. (2013) and Koester & Kepler (2015) , but only 11 sources have derived
masses. In Fig. 12, from top to bottom panel, these are comparisons of mass,
effective temperature, surface gravity and S/N between our results and results
from Kleinman et al. (2013) and Koester & Kepler (2015), respectively. Based
on these direct comparisons, our results are generally consistent with results
from SDSS. It is also true that DBs with higher S/N tend to have more
consistent parameters than DBs with lower S/N. And SDSS DB spectra have higher
S/N than SDSS spectra, when the S/N of LAMOST DBs are less than $\sim$ 50\.
Even though there are only three sources, it’s likely the opposite when the
S/N of LAMOST DBs are greater than $\sim$ 50.

Figure 12: Comparisons between LAMOST DB parameters and SDSS parameters from
Kleinman et al. (2013) and Koester & Kepler (2015). From top to bottom: mass,
effective temperature, surface gravity and S/N. Black circles represent DBs
with S/N of LAMOST spectra between 10 and 20, while blue crosses are DAs with
S/N of LAMOST spectra greater than 20. The red solid lines are unit slope
relation.

##  4 On going and future WD candidate selection for LAMOST

We have been selecting potential WD targets for future, low-resolution, LAMOST
spectral fibre selection. In this section, we describe our pre-Gaia DR2
criteria for the second phase survey. Even though with the release of Gaia 2nd
data release, a white dwarf candidates sample as large as 486 641 has been
revealed (Gentile Fusillo et al., 2018), and their $T_{\rm eff}$, log $g$,
radii and mass can be inferred from accurate photometry and trigonometric
parallax. However, the importance of obtaining the optical white dwarf spectra
can not be neglected. One important application is to discover more rare WDs
with emission lines caused by gaseous debris disk or irradiation from unseen
substellar object (Gänsicke et al., 2006; Melis et al., 2012; Guo et al.,
2015a; Manser et al., 2019). Another example is to identify more metal
polluted WDs (DZs), which can be a unique tool to analyse the chemical
composition of their tidally disrupted planetesimal (Gänsicke et al., 2012;
Farihi, Gänsicke & Koester, 2013). As a matter of fact, in order to obtain WD
optical spectra, future large multi-object spectroscopic surveys are planning
to observe these white dwarf candidates from Gaia. For instance, SDSS-V
(Kollmeier et al., 2017), 4most (de Jong et al., 2012), WEAVE (Dalton et al.,
2012), and DESI (DESI Collaboration et al., 2016).

At the end of the LAMOST first phase survey in 2017 June, we began a process
of selecting WD candidates, based on reduced proper motion. The photometric
data we used is taken from the Xuyi Schmidt Telescope Photometric Survey of
the Galactic Anti-center (Liu et al., 2014; Guo et al., 2018, XSTPS-GAC) and
Pan-STARRS (Kaiser et al., 2010), while the proper motion data are from the
Gaia-PS1-SDSS (Tian et al., 2017, GPS1) proper motion catalog. XSTPS-GAC is a
photometric sky survey in the SDSS $gri$ bands, and because LAMOST sources are
selected from XSTPS-GAC, it is highly suitable for WD candidate
identification. The total number of sources in XSTPS-GAC is 110 168 720, and
after cross-matching with GPS1 within 3 arcsec, there are 56 059 242 sources
in common. It is worth mentioning that this is a simple direct cross-matching
without considering the epochs of observations and proper motion of stars. We
use equation 1 to calculate reduced proper motion, and plot this against $g-i$
in order to identify WD candidates, where Fig. 13 shows our exact parameter
cuts.

Common sources are plotted in the $g$-$i$ colour versus RPM space, over-
plotted with the density contours. Red triangles represent 2 030 known DAs
among these common sources, while blue triangles represent 127 known DBs in
the same sample. Based on their location, WDs should locate in the same
region. Therefore, we defined a triangle region to separate the WDs and the
other types of star. The triangle region is defined by cyan solid line, X axis
and Y axis. Black dots are common sources locate in the defined region, which
represent selected white dwarf candidates.

