Observational Properties of 155 O- and B-type Massive Pulsating Stars (2024)

Massive stars generally refer to O- and B-type (OB-type) stars, which have the characteristics of high mass, temperature, and luminosity (Morton & Adams 1968; Panagia 1973; Morgan & Keenan 1973). They are related to many important objects and physical processes, such as neutron stars, black holes, supernovae, and gravitational-wave events (Sadowski et al. 2008; Yoon et al. 2010; Langer et al. 2020; Han et al. 2020). Despite recent advances, there are still many deficiencies in the study of massive stars, such as internal element mixing, stellar-wind mass loss, magnetic activity, internal angular momentum transport, and so on. To make up for these deficiencies, it is very important to study the structure and evolution of massive stars by the method of asteroseismology, because it is the only way to obtain their internal structure information at present.

Slowly pulsating B stars (SPB stars) and β Cephei pulsating variable stars (BCEP stars) are the only two recognized classes of OB-type pulsating variable stars in the upper main sequence. SPB stars generally have a spectral type of late B type (about B3 to B9) and a mass from 2.5 to 8 M_⊙. They pulsate in a nonradial multiperiodic g-mode with a period range of 0.5–3 days (Aerts et al. 2010). BCEP stars oscillate in low-order p- and g-modes (Stankov & Handler 2005) with a typical period range of 2–7 hr. They are late O-type or early B-type stars (earlier than B5) with a rough mass range of 7–20 M_⊙ (Dziembowski et al. 1993). The pulsations of SPB stars and BCEP stars seem to be excited by the κ mechanism driven by the ionization zone of iron-group elements.

Stankov & Handler (2005) published a catalog of 93 confirmed BCEP stars including 14 stars discovered by Pigulski (2005). Three new BCEP stars were detected by Burssens et al. (2019) from the K2 mission. Recently, the KELT exoplanet survey detected a total of 113 BCEP stars including 86 new discoveries (Labadie-Bartz et al. 2020). Some researchers have made ground-based surveys for SPB stars, such as Aerts et al. (1999), Mathias et al. (2001), De Cat & Aerts (2002), and De Cat et al. (2007). More than 15 new SPB candidates were identified from the CoRoT space mission (Degroote et al. 2009). Balona et al. (2011) detected 15 pulsating stars showing the low-frequency (LF) characteristics of SPB stars from the Kepler space mission (Borucki et al. 2010), of which seven stars also showed a weak and isolated high frequency (HF).

NASA launched the Transiting Exoplanet Survey Satellite (TESS; Ricker et al. 2015) in 2018 April. For TESS, the sky is divided into 26 sectors, including 13 sectors of the southern sky and northern sky, respectively. Each sector is observed continuously for 27 days, and the whole sky can be repeated for about 2 yr. Every sector with the 24 × 96 degree field of view provides light curves with a 2 minute short cadence for about 20,000 targets and also provides full-frame images every 30 minutes. The primary TESS mission is to detect Earth-sized planets transiting bright and nearby stars. At the same time, its massive and high-precision photometric data also provides an unprecedented opportunity for the research of binaries and variable stars, especially for bright variables (e.g., Balona & Ozuyar 2020; Shi et al. 2022). Most recently, Balona & Ozuyar (2020) published a catalog of 766 pulsating main-sequence B-type stars observed by TESS in sectors 1–18, which greatly expands the list of existing samples.

The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST, also called the Guo Shou Jing telescope) is a special quasi-meridian reflecting Schmidt telescope located at the Xinglong Station of National Astronomical Observatory in China (Wang et al. 1996; Cui et al. 2012). It has a field of view of 5 square degrees and can obtain 4000 spectra in a single exposure. The telescope is equipped with a low-resolution spectrograph and a medium-resolution spectrograph. The low-resolution spectrograph has a wavelength range of 3700–9000 Å, including both a blue arm (3700–5900 Å) and a red arm (5700–9000 Å). The medium-resolution spectrograph is also divided into both a blue arm (4950–5350 Å) and a red arm (6300–6800 Å). LAMOST has obtained a large number of stellar spectral data (e.g., Zhao et al.2012; Luo et al. 2015), including many binary systems (e.g., Qian et al. 2017, 2018; Zhang et al. 2019; Qian et al. 2020), many pulsating stars (e.g., Qian et al. 2018, 2019) and more than 250,000 candidate binary or variable stars (Qian et al. 2019).

