Gravity-mode main-sequence asteroseismology of 16 open clusters and associations

Introduction

Asteroseismology is the study of stellar oscillations and what they reveal about stellar interiors (see the reviews by C. Aerts et al. [3]; D. M. Bowman & L. Bugnet [30]). Over the past decade, space-based photometric missions such as M. Auvర్గne et al. 2009, Kepler (W. J. Borucki et al. [25]), and TESS (G. R. Ricker et al. [149]) have driven major advances in the field and deepened our understanding of stellar physics (e.g. C. Aerts [1]). In particular, gravity (g) modes are highly sensitive to the physical conditions in and near stellar cores, and therefore provide direct probes of near-core regions. In early-type main-sequence stars ($T_{\rm eff} \gtrsim7000\,\mathrm{K}$), high-radial-order ($20 \lesssim n \lesssim100$),

Corresponding author: Gang Li Email: [email protected]

photometric missions such as CoRoT (M. Auvर्गne et al. 2009), Kepler (W. J. Borucki et al. [25]), and TESS (G. R. Ricker et al. [149]) have driven major advances in the field and deepened our understanding of stellar physics (e.g. C. Aerts [1]). In particular, gravity (g) modes are highly sensitive to the physical conditions in and near stellar cores, and therefore provide direct probes of near-core regions. In early-type main-sequence stars ($T_{\rm eff} \gtrsim7000\,\mathrm{K}$), high-radial-order ($20 \lesssim n \lesssim100$), low-degree ($\ell\lesssim2$) g modes can reach observable amplitudes at the surface because their envelopes contain only shallow (or no) convective layers (e.g. T. Van Reeth et al. [178]; G. Li et al. (2020b)). Stars exhibiting g-mode pulsations are either γ Doradus stars (A- to F-type; L. A. Balona et al. [13]; A. B. Kaye et al. [86]) or Slowly Pulsating B-type (SPB) stars (C. Waelkens [183]; P. De Cat & C. Aerts [45]). Here we use the umbrella term “g-mode pulsators” for both classes. These g-mode pulsators have proved to be powerful probes of multiple physical processes, including near-core rotation (T. Van Reeth et al. [177]; G. Li et al. (2020b); S. Garcia et al. [61]), convective-core overshooting and mixing in the radiative envelope (A. Miglio et al. [116]; M. G. Pedersen et al. [140]; J. S. G. Mombarg et al. [121]), angular-momentum (AM) transport (R. M. Ouazzani et al. [132]; F. D. Moyano et al. [124]; J. S. G. Mombarg et al. [117]; J. S. G. Mombarg & S. Mathis [120]), and even deep-seated magnetic fields (M. Takata et al. [173]; S. Ihallaine et al. (2026)).

Despite these successes, comprehensive modelling of gravity-mode main-sequence pulsators remains computationally demanding. Detailed modelling is at least a seven-dimensional problem (C. Aerts et al. [5]), and several physical descriptions cannot yet be derived from first principles and lack robust calibration, such as mixing length and convective overshooting (e.g. M. Joyce & J. Tayar [85]). In addition, the most basic parameters of stellar evolution, mass, age, and metallicity, often lack accurate measurements, which leads to severe parameter degeneracies. This forces us to explore a wide parameter space and makes the computation of evolutionary grids time-consuming.

Furthermore, the underlying physics of AM transport and envelope mixing also remains uncertain: multiple processes may operate simultaneously. For example, AM transport may be driven by meridional circulation (J. P. Zahn [188]; A. Maeder & J.-P. Zahn [109]), shear instabilities (A. Heger et al. [72]), magnetic dynamos (H. C. Spruit [167]; J. Fuller et al. [58]), or internal gravity waves (T. M. Rogers et al. [150]; R. P. Ratnasingam et al. [145]; T. M. Rogers & R. P. Ratnasingam [152]; S. Mathis [111]) (see C. Aerts et al. [4] for a review). Chemical mixing in radiative envelopes may arise from shear mixing (A. Maeder [107]), internal gravity waves (T. M. Rogers & J. N. McElwaine [151]; A. Varghese et al. [181, 180]; J. S. G. Mombarg et al. (2025)), or surface fossil magnetic fields (Z. Keszthelyi et al. [89]) (see A. Maeder [108] and M. Salaris & S. Cassisi [158] for reviews). Yet their relative contributions and calibrations are still poorly constrained.

Seeking additional constraints on stars greatly helps to expand the scope of asteroseismic modelling. Binaries with two pulsating components are already highly valuable (e.g. C. Johnston et al. [84]; S. J. Murphy et al. [128]; M. Hon et al. [78]; P. G. Beck et al. [19]), provided that the two stars are coeval and chemically homogeneous (e.g. A. L. Kraus & L. A. Hillenbrand [94]; G. Valle et al. [176]). Previous synergistic binary-asteroseismology studies have strongly tested current stellar evolutionary theory, in both main-sequence and post-main-sequence phases (e.g. V. S. Schmid & C. Aerts [162]; Z. Guo et al. [69]; Y. Li et al. (2018); S. Sekaran et al. [165]; S. J. Murphy et al. [128]; L. S. Schimak et al. [161]).