Our reduced proper motion cuts yielded 30 441 WD candidates. Next, we cross-
matched these objects with the literature, finding 20 628 sources are
previously unrecognised WD candidates (at that time). These candidates were
entered into the target selection software designed for LAMOST. Some of those
white dwarf candidates have already been observed and included in DR6, while
the rest will appear in the 2nd phase.

$RPM=g+5\times log(PM)+5$ (1)

Figure 13: Colour g-i versus RPM. The coloured density map and contours
demonstrate the majority of common stars locate at the central region. Red
triangles represent known DAs in the common source sample, while blue
triangles represent known DBs. The cyan solid line is defined to separate WDs
from majority of stars. The black dots are selected white dwarf candidates,
based on the RPM approach.

After the second release of Gaia data in 2018 April, Gentile Fusillo et al.
(2018) has revealed a white dwarf candidate sample as large as 486 k.
Unfortunately, our selection of WDs for LAMOST second phase has completed in
2017. Nonetheless, plan has been made to utilise this high fidelity catalog to
form a proper sample for LAMOST to observe in the future.

##  5 Summary

In this work, we study the DAs and DBs identified in LAMOST DR5. The LAMOST
pipeline classification, colour-colour cut and random forest method were
utilised to select DA candidates. Visual inspection produced 2 620 authentic
DA spectra. For DBs, a random forest, machine learning algorithm was used to
select the candidates. From 12 572 DB candidates, 182 were visually confirmed.
Regarding the efficiency, larger training sample in the future can definitely
be helpful. After cross-matching with SIMBAD and the literature, 393 DAs and
46 DBs are found to be new identifications.

Those identified WDs were analysed. For all DAs where their spectral S/N
$>10$, and DBs with same S/N $>10$, their spectra were fitted with white dwarf
atmosphere models to derive effective temperature and surface gravity
(Koester, 2010). From these two parameters the mass and cooling age were
calculated from evolutionary models.

Proper motions, magnitude and parallax of Gaia DR2 are also provided in our
catalog (Table. 4). In addition, distributions of mass, effective temperature,
surface gravity, cooling age and distance were built to study the property of
our sample.

For DAs, the peak of the mass distribution is in general agreement with
previous results. Both low- and high-mass residuals are present in the mass
distributions. For DBs, the peak of the mass distribution is located around
0.65 M⊙, and also consistent with other studies. However, there are only 70
DBs with sufficiently high S/N to derive reliable parameters, and the
resulting distributions are too sparsely populated to draw any conclusions.
The parameters of LAMOST DAs and DBs have been compared for sources in common
with previous work, and found to be in good agreement for spectra with
relatively high S/N. We also found that for spectra with LAMOST S/N less than
$\sim$ 50, SDSS spectra tend to have larger S/N, while for spectra with S/N
greater than $\sim$ 50, LAMOST spectra have larger S/N.

Even after the release of Gaia DR2 (Gaia Collaboration, et al., 2018a) and the
white dwarf candidates catalog in Gaia (Gentile Fusillo et al., 2018), the
observation of optical white dwarf spectra is still of great importance.

Optical spectral identification is of increasing importance in the Gaia era.
Therefore, we selected 20 628 white dwarf candidates from XSTPS-GAC and GPS1,
then put them into the input catalog of low-resolution observation for the
transition year and 2nd phase of LAMOST, which began in 2017. Since the white
dwarf candidates catalog from Gaia DR2 has been published, we will try to add
those observable candidates into LAMOST inout catalog in the near future as
well.

## Acknowledgments

We thank the anonymous referee for helpful suggestions and advices, which
improved this paper a lot. We thank M.Barlow, J.Farihi and A.Swan for a
careful reading of the manuscript and helping with the improvement of English
writing. We also thank D. Koester and P. Bergeron for providing white dwarf
models. Balmer/Lyman lines in the models were calculated with the modified
Stark broadening profiles of Tremblay & Bergeron (2009), kindly made available
by the authors. This work is supported by the National Natural Science
Foundation of China (Grant No. 11890694, No. 11473001 and 11078006). The
authors also acknowledge support by the National Key Basic Research Program of
China (Grant No. 2014CB845700). We also acknowledge the support from the 2m
Chinese Space Station Telescope project: CMS-CSST-2021-A10. This work was
partially supported by the Scholar Program of Beijing Academy of Science and
Technology (DZ:BS202002). This work is also supported by the China
Postdoctoral Science Foundation (Grant No. 2017M610695) and the Astronomical
Big Data Joint Research Centre, co-founded by the National Astronomical
Observatories, Chinese Academy of Sciences and the Alibaba Cloud.