The Gaia satellite was launched in 2013 December and is a cornerstone mission of the European Space Agency. It has provided very high-precision astrometry data for nearly 2 billion stars (Gaia Collaboration et al. 2016, 2018, 2021). Its parallax data is a key parameter to calculate the luminosity of stars, which provides an important way to research variables (e.g., Murphy et al. 2019) or to test the reliability of research results (e.g., Shi et al. 2021a, 2021c). Gaia Data Release 3 also derived the stellar atmospheric parameters from the Blue and Red Photometer low-resolution spectral data and the Radial Velocity Spectrometer spectrum by different methods, such as the General Stellar Parameterizer from Photometry (GSP-Phot) and the Extended Stellar Parameterizer for Hot Stars (ESP-HS).

In this paper, we identify 155 OB-type pulsating stars observed by TESS, LAMOST, and Gaia, and their observational and physical properties are also analyzed. First, the TESS light curves of these samples are analyzed by a Fourier spectrum. Second, some statistical analyses are made according to their parallax information and effective temperatures.

From the Mikulski Archive for Space Telescopes database, we downloaded the light curves observed by TESS with a 2 minute short cadence. Then, we choose to use the light curves that have been corrected for long-term drifts by using pre-search data conditioning (Jenkins et al. 2010) and process them using the steps described by Shi et al. (2021a, 2021b). A total of 155 OB-type pulsating stars or candidates are identified by a simple program-aided visual classification. The information is listed in Tables 1 and 2 for these pulsating stars or candidates, respectively. We have also carried out a crossmatch of these samples with the catalog of 766 pulsating main-sequence B-type stars (Balona & Ozuyar 2020), and a total of 10 objects are listed in this catalog and shown in Table 3.

Table 1.The Catalog of OB-type Massive Pulsating Stars Observed by TESS, LAMOST, and Gaia

