Searching for Hot Subdwarf Stars in LAMOST DR1-II. Pure spectroscopic identification method for hot subdwarfs

TL;DR

This paper introduces a new machine learning method called HELM for spectroscopic identification of hot subdwarf stars, successfully discovering 56 such stars in LAMOST DR1 data and confirming known spectral features.

Contribution

The paper presents the HELM algorithm, a novel machine learning approach that directly analyzes spectra for hot subdwarf identification without needing photometric data.

Findings

Identified 56 hot subdwarf stars in LAMOST DR1.

Confirmed the two He sequences in the Teff - log(nHe/nH) diagram.

Demonstrated HELM's reliability and applicability to other spectral objects.

Abstract

Employing a new machine learning method, named hierarchical extreme learning machine (HELM) algorithm, we identified 56 hot subdwarf stars in the first data release (DR1) of the Large Sky Area Multi-Object Fibre Spectroscopic Telescope (LAMOST) survey. The atmospheric parameters of the stars are obtained by fitting the profiles of hydrogen (H) Balmer lines and helium (He) lines with synthetic spectra calculated from non-Local Thermodynamic Equilibrium (NLTE) model atmospheres. Five He-rich hot subdwarf stars were found in our sample with their log(nHe/nH) > -1 , while 51 stars are He-poor sdB, sdO and sdOB stars. We also confirmed the two He sequences of hot subdwarf stars found by Edelmann et al. (2003) in Teff - log(nHe/nH) diagram. The HELM algorithm works directly on the observed spectroscopy and is able to filter out spectral properties without supplementary photometric data. The results presented in this study demonstrate that the HELM algorithm is a reliable method to search for hot subdwarf stars after a suitable training is performed, and it is also suitable to search for other objects which have obvious features in their spectra or images.

Tables

Table 1. Table 1: Information for the 74 stars analyzed in this study. From left to right of the table, it gives the LAMOST designation of the objects, right ascension, declination, effective temperature, gravity, helium abundance, spectral classification type, SNR in u band, apparent magnitude in u and g band from SDSS and apparent magnitude in G band from Gaia DR2, respectively.

Designationa	rab	dec	$T_{\mathrm{eff}}$	$\log g$	$\log {\left(n\mathrm{He}/nH\right)}^c$	Sptype	SNR	uSDSS	gSDSS	G GaiaDR2
LAMOST	LAMOST	LAMOST	$\left(K\right)$	($\mathrm{cm}{s}^{-2}$)			u-band	(mag)	(mag)	(mag)
J002124.79+402857.1	5.3532989	40.482537	25850$\pm$ 580	5.42$\pm$0.11	-2.57$\pm$0.18	sdB He4	18.7	-	15.19	15.51
J002355.23+420905.5∗	5.9801396	42.151544	30150$\pm$ 280	5.47$\pm$0.06	-2.31$\pm$0.14	sdB He6	18.6	-	15.46	15.79
J003627.19+271000.7	9.113308	27.166863	-	-	-	MS	45.0	14.93	14.67	14.64
J003801.72+343156.2	9.5071771	34.53228	40850$\pm$ 610	5.49$\pm$0.10	-0.23$\pm$0.09	He-sdOB He33	17.9	-	13.66	13.90
J004949.26+352200.9∗	12.455266	35.366938	34960$\pm$ 690	5.83$\pm$0.12	-1.49$\pm$0.10	sdOB He13	25.3	-	14.54	14.82
J010448.81+362742.4∗	16.203409	36.461784	32260$\pm$ 60	5.74$\pm$0.02	-1.63$\pm$0.03	sdOB He11	90.6	12.55	12.95	12.40
J010945.73+374538.5∗	17.440552	37.760704	29980$\pm$ 100	5.49$\pm$0.03	-3.54$\pm$0.26	sdB He2	25.6	13.96	14.61	13.87
J011857.19-002545.5∗	19.738333	-0.429333	29060$\pm$ 140	5.48$\pm$0.04	-3.16$\pm$0.25	sdB He2	15.7	14.49	14.60	14.82
J013134.51+323723.7	22.893792	32.623252	60390$\pm$ 720	5.48$\pm$0.05	-1.40$\pm$0.10	sdO He8	10.9	-	15.00	15.30
J014710.62+303213.2	26.794254	30.537002	22110$\pm$ 210	5.00$\pm$0.07	-2.05$\pm$0.12	sdB He6	18.8	-	14.10	14.35
J015054.28+310746.7	27.72618	31.129651	28540$\pm$ 180	5.70$\pm$0.04	-1.69$\pm$0.05	sdB He10	16.9	-	13.97	14.32
J020932.45+430712.5∗	32.385219	43.12014	27580$\pm$ 500	5.42$\pm$0.03	-2.73$\pm$0.16	sdB He5	11.8	14.42	14.86	14.34
J022517.07+031218.2	36.3211422	3.2050785	-	-	-	WD	15.1	16.24	16.70	16.95
J023551.35+011845.1	38.963972	1.312544	-	-	-	WD	10.4	16.97	16.41	16.17
J030025.22+003224.3	45.10512	0.54009	-	-	-	MS	13.1	23.89	21.76	20.36
J031756.92+322950.4	49.487181	32.497341	33860$\pm$ 430	6.07$\pm$0.15	-1.62$\pm$0.12	sdB He13	15.9	-	15.58	15.72
J035926.96+270508.6	59.862336	27.08573	35160$\pm$ 380	5.51$\pm$0.04	-2.74$\pm$0.35	sdOB He2	14.0	-	14.97	15.10
J040613.24+465133.6	61.555205	46.859349	-	-	-	MS	15.2	14.77	-	14.59
J051425.36+332344.3	78.605685	33.395662	-	-	-	MS	10.4	-	15.04	13.38
J053656.48+395518.7∗	84.235335	39.92188	38490$\pm$ 350	5.54$\pm$0.07	-0.65$\pm$0.07	sdOB He16	14.7	-	13.67	13.92
J054447.48+272032.0	86.197835	27.342228	-	-	-	WD	10.3	-	17.08	16.93
J055151.32+220437.0	87.96384	22.076954	29610$\pm$ 110	5.66$\pm$0.03	-2.22$\pm$0.05	sdB He5	24.4	-	12.85	13.17
J055227.67+155311.4	88.115311	15.886516	-	-	-	WD	23.1	-	12.52	13.03
J055348.85+325601.7	88.453581	32.93382	30490$\pm$ 110	5.68$\pm$0.02	-2.15$\pm$0.04	sdB He5	44.0	-	14.02	14.17
J055411.88+220459.7	88.549534	22.083273	-	-	-	MS	10.2	-	13.28	13.17
J055926.92+271321.0	89.862203	27.222502	-	-	-	MS	10.9	-	19.20	17.99
J062704.91+345809.5∗	96.770481	34.969325	25080$\pm$ 380	5.26$\pm$0.08	-3.57$\pm$0.62	sdB He1	10.8	-	14.19	14.43
J062836.51+325031.5	97.152155	32.842084	42740$\pm$ 570	5.30$\pm$0.12	0.20$\pm$0.10	He-sdOB He37	21.5	-	14.51	14.71
J063210.36+281041.7	98.043207	28.178276	45130$\pm$ 330	5.51$\pm$0.12	0.33$\pm$0.06	He-sdOB He40	17.7	-	14.82	15.10
J063526.61+323109.8	98.86089	32.519401	-	-	-	MS	11.6	-	15.95	15.15
J063952.15+515700.9	99.967315	51.950267	29720$\pm$ 110	5.37$\pm$0.04	-3.00$\pm$0.73	sdB He1	35.8	-	-	11.96
J064618.36+292013.2∗	101.57652	29.337016	38740$\pm$ 450	5.90$\pm$0.05	$-4.00>$	sdO He0	73.4	-	-	13.59
J064814.13+171056.2	102.05891	17.182305	-	-	-	MS	10.6	-	14.96	13.23
J065446.63+244926.8	103.69431	24.82412	58700$\pm$3600	5.17$\pm$0.05	-2.04$\pm$0.10	sdO He2	55.7	-	13.65	13.99
J065532.98+220349.6	103.88743	22.063784	45090$\pm$ 890	5.62$\pm$0.05	-1.71$\pm$0.08	sdO He6	30.5	-	-	13.70
J065647.77+242958.8	104.19908	24.499685	-	-	-	MS	18.7	-	-	10.19
J065748.42+253251.1	104.45177	25.547541	44930$\pm$1160	6.48$\pm$0.10	$-4.00>$	sdB He19	16.1	-	15.89	16.05
J065816.71+094343.1	104.56965	9.7286415	36270$\pm$ 320	5.03$\pm$0.03	-1.70$\pm$0.08	sdOB He11	17.1	-	13.27	13.59
J070619.19+242910.5	106.57996	24.486267	61820$\pm$6030	5.30$\pm$0.04	-2.00$\pm$0.13	sdO He4	15.0	-	15.77	15.81
J071202.40+113332.4	108.01	11.559014	24720$\pm$ 180	5.10$\pm$0.04	-2.63$\pm$0.07	sdB He5	33.0	-	-	12.46