The LAMOST FELLOWSHIP is supported by Special Funding for Advanced Users,
budgeted and administrated by the Centre for Astronomical Mega-Science,
Chinese Academy of Sciences.

The Guo Shou Jing Telescope (the Large Sky Area Multi-Object Fibre
Spectroscopic Telescope, LAMOST) is a National Major Scientific Project which
is built by the Chinese Academy of Sciences, funded by the National
Development and Reform Commission, and operated and managed by the National
Astronomical Observatories, Chinese Academy of Sciences.

## DATA AVAILABILITY

The spectra data underlying this article are publicly available from LAMOST
archive (http://dr5.lamost.org/). Table 3, 4, 5, and 6 are partially shown in
the article. They are fully accessible through publisher in supplementary
material. Table 5 and 6 are WDs identified in our previous work (LAMOST DR2)
with updated classifications and parameters.

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Table 3:  Basic parameters of WDs from LAMOST DR 3, 4 & 5\.
(Only part of the catalogue is shown here. The full table can be found in the
supplementary material.)

GIDa |  ObsIDb |  Designationc | RA | DEC |  Obs-dated |  Mjd-Planid$\\_$spid-Fiberide | Type
---|---|---|---|---|---|---|---
1$\\_$2 | 247515227 | J002633.24+390902.9 | 6.638503 | 39.150817 | 2014-09-10 |  56911-HD002951N381926B01$\\_$sp15-227 | DAZ
1$\\_$2 | 354311163 | J002633.13+390904.0 | 6.6380824 | 39.151121 | 2015-09-14 |  57280-M31007N36M1$\\_$sp11-163 | DAZ
2$\\_$2 | 249301140 | J041010.37+180222.8 | 62.543227 | 18.039691 | 2014-09-26 |  56927-GAC062N19B1$\\_$sp01-140 | DA
2$\\_$2 | 318401139 | J041010.37+180222.8 | 62.543227 | 18.039691 | 2015-02-13 |  57067-GAC062N19B2$\\_$sp01-139 | DA
3$\\_$2 | 250301120 | J042355.72+162113.2 | 65.982207 | 16.353693 | 2014-10-05 |  56936-GAC065N18B1$\\_$sp01-120 | DA
3$\\_$2 | 250401120 | J042355.78+162114.9 | 65.982452 | 16.354149 | 2014-10-05 |  56936-GAC065N18B2$\\_$sp01-120 | DA
4$\\_$2 | 250407081 | J042839.47+165811.7 | 67.164496 | 16.969927 | 2014-10-05 |  56936-GAC065N18B2$\\_$sp07-081 | DA
4$\\_$2 | 420109239 | J042839.40+165812.0 | 67.1642003 | 16.9700186 | 2016-02-05 |  57424-KP042325N164638B01$\\_$sp09-239 | DA
5$\\_$2 | 252902097 | J024746.29+000331.6 | 41.942909 | 0.0587914 | 2014-10-13 |  56944-EG025338N015809M01$\\_$sp02-097 | DA
5$\\_$2 | 367416195 | J024746.39+000331.1 | 41.943312 | 0.058658 | 2015-10-08 |  57304-EG025335S013827B01$\\_$sp16-195 | DA
6$\\_$2 | 252908132 | J025817.87+010946.0 | 44.574461 | 1.1627782 | 2014-10-13 |  56944-EG025338N015809M01$\\_$sp08-132 | DA+M
6$\\_$2 | 300710119 | J025817.87+010946.0 | 44.574461 | 1.1627782 | 2015-01-20 |  57043-EG030739N012421M01$\\_$sp10-119 | DA+M
7$\\_$3 | 254115228 | J040342.10+145928.7 | 60.9254278 | 14.9913211 | 2014-10-15 |  56946-HD040531N141710B01$\\_$sp15-228 | DA