TESS ID	π	V	Teff	Flag		Fourier	Comments	Period	Amplitude
	(mas)	(mag)	(K)			Spectra		(days)	(mmag)
2944381	0.57	9.91	12,080(179)	1	2.79	LF	SPB	1.6182(2)	2.52(1)
2945216	0.30	10.70	27,206(811)	1	3.94	LF	SPB	4.316(2)	0.88(1)
3030849	0.52	10.29	14,399(198)	1	3.00	LF	SPB	1.34811(9)	6.34(3)
4136259	2.94	7.76	12,891(272)	1	2.20	LF	SPB	0.84957(5)	1.61(1)
5612096	6.37	5.36	16,256	2	2.73	LF	SPB(C)	1.4735(1)	14.48(8)
45646950	0.52	12.79	16,622(321)	1(Be)	3.16	LF	SPB	0.7793(1)	3.44(4)
45709015	0.68	9.95	18,428(419)	1	3.32	LF	SPB	1.8932(6)	1.13(2)
53327951	0.47	8.72	15,546	2(Be)	3.75	LF	SPB	1.0217(2)	3.32(3)
55079633	0.29	9.89	25,885(888)	1	4.13	LF	SPB	9.145(7)	2.72(2)
63748979	0.73	12.24	13,590	2(Be)	2.51	LF	SPB(C)	0.8179(2)	8.3(1)
68989297	2.13	8.70	17,314(338)	1	2.43	LF	SPB	2.28948(7)	17.74(1)
75508636	0.95	9.62	17,944(194)	1	2.93	LF	SPB	1.3141(2)	1.59(2)
77881231	0.78	10.94	11,412(111)	1	2.05	LF	SPB	1.7827(1)	15.28(4)
96951421	0.60	9.22	14,500	4(Be)	3.22	LF	SPB	1.13355(7)	28.8(1)
127584684	0.48	10.32	20,788(485)	1	3.38	LF	SPB	4.346(3)	0.75(1)
137815897	0.45	10.15	18,486(281)	1	3.28	LF	SPB(C)	1.09276(8)	1.72(1)
138366301	0.53	10.00	15,909(232)	1	3.04	LF	SPB	2.558(3)	0.67(2)
155305056	0.21	9.14	21,035	2(Be?)	4.55	LF	SPB	0.62176(8)	5.09(4)
158662338	0.34	12.96	11,705(131)	1	1.94	LF	SPB(C)	1.3604(4)	19.7(2)
172426403	1.09	9.34	16,207(277)	1	2.71	LF	SPB	1.5994(5)	2.52(2)
190059323	1.38	8.15	9549	2	2.45	LF	SPB	1.352(1)	0.15(1)
202270396	0.42	12.75	13,030	2	2.04	LF	SPB(C)	0.6205(1)	8.2(1)
236101031	0.55	9.57	20,258(329)	1	3.46	LF	SPB	2.927(1)	4.67(3)
247638066	3.64	5.99	12,210	2	2.68	LF	SPB	3.8000(1)	1.43(1)
252287651	0.93	8.86	13,956(1237)	1	2.94	LF	SPB	3.218(2)	0.94(1)
261361813	2.04	8.33	13,168(177)	1	2.34	LF	SPB	3.982(2)	1.45(1)
269079069	2.12	7.98	13,906(188)	1	2.48	LF	SPB	1.114714(4)	14.38(6)
273537365	1.36	9.82	15,470(264)	1	2.36	LF	SPB	1.6774(7)	2.54(3)
286043331	1.15	9.93	13,528(214)	1	2.26	LF	SPB	3.0586(5)	1.95(1)
293929714	3.49	6.39	16,849	2	2.91	LF	SPB	1.5409(3)	5.89(4)
320273520	0.97	9.52	13,502(163)	1	2.55	LF	SPB	2.59(1)	0.13(1)
328231445	7.34	5.61	13,040	2	2.28	LF	SPB	0.33485(4)	0.19(1)
355826643	1.64	8.80	16,335	2	2.66	LF	SPB	1.6335(2)	0.88(1)
404745241	3.00	7.68	12,913(245)	1	2.23	LF	SPB	1.2076(2)	5.36(4)
426419494	0.52	13.02	12,830(184)	1	1.63	LF	SPB	0.48409(1)	7.76(4)
429750051	0.55	9.06	24,332	2	4.18	LF	SPB	3.991(2)	6.16(6)
712312017	3.15	8.25	12,321(202)	1	1.92	LF	SPB	0.35934(6)	1.74(4)
1827744	1.01	9.82	14,999(202)	1	2.52	LF+HF	SPB	0.433897(4)	2.85(1)
2334539	0.95	9.37	20,005(407)	1	3.06	LF+HF	SPB	1.7416(6)	0.49(1)
3097389	0.49	9.26	20,000(51)	1	3.79	LF+HF	SPB	3.668(3)	0.32(1)
17126940	0.53	13.49	32,447	2	3.28	LF+HF	SPB	3.340(4)	1.28(2)
19935717	0.76	10.77	15,590(247)	1(Be)	2.56	LF+HF	SPB	0.48104(3)	2.32(3)
20309687	0.78	10.19	16,893(269)	1	2.87	LF+HF	SPB	0.43838(3)	1.08(1)
23992299	0.11	13.21	15,398(206)	1	3.03	LF+HF	SPB	1.1823(5)	5.13(8)
27847920	0.34	10.62	16,785(295)	1	3.24	LF+HF	SPB	0.483028(2)	1.99(2)
56750848	1.16	8.64	22,741(4422)	1(Be)	3.24	LF+HF	SPB	5.175(3)	4.97(6)
59468515	1.06	10.07	17,883(383)	1	2.60	LF+HF	SPB	0.47572(2)	1.11(1)
69225473	3.39	7.96	14,504	2	2.14	LF+HF	SPB	2.4936(3)	2.79(1)
76543999	0.99	8.22	18,519	2(Be?)	3.43	LF+HF	SPB	0.47182(1)	7.30(4)
76641076	0.27	9.72	25,029(518)	1	4.47	LF+HF	SPB	0.57454(4)	5.74(6)
78140949	1.00	9.73	14,047(237)	1	2.57	LF+HF	SPB	0.38759(2)	1.72(1)
78261043	0.40	9.45	19,379	2	3.87	LF+HF	SPB	3.949(2)	2.90(4)
80980016	0.49	9.39	21,190(426)	1	3.78	LF+HF	SPB	3.716(2)	0.97(1)