Table 2. Table 1: Continued

Designationa	rab	dec	$T_{\mathrm{eff}}$	$\log g$	$\log {\left(n\mathrm{He}/nH\right)}^c$	Sptype	SNR	uSDSS	gSDSS	G GaiaDR2
LAMOST	LAMOST	LAMOST	$\left(K\right)$	($\mathrm{cm}{s}^{-2}$)			u-band	(mag)	(mag)	(mag)
J072835.11+280239.1	112.1463	28.044199	86250$\pm$16170	5.77$\pm$0.16	0.04$\pm$0.12	He-sdO He40	10.1	-	15.45	15.78
J073446.14+342120.8	113.69226	34.355805	25510$\pm$ 680	5.15$\pm$0.07	-2.42$\pm$0.09	sdB He6	20.6	-	15.20	15.46
J073756.25+311646.5	114.48439	31.279597	30600$\pm$ 130	5.45$\pm$0.03	-2.47$\pm$0.12	sdB He5	11.2	-	-	13.58
J074121.90+265425.8∗	115.34127	26.907168	29530$\pm$ 460	5.30$\pm$0.07	$-4.00>$	sdB	11.6	-	15.52	15.59
J074435.14+302108.7∗	116.14643†	30.352421	28980$\pm$ 200	5.51$\pm$0.03	-2.95$\pm$0.10	sdB He3	30.6	-	14.39	14.74
J074855.82+304247.0∗	117.23262†	30.713059	30910$\pm$ 110	5.80$\pm$0.03	-2.02$\pm$0.04	sdB He4	31.8	-	13.76	14.06
J075139.26+064604.8	117.91362	6.7680011	39850$\pm$ 180	5.61$\pm$0.04	-0.16$\pm$0.03	He-sdOB He30	39.9	-	13.21	13.50
J075412.37+294957.0∗	118.55157	29.832504	30910$\pm$1230	5.77$\pm$0.28	-1.87$\pm$0.32	sdB He7	14.5	-	14.24	14.57
J075922.99+164601.6	119.845827	16.767125	37930$\pm$ 920	5.25$\pm$0.05	-2.89$\pm$0.27	sdO He1	23.9	13.84	14.94	14.42
J080327.92+342140.6∗	120.86637	34.361297	38130$\pm$1350	5.58$\pm$0.11	-3.28$\pm$0.60	sdO He3	26.1	-	14.75	15.06
J080611.66+334425.6	121.5486	33.740449	-	-	-	WD	10.5	-	16.13	16.33
J080628.65+242057.4∗	121.61938	24.349293	27990$\pm$ 350	5.48$\pm$0.04	-2.50$\pm$0.14	sdB He4	14.4	-	14.70	15.00
J080758.25+272434.3	121.99274	27.409538	38370$\pm$1190	5.58$\pm$0.08	-3.41$\pm$0.66	sdO He2	50.4	-	13.76	14.11
J084535.66+194150.2	131.3986†	19.697288	22070$\pm$ 420	5.00$\pm$0.06	-1.80$\pm$0.06	sdB He7	18.4	13.13	13.49	13.26
J085649.36+170116.0∗	134.2056708†	17.021125	28810$\pm$ 150	5.65$\pm$0.01	-3.19$\pm$0.17	sdB He2	56.3	14.67	12.73	12.81
J085851.11+021012.9∗	134.71299	2.1702667	48580$\pm$1150	5.61$\pm$0.07	-1.83$\pm$0.09	sdO He6	16.8	-	13.30	13.63
J093512.20+310959.3∗	143.8008625	31.166475	33870$\pm$ 110	5.62$\pm$0.04	-1.47$\pm$0.07	sdOB He11	13.4	15.06	15.34	15.63
J112350.68+233645.8∗	170.961175	23.6127333	27560$\pm$ 350	5.32$\pm$0.04	-2.39$\pm$0.11	sdB He5	15.8	13.76	13.90	14.15
J120624.36+570935.7∗	181.6015083†	57.1599222	34960$\pm$ 230	5.70$\pm$0.04	-1.81$\pm$0.06	sdOB He9	18.4	14.28	14.60	14.85
J123652.66+501513.8∗	189.219429	50.253856	43250$\pm$2210	5.40$\pm$0.12	-2.42$\pm$0.30	sdO He2	22.7	13.96	14.38	14.65
J125229.60-030129.6∗	193.12335	-3.0248924	30790$\pm$ 480	5.59$\pm$0.09	$-3.36>$	sdB He0	13.4	15.46	15.71	15.65
J133640.95+515449.4	204.170631	51.913729	88450$\pm$21230	5.13$\pm$1.00	-2.77$\pm$1.04	sdOB -	53.5	12.79	12.76	12.97
J135153.11-012946.6	207.9713167	-1.4962778	31040$\pm$ 560	6.03$\pm$0.12	$-2.77>$	sdB He0	11.2	15.31	15.45	15.66
J141736.40-043429.0	214.401671	-4.574742	37750$\pm$ 380	5.82$\pm$0.06	-1.53$\pm$0.05	sdOB He12	24.6	13.52	13.96	13.71
J144052.82-030852.6∗	220.220106	-3.147965	29320$\pm$ 40	5.44$\pm$0.03	-2.74$\pm$0.05	sdB He0	45.2	13.60	14.02	13.82
J161200.65+514943.5∗	243.0027458	51.82875	45130$\pm$1610	5.09$\pm$0.13	-3.31$\pm$0.29	sdB He2	10.9	13.26	13.54	13.67
J164718.35+322832.9	251.826491	32.475813	-	-	-	WD	38.9	13.47	13.83	13.59
J171013.21+532646.0	257.555047	53.446121	28120$\pm$ 340	5.83$\pm$0.03	-2.42$\pm$0.12	sdB He3	13.1	12.28	12.87	12.60
J171718.79+422609.2	259.32832	42.435913	55490$\pm$2130	5.78$\pm$0.03	-3.01$\pm$0.29	sdO He0	30.4	12.26	12.77	12.48
J175311.46+062541.5	268.2977592	6.4282084	-	-	-	MS	11.6	14.68	13.66	14.58
J192216.18+405757.4	290.567417	40.965972	-	-	-	MS	20.7	13.54	-	13.51
J192609.46+372008.1∗	291.539417	37.335611	31060$\pm$ 240	5.97$\pm$0.04	-1.65$\pm$0.04	sdB He11	23.8	13.45	-	13.61
J213406.74+033415.4	323.528123	3.570953	40310$\pm$1390	6.12$\pm$0.12	-1.60$\pm$0.18	sdB -	21.2	11.50	11.78	11.55
J223419.15+091620.5	338.57981	9.272378	-	-	-	MS	13.2	13.89	13.93	13.87