Even more powerfully, clusters with many coeval pulsating stars provide a much stronger set of constraints and tests of stellar models (e.g. L. Piau et al. [142]; K. Brogaard et al. [36]). Recent studies highlight both the promise and current limitations: J. Tayar & M. Joyce [175] found large star-to-star scatter in red-giant asteroseismic ages within the same cluster, sometimes in apparent tension with isochrone ages. On the other hand, D. J. Fitzwinski et al. (2024) showed that joint modelling of g-mode asteroseismology, gyrochronology, and isochrone fitting yields a more robust age for the young open cluster UBC1. In addition to a common age, global stellar parameters such as temperature, luminosity, and mass can be inferred from the stars’ locations on the colour-magnitude diagram (CMD). G. Li et al. (2025) modelled several g-mode pulsators in NGC 2516 and inferred a seismic cluster age of 132 $\pm$ 8 Myr, but reported discrepancies between seismic and isochrone masses. These discrepancies may arise from inconsistencies between surface and interior properties, or may indicate that a detailed treatment of the effects of rotation on the CMD is needed. A series of recent studies has demonstrated the potential of cluster–asteroseismology synergistic research.

Asteroseismology in clusters has been burgeoning over the past decade. Early efforts used CoRoT data (e.g. K. Zwintz et al. [191]). The Kepler field contained four well-known clusters, NGC 6791, NGC 6819, NGC 6811, and NGC 6866 (e.g. D. Stello et al. 2011; S. Hekker et al. 2011; S. Basu et al. 2011; E. Corsaro et al. 2012; L. A. Balona et al. 2013a,b; K. Brogaard et al. 2021a; I. L. Colman et al. 2022; K. Brogaard et al. 2023), and asteroseismology helped constrain the properties of these clusters in the pre-Gaia era. The K2 mission scanned along the ecliptic plane and covered many additional clusters (e.g. M. N. Lund et al. [106]; D. Stello et al. [171]; E. L. Sandquist et al. [160]; S. J. Murphy et al. [126]), enabling the detection of a seismic signature of deepening convective envelopes in post-main-sequence solar-like oscillators in M 67 [148].

Data from the ongoing TESS mission is also useful for asteroseismology in clusters, despite the shorter observing baselines and crowding in its large pixels. In particular, pressure-mode (p-mode) pulsators in open clusters—whose amplitude spectra can often be resolved with shorter light curves—have been identified with TESS data, including in the Pleiades [20], NGC 3532 [23], the Cep–Her complex [125], NGC 1901 [22], and NGC 2126 [46]. Gravity-mode period-spacing patterns have also been discovered using year-long light curves in the TESS continuous viewing zone in UBC 1 and NGC 2516 [55] (G. Li et al. 2024). Such patterns have also been observed in shorter TESS light curves in the Pleiades and NGC 3532 [54].

In this paper, we present g-mode period-spacing patterns for 68 member stars across 16 stellar groups. Throughout this work, we use “stellar groups” as an umbrella term encompassing open clusters, young stellar associations, and substructures within larger stellar complexes. Our homogeneous sample of early-type main-sequence stars with measured near-core rotation rates and asymptotic spacings establishes a benchmark data set for calibrating AM transport and internal mixing in future stellar-evolution models. The paper is organised as follows. § 2 describes the properties of the stellar groups studied in this work. § 3 details the asteroseismic signal extraction, including frequency pre-whitening, period-spacing pattern identification, and fitting under the traditional approximation of rotation (TAR). We present an overview of our seismic measurements in § 4, including the distribution of near-core rotation rates in § 4.1, their mass-dependent evolution in Section 4.2, and the corresponding results for asymptotic spacings in Sections 4.3 and § 4.4. We present a newly discovered pre-main-sequence pulsator in § 5, and discuss the pulsating blue stragglers in our sample in § 6. Finally, § 7 summarises our main conclusions.

The Stellar Groups in This Work

The Collected Stellar Groups

Gaia has enabled the large-scale identification of open clusters, leading to the release of various open-cluster catalogues [e.g. 39, 41, 143, 141, 79]. In this work, we relied on the all-sky cluster catalog and membership lists derived from Gaia DR3 by E. L. Hunt & S. Reffert [79].

Some clusters in this work were compiled before the publication of E. L. Hunt & S. Reffert [79], while some others are not included in their catalogue. For these systems, we adopted membership lists from elsewhere in the literature. In particular, we used the Gaussian-mixture-model memberships for the four well-known open clusters in the Kepler field (H. Wang et al. 2026), the NGC 2516 memberships from S. Meingast et al. [114], the NGC 3532 memberships from X. Pang et al. [135], the Pleiades memberships combined from J. Gagné & J. K. Faherty [59] and S. Meingast et al. [114] (see D. J. Fritzewski et al. [54]), the Huluwa 1–5 subgroup definitions and memberships for Vela OB2 from X. Pang et al. [134], and the Cep–Her complex memberships from R. Kerr et al. [88], as adopted by S. J. Murphy et al. [125].