81259541	0.97	8.46	23,542	2	3.52	LF+HF	SPB	0.344228(7)	13.35(7)
117103922	0.83	8.95	20,748(341)	1	3.41	LF+HF	SPB	0.82294(8)	1.33(1)
162616331	0.37	11.66	14,676(179)	1	2.58	LF+HF	SPB	0.45571(5)	0.51(2)
200516204	1.40	9.48	12,490(175)	1(Be)	2.15	LF+HF	SPB	0.45750(2)	4.85(3)
234704735	0.38	11.30	14,587(476)	1(Be)	3.05	LF+HF	SPB	0.33594(3)	4.32(5)
234853418	1.10	9.82	14,904(293)	1	2.52	LF+HF	SPB	0.438725(1)	1.44(1)
234923805	0.60	12.68	19,494	2(Be)	2.34	LF+HF	SPB	2.573(2)	2.71(4)
234927025	1.43	9.20	13,937(367)	1(Be)	2.70	LF+HF	SPB	0.5878(1)	0.88(1)
234933597	0.70	7.74	15,050	2(Be)	4.46	LF+HF	SPB	1.65737(2)	2.53(2)
250137613	2.92	6.42	15,174	2	2.91	LF+HF	SPB	1.327400(4)	6.80(2)
264613665	0.41	11.20	22,876(462)	1	3.22	LF+HF	SPB	2.466(2)	2.61(3)
266656195	1.14	7.77	18,049(1749)	1(Be)	3.37	LF+HF	SPB	3.015(3)	10.6(2)
269267602	0.57	10.86	17,514(306)	1	2.80	LF+HF	SPB	1.85131(2)	2.60(2)
269617027	0.94	9.36	13,700(262)	1	2.76	LF+HF	SPB	1.09744(6)	5.24(4)
273038264	0.27	10.96	22,179(353)	1	3.62	LF+HF	SPB	0.7574(4)	0.83(3)
282207882	0.71	9.43	15,014(370)	1	3.08	LF+HF	SPB	0.33785(3)	2.66(3)
309335864	0.78	9.16	19,477(566)	1(Be)	3.28	LF+HF	SPB	0.54676(4)	2.00(2)
358301744	1.08	8.98	15,907(193)	1	2.89	LF+HF	SPB	0.49892(4)	0.53(1)
427352300	2.79	7.60	12,767	2	2.33	LF+HF	SPB	5.69(1)	0.45(1)
9745058	1.10	10.72	18,856	3(Be)	2.36	HF+LF	SPB	0.26122(1)	2.94(3)
72520779	0.49	11.62	13,574(179)	1	2.42	HF+LF	SPB	0.33241(1)	12.40(5)
78499882	0.60	10.00	15,407	2(Be)	2.98	HF+LF	SPB	0.28280(1)	5.25(6)
117007503	0.78	10.15	18,234(332)	1	2.89	HF+LF	SPB	0.204284(3)	2.81(2)
129011169	1.79	9.89	11,013(113)	1	1.64	HF+LF	SPB	0.27051(2)	1.59(2)
201960635	0.49	11.02	17,633(442)	1(Be)	2.91	HF+LF	SPB	0.2364358(4)	1.92(2)
234172192	0.70	9.72	14,367(474)	1	2.93	HF+LF	SPB	0.330332(8)	12.81(4)
408991617	0.94	10.14	15,981(256)	1	2.52	HF+LF	SPB	0.173038(9)	1.66(2)
414916124	1.37	10.93	11,896(135)	1	1.60	HF+LF	SPB	0.32183(2)	4.09(3)
446041643	1.89	9.52	15,266(196)	1	2.10	HF+LF	SPB	0.222960(2)	6.81(2)
20412106	1.12	8.25	13,419(190)	1	2.97	LF+HF	SPB(C)	0.50573(2)	0.58(1)
68816670	2.07	8.61	15,567(199)	1	2.38	LF+HF	SPB	0.93473(6)	2.41(2)
115730751	0.83	10.39	16,942(416)	1	2.66	LF+HF	SPB	2.9687(7)	1.37(2)
8300380	1.47	9.45	16,642	2	2.50	HF+LF	SPB	0.199347(8)	0.63(3)
76211045	0.60	9.61	21,521(367)	1	3.61	LF+HF	SPB	0.31331(3)	0.40(1)
29277573	0.81	8.60	14,858	2(Be)	3.24	LF+HF	BCEP	0.0882321(6)	2.41(2)
45802921	0.56	10.37	22,296(644)	1	3.46	LF+HF	BCEP	0.107432(4)	0.35(1)
48217508	0.46	9.84	18,387(388)	1	3.36	LF+HF	BCEP	0.0957064(9)	1.29(1)
12672166	0.55	9.78	24,374(1144)	1	3.79	HF+LF	BCEP	0.145089(5)	1.32(2)
45799839	0.54	10.16	21,409(722)	1	3.55	HF+LF	BCEP	0.132007(1)	4.05(3)
232846315	0.47	9.46	20,000(46)	1	3.68	HF+LF	BCEP	0.1318001(2)	4.28(5)
234834992	0.67	8.16	24,102	3	4.25	HF+LF	BCEP	0.1653974(4)	0.33(1)
234879286	0.62	11.14	23,537(684)	1	2.98	HF+LF	BCEP	0.076697(3)	1.01(2)
272625912	0.35	10.00	25,740(526)	1	4.26	HF+LF	BCEP	0.3025623(6)	15.4(1)
336987555	0.95	9.14	21,740(517)	1	3.43	HF+LF	BCEP	0.123298(3)	0.35(1)
348506791	0.39	8.50	30,419(637)	1	4.63	HF	BCEP(C)	0.217349(6)	13.9(1)
348608238	0.43	10.62	24,449(452)	1	3.53	HF+LF	BCEP(C)	0.176728(8)	2.30(2)
348671609	0.39	10.01	21,794(331)	1	3.74	HF+LF	BCEP(C)	0.226561(7)	5.82(3)
372115570	0.42	10.09	24,377(399)	1	3.80	HF+LF	BCEP(C)	0.252373(9)	5.25(3)
9153664	1.92	8.73	12,548	2	2.16	HF	BCEP/SPB	0.217741(3)	16.11(4)
458654855	6.68	5.91	12,228	2	2.18	HF+LF	BCEP/SPB	0.157130(1)	0.50(1)