Equations

$$y=1.0-aexp\left[-{\left(\frac{|\lambda -{\lambda }_0|}{b}\right)}^c\right],$$

$$y=n-aexp\left[-{\left(\frac{|\lambda -{\lambda }_0|}{b}\right)}^c\right].$$

$$20\frac{\mathrm{HeI}\lambda 4471+\mathrm{HeII}\lambda 4541}{{\mathrm{H}}_{\gamma }-0.83\mathrm{HeII}\lambda 4541}$$

$$40-20\frac{{\mathrm{H}}_{\gamma }-0.83\mathrm{HeII}\lambda 4541}{\mathrm{HeI}\lambda 4471+\mathrm{HeII}\lambda 4541}$$

$$\log (n\mathrm{He}/n\mathrm{H})=-3.53+1.35\left(\frac{T_{\mathrm{eff}}}{10^{4}K}-2.00\right),$$

$$\log (n\mathrm{He}/n\mathrm{H})=-4.79+1.26\left(\frac{T_{\mathrm{eff}}}{10^{4}K}-2.00\right).$$

$$\log (n\mathrm{He}/n\mathrm{H})=-4.26+0.69\left(\frac{T_{\mathrm{eff}}}{10^{4}K}-2.00\right).$$

Full text

1 Introduction

Hot subdwarf stars (spectral types i.e.: sdB, sdO and related objects) are low mass stars in a core or shell helium (He) burning stage (Heber 2009, 2016). These stars lose nearly their whole hydrogen (H) envelopes during the evolution on the red giant branch (RGB), therefore they present very high effective temperatures ($T_{\mathrm{eff}}$ $\geq$ 20 000 K) on reaching the horizontal branch (HB) stage. Hot subdwarf stars are considered to be the main source of UV-excess found in elliptical galaxies (O’Connell 1999; Han et al. 2007). These stars also turned out to be important objects in studying close binary interactions, since many hot subdwarf stars are found in close binaries (Maxted et al. 2001; Napiwotzki et al. 2004; Copperwheat et al. 2011). The most common types of companion stars in hot subdwarf binaries are main-sequence (MS) stars, white dwarfs (WDs), brown dwarfs and planets. Hot subdwarf stars with massive WD companions are considered to be the progenitors of type Ia supernovae (Wang et al. 2009; Geier et al. 2011; Geier 2015). The atmospheres of hot subdwarf stars are good places to study diffusion processes, such as gravitational settling and radiative levitation. Moreover, pulsating sdB/O stars are extensively used in asteroseismology to study stellar interiors and rotation. For a recent review on hot subdwarf stars see Heber 2016.

The formation mechanism of hot subdwarf stars is still unclear. Since about half of the hot subdwarf B type (sdB) stars are found in close binaries, Han et al. (2002, 2003) carried out a detailed binary population synthesis to study the formation of sdB stars. They found that common envelope (CE) ejection, mass transfer through Roche lobe overflow (RLOF) or merger of two helium core white dwarfs (He-WDs) could produce sdB stars in a close binary, wide binary and single system respectively. Based on these results, Chen et al. (2013) predicted that the orbital period of sdB binaries formed from RLOF mass transfer could be up to 1200 days, if atmospheric RLOF and a different angular momentum loss are considered in binary evolution. This result could explain the formation of sdB stars found in wide binaries. Furthermore, Xiong et al. (2017) found that two distinct groups of sdB stars could be formed through the detailed CE ejection channel. One group is flash-mixing sdB stars without H-rich envelopes, and the other is canonical sdB stars with H-rich envelopes. In addition, Zhang et al. (2012, 2017) studied the formation channel in detail for single sdB stars through the merger of two He-WDs or the merger of a He-WD with a low-mass MS companion. Their results could account for some He-rich sdB stars found in the field. The counterpart of hot sudwarf stars in globular clusters (GCs) are known as extreme horizontal branch (EHB) stars. Some of these stars with particularly high effective temperatures (e.g., $T_{\mathrm{eff}}$ $\geq$ 32 000 K ) form a blue hook in the ultraviolet (UV) color-magnitude diagram (CMD) of GCs (Brown et al. 2016), and they are known as blue hook stars in GCs. Lei et al. (2015, 2016) proposed that tidally-enhanced stellar wind during binary evolution may lead to huge mass loss of the primary stars at RGB and could produce blue hook stars in GCs after undergoing late core He flash.

Thanks to large surveys over the past decade a significant number of previously unknown hot subdwarfs have been catalogued, e.g., Kepler ($\varnothing$stensen et al. 2010), Galaxy Evolution Explorer (GALEX, Vennes et al. 2011; Németh et al. 2012; Kawka et al. 2015), the Sloan Digital Sky Survey (SDSS, Geier et al. 2015; Kepler et al. 2015, 2016) and the Large Sky Area Multi-Object Fibre Spectroscopic Telescope (LAMOST) survey (Luo et al. 2016). $\varnothing$stensen (2006) compiled a widely used hot subdwarf database by searching extensive literatures, in which more than 2300 hot subdwarf stars are archived. Furthermore, Geier et al. (2017) compiled a catalogue of known hot subdwarf stars and candidates retrieved from literatures and unpublished databases. This catalogue contains 5613 objects with multi-band photometry, proper motions, classifications, atmospheric parameters, radial velocities and information on light curve variability. Using the first data release (DR1) of the LAMOST survey, Luo et al. (2016) identified 166 hot subdwarf stars, among which 122 objects are single-lined, while the other 44 objects present double-lined composite spectra (e.g., Mg I triplet lines at 5170 $\mathrm{\AA}$ or Ca II triplet lines at 8650 $\mathrm{\AA}$) , which demonstrates the binary nature of these stars.