For the Kepler field, by crossmatching with the catalogue by E. L. Hunt & S. Reffert [79], we found that, in addition to the four well-known clusters, three further open clusters were identified: CWNU 1183 ($\sim50$ Myr), ASCC 108 ($\sim190$ Myr), and Theia 4877 ($\sim720$ Myr). However, these clusters were sparsely sampled by Kepler, with light curves available for only a few member stars.

For stellar groups observed by TESS, we did not perform photometric reductions for every group across the sky. Instead, we prioritised targets based on asteroseismic requests from our collaborators (e.g., for spectroscopic follow-up, rotation measurements, or complementary g-mode analyses). In practice, whenever such a group had at least two consecutive TESS sectors of coverage, we reduced and analysed the corresponding light curves to search for g-mode period-spacing patterns.

In total, we collected 16 stellar groups for g-mode asteroseismic analysis, listed in the first column of Table 1.

Stellar group	Age (Myr)	$A_V$ (mag)	Distance (pc)	TIC or KIC	Gaia DR3 source id	RA (deg)	Dec (deg)	$f_{\rm rot}$ (d$^{-1}$)	$\Pi_0$ (s)	Mass (M$_\odot$)
Perseus	$6.5^{+2.2}_{-2.2}$	1.2	$286^{+5}_{-5}$	TIC 26532226*	216759169703741952	57.308996	31.734505	$1.23^{+0.09}_{-0.09}$	$4130^{+400}_{-400}$	$1.52^{+0.07}_{-0.10}$
Vela OB2	Huluwa	$14^{+8}_{-8}$	0.35	$352.0^{+2.9}_{-2.9}$	TIC 56640851*	5543536661448630528	127.241234	-34.493455	$2.634^{+0.007}_{-0.007}$	$4302^{+70}_{-60}$
Cep-Her	ORPH	$32^{+8}_{-8}$	0.27	$341.2^{+1.5}_{-1.6}$	TIC 349011395*	4531730361801104512	282.504541	22.909099	$2.128^{+0.013}_{-0.014}$	$4350^{+70}_{-70}$
Cep-Her	ORPH	$32^{+8}_{-8}$	0.24	$341.2^{+1.5}_{-1.6}$	TIC 346151391*	4531762659948423936	280.041233	21.097964	$0.965^{+0.010}_{-0.009}$	$4794^{+90}_{-80}$
Cep-Her	CUPV	$67^{+13}_{-13}$	0.083	$341.2^{+1.5}_{-1.6}$	TIC 303754397*	2181689321609724544	309.023173	53.203000	$1.956^{+0.026}_{-0.028}$	$3429^{+190}_{-190}$
Cep-Her	CINR	$36^{+8}_{-8}$	0.087	$341.2^{+1.5}_{-1.6}$	TIC 277011700*	2181783295493195264	306.492739	52.483826	$1.57^{+0.03}_{-0.03}$	$4632^{+280}_{-260}$
Cep-Her	CINR	$36^{+8}_{-8}$	0.076	$341.2^{+1.5}_{-1.6}$	TIC 277570969*	2184113366783588096	311.067054	56.173412	$0.750^{+0.017}_{-0.018}$	$9688^{+400}_{-400}$	$3.42^{+0.10}_{-0.10}$
CWNU 1183	$46^{+40}_{-20}$	0.11	$471.7^{+0.6}_{-0.6}$	KIC 3868382	2073188036719192960	295.851255	38.996251	$0.8441^{+0.0004}_{-0.0004}$	$4453^{+9}_{-10}$	$1.676^{+0.027}_{-0.05}$
Pleiades	$125^{+8}_{-8}$	0.10	$134.841^{+0.018}_{-0.018}$	TIC 385552372	65296357738731008	56.393686	24.463107	$2.54^{+0.07}_{-0.07}$	$4860^{+1800}_{-1800}$	$1.568^{+0.017}_{-0.03}$
Pleiades				TIC 67828699	63502259702709888	56.383383	21.246480	$2.990^{+0.020}_{-0.020}$	$5150^{+260}_{-260}$	$1.89^{+0.04}_{-0.04}$