Note. The numbers in the parentheses are the errors of the data. The targets with the H_α emission-line profile detected from LAMOST are marked as Be in the parentheses of Column (5). The capital letter C in the parentheses of Column (8) represents those targets that may be contaminated by neighboring stars in the TESS photometry apertures.

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Table 2.The Candidates of OB-type Pulsating Stars Observed by TESS, LAMOST, and Gaia

TESS ID	π	V	Teff	Flag		Comments
	(mas)	(mag)	(K)
16700873	0.14	13.00	16,607(502)	1	3.06	?
16732768	0.58	10.64	29,346	2	3.65	?
17125739	0.54	11.12	26,061	2	3.59	?(C)
17449204	0.52	10.96	12,333	2(Be?)	3.51	?
17449469	0.55	12.40	32,610	2(Oe)	3.93	?
45717172	0.57	7.43	22,590	2	4.58	?
62706478	1.38	8.20	13,660(367)	1	2.74	?
63366439	0.60	10.77	13,160(163)	1	2.41	SPB+ROT
63457231	0.79	9.88	24,689	2(Be?)	3.74	?
75509134	1.19	8.92	22,063(281)	1(Be)	3.20	?
76216928	0.80	9.51	16,065(288)	1(Be)	3.03	?
78431470	0.63	7.04	22,653	2	4.53	?
78515820	0.23	10.89	20,182	2	4.11	?
121067499	0.94	8.12	20,315	2	3.61	?
121605728	2.35	4.40	15,997	2	3.97	?
127586563	0.31	10.90	25,722(631)	1	4.12	SPB+ROT
139424697	0.45	12.03	25,090	2	2.77	?
143216039	1.41	8.11	10,400	2	2.55	?
143860583	1.21	8.63	17,400(357)	1	3.01	?
167031605	0.99	9.91	10,919(158)	1	2.22	SPB+EB
200519617	1.22	7.51	21,303(1856)	1(Be)	3.60	?
216236227	0.35	8.52	23,329	2	4.62	?(C)
234038269	1.32	9.93	11,695(198)	1	2.02	?
234841110	1.39	9.27	25,345(846)	1(Be?)	3.05	?(C)
234933368	0.47	12.46	19,341	2(Be)	3.31	?
237668110	1.39	7.85	19,127(1283)	1(Be)	3.26	SPB+ROT
239880242	2.36	8.23	11,867(267)	1(Be)	2.15	?
245048006	1.08	9.25	13,911(162)	1	2.76	?
261534342	1.09	8.73	14,500	4	2.88	?
272368236	0.57	7.50	29,111	2	4.57	SPB+EB
272843619	0.28	10.61	18,703(304)	1	3.54	?(C)
290646079	0.27	11.40	13,741(129)	1	2.90	?
302538146	3.40	7.00	14,725	2(Be)	2.55	SPB+ROT
317144497	0.41	9.33	12,288	2	3.80	?
319574477	0.63	9.16	26,558(964)	1	3.82	?
319655114	0.47	9.01	36,131(1596)	1	4.39	?(C)
320935848	0.14	11.39	20,950(10)	1(Be)	3.95	?
334155902	1.81	9.72	10,619(102)	1	1.67	?
343878395	0.65	10.14	10,700	4(Be)	4.22	SPB+ROT
344241254	5.35	6.66	9760	2	1.88	?
348023238	0.44	9.18	27,335(534)	1	4.14	BCEP+ROT(C)
349070699	0.67	8.36	23,474	2(Be)	3.89	SPB+ROT
366657610	6.68	7.56	11,392	2	1.45	ROT+SPB
412187395	1.84	9.20	12,712(144)	1(Be)	2.04	?
415674825	1.47	10.62	12,056	2	1.60	?
429715043	0.52	10.72	23,159	2(Be)	3.40	SPB+ROT
429749401	0.51	8.79	32,098(458)	1(Oe)	4.65	SPB+ROT
434303361	0.46	9.79	12,302	2	3.31	?(C)
436722939	0.63	7.80	12,926	2	3.60	SPB+ROT
445988959	2.73	7.05	14,017	2(Be)	2.64	?
470314334	0.99	10.01	14,856(240)	1	2.54	SPB+EB(C)
470472700	0.20	9.69	23,936	2(Be?)	4.98	?