We need even more spectroscopically identified hot subdwarf stars and candidates to improve our understanding on their formation and evolution. Fortunately, large spectroscopic surveys provide us a good opportunity to search for new hot subdwarf stars, e.g., SDSS (York et al. 2000) and LAMOST (Cui et al. 2012; Zhao et al. 2006, 2012). The traditional method extensively used to search for hot subdwarf stars in large spectroscopic surveys is based on color cuts, followed by visual inspections. However, this method requires homogeneous photometry for the spectra to obtain their colors in different band (e.g., u-g and g-r, Geier et al. 2011), thus it might not work well in spectral database without any or lack of homogeneous photometric information, such as the database of LAMOST.

Employing the Hierarchical Extreme Learning Machine (HELM) algorithm, Bu et al. (2017, hereafter Paper I) explored a machine learning method to search for hot subdwarf stars in LAMOST spectra. The Extreme Learning Machine (ELM) is a special type of single hidden-layer feed-forward network, while HELM is the hierarchical framework of the ELM algorithm (Huang et al. 2006). It is inspired by the deep learning algorithms, and built in a multilayer manner. HELM has been frequently used in many fields, such as image-quality assessment (Mao et al. 2014), human action recognition (Minhas et al. 2010) and hyper-spectral image classification (Li et al. 2015). Using the HELM algorithm in Paper I, we obtained an accuracy and efficiency of classifying single-lined hot subdwarf stars in LAMOST spectra up to 92% and 96% respectively, which demonstrated the reliability of the method to search for hot subdwarf stars in the LAMOST survey spectral database.

Like in the seminal study of Paper I, we applied the HELM algorithm method to LAMOST DR1 and identified 56 hot subdwarf stars. We obtained the atmospheric parameters of these stars by fitting their spectra with synthetic spectra calculated from NLTE model atmospheres (Németh et al. 2012, 2014). The structure of the paper is as follows. In Section 2, we briefly introduced the LAMOST spectral survey and sample filtering method based on the HELM algorithm. In Section 3, we introduced the selection criteria to sort out hot subdwarf stars selected from the candidates by the HELM algorithm. We give our results in Section 4. Finally, a discussion and a summary of this study are presented in Section 5 and 6, respectively.

2 The Lamost survey and sample filtering with the HELM algorithm

2.1 The LAMOST survey and database DR1

LAMOST is a special reflecting Schmidt telescope designed with both large aperture (effective aperture of 3.6 - 4.9 m) and a wide field of view (FOV, 5*∘*, Cui et al. 2012). LAMOST is equipped with 16 low resolution spectrographs connected to 4000 optical fibres, which are precisely positioned on the focal surface. As the telescope with the highest rate of spectral acquisition all over the world, LAMOST could obtain the spectra of 4000 objects simultaneously.

LAMOST conducted its pilot survey between October 2011 and June 2012, while the regular survey started in September 2012 and finished its first year’s operation in June 2013. The data from both the pilot survey and the first year regular survey make up the database of LAMOST DR1 (Luo et al. 2015). DR1 contains totally 2 204 696 spectra with a resolution ($\lambda/\Delta\lambda$) of 1800 in the wavelength range 3690-9100$\mathrm{\AA}$, among which 1 790 879 spectra have their signal-to-noise ratio (SNR) $\geq$10, and 1 944 329 spectra are classified as stellar spectra. Although the number of stellar spectra in LAMOST DR1 is large, many of them lack photometric measurements in certain bands, such as the u band, and it prevents one to use colors for object classifications. Therefore, LAMOST DR1 provides us an appropriate database to test our new method (HELM algorithm) in searching for hot subdwarf stars directly from observed spectra, without a need for color information (also see the discussion in Section 5).

2.2 The HELM algorithm and our training sample

HELM stands for the hierarchical framework of the ELM algorithm (see Paper I for more details), which was proposed by Tang et al. (2015). It usually contains two parts: an unsupervised learning part and a supervised part. The unsupervised part in HELM could include many layers. To give higher-level features of the training sample, the input of each layer is the output of the previous layer. On the other hand, the supervised part contains only one layer, and it takes the output of the last unsupervised layer as its input. In the experiments of Paper I, The HELM algorithm could filter out single-lined hot subdwarf stars from LAMOST spectra with an accuracy of 0.92 and efficiency of 0.96, respectively. When applied to the selection of double-lined hot subdwarfs, the HELM presented an accuracy and efficiency of 0.80 and 0.71, respectively. These results are better when we compare them with other popular algorithms (see section 4.2 in Paper I), which demonstrates that the HELM algorithm is an accurate and efficient new method to search for hot subdwarf stars in large spectroscopic surveys.

The training sample used in the experiments of Paper I are the spectra of hot subdwarf stars identified in Luo et al. (2016) combined with 4600 LAMOST DR1 spectra of various types of objects, including stars of different spectral types, galaxies, quasars and objects with ambiguous spectral features. There are a total of 166 hot subdwarf spectra in our training sample, among which 122 stars are single-lined hot subdwarfs, while 44 spectra show strong Mg I triplet lines at 5170 $\mathrm{\AA}$ or Ca II triplet lines at 8650 $\mathrm{\AA}$ indicating the binary nature of these stars. According to Table 2 in Luo et al. (2016), the 122 single-lined hot subdwarf stars consist of 77 sdB stars, 15 He-sdO stars, 12 sdO stars, 10 He-sdB stars and 8 blue horizontal branch (BHB) stars. All the sample spectra are divided into three groups to carry out the experiments in HELM and other popular algorithms (see Paper I for details).

3 Target selection

By applying the HELM algorithm outlined in Paper I, we obtained more than 7000 hot subdwarf candidates from LAMOST DR1, among which 1034 spectra have an $u$-band SNR larger than 10. We have selected our final hot subdwarf sample from these candidates. Blue horizontal branch (BHB) stars, B-type main-sequence (B-MS) stars and WDs show very similar features (e.g., strong H Balmer lines) in their spectra as hot subdwarf stars (Moehler et al. 1990). Some of these stars have similar temperatures to hot subdwarf stars, especially to He-poor sdB stars. Therefore, the hot subdwarf candidate sample selected by the HELM algorithm method is contaminated by the above mentioned object types. Three steps are used to select hot subdwarf stars from our candidates.