7$\\_$3 | 381910034 | J040342.21+145929.8 | 60.925876 | 14.991617 | 2015-11-03 |  57330-GAC062N15B1$\\_$sp10-034 | DA
7$\\_$3 | 382010034 | J040342.19+145928.4 | 60.925814 | 14.991239 | 2015-11-03 |  57330-GAC062N15B2$\\_$sp10-034 | DA
8$\\_$2 | 256106072 | J225745.89+074320.5 | 344.44124 | 7.722373 | 2014-10-25 |  56956-EG224840N075042M01$\\_$sp06-072 | DA
8$\\_$2 | 380401098 | J225745.89+074320.5 | 344.44124 | 7.722373 | 2015-11-01 |  57328-EG225829N094931M01$\\_$sp01-098 | DA
9$\\_$2 | 256113149 | J225605.44+081936.3 | 344.0227 | 8.32677 | 2014-10-25 |  56956-EG224840N075042M01$\\_$sp13-149 | DA
9$\\_$2 | 380402065 | J225605.44+081936.3 | 344.0227 | 8.32677 | 2015-11-01 |  57328-EG225829N094931M01$\\_$sp02-065 | DA
10$\\_$2 | 256201054 | J055944.97+171203.3 | 89.937392 | 17.20094 | 2014-10-25 |  56956-GAC090N18M1$\\_$sp01-054 | DA
10$\\_$2 | 420409046 | J055944.97+171203.4 | 89.937412 | 17.200946 | 2016-02-06 |  57425-GAC089N16M1$\\_$sp09-046 | DA
11$\\_$2 | 256601015 | J061518.94+153059.4 | 93.828958 | 15.5165 | 2014-10-26 |  56957-GAC093N17M1$\\_$sp01-015 | CV
11$\\_$2 | 400112059 | J061518.94+153059.4 | 93.828958 | 15.5165 | 2016-01-04 |  57392-GAC092N13M1$\\_$sp12-059 | CV
12$\\_$2 | 257606145 | J071004.93+292403.2 | 107.52056 | 29.400907 | 2014-11-01 |  56963-GAC105N29B1$\\_$sp06-145 | DA
12$\\_$2 | 281116178 | J071004.93+292403.2 | 107.52056 | 29.400907 | 2014-12-18 |  57010-GAC108N27B1$\\_$sp16-178 | DA
13$\\_$3 | 259201037 | J075853.02+161645.1 | 119.72092 | 16.279214 | 2014-11-04 |  56966-GAC120N18B1$\\_$sp01-037 | CV
13$\\_$3 | 392716175 | J075853.02+161645.1 | 119.72092 | 16.279214 | 2015-12-21 |  57378-GAC120N14B1$\\_$sp16-175 | CV
13$\\_$3 | 392816175 | J075853.02+161645.1 | 119.72092 | 16.279214 | 2015-12-21 |  57378-GAC120N14B2$\\_$sp16-175 | CV
14$\\_$2 | 265114068 | J060911.91+352549.3 | 92.299661 | 35.430376 | 2014-11-12 |  56974-GAC094N35B1$\\_$sp14-068 | DA
14$\\_$2 | 385314070 | J060912.00+352549.1 | 92.300011 | 35.430329 | 2015-12-01 |  57358-GAC094N35B2$\\_$sp14-070 | DA
15$\\_$2 | 266807242 | J022301.66+061649.5 | 35.756946 | 6.2804389 | 2014-11-16 |  56978-EG021841N081050M01$\\_$sp07-242 | CV
15$\\_$2 | 474703167 | J022301.66+061649.5 | 35.756946 | 6.280439 | 2016-11-02 |  57695-EG022616N061733M01$\\_$sp03-167 | CV

  * •

Notes:
aGroup ID. i.e. “1_2" means group 1 has 2 spectra.
bObservation ID, which is also unique for each spectrum.
cDesignation from LAMOST. The exact number could be slight different for the
same group.
dObservation date of the spectrum.
eUnique spectrum ID.

Table 4: Determined WD parameters and parameters from Gaia DR2.
(Only part of the catalogue is shown here. The full table can be found in the
supplementary material.)