Pleiades				TIC 5536869	62413988007668352	49.457440	22.831990	$1.88^{+0.07}_{-0.07}$	$5245^{+1100}_{-1100}$	$1.97^{+0.05}_{-0.05}$
NGC 2516	$132^{+8}_{-8}$	0.20	$407.09^{+0.09}_{-0.09}$	TIC 341043961	5295292121571898880	118.323853	-57.552839	$3.011^{+0.011}_{-0.012}$	$5035^{+90}_{-110}$	$1.499^{+0.021}_{-0.05}$
NGC 2516				TIC 308307454	5290771204639131648	120.228699	-60.754088	$0.97^{+0.03}_{-0.04}$	$4340^{+150}_{-160}$	$1.515^{+0.023}_{-0.05}$
NGC 2516				TIC 358466729	5290739146997100160	119.262316	-60.610183	$2.1191^{+0.003}_{-0.0029}$	$4726^{+80}_{-90}$	$1.533^{+0.023}_{-0.05}$
NGC 2516				TIC 410452218	5290650705036608256	119.914707	-61.194376	$2.803^{+0.010}_{-0.01}$	$4799^{+90}_{-90}$	$1.628^{+0.025}_{-0.06}$
NGC 2516				TIC 281582674	5289355171098491520	115.990674	-61.694069	$2.953^{+0.006}_{-0.006}$	$4841^{+60}_{-60}$	$1.70^{+0.04}_{-0.04}$
NGC 2516				TIC 364398040	5290820029826947968	119.628849	-60.629526	$2.947^{+0.014}_{-0.014}$	$4865^{+120}_{-120}$	$1.77^{+0.03}_{-0.07}$
NGC 2516				TIC 372912679	5290642699218901376	119.483950	-61.365514	$3.005^{+0.011}_{-0.013}$	$4821^{+100}_{-110}$	$1.82^{+0.03}_{-0.08}$
NGC 2516				TIC 308992761	5276258269626067840	123.282602	-61.365514	$3.005^{+0.011}_{-0.013}$	$4821^{+100}_{-110}$	$1.82^{+0.03}_{-0.08}$
UBC 1	$225^{+80}_{-80}$	0.062	$322.42^{+0.16}_{-0.16}$	TIC 421313449	2142861741434813440	288.972108	57.893139	$1.265^{+0.027}_{-0.027}$	$7530^{+700}_{-800}$	$3.54^{+0.40}_{-0.29}$
ASCC 108	$265^{+5}_{-5}$	0.37	$1152^{+17}_{-17}$	TIC 4774208	2073453179242124416	289.194971	39.860692	$0.544^{+0.009}_{-0.009}$	$4549^{+24}_{-24}$	$1.649^{+0.023}_{-0.023}$
NGC 3532	$340^{+10}_{-20}$	0.12	$471.88^{+0.11}_{-0.11}$	TIC 4497303	2073647624945728000	298.193925	-58.956847	$2.574^{+0.019}_{-0.019}$	$4300^{+22}_{-22}$	$1.68^{+0.04}_{-0.04}$
NGC 6866	$590^{+170}_{-170}$	0.31	$1402.0^{+2.2}_{-2.2}$	TIC 8330312	2076066474968988288	300.952501	44.119388	$1.338^{+0.005}_{-0.005}$	$4241^{+90}_{-90}$	$1.51^{+0.05}_{-0.05}$
NGC 6866				TIC 8264304	2076048752958379744	300.921448	44.111050	$1.552^{+0.020}_{-0.020}$	$3897^{+240}_{-240}$	$1.51^{+0.05}_{-0.05}$
NGC 6866				KIC 8197019	2076063122179130624	300.848740	44.077964	$1.886^{+0.010}_{-0.009}$	$3896^{+100}_{-100}$	$1.52^{+0.05}_{-0.05}$
Stellar group	Age (Myr)	$A_V$ (mag)	Distance (pc)	TIC or KIC	Gaia DR3 source id	RA (deg)	Dec (deg)	$f_{\rm rot}$ (d$^{-1}$)	$\Pi_0$ (s)	Mass ($M_\odot$)
				KIC 8264720	2081882459267654400	301.023483	44.173077	$1.450^{+0.013}_{-0.014}$	$4232^{+150}_{-150}$	$1.55^{+0.04}_{-0.05}$
				KIC 8198031	2075873422065500800	301.111555	44.063979	$1.8549^{+0.0014}_{-0.0013}$	$4144^{+21}_{-21}$	$1.55^{+0.04}_{-0.05}$
				KIC 8330056	2076066145836177408	300.887723	44.201764	$1.9125^{+0.0012}_{-0.0012}$	$4096^{+15}_{-15}$	$1.55^{+0.04}_{-0.05}$