3.1 Excluding BHB stars and WDs from our sample

BHB stars are horizontal branch stars bluer than the RR Lyrae instability strip in the color-magnitude diagram (CMD). These stars present effective temperatures in the range of about 7 000 - 20 000 K and surface gravities (e.g., log $g$) in the range of $\log\ {g}\ =\ 2.5-4.5$ cm s*-2*, respectively (Catelan 2009). Xue et al. (2008) used the $D_{0.2}$ and $f_{\mathrm{m}}$ method to discriminate BHB stars from blue straggler (BS) and B-MS stars. In this method, $D_{0.2}$ is the full width of the Hδ line at 20% below the local continuum, while $f_{\mathrm{m}}$ is the flux relative to the continuum at the line core (Beers et al. 1992; Sirko et al. 2004). Xue et al. (2008) used the criteria: $17\mathrm{\AA}\leq D_{0.2}\leq 28.5\mathrm{\AA}$ and $0.1\leq f_{\mathrm{m}}\leq 0.3$, to select BHB stars from their samples.

Both the values of $D_{0.2}$ and $f_{\mathrm{m}}$ are sensitive to effective temperature and gravity in hot stars (Xue et al. 2008), which makes it a suitable measure to distinguish our sample spectra in the $D_{\rm 0.2}$ - $f_{\rm m}$ diagram. Since BHB stars have lower temperatures and gravities than hot subdwarf stars and regular WDs present higher temperatures and gravities than hot subdwarf stars, these spectral classes can be clearly separated according to their $D_{\rm 0.2}$ and $f_{\rm m}$ values (Greenstein & Sargent 1974). We use the scale width versus shape method (Clewley et al. 2002; Xue et al. 2008) to fit the $\mathrm{H}_{\delta}$ line and obtain the value of $D_{0.2}$ and $f_{\mathrm{m}}$ for each spectrum in our sample. This method is based on a Sérsic profile fit (Sérsic 1968) to Balmer lines in the following form:

[TABLE]

where $y$ is the normalized flux, $\lambda$ is the wavelength and $\lambda_{0}$ is the nominal central wavelength of the Balmer line. The coefficients $a$, $b$ and $c$ are free parameters. As described in Xue et al. (2008), to account for imperfect normalization of spectra, we used five free parameters: $a$, $b$, $c$, $\lambda_{0}$ and $n$ to fit the normalized spectrum to the Sérsic profile:

[TABLE]

The three panels in Fig 1 show the results of fitting the $\mathrm{H}_{\delta}$ profile of a sdB star, a BHB star and a WD, respectively. In each panel, solid curves represent an extracted spectrum near the $\mathrm{H}_{\delta}$ line, while blue dashed curves denote our best fitting line profiles. Panel (a) shows the spectrum of the sdB star PG 1605+072 taken from Luo et al. (2016) with $T_{\mathrm{eff}}$ = 32 550$\pm$370 K and $\mathrm{log}\ g$= 5.29$\pm$0.07 cm s*-2*. By adopting the fitting method described above, we got $D_{0.2}$ = 9.37 $\mathrm{\AA}$ and $f_{\mathrm{m}}$ = 0.63. Panel (b) shows the spectrum of the BHB star SDSSJ171935.27+262234.9 from Xue et al. (2008) with $T_{\mathrm{eff}}$ = 7846 K and $\mathrm{log}\ g$ = 3.46 cm s*-2* (no error bars for this star are presented in Xue et al. 2008 ), while its $D_{0.2}$ and $f_{\mathrm{m}}$ are 22.53 $\mathrm{\AA}$ and 0.28, respectively. One can see obviously that the BHB star presents much deeper $\mathrm{H}_{\delta}$ line (i.e., smaller value of $f_{\mathrm{m}}$) and much wider $D_{0.2}$ than the sdB star in Panel (a) due to its significantly lower effective temperature and gravity. The spectrum of the WD SDSS J094126.79+294503.4 in Panel (c) is taken from the catalogue of Eisenstein et al. (2006) with its $T_{\mathrm{eff}}$ = 20 818 K and $\mathrm{log}\ g$ = 8.0 cm s*-2*. Although this WD shows a similar depth of the $\mathrm{H}_{\delta}$ line (i.e., $f_{\mathrm{m}}$ = 0.55) to the sdB star showed in Panel (a), it presents a much larger $D_{0.2}$ (39.42 $\mathrm{\AA}$) than the sdB star (9.37 $\mathrm{\AA}$) due to its higher gravity.

To better demonstrate the differences of $D_{0.2}$ and $f_{\mathrm{m}}$ among BHB stars, hot subdwarfs and WDs, we selected some known BHB stars, hot subdwarfs and WDs from published catalogues and put them into the $D_{0.2}$ - $f_{\mathrm{m}}$ diagram in Panel (a) of Fig 2. Black solid triangles denote BHB stars identified from Xue et al. (2008), blue open circles represent hot subdwarfs selected from the catalogue of Geier et al. (2017), and green open squares are WDs from Eisenstein et al. (2006). BHB stars are concentrated quite well in the upper left corner of Panel (a), and subdwarfs distribute in a strip from the middle center to the bottom right, while WDs locate on the upper right and middle area of the panel (note that most of of the selected WDs have $D_{\rm 0.2}$ values larger than 35 Å and are off the panel). As expected, there is a remarkable gap between BHB stars and hot subdwarf stars near $D_{0.2}$ = 17.0 Å  which is marked by the red dashed horizontal line in Panel (a). Since WDs present much larger values of $D_{0.2}$ than BHB and hot subdwarf stars, $D_{0.2}$ = 17.0 can be used as a criterion to distinguish hot subdwarf stars from BHB stars and WDs in our sample.

Panel (b) of Fig 2 shows the values of $D_{0.2}$ and $f_{\mathrm{m}}$ for the 1034 sample spectra selected by HELM (see Section 2 and Paper I). To compare with Panel (a) clearly, we plot a dashed horizontal line at $D_{0.2}$ = 17.0 Å in Panel (b) as well, which denotes the gap between BHB stars and hot subdwarf stars in Panel (a). Our sample in Panel (b) shows an analogous distribution to the stars in Panel (a), with the notable exception that the obvious gap at $D_{\rm 0.2}\ =\ 17.0$ Å is not seen in Panel (b). This is due to the fact that the selected BHB stars in Panel (a) are stars with temperatures in the range of $T_{\rm eff}\ =\ 7000-10\,000$ and surface gravity in a range of $\log{g}\ =\ 2.5-4.0$ cm s*-2* (Xue et al. 2008), which are much lower than the temperatures and gravities of hot subdwarf stars (e.g., $T_{\mathrm{eff}}\geq$ 20 000$K$ and log$\ g\geq 5.0\ \mathrm{cm\,s}^{-2}$, Heber 2016), while the stars selected by HELM form a more evenly distributed mix of stars and the gap in the $D_{\rm 0.2}-f_{\rm m}$ diagram is filled up. Therefore, our sample contains not only BHB stars with low temperatures, hot subdwarf stars and WDs, but also includes high temperature BHB stars (e.g., 10 000 - 20 000 K) and B-MS stars, because these stars present similar temperatures to hot subdwarf stars in lower temperatures (e.g., He-poor sdB stars). Therefore, high temperature BHB stars and B-MS stars fill the gap presented in Panel (a) and make a continuous distribution for our sample in $D_{0.2}$ - $f_{\mathrm{m}}$ diagram. Note that there are a few stars in the upper right and middle area of Panel (b), which are typically occupied by WDs in Panel (a). This demonstrates that a few WDs are in our sample, and HELM is very efficient at distinguishing hot subdwarf stars from WDs. Nevertheless, the criterion of $D_{0.2}$ = 17.0 Å still excludes most BHB stars with low temperatures and WDs, while preserving hot subdwarf stars in our sample.