[hb]

GIDa |  ObsIDb |  S/Ngc | $T_{\rm eff}$ |  log $g$ | Mass | Age |  Plxd |  PMrae |  PMdece |  magGf | Type
---|---|---|---|---|---|---|---|---|---|---|---
|  |  | (K) |  |  (M⊙) | (Myr) | (mas) | (mas/yr) | (mas/yr) |  |
1$\\_$2 | 247515227 | 11 |  |  |  |  |  15.8342$\pm$0.066 |  142.505$\pm$0.102 |  -130.002$\pm$0.087 | 15.800 | DAZ
1$\\_$2 | 354311163 | 3 |  |  |  |  |  15.8342$\pm$0.066 |  142.505$\pm$0.102 |  -130.002$\pm$0.087 | 15.800 | DAZ
2$\\_$2 | 249301140 | 105 |  |  |  |  |  29.3892$\pm$0.0572 |  72.19$\pm$0.14 |  -85.906$\pm$0.096 | 14.244 | DA
2$\\_$2 | 318401139 | 124 |  15312$\pm$1369 |  8.04$\pm$0.27 |  0.64$\pm$0.16 |  199$\pm$114 |  29.3892$\pm$0.0572 |  72.19$\pm$0.14 |  -85.906$\pm$0.096 | 14.244 | DA
3$\\_$2 | 250301120 | 22 |  |  |  |  |  22.2272$\pm$0.0519 |  114.412$\pm$0.103 |  -27.715$\pm$0.079 | 14.347 | DA
3$\\_$2 | 250401120 | 39 |  20526$\pm$1688 |  8.24$\pm$0.27 |  0.77$\pm$0.17 |  109$\pm$73 |  22.2272$\pm$0.0519 |  114.412$\pm$0.103 |  -27.715$\pm$0.079 | 14.347 | DA
4$\\_$2 | 250407081 | 115 |  |  |  |  |  20.8952$\pm$0.0567 |  102.692$\pm$0.115 |  -26.885$\pm$0.068 | 14.074 | DA
4$\\_$2 | 420109239 | 116 |  26029$\pm$1851 |  8.14$\pm$0.29 |  0.72$\pm$0.18 |  27$\pm$4 |  20.8952$\pm$0.0567 |  102.692$\pm$0.115 |  -26.885$\pm$0.068 | 14.074 | DA
5$\\_$2 | 252902097 | 9 |  |  |  |  |  8.1485$\pm$0.0776 |  130.453$\pm$0.136 |  -41.637$\pm$0.125 | 16.488 | DA
5$\\_$2 | 367416195 | 35 |  19475$\pm$1519 |  8.07$\pm$0.27 |  0.66$\pm$0.16 |  92$\pm$65 |  8.1485$\pm$0.0776 |  130.453$\pm$0.136 |  -41.637$\pm$0.125 | 16.488 | DA
6$\\_$2 | 252908132 | 7 |  |  |  |  |  |  |  | 17.818 | DA+M
6$\\_$2 | 300710119 | 5 |  |  |  |  |  |  |  | 17.818 | DA+M
7$\\_$3 | 254115228 | 101 |  14421$\pm$2543 |  8.43$\pm$0.27 |  0.88$\pm$0.17 |  442$\pm$283 |  24.0527$\pm$0.0541 |  141.19$\pm$0.107 |  -24.07$\pm$0.084 | 15.038 | DA
7$\\_$3 | 381910034 | 53 |  |  |  |  |  24.0527$\pm$0.0541 |  141.19$\pm$0.107 |  -24.07$\pm$0.084 | 15.038 | DA
7$\\_$3 | 382010034 | 42 |  |  |  |  |  24.0527$\pm$0.0541 |  141.19$\pm$0.107 |  -24.07$\pm$0.084 | 15.038 | DA