Note. The numbers in the parentheses are the errors of the data. The targets with the H_α emission-line profile detected from LAMOST are marked as Be or Oe in the parentheses of Column (5). The capital letter C in the parentheses of Column (7) represents those targets that may be contaminated by neighboring stars in the TESS photometry apertures.

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Meanwhile, the parallax π of these samples is observed by the Gaia Survey and listed in Column (2) of Tables 1 and 2. The visual magnitude m_V of these samples is from the TESS Input Catalog (TIC; Stassun et al. 2018) or SIMBAD (Wenger et al. 2000) and is listed in Column (3) of Tables 1 and 2. Whether there are neighboring stars contaminating the TESS photometry apertures is checked on SIMBAD, and we mark the targets that may be contaminated with a capital letter C in parentheses in Column (8) of Table 1 and Column (7) of Table 2.

Gaia ESP-HS and GSP-Phot derived the surface effective temperatures for most of these samples. Meanwhile, LAMOST observed the low- or medium-resolution spectra of most of these samples, and their stellar atmospheric parameters were given by Guo et al. (2021). Figure 1 shows the comparison between the temperature of Gaia ESP-HS and that of LAMOST derived by Guo et al. (2021) (LAMOST_Guo), where these targets with temperatures below 30,000 K give consistent results. This means that their temperature should be reliable except for individual targets. However, the consistency of other atmospheric parameters is very poor, so only the effective temperature is quoted in this paper.

The effective temperatures T_eff of these samples are listed in Column (4) of Tables 1 and 2, and Column (5) assigns a priority flag according to the method of deriving T_eff. First, second, third, and fourth priority is given to Gaia ESP-HS, LAMOST_Guo, Gaia GSP-Phot, and the temperature estimation from the spectral type given by LAMOST, respectively. The uncertainties of effective temperature given by Gaia ESP-HS are listed in the parentheses in Column (4) in Tables 1 and 2. The average uncertainties of effective temperature estimated by Guo et al. (2021) are σ_Teff = 1642 K for low-resolution spectra and σ_Teff = 2185 K for medium-resolution spectra. The effective temperatures from low-resolution spectra have a smaller uncertainty than those from medium-resolution spectra, which may be due to the wider wavelength coverage of the low-resolution spectra (Guo et al. 2021). Those surface effective temperatures given by the third and fourth priority may lead to more errors than those given by Guo et al. (2021).

We check the H_α emission-line profile from LAMOST data and marked these Oe/Be stars and candidates (with a question mark) in the parentheses of Column (5) of Tables 1 and 2. Figure 2 shows an example of low-resolution spectra from LAMOST for a Be star. The existence of the emission lines may affect the effective temperature determinations.