After applying the selection criterion of $D_{0.2}<17.0$ Å  we obtained 578 hot subdwarf candidate spectra, among which 161 spectra present obvious Mg I triplet lines at 5170 $\mathrm{\AA}$ or Ca II triplet lines at 8650 $\mathrm{\AA}$. These lines are characteristic of cool stars and such subdwarfs are double-lined composite spectrum binary candidates, that will be studied in a forthcoming publication. Therefore, our hot subdwarf sample selected by $D_{0.2}$-$f_{\mathrm{m}}$ method consists of 417 spectra, for which the atmospheric parameters were determined by fitting their H Balmer and He lines.

The $D_{0.2}$-$f_{\mathrm{m}}$ method is able to exclude most of the BHB stars and WDs in our sample. However, as the method is based on measuring the width and depth of Hδ line, some hot subdwarfs with weak or no obvious Hδ lines (e.g., He-sdO, He-sdB) could be also removed from our sample. Furthermore, the values of $D_{0.2}$ and $f_{\mathrm{m}}$ for some spectra are difficult to obtain from poor quality spectra near the Hδ line. To assess the completeness of our sample we used XTgrid (Németh et al. 2012; Vennes et al. 2011, see next section for detail) to make a spectral classification for the 456 spectra which were removed by the $D_{0.2}$-$f_{\mathrm{m}}$ method. With this procedure we could recover a further 48 hot subdwarf candidates from low quality spectra. The atmospheric parameters of these 48 spectra together with the 417 spectra selected by $D_{0.2}$-$f_{\mathrm{m}}$ method (i.e., 465 spectra in total) are determined by fitting their LAMOST optical spectra with synthetic spectra (see next section). All objects with atmospheric parameters characteristic of hot subdwarfs were selected as hot subdwarf candidates.

3.2 Atmospheric parameters of hot subdwarf candidates

To determine the atmospheric parameters of the final hot subdwarf sample we fitted NLTE models to the observations. We used the NLTE model atmosphere code Tlusty (version 204; Hubeny & Lanz (2017) to calculate models with H and He composition and corresponding synthetic spectra with Synspec (version 49; Lanz et al. 2007). Details of the model calculations are described by Németh et al. (2014). The spectral analysis was done by a steepest-descent iterative $\chi^{2}$ minimization procedure, which is implemented in the fitting program XTgrid (Németh et al. 2012; Vennes et al. 2011). This algorithm fits the entire optical range and attempts to reproduce the observed line profiles simultaneously. Final parameter errors are determined by departing from the best fitting parameters in one dimension until the statistical limit for the 60% confidence level of a single parameter is reached, separately for positive and negative error bars. To match the resolution of LAMOST spectra we convolved the synthetic spectra with a Gaussian profile at a constant resolution ($R\ =\ 1800$).

Fig 3 shows the best fitting models for four representative hot subdwarf spectra from our sample. In this figure, gray solid curves denote the normalized stellar spectra111The continuum for each spectrum was fitted automatically in XTgrid, while red dashed curves represent the best fitting synthetic spectra. The positions of the strongest H Balmer lines, He I and He II lines are marked in Fig 3 as well. The label ’He’ plus an integer for each spectrum is the helium class following the hot subdwarf classification scheme of Drilling et al. (2013), which is based on He line strength (see Sect 4 for details). The top spectrum is a He-sdOB star with dominant He I lines and weak H Balmer lines, while the second spectrum from the top is a sdOB star, which shows dominant H Balmer lines with both weak He I and He II lines. The third spectrum from the top is a typical sdB star, which presents broad H Balmer lines with weak He I lines. Finally, the spectrum at the bottom of the figure is classified as a sdO star, because of its dominant H Balmer lines with weak He II line at 4686 $\mathrm{\AA}$ while no He l lines can be detected.

By employing XTgrid , we obtained the atmospheric parameters (e.g., $T_{\mathrm{eff}}$, $\mathrm{log}\ g$ and He abundance) for the 465 spectra selected in Section 3. We classified stars with $T_{\mathrm{eff}}\geq$ 20 000 K and $\mathrm{log}\ g\geq$ 5.0 as hot subdwarf stars, with $T_{\mathrm{eff}}<$ 20 000K and $\mathrm{log}g<$ 5.0 as hot BHB stars, while stars with $\mathrm{log}\ g<$ 4.5 as B-MS stars following the classification scheme of Németh et al. (2012). After this procedure, we selected 76 hot subdwarf candidates based on their atmospheric parameters. We checked our results by Gaia Hertzsprung-Russell diagram (HRD) in next section.

3.3 Cross matching our results with the HRD of Gaia DR2

The second data release (DR2) from Gaia (Gaia Collaboration et al. 2018a) provides high-precision astrometry and photometry for about 1.3 billion sources over the full sky. Based on this huge database, Gaia Collaboration et al. (2018b) built the Gaia DR2 HRD by using the most precise parallax and photometry (see Sect 2 in Gaia Collaboration et al. 2018b for their detailed selection filters). To check our final results, we cross matched the 76 hot subdwarf candidates with the database of Gaia DR2, and got 75 common objects within the radius of five arcseconds, among which one object had negative parallax, and it was removed from our sample. Fig 4 shows the HRD from Gaia Collaboration et al. (2018b) together with the 74 stars in common with this study. Gray dots denote the objects from Gaia DR2 selected by Gaia Collaboration (65 921 112 stars in total, see Fig 1 of Gaia Collaboration et al. 2018b), while blue triangles, yellow squares and red circles are the common stars in our sample. We found 56 stars (e.g., blue triangles) to be located in the hot subdwarf region of the HRD. Therefore, these 56 objects are finally identified as hot subdwarf stars in this study. On the other hand, we found 12 stars (e.g., yellow squares) distributed along the wide MS222Extinction is not considered in the HRD of Fig 1 in Gaia Collaboration et al. (2018b), therefore the MS is wider and can not be distinguished very clearly from the RGB. But the WD and hot subdwarf sequences are presented more clearly in this HRD. , and 6 stars (e.g., red circles) are along the WD sequence.

4 Results

Using the method described in Section 3, we identified 56 hot subdwarf stars. We followed the spectral classification scheme in Moehler et al. (1990) and Geier et al. (2017) to classify hot subdwarf stars: stars showing strong H Balmer lines with weak or no He I lines are classified as sdB stars; stars showing strong H Balmer lines accompanied by He II absorption are considered as sdO stars; stars having H Balmer lines accompanied both by weak He I and He II lines are classified as sdOB stars and stars with dominant He I lines and weak H Balmer lines are He-sdOB stars, while stars with dominant He II lines are He-sdO stars. Based on this simple classification scheme, we identified 31 sdB stars, 11 sdO stars, 9 sdOB stars, 4 He-sdOB and 1 He-sdO stars.