8$\\_$2 | 256106072 | 7 |  |  |  |  |  4.557$\pm$0.2331 |  -15.071$\pm$0.374 |  -40.83$\pm$0.269 | 18.302 | DA
8$\\_$2 | 380401098 | 12 |  |  |  |  |  4.557$\pm$0.2331 |  -15.071$\pm$0.374 |  -40.83$\pm$0.269 | 18.302 | DA
9$\\_$2 | 256113149 | 6 |  |  |  |  |  6.3772$\pm$0.1 |  -19.921$\pm$0.199 |  -1.312$\pm$0.136 | 16.738 | DA
9$\\_$2 | 380402065 | 37 |  23254$\pm$2294 |  7.65$\pm$0.34 |  0.47$\pm$0.13 |  20$\pm$7 |  6.3772$\pm$0.1 |  -19.921$\pm$0.199 |  -1.312$\pm$0.136 | 16.738 | DA
10$\\_$2 | 256201054 | 57 |  |  |  |  |  12.713$\pm$0.0718 |  0.726$\pm$0.121 |  -19.04$\pm$0.1 | 15.841 | DA
10$\\_$2 | 420409046 | 87 |  18982$\pm$1348 |  8.31$\pm$0.25 |  0.81$\pm$0.16 |  162$\pm$98 |  12.713$\pm$0.0718 |  0.726$\pm$0.121 |  -19.04$\pm$0.1 | 15.841 | DA
11$\\_$2 | 256601015 | 4 |  |  |  |  |  1.2902$\pm$0.1754 |  -0.069$\pm$0.31 |  -8.973$\pm$0.311 | 17.961 | CV
11$\\_$2 | 400112059 | 3 |  |  |  |  |  1.2902$\pm$0.1754 |  -0.069$\pm$0.31 |  -8.973$\pm$0.311 | 17.961 | CV
12$\\_$2 | 257606145 | 19 |  |  |  |  |  14.4462$\pm$0.0781 |  -1.383$\pm$0.114 |  -101.355$\pm$0.102 | 15.515 | DA
12$\\_$2 | 281116178 | 28 |  15710$\pm$1559 |  7.97$\pm$0.31 |  0.60$\pm$0.17 |  162$\pm$95 |  14.4462$\pm$0.0781 |  -1.383$\pm$0.114 |  -101.355$\pm$0.102 | 15.515 | DA
13$\\_$3 | 259201037 | 43 |  |  |  |  |  4.79$\pm$0.0572 |  -26.015$\pm$0.116 |  -0.264$\pm$0.063 | 15.515 | CV
13$\\_$3 | 392716175 | 26 |  |  |  |  |  4.79$\pm$0.0572 |  -26.015$\pm$0.116 |  -0.264$\pm$0.063 | 15.515 | CV
13$\\_$3 | 392816175 | 41 |  |  |  |  |  4.79$\pm$0.0572 |  -26.015$\pm$0.116 |  -0.264$\pm$0.063 | 15.515 | CV
14$\\_$2 | 265114068 | 16 |  |  |  |  |  20.6106$\pm$0.0851 |  -0.299$\pm$0.107 |  51.212$\pm$0.096 | 15.681 | DA
14$\\_$2 | 385314070 | 33 |  10214$\pm$360 |  8.39$\pm$0.35 |  0.85$\pm$0.23 |  1064$\pm$711 |  20.6106$\pm$0.0851 |  -0.299$\pm$0.107 |  51.212$\pm$0.096 | 15.681 | DA
15$\\_$2 | 266807242 | 34 |  |  |  |  |  1.3651$\pm$0.1253 |  5.159$\pm$0.164 |  -8.974$\pm$0.154 | 17.051 | CV
15$\\_$2 | 474703167 | 43 |  |  |  |  |  1.3651$\pm$0.1253 |  5.159$\pm$0.164 |  -8.974$\pm$0.154 | 17.051 | CV