The Fourier spectra of these OB-type pulsating samples are analyzed using the Period04 software (Lenz & Breger 2005), which is based on classical Fourier analysis. The signal-to-noise ratio (S/N) of the frequency is calculated with a box size of 1 day⁻¹ and the original residuals, and the errors of frequencies and amplitudes are calculated according to Montgomery & Odonoghue (1999).

We assume the value of 3 cycles day⁻¹ as a rough boundary between LF and HF in the Fourier spectra, according to the properties of the p-mode and g-mode (e.g., Stankov & Handler 2005; Aerts et al. 2010); the classification of these variable stars will be considered more later. Columns (7) and (8) of Table 1 give the descriptions of the Fourier spectra and the recommended variable star type, respectively. A star is classified as SPB if it only has the LF, i.e., there is not a frequency of more than 3 cycles day⁻¹ with an S/N greater than 5.4 for a 2 minute short cadence (Baran & Koen 2021).

In many cases, a star is detected to have LF and HF at the same time, which will be marked as LF+HF or HF+LF according to in which range frequencies seem to dominate. If there are several independent HFs, a star should be a BCEP star, because BCEP stars can oscillate in the p- and g-modes (Stankov & Handler 2005) or because those LFs are just combination frequencies of HFs. In reality, it is classified as an SPB if those HFs are combination frequencies of LFs. For example, Kurtz et al. (2015) attribute frequency groups in the Fourier spectra to g-mode pulsations and combination frequencies. There are two targets (TIC9153664 and TIC458654855) that should be classified as BCEP according to their Fourier spectra but are marked as BCEP/SPB, which will be described in the next section.

These samples identified as SPB, BCEP, and BCEP/SPB are listed in Table 1, and their Fourier spectra are shown in Figures 3 and 4. Their dominant frequencies and amplitudes are listed in Columns (9) and (10) of Table 1, and the errors in the last column are in parentheses. We found that almost all targets with HF also have LF, except TIC9153664 and TIC348506791. Moreover, it seems that the two targets also have some frequencies less than 3 cycles day⁻¹ from the Fourier spectra, but their S/N is less than 5.4. This may be because less data coverage (only one sector) of TIC9153664 and TIC348506791 makes these LFs with a low S/N.

Generally, rotational variability is caused by spots or the stellar wind (Burssens et al. 2020), etc, which in Fourier spectra show as a series (possibly more than two) of harmonic frequencies of the rotation frequency, similar to the eclipsing binary, but no obvious eclipse can be seen in the light curve. Table 2 lists 52 candidate targets, including the following situations:

(a) a pulsating variable star may be in an eclipsing binary (EB) or a rotational variable (ROT), including SPB+EB and BCEP+EB or SPB+ROT and BCEP+ROT;

(b) if a variable star could not detect coherent periodic signals and is suspected of exhibiting internal gravity waves or rotational variation, it will be marked as a question mark.

The luminosity of these OB-type pulsating stars or candidates are shown in Column (6) of Tables 1 and 2, which are calculated using

where the bolometric correction BC is estimated based on the surface effective temperature using the calibration derived by Pecaut & Mamajek (2013), and the interstellar extinction A_V is calculated from Schlafly & Finkbeiner (2011). The average uncertainties of is estimated as about 0.1 dex, from the standard deviations for the visual magnitude m_V about 0.01 mag, for the bolometric correction BC about 0.02 mag, for the interstellar extinction A_V about 0.10 mag, and for the Gaia parallax about 0.05 mas.

The H-R diagram of these OB-type pulsating stars and candidates is displayed in Figure 5. In this figure, the evolutionary tracks for the mass of 2.5, 7, and 20 M_⊙, and the theoretical zero-age main sequence for Z = 0.02 were created with the stellar evolution code Modules for Experiments in Stellar Astrophysics (Paxton et al. 2011, 2013, 2015, 2018, 2019). The blue and magenta dotted line shows the instability regions of the SPB and BCEP stars for Z = 0.02 and a spherical harmonic degree l ≤ 3 from Miglio et al. (2007), respectively.

We rechecked some targets that deviated from the instability regions in the H-R diagram. It is found that the effective temperature of some targets may be unreliable, such as TIC234933597, 53327951, 29277573, 190059323, 9745058, and 17126940, which do not have the effective temperature given by Gaia ESP-HS, only by LAMOST_Guo or Gaia GSP-Phot with low reliability. However, the effective temperature for most targets should be reliable, even for some targets that deviate significantly in the H-R diagram. For example, Gaia ESP-HS and LAMOST_Guo both gave the same effective temperature for TIC234879286, 426419494, 414916124, 234923805, and 129011169, and their effective temperature should be reliable.