				KIC 8263970	2076063568855737728	300.841745	44.106563	$1.9462^{+0.0012}_{-0.0012}$	$4183^{+18}_{-18}$	$1.56^{+0.04}_{-0.05}$
				KIC 8265126	2081881905204354048	301.124823	44.175800	$0.891^{+0.004}_{-0.004}$	$4198^{+50}_{-40}$	$1.57^{+0.04}_{-0.05}$
				KIC 8127448	2076047591576773120	300.406599	43.947894	$1.145^{+0.013}_{-0.013}$	$4256^{+110}_{-110}$	$1.57^{+0.04}_{-0.05}$
				KIC 8264708	2075877648313310848	301.020006	44.159308	$1.6361^{+0.0012}_{-0.0011}$	$4240^{+40}_{-40}$	$1.66^{+0.04}_{-0.07}$
				KIC 8330092	2076066725646925824	300.895527	44.247220	$1.36^{+0.04}_{-0.04}$	$3643^{+210}_{-200}$	$1.67^{+0.04}_{-0.07}$
				KIC 8197788*	2075876583161403392	301.046622	44.092546	$2.290^{+0.012}_{-0.012}$	$4512^{+90}_{-90}$	$1.86^{+0.05}_{-0.08}$
				KIC 8264667	2075877609644932608	301.010774	44.157189	$0.684^{+0.005}_{-0.005}$	$4240^{+130}_{-130}$	$2.03^{+0.05}_{-0.13}$
				KIC 8264550	2075877884522838400	300.979905	44.178839	$1.536^{+0.014}_{-0.014}$	$4521^{+170}_{-160}$	$2.25^{+0.11}_{-0.15}$
				KIC 8264293*	2076065699159591296	300.919389	44.195388	$2.427^{+0.015}_{-0.016}$	$7935^{+400}_{-400}$	$3.18^{+0.17}_{-0.10}$
NGC 2632	$700^{+100}_{-100}$	0.16	$183.49^{+0.04}_{-0.04}$	TIC 175239414*	664329190407201280	129.993050	20.158186	$2.119^{+0.005}_{-0.004}$	$3842^{+40}_{-40}$	$1.69^{+0.05}_{-0.04}$
				TIC 184873310*	664845308036464256	130.720922	20.819176	$1.083^{+0.028}_{-0.029}$	$4113^{+190}_{-180}$	$1.72^{+0.05}_{-0.04}$
				TIC 14503989*	663386977661550336	125.459595	19.489010	$0.958^{+0.004}_{-0.004}$	$4255^{+20}_{-21}$	$1.74^{+0.04}_{-0.06}$
Theia 4877	$720^{+400}_{-270}$	0.22	$1268^{+4}_{-4}$	KIC 8240902	2078327841249527168	294.484252	44.155876	$0.896^{+0.004}_{-0.004}$	$4437^{+50}_{-50}$	$1.55^{+0.04}_{-0.04}$
NGC 1901	$820^{+120}_{-120}$	0.12	$416.34^{+0.25}_{-0.25}$	TIC 30935460*	4661283304330138112	76.225559	−68.685193	$1.11^{+0.07}_{-0.08}$	$3565^{+1200}_{-900}$	$1.540^{+0.04}_{-0.029}$
				TIC 179437576*	4658745635794924160	80.047359	−68.040575	$1.1519^{+0.0006}_{-0.0005}$	$3970^{+14}_{-14}$	$1.60^{+0.04}_{-0.03}$
NGC 6811	$1100^{+200}_{-200}$	0.088	$1110.1^{+1.3}_{-1.3}$	KIC 9716563	2128134824634071424	294.410699	46.486817	$0.9081^{+0.0009}_{-0.0008}$	$3861^{+10}_{-10}$	$1.453^{+0.04}_{-0.018}$
				KIC 9716350	2128145166915272832	294.324900	46.462534	$0.8631^{+0.0026}_{-0.0026}$	$4079^{+60}_{-60}$	$1.458^{+0.04}_{-0.018}$
				KIC 9654789*	2128119568910037632	294.119940	46.310836	$1.1423^{+0.0009}_{-0.0009}$	$3856^{+18}_{-19}$	$1.474^{+0.04}_{-0.020}$
				KIC 9655399*	2128109089189944448	294.078348	46.331?	$1.0263^{+0.0012}_{-0.0012}$	$3999^{+15}_{-15}$	$1.479^{+0.04}_{-0.020}$
				KIC 995?
NGC 6819	$2300^{+300}_{-300}$	0.32	$2510^{+5}_{-5}$	KIC 502?
NGC 6791	$8200^{+400}_{-400}$	0.65	$4189^{+9}_{-9}$	KIC 243?