Drilling et al. (2013) designed an MK (Morgan-Keenan)-like system of spectral classification for hot subdwarf stars, in which a spectral class, a luminosity class and a helium class are used to classify hot subdwarf stars. The spectral class is based on the MK standards of spectral classes O and B stars, and the luminosity class is based on the H and He line widths (see Sect 3 in Drilling et al. 2013). On the other hand, the helium class is described by an integer from 0 to 40 denoting the strengths of the He lines relative to the H Balmer lines, and it is roughly equal to the following function of the relative line depths:

[TABLE]

for helium class 0-20, and

[TABLE]

for helium class 20-40. We also appended this helium class for our hot subdwarf stars (see Table 1).

The atmospheric parameters of the 56 identified hot subdwarf stars together with the information of 12 MS stars and 6 WDs are listed in Table 1. The atmospheric parameters of the MS stars and WDs are not presented. In column 1-11 of Table 1, we have presented the LAMOST designation, right ascension, declination, effective temperature , surface gravity and He abundance obtained in this study, spectral classification type, SNR in the u band, apparent magnitudes in the u and g band of SDSS, apparent magnitudes in the G band of Gaia DR2, respectively. We also cross-matched our hot subdwarf stars with the hot subdwarfs list in Geier et al. (2017) and Németh et al. (2012). In Table 1, the common hot subdwarf stars with Geier et al. (2017) are labeled by ∗, and the common hot subdwarf stars with Németh et al. (2012) are marked by †.

4.1 Comparison with other studies

Among the 56 hot subdwarf stars in our study, 25 stars have been already catalouged by Geier et al. (2017), and 5 stars are listed in Németh et al. (2012). To check the results presented in our study, we compared the atmospheric parameters obtained in this study with the ones from Geier et al. (2017) and Németh et al. (2012) where their parameters are available.

We have 25 common hot subdwarf stars with Geier et al. (2017), but only 11 stars with their $T_{\mathrm{eff}}$ and $\mathrm{log}\ g$ are available in the catalogue, and 10 stars with their He abundances are available in the catalogue. The subplots from left to right of Panel (a) in Fig 5 present the comparison of $T_{\mathrm{eff}}$, $\mathrm{log}\ g$ and $\mathrm{log}(n\mathrm{He}/n\mathrm{H})$, respectively. As we see that both $T_{\mathrm{eff}}$ and $\mathrm{log}(n\mathrm{He}/n\mathrm{H})$ obtained in this study matched well with the values from Geier et al. (2017). Although, the comparison of $\mathrm{log}\ g$ in the middle subplot of Panel (a) presents a more dispersive distribution than the other two parameters, but our results are still comparable with the values from literature.

We also have 5 common hot subdwarf stars with Németh et al. (2012), which are marked in Table 1. These stars are from the GALEX survey with low-resolution spectra. Similar as we see in Panel (a), both $T_{\mathrm{eff}}$ and $\mathrm{log}(n\mathrm{He}/n\mathrm{H})$ from this study match very well with the values from Németh et al. (2012, see the left and right subplots in Panel (b)). However, most of the $\mathrm{log}\ g$ obtained in this study seem to be a little larger than the values from Németh et al. (2012, see the middle subplot in Panel(b)). This could be due to the fact that the synthetic spectra used to fit the observed spectra in our study are calculated from atmospheric models only with H and He composition (Németh et al. 2014), while the synthetic spectra used in Németh et al. (2012) are calculated from atmospheric models not only with H and He composition but also include C, N and O composition. Furthermore, the observed spectra in our sample (obtained in LAMOST survey) are different from the spectra in Németh et al. (2012, obtained in GALEX survey), and the qualities (e.g., SNR) for the spectra are also different. Beyond these effects the major reason for the differences in the surface gravity is the inclusion of H Stark broadening tables from Tremblay & Bergeron (2009) directly in the model atmosphere calculation in Tlusty version 204, unlike in version 200 used by Németh et al (2012).

4.2 Parameter diagrams

Fig 6 shows the distribution of all hot subdwarf stars from our study in the $T_{\rm eff}-\log\ {g}$ diagram. The thick solid line denotes the He main-sequence (He MS) from Paczyński (1971), while the two dashed lines represent the zero-age HB (ZAHB) and terminal-age HB (TAHB) for hot subdwarf stars with [Fe/H] = -1.48 from Dorman et al. (1993). The thin solid, dot-dashed and dotted curves are the sdB evolution tracks from Han et al. (2002). From right to left, these sdB evolution tracks have the masses of 0.5, 0.6 and 0.7 $\mathrm{M}_{\odot}$ respectively. The thin solid curves present a H-rich envelope mass of 0.0 $\mathrm{M}_{\odot}$, the dot-dashed curves for 0.001 $\mathrm{M}_{\odot}$, and the dotted curves for 0.005 $\mathrm{M}_{\odot}$.

We split our sample into three groups based on their He abundance following the scheme of Németh et al. (2012). In Fig 6, filled circles denote hot subdwarf stars with their $\mathrm{log}(n\mathrm{He}/n\mathrm{H})\leq-2.2$. Most of these stars are He-poor sdB stars, and they are located near $T_{\mathrm{eff}}$ = 29 000 K, and $\mathrm{log}\ g$ = 5.5 cm s*-2*. A few of the stars in this He abundance range show very high temperatures (e.g., $T_{\mathrm{eff}}\geq$50 000 K), which suggests that they have already finished their core helium burning stage and now evolve towards the WD cooling tracks. Open triangles in Fig 6 represent hot subdwarf stars with $-2.2<\mathrm{log}(n\mathrm{He}/n\mathrm{H})<-1.0$. Most of these stars are found near $T_{\mathrm{eff}}$ = 32 000 K, and $\mathrm{log}g$ = 5.75 cm s*-2*. These stars show higher gravities than previous group and their temperatures show a large dispersion. The third group contains stars with He abundances in the range of $-1.0\leq\mathrm{log}(n\mathrm{He}/n\mathrm{H})$, which are denoted by open squares in Fig 6. Actually, we just found five hot subdwarf stars in this He abundance range, four of them are classified as He-sdOB stars and one is classified as He-sdO star based on our classification scheme.