Figure 6 shows the relation between the dominant pulsation period and the surface effective temperature (P-T) for these OB-type pulsating stars, where the size of the circles indicates their pulsation amplitude of the dominant frequency. Except TIC9153664 and TIC458654855, although there are a few targets with an unreliable effective temperature, those SPB and BCEP stars can be separated by a simple straight line in the P-T diagram.

The relation of their dominant pulsation period and luminosity (P-L) is shown in Figure 7, in which those SPB and BCEP stars show rough linear distributions. The least-square method derived the fitting equation, for all SPB stars:

for those SPB stars with pure LF:

and for those BCEP stars:

Equations (3) and (4) have the same slope but are different from Equation (5), indicating that those SPB with pure LF and with combination frequencies in HF belong to the same kind of variables and are different from those of BCEP stars. Similar to the P-T diagram, those SPB and BCEP stars can also be separated by a simple straight line in the P-L diagram.

As can be seen in the H-R diagram, these SPB and BCEP stars are mainly located in their instability regions, and most are in the evolutionary stage of the main sequence with a mass range of 2.5–20 M_⊙ for SPB and 7–20 M_⊙ for BCEP.

TIC9153664 and 458654855 both show Fourier spectra similar to those BCEP stars, but they are not only distributed in the same region as those SPB stars in the H-R diagram but also in the P-T and P-L diagrams. Therefore, they are marked as BCEP/SPB.

We identify 155 OB-type pulsating stars or candidates, including 38 Oe/Be stars or candidates, by visual classification from the data of TESS, LAMOST, and Gaia. Then, we calculated their luminosity, and obtained their H-R diagram by combining it with their effective temperature. Among the 155 objects, 87 samples are identified as SPB stars including 37 objects with pure LFnd 50 objects with both LF and HF pulsation, where these HF pulsations are combined with LFs. A total of 14 targets with both LF and HF are identified as BCEP stars, and our results also indicate that there is no pure HF pulsating star. The H-R diagram shows that these SPB and BCEP stars are mainly located in their instability regions and the evolutionary stage of the main sequence with a mass range of 2.5–20 M_⊙ for SPB and 7–20 M_⊙ for BCEP.

Except for those targets with unreliable temperatures, there are a few stars located around the instability regions in the H-R diagram that may be the pulsating subdwarfs or the main-sequence pulsating dwarfs with a different metallicity. Some objects (such as TIC23992299, 16700873, 290646079, and 426419494) are located 20°–50° off the Galactic plane, indicating they should not be young objects, possibly because they are massive stars originating from binary mergers (e.g., Schneider et al. 2016 and Wang et al. 2022) or runaway stars from the Galactic plane. Of course, they could also simply be subdwarfs as classified in SIMBAD.

TIC9153664 and 458654855 both show Fourier spectra similar to that of BCEP stars, but they are not only distributed in the same region as those SPB stars in the H-R diagram but also in the P-T and P-L diagrams. If their positions in the H-R diagram are correct, they are likely to be a special kind of target. Their HFs may likely be g-mode frequencies shifted to higher apparent values by rapid rotation (e.g., Bouabid et al. 2013). In addition, the results of Stromgren–Crawford uvbyβ photometry (Paunzen 2015) seem to indicate that both stars are of spectral type A and rather evolved, which is consistent with their relatively high luminosity as main-sequence A-type stars and their locations outside the Galactic plane (+19° and +28°, respectively). In this case, they could just as well simply be δ Sct pulsators.

We also derive the preliminary results of the P-L relation for SPB and BCEP stars by the least-square method, which may reveal potential for massive pulsating stars to be used as a standard candle to measure distances. However, more samples and further research are needed to improve their accuracy, especially for BCEP stars.

Although the SPB and BCEP stars have overlapping regions in the H-R diagram, they can be distinguished in the P-T and P-L diagrams. In addition to the H-R diagram, the P-T and P-L diagrams are also very useful for the classification of SPBs and BCEPs.

These OB-type pulsating stars are very important sources for further study of massive stars via the method of asteroseismology, which has the potential to dramatically increase our understanding of the theory of evolution and structure for this type of star. In the future, it is necessary to study these objects from various views in more detail.