NOTE—Stars marked with an asterisk are newly reported in this work. Existing distances are the median posterior values from Hunt & Reffert [79] where available; the distance uncertainties span the 16th–84th percentiles. The values for Vela OB2 and Perseus Alcaeus are from Olivares et al. [130]. Their extinction values, while the listed distance uncertainty is propagated from the tabulated parallax uncertainty. The Cep-Her extinction uncertainty is propagated from the listed distance and its propagated uncertainty. The mean of the five Cep-Her stars, using the geometric distances adopted by Kerr et al. [87].

Our collection spans a wide age range. We have four stellar groups younger than $\sim50$ Myr (Alcaeus in Perseus, Huluwa in Vela OB2, and the Orpheus and Cinyras associations in Cep–Her), providing the opportunity to discover pre-main-sequence (PMS) g-mode pulsators. Beyond the PMS phase, our sample extends from an age of $\sim67$ Myr (the Cupavo association in the Cep–Her complex) to $\sim1100$ Myr with NGC 6811. Unfortunately, we could not collect any normal $\gamma$ Dor pulsators in stellar groups with ages between $\sim1100$ Myr and $\sim2300$ Myr. This age interval roughly corresponds to the epoch when many open clusters dissolve into the Galactic field, and when stars with masses of $\sim1.5\,\mathrm{M}_{\odot}$, typical of $\gamma$ Dor stars, leave the main sequence. Interestingly, NGC 6819 ($\sim2300$ Myr) and NGC 6791 ($\sim8200$ Myr) show rich populations of blue stragglers located in the g-mode instability strip. We indeed found one g-mode pulsator with clear period-spacing patterns in each of the two clusters. Detailed descriptions of our PMS pulsators and blue-straggler pulsators are given in Sections 5 and 6.

Adopted Ages of the Stellar Groups

Table 1 lists all 16 stellar groups. We found substantial discrepancies between the ages given by E. L. Hunt & S. Reffert [79] and the well-established ages in the literature. We therefore reviewed the literature and adopted the stellar-group ages listed in the second column of Table 1. We provide the details of the adopted ages, in chronological order, in the following paragraphs.

T. Pavlidou et al. [137] identified Alcaeus as a subgroup of the Perseus star-forming region and estimated its age to be around 5 Myr. M. Kounkel et al. [92] reported an age of 4.5 Myr for Alcaeus. J. Olivares et al. [130] found an age of 10 Myr, while T. Pavlidou et al. [136] most recently reported 5–8 Myr. We therefore adopted 6.5 $\pm$ 2.2 Myr for Alcaeus, calculated as the mean and standard deviation of the previous measurements.

For Vela OB2, we adopted the Huluwa membership and age scale of X. Pang et al. [134], who divided the structure into five subgroups, Huluwa 1–5, with ages of 10–22 Myr for the older Huluwa 1–3 and 7–20 Myr for the younger Huluwa 4–5. Within this framework, we adopted 14 $\pm$ 8 Myr for Huluwa, encompassing the full age range reported by X. Pang et al. [134]. An independent spectroscopic and three-dimensional kinematic analysis by J. J. Armstrong et al. [6] adopted a different decomposition of the region, distinguishing the extended Vela OB2 association from the $\gamma$ Vel and P Puppis clusters, while deriving ages broadly consistent with the 10–20 Myr range. Thus, the Huluwa subgroup labels and ages used here should be understood specifically within the framework of X. Pang et al. [134].

We identified five g-mode pulsators in three young associations within the Cep–Her complex. We assigned their ages following R. Kerr et al. [87]: 32 $\pm$ 8 Myr for Orpheus, 36 $\pm$ 8 Myr for Cinyras, and 67 $\pm$ 13 Myr for Cupavo.

For CWNU 1183 in the Kepler field, O. Ironi et al. [83] derived an age of 48 $\pm$ 6 Myr but noted that the age uncertainty may be underestimated. We therefore adopted the age from E. L. Hunt & S. Reffert [79], who reported a consistent result with a larger uncertainty, $46^{+40}_{-20}$ Myr.

Ages for some other clusters were adopted as follows. For NGC 2516, we used 132 $\pm$ 8 Myr, measured by four g-mode pulsators simultaneously (G. Li et al. 2025). The age was also supported by the gyrochronological age of this cluster by D. J. Fritzewski et al. [53]. For the Pleiades, the most widely accepted age is 125 $\pm$ 8 Myr from the lithium-depletion boundary J. R. Stauffer et al. [168], although this age is sensitive to both the membership list used and the underlying model physics, particularly the treatment of magnetic fields S. E. Dahm [44]. D. J. Fritzewski et al. [54] pointed out that the g-mode properties of Pleiades member stars are similar to those of NGC 2516, supporting a similar age. We adopted 225 $\pm$ 75 Myr for UBC 1, derived by asteroseismology and gyrochronology by D. J. Fritzewski et al. [55]. D. Yazıcı et al. [187] reported an isochrone-fitting age of 265 $\pm$ 5 Myr for ASCC 108. C. He et al. [71] performed isochrone-fitting for NGC 3532 and derived an age of $340^{+?}_{-20}$ Myr.

Age measurements for NGC 1901 are quite scattered. E. L. Hunt & S. Reffert [79] reported an age of $283^{+220}_{-120}$ Myr, and G. Carraro et al. [40] reported 400 $\pm$ 100 Myr. Older ages have also been suggested: J. Kos et al. [91] reported $\log(\mathrm{age}/\mathrm{yr}) = 8.84$ ($\sim692$ Myr) from Padova isochrone fitting, M. Bernizoni et al. (2026) derived an age from gyrochronology of 820 $\pm$ 120 Myr, T. Cantat-Gaudin et al. [39] reported 891 Myr, and S. Malhotra et al. [110] obtained $\log(\mathrm{age}/\mathrm{yr}) = 8.987$ ($\sim971$ Myr). We adopted the gyrochronological age because our g-mode asteroseismic results favoured an older age (see the discussion in Section 4.4).