  * •

Notes:
aGroup ID. i.e. “1_2" means group 1 has 2 spectra.
bUnique ID for each spectrum.
cSignal to Noise ratio in g band. Note only spectra with S/N>=15 in g band are
fitted.
dParallax from Gaia DR2 in mas.
eProper motions in ra and dec from Gaia DR2 in units of mas/yr.
fG band photometry from Gaia DR2.

Table 5: Mis-classified white dwarfs in LAMOST DR2.
(Only part of the catalogue is shown here. The full table can be found in the
supplementary material.)

[hb]

GIDa | RA | DEC |  Designationb |  Mjd-Planid$\\_$spid-Fiberidc | snrg | Old type | Update
---|---|---|---|---|---|---|---
64$\\_$2 | 98.8159 | 2.39865 | J063515.81+022355.1 |  55976-GAC$\\_$099N04$\\_$V1$\\_$sp02-124 | 11.73 |  DA$\\_$in$\\_$nebula? | star
64$\\_$2 | 98.8159 | 2.39865 | J063515.81+022355.1 |  55976-GAC$\\_$099N04$\\_$V5$\\_$sp02-124 | 10.78 |  DA$\\_$in$\\_$nebula? | star
111$\\_$3 | 106.68858 | 22.26037 | J070645.25+221537.3 |  56611-GAC108N21V3$\\_$sp14-199 | 28.55 | DA+M? | star
111$\\_$3 | 106.68858 | 22.26037 | J070645.25+221537.3 |  56621-GAC108N21V1$\\_$sp14-199 | 11.85 | DA+M? | star
111$\\_$3 | 106.68858 | 22.26037 | J070645.25+221537.3 |  56621-GAC108N21V3$\\_$sp14-199 | 15.67 | DA+M? | star
113$\\_$2 | 58.28319 | 34.53968 | J035307.96+343222.8 |  56618-VB057N34V1$\\_$sp08-238 | 17.45 | DAZ | star
113$\\_$2 | 58.28319 | 34.53968 | J035307.96+343222.8 |  56618-VB057N34V2$\\_$sp08-238 | 10.69 | DAZ | star
141$\\_$1 | 80.71046 | 29.65543 | J052250.50+293919.5 |  55859-M5904$\\_$sp15-198 | 3.41 | DA? | star
142$\\_$1 | 10.58862 | 39.37988 | J004221.26+392247.5 |  55862-M6201$\\_$sp16-091 | 5.67 | DA? | star
143$\\_$1 | 12.11577 | 39.62563 | J004827.78+393732.2 |  55862-M6201$\\_$sp16-122 | 5.27 | DA? | star
151$\\_$1 | 89.49879 | 29.20391 | J055759.71+291214.0 |  55876-GAC$\\_$089N28$\\_$B2$\\_$sp04-060 | 5.97 | DA? | star
152$\\_$1 | 89.49431 | 29.98647 | J055758.63+295911.2 |  55876-GAC$\\_$089N28$\\_$B2$\\_$sp15-134 | 3.53 | DA? | star
153$\\_$1 | 91.57595 | 28.03239 | J060618.22+280156.5 |  55876-GAC$\\_$089N28$\\_$B3$\\_$sp06-113 | 4.95 | DA? | star
154$\\_$1 | 89.50101 | 29.54909 | J055800.24+293256.7 |  55876-GAC$\\_$089N28$\\_$B3$\\_$sp15-102 | 7.67 | DA? | star
156$\\_$1 | 88.77986 | 29.0578 | J055507.16+290328.0 |  55876-GAC$\\_$089N28$\\_$B1$\\_$sp04-001 | 5.23 | DA? | star
158$\\_$1 | 53.9205 | 4.24866 | J033540.91+041455.1 |  55886-F8606$\\_$sp05-206 | 5.68 | DA? | star
170$\\_$1 | 71.51261 | 26.14234 | J044603.02+260832.4 |  55890-GAC$\\_$067N28$\\_$M1$\\_$sp01-236 | 5.18 | DA? | star
171$\\_$1 | 74.26587 | 27.71918 | J045703.80+274309.0 |  55890-GAC$\\_$067N28$\\_$M1$\\_$sp06-197 | 6.43 | DA? | star
173$\\_$1 | 106.81713 | 26.6493 | J070716.11+263857.4 |  55890-GAC$\\_$106N28$\\_$M1$\\_$sp01-154 | 9.85 | DA+M? | DA
182$\\_$1 | 50.2794 | 4.86407 | J032107.05+045150.6 |  55892-F9204$\\_$sp04-169 | 8.39 | DBA? | hotSD

  * •

Notes:
aGroup ID. i.e. “1_2" means group 1 has 2 spectra.
bDesignation from LAMOST. The exact number could be slight different for the
same group.
cUnique spectrum ID.

Table 6: DA White dwarfs with updated parameters in LAMOST DR2.
(Only part of the catalogue is shown here. The full table can be found in the
supplementary material.)