Fig 7 shows the $T_{\mathrm{eff}}$-$\mathrm{log}(n\mathrm{He}/n\mathrm{H})$ diagram for our hot subdwarf stars. The solar He abundance is marked by a horizontal red dashed line. The diamonds represent the stars for which only an upper limit of $\mathrm{log}(n\mathrm{He}/n\mathrm{H})$ could be obtained. Edelmann et al. (2003) found two He sequences, which are positive correlations between the effective temperature and He abundance (i.e., a He-rich sequence and a He-weak sequence) when the analyzed spectra of hot subdwarf stars were from the Hamburg Quasar Survey. The He-rich sequence of their sample follows the fitting formula:

[TABLE]

while the He-weak sequence in their study follows the formula:

[TABLE]

These two lines are shown by the dotted and the solid lines in Fig 7, respectively. We found results similar to those described by Edelmann et al. (2003), the two He sequences of hot subdwrf stars are also present in our sample. Moreover, the He-rich sequence in Fig 7 could be fitted well by the line described in equation (5), which is from Edelmann et al. (2003). However, a He-weak sequence in our sample follows a different trend than the He-weak sequence by Edelmann et al. (2003). On the other hand, the He-weak sequence in our sample is consistent with the one presented in Németh et al. (2012). They used another line to fit the He-weak sequence in their study:

[TABLE]

We also plot the linear regression by equation (7), which is denoted by a dot-dashed line in Fig 7. The trend of this line is consistent with our He-weak sequence. Furthermore, Edelmann et al. (2003) also found two less clear sequences of hot subdwarf stars in the $\mathrm{log}$ g-$\mathrm{log}(n\mathrm{He}/n\mathrm{H})$ plane. However, we did not find a similar result in our sample (see Fig 8).

5 Discussion

The traditional method to search for hot subdwarf stars in large spectroscopic surveys is to make color cuts followed by visual inspections. This method requires homogeneous photometric information to obtain the colors of the stars (e.g., u-g and g-r; Geier et al. 2011). Therefore, the traditional method is not suitable for large spectral databases without supplementary photometric measurements, such as the spectral database of LAMOST. The HELM algorithm, as described in Paper I and in this study, does not need color information to filter out spectra with certain spectral properties. This makes HELM a suitable method to screen large spectroscopic surveys for hot subdwarf stars, or any other objects with distinct spectral features.

One may note that He-rich hot subdwarf stars are under-represented in our samples (e.g., only 5 stars with $\mathrm{log}(n\mathrm{He}/n\mathrm{H})>-1.0$, see Fig 7 in this paper), this could be due to the fact that the number of He-rich hot subdwarf stars in the training sample is small. Our training spectra were the hot subdwarfs from Luo et al. (2016), which consists of 77 sdB stars, 12 sdO stars, 10 He-sdB stars and 15 He-sdO stars. According to the classification scheme of Luo et al. (2016), both sdB and sdO stars are He-poor hot subdwarf stars with dominant H Balmer lines, while both He-sdB and He-sdO stars are He-rich stars with dominant He I or He II lines. That is, there are many more hot subdwarf stars with dominant H Balmer lines (He-poor stars) than the stars with dominant He lines (He-rich stars) in our training sample, e.g., 77 versus 25. In addition to this, we did not separate these different type of subdwarf stars during the experiments. Instead, we trained HELM with all the sample spectra together, thus the larger the number of stars of a particular type in the training sample, the greater the precision with which this stellar type may be identified in the science sample. These factors could be accounted for the lack of He-rich hot subdwarf stars in our results.

The quantity and quality of the training spectra are both very important factors in the HELM algorithm method, and have a direct influence on the results (Tang et al. 2015). Before we started this work, only 166 hot subdwarf stars (including 122 single-lined stars and 44 double-lined stars) with LAMOST spectra were published in Luo et al. (2016). Therefore, the number of hot subwarf stars is limited in our training spectra. Moreover, among 122 single-lined hot subdwarf stars, 8 stars are classified as BHB stars in Luo et al. (2016), and only about 50 have a SNR larger than 10. As a result, although the initial candidates selected by HELM algorithm contains more than 7000 spectra, but nearly 6000 spectra have a $u$-band SNR below 10, which demonstrates a poor quality of the spectra for a follow-up study. These spectra have been discarded from our analysis as we mention in Section 3. With these considerations the total number of hot subdarfs in the LAMOST target list is likely much higher.

Having used machine learning tools to search for hot subdwarf stars in LAMOST, we can outline some future improvements that will be required for a better efficiency and accuracy of the method. For example, we plan to add the standard hot subdwarf stars listed in Drilling et al. (2013) into our training sample, since it provides detailed classification for all kinds of hot subdwarf stars with different types, which will be quite useful to classify hot subdwarf stars by the HELM algorithm. We also plan to cross match the LAMOST database with the newest hot subdwarf catalogue (e.g., Geier et al. 2017), then we will be able to add many high quality hot subdwarf spectra to our training sample. From these improvements we expect a large number of new subdwarfs to be uncoverd from the LAMOST survey in the near future. These works are already on the way and will make important contributions on the study of the formation and evolution of hot subdwarf stars.

6 Summary

We have applied the HELM algorithm in our study to search for hot subdwarf stars in LAMOST DR1. 56 hot subdwarf stars are identified among 465 candidates with single-lined spectra, and their atmospheric parameters have been obtained by fitting the profiles of H Balmer and He lines with the synthetic spectra calculated from NLTE model atmospheres. 31 sdB stars, 11 sdO stars, 9 sdOB stars, 4 He-sdOB and 1 He-sdO stars were found in our study. These stars confirm the two He sequences of hot subdwarf stars in $T_{\mathrm{eff}}$-$\log{(n{\rm He}/n{\rm H})}$ diagram, which were first found by Edelmann et al. (2003).

Our study has shown the strength of the HELM algorithm to filter out targets with specific spectral properties from large sets of spectroscopic data directly, without the need of any photometric observations or pre-selection. Though the total number of hot subdwarf stars identified may seem low compared to the sample size, it is mainly due to the limited quantity and quality of the training spectra. We expect that many more hot subdwarf stars will be found in the LAMOST database using machine learning method in the future after our experiences are implemented in the algorithm. We used the HELM algorithm for the first time to search for hot subdwarf stars in a large spectroscopic survey, and the results presented in our study demonstrate that this method could be applied to search for other types of object with obvious features in their spectra or images.

{ack}

We thank the referee, A. E. Lynas-Gray, for his valuable suggestions and comments, which improved the manuscript much. This work was supported by the National Natural Science Foundation of China Grant Nos, 11390371, 11503016, 11873037，11603012 and U1731111, Natural Science Foundation of Hunan province Grant No. 2017JJ3283, the Youth Fund project of Hunan Provincial Education Department Grant No. 15B214, the Astronomical Big Data Joint Research Center, co-founded by the National Astronomical Observatories, Chinese Academy of Sciences and the Alibaba Cloud, Young Scholars Program of Shandong University, Weihai 2016WHWLJH09, Natural Science Foundation of Shandong Province ZR2015AQ011, China post-doctoral Science Foundation 2015M571124. This research has used the services of www.Astroserver.org under reference W00QEL. P.N. acknowledges support from the Grant Agency of the Czech Republic (GAČR 18-20083S). The LAMOST Fellowship is supported by Special Funding for Advanced Users, budgeted and administered by the Center for Astronomical Mega-Science, Chinese Academy of Sciences (CAMS). Guoshoujing Telescope (the Large Sky Area Multi-Object Fiber Spectroscopic Telescope LAMOST) is a National Major Scientific Project built by the Chinese Academy of Sciences. Funding for the project has been provided by the National Development and Reform Commission. LAMOST is operated and managed by the National Astronomical Observatories, Chinese Academy of Sciences.