Age measurements for NGC 2632 and NGC 6866 remain highly model dependent. For NGC 2632, T. D. Brandt & C. X. Huang [31] reported an age of 810 $\pm$ 70 Myr after including rotation, compared with the previously well-accepted age of around 600 Myr. In contrast, S. Gossage et al. [66] reproduced an age of 610 $\pm$ 25 Myr based on models with different initial rotation assumptions, as summarized in their tbl:3. We therefore adopted an average age of $700 \pm100$ Myr. For NGC 6866, H. Wang et al. (2026) reported a PARSEC-isochrone age of $690^{+140}_{-30}$ Myr, a MESA-isochrone age of $467^{+70}_{-50}$ Myr, and a g-mode asteroseismic age of $759^{+54}_{-82}$ Myr. In addition, K. Brogaard et al. [38] reported an age of $430 \pm50$ Myr based on red-giant oscillations. We thus adopted an average age of $590 \pm170$ Myr for NGC 6866.

We did not find a dedicated age study for Theia 4877, so we adopted the age from E. L. Hunt & S. Reffert [79], which is $720^{+400}_{-270}$ Myr. For NGC 6811, we adopted an age of $1.1 \pm0.2$ Gyr, measured using an eclipsing binary in the cluster by E. L. Sandquist et al. [159] and consistent with S. Meibom et al. [113].

Several age estimates are available for NGC 6819. S. Basu et al. [17] reported an age of $2.4 \pm0.4$ Gyr based on 12 red-giant stars in NGC 6819 and summarized that the seismic age is consistent with ages determined from several isochrone models. We also included the age measured from eclipsing binaries (L. N. Brewer et al. [33]), and the white-dwarf cooling-sequence age by L. R. Bedin et al. [21]. Therefore, we adopted a mean age of $2.3 \pm0.3$ Gyr for NGC 6819.

For NGC 6791, solar-like asteroseismic age estimates include $7.9 \pm1.0$ Gyr from S. Basu et al. [17] and $8.2 \pm0.3$ Gyr from J. M. McKeever et al. [112]. Other estimates include an age of $8.3 \pm0.3$ Gyr from binary systems (K. Brogaard et al. [37]), a white-dwarf cooling-sequence age of $8.0 \pm0.2$ Gyr (E. García-Berro et al. [63]), and a CMD age of $8.5 \pm0.7$ Gyr (G. Dufresne et al. [47]). We adopted the average value of $8.2 \pm0.4$ Gyr for NGC 6791.

We also note that L. G. Bouma et al. [29] recovered gyrochronological ages of $117 \pm6$ Myr for the Pleiades, $306^{+11}_{-9}$ Myr for NGC 3532, $738^{+22}_{-20}$ Myr for NGC 2632/Praesepe, $946^{+16}_{-15}$ Myr for NGC 6811, and $2518^{+32}_{-33}$ Myr for NGC 6819 using the gyro-interp framework; these values are broadly consistent with the ages adopted in this work.

Asteroseismic Signal Extraction

In this section, we briefly outline our analysis of the g-mode asteroseismic signals, following procedures that have been applied to hundreds of g-mode pulsators in the Kepler and TESS data (e.g. T. Van Reeth et al. [179, 177]; G. Li et al. 2020b; S. Garcia et al. [62]).

Target Selection and CMD Construction

To construct CMDs for each stellar group and select its early-type members, we downloaded Gaia $G$-band magnitudes and the colour index $G_{\mathrm{BP}} - G_{\mathrm{RP}}$ from the Gaia Archive¹, using the membership tables described above. We selected only early-type main-sequence stars for the subsequent asteroseismic analysis, because stars cooler than the red edge of the classical instability strip (roughly 7000 K) do not exhibit classical pulsations, and any solar-like oscillations would remain undetectable given the long cadence and low amplitudes. This temperature criterion approximately corresponds to the well-known Kraft break ([93, 24]), where stars transition from having substantial convective envelopes to much thinner ones. We identified this criterion visually, as the slope of the main sequence changes slightly near this temperature.

To place all stellar-group members and $\gamma$ Dor stars on a homogeneous intrinsic Gaia CMD, we corrected the Gaia photometry for interstellar extinction and reddening. For the 13 groups included in the catalogue of E. L. Hunt & S. Reffert [79], namely CWNU 1183, the Pleiades, NGC 2516, UBC 1, ASCC 108, NGC 3532, NGC 6866, NGC 2632, Theia 4877, NGC 1901, NGC 6811, NGC 6819, and NGC 6791, we adopted the median posterior extinction, $A_{V,50}$, and distance modulus, $\mu_{50}$, reported in that catalogue. We converted $A_V$ to the Gaia passbands using

following B. Bauer-Fasching et al. [18]. The extinction-corrected colour and absolute magnitude were then calculated as

where $\mu= 5 \log_{10}(d/10\ \mathrm{pc})$. The same corrections were applied to the stellar-group members and the identified $\gamma$ Dor stars.

For Huliwa, we adopted $A_V = 0.35$ mag from X. Pang et al. [134] and used the individual stellar distances provided in its membership catalogue. For Alcaeus, we adopted $A_V = 1.19$ mag, obtained as the median of the individual maximum-a-posteriori extinction estimates reported by J. Olivares et al. [130], and used their mean distance of 286 pc. For the Cep–Her complex, we used the per-star dereddened Gaia colour, extinction-corrected absolute $G$ magnitude, and distance estimates provided by R. Kerr et al. [87]; therefore, no additional cluster-wide extinction correction was applied.

Light-curve Reduction

For the Kepler data, we first queried the official mission light curves from the Mikulski Archive for Space Telescopes (MAST), and downloaded the simple-aperture-photometry flux (SAP FLUX) time series for our analysis. For stars in NGC 6819 and NGC 6791, we also used the image-subtraction light curves from the Kepler Increased Resolution Image Subtraction (IRIS) catalogue of I. L. Colman et al. [42], which were extracted from the Kepler superstamp images.

The light curve reduction for the TESS data was more complex. We extracted custom light curves from the full-frame images following the procedure described by S. Garcia et al. [62]. Briefly, we downloaded $20 \times20$ pixel TESS cutouts, defined target and background apertures on a median image, performed aperture photometry to obtain the simple-aperture-photometry (SAP) flux, corrected instrumental systematics using principal-component-analysis (PCA) cotrending, removed quality-flagged cadences and outliers, and finally stitched and normalised the multi-sector light curves. We also computed the contamination rate, defined as the fraction of flux from nearby stars entering the target aperture. For some targets, we manually adjusted the aperture to reduce the contamination as much as possible. We selected the background aperture to be at least six pixels away from the target centre, as we found that some large-amplitude variables could induce significant variations even in the background.

The Kepler long-cadence light curves and TESS calibrated full-frame images used in this work were obtained from the Mikulski Archive for Space Telescopes (MAST). The corresponding dataset DOIs are 10.17909/T9488N for Kepler and 10.17909/0cp4-2j79 for TESS. The compiled stellar data used in this work are available at 10.17909/sq4y-sy72.

Frequency Extraction

For the Kepler data, we used the full four-year light curve as input to our frequency-extraction code. For the TESS data, to mitigate systematic uncertainties and window-function effects, we selected the light curves with the longest continuous TESS coverage, avoiding sparse temporal coverage (e.g., short segments separated by multi-year gaps). The TESS sectors used for the frequency extraction are listed in Table 2.

Cluster	TIC	TESS sector(s)
Cep-Her	TIC303754397	15, 16
Cep-Her	TIC346151391	53, 54
Cep-Her	TIC277011700	14, 15, 16
Cep-Her	TIC277570969	82, 83, 84
Cep-Her	TIC349011395	53, 54
NGC2632	TIC175239414	44, 45, 46
NGC2632	TIC184873310	44, 45, 46
NGC2632	TIC14503989	44, 45, 46
NGC1901	TIC179437576	Years 1, 3, and 5
NGC1901	TIC30935460	Years 1, 3, and 5
Hulwa	TIC56640851	88, 89
Alcaeus	TIC26532226	42, 43, 44

We adopted the iterative pre-whitening algorithm described by G. Li et al. (2019a). In each iteration, we calculated the amplitude spectrum, identified the highest peak, and fitted a sinusoidal function to the light curve within a narrow range around that peak in frequency and amplitude. The residuals between the best-fitting sinusoid and the original light curve were then used as input for the next iteration. We stopped when no peak exceeded a signal-to-noise ratio (SNR) of four, with the noise level calculated within a $\pm2.5\,\mathrm{d}^{-1}$ window.

Note. For published cluster studies, details of the TESS sectors used and the frequency extraction are provided in G. Li et al. (2024) for NGC 2516, G. Li et al. (2026) for NGC 3532, D. J. Fritzewski et al. [54] for Pleiades, and D. J. Fritzewski et al. [55] for UBC 1.

Traditional Approximation of Rotation (TAR) Fit

After extracting all frequencies from the light curves, we focused on the low-frequency region ($\lesssim5\,\mathrm{d}^{-1}$) to identify g modes. Period spacings ($\Delta P$) are defined as the period differences between adjacent g-mode overtones with the same angular degree $\ell$ and azimuthal order $m$ (i.e., $\Delta n = 1$). In the asymptotic limit, the period spacing is constant with radial order for a non-rotating and chemically homogeneous star (H. Shibahashi [166]; M. Tassoul [174]). However, rotation causes the period spacing to vary quasi-linearly with period ([26, 177, 133]). We therefore searched for period-spacing patterns showing approximately linear variations of $\Delta P$ with period, following the approach of G. Li et al. (2019a).

We next assigned $(\ell, m)$ to the identified period-spacing patterns. H