[hb]

ObsIDa |  Designationb | Obsdate | RA | DEC | snrg |  Teffc |  loggc |  massc |  agec
---|---|---|---|---|---|---|---|---|---
112211 | J221640.39+012741.2 | 2011-10-24 | 334.168324 | 1.461445 | 10.49 |  10872$\pm$360 |  8.28$\pm$0.36 |  0.78$\pm$0.23 |  740$\pm$400
116148 | J220522.86+021837.5 | 2011-10-24 | 331.345250 | 2.310432 | 14.26 |  13000$\pm$2793 |  7.76$\pm$0.35 |  0.48$\pm$0.16 |  218$\pm$167
403199 | J004128.66+402324.0 | 2011-10-24 | 10.369458 | 40.390026 | 19.99 |  27493$\pm$2182 |  7.60$\pm$0.35 |  0.46$\pm$0.13 |  11$\pm$3
1102134 | J025737.24+264047.8 | 2011-10-27 | 44.405201 | 26.679970 | 15.86 |  10838$\pm$359 |  8.51$\pm$0.33 |  0.93$\pm$0.21 |  1134$\pm$1078
1115183 | J030214.72+285707.4 | 2011-10-27 | 45.561340 | 28.952057 | 13.54 |  16814$\pm$1427 |  7.53$\pm$0.31 |  0.39$\pm$0.10 |  66$\pm$23
1506145 | J071004.83+292402.8 | 2011-10-28 | 107.520140 | 29.400780 | 12.06 |  12000$\pm$3141 |  6.88$\pm$0.50 |  0.21$\pm$0.10 |  113$\pm$147
1615243 | J004036.79+413138.7 | 2011-10-28 | 10.153296 | 41.527443 | 21.71 |  13564$\pm$2707 |  7.83$\pm$0.32 |  0.52$\pm$0.17 |  209$\pm$183
1616129 | J003956.55+422929.5 | 2011-10-28 | 9.985629 | 42.491542 | 10.24 |  9861$\pm$303 |  7.76$\pm$0.55 |  0.47$\pm$0.26 |  472$\pm$266
2101118 | J005340.52+360116.8 | 2011-11-08 | 13.418857 | 36.021358 | 32.82 |  28460$\pm$1577 |  7.85$\pm$0.33 |  0.57$\pm$0.15 |  10$\pm$1
2102081 | J004159.19+362352.3 | 2011-11-08 | 10.496630 | 36.397865 | 10.03 |  22062$\pm$2314 |  7.60$\pm$0.33 |  0.44$\pm$0.13 |  24$\pm$9
6610008 | J032942.79+053755.8 | 2011-11-20 | 52.428301 | 5.632185 | 11.08 |  19155$\pm$1518 |  8.04$\pm$0.27 |  0.65$\pm$0.16 |  91$\pm$67
6807221 | J063532.48+261958.6 | 2011-11-20 | 98.885366 | 26.332951 | 14.00 |  35843$\pm$2393 |  8.00$\pm$0.42 |  0.67$\pm$0.21 |  5$\pm$2
6904155 | J080800.00+290152.5 | 2011-11-20 | 122.000010 | 29.031273 | 19.48 |  25340$\pm$2300 |  7.93$\pm$0.32 |  0.60$\pm$0.15 |  17$\pm$8
7015243 | J004036.79+413138.7 | 2011-11-20 | 10.153296 | 41.527443 | 19.41 |  13000$\pm$2414 |  7.86$\pm$0.35 |  0.53$\pm$0.19 |  249$\pm$201
7516178 | J071004.83+292402.8 | 2011-11-23 | 107.520140 | 29.400789 | 12.04 |  13758$\pm$1742 |  8.16$\pm$0.30 |  0.71$\pm$0.19 |  324$\pm$226
7801231 | J100551.51-023417.8 | 2011-11-24 | 151.464628 | -2.571630 | 19.69 |  20835$\pm$1816 |  7.99$\pm$0.30 |  0.62$\pm$0.17 |  55$\pm$58

  * •

Notes:
aUnique ID for each spectrum.
bDesignation from LAMOST. The exact number could be slight different for the
same group.
cUndated parameters using fitting method adopted in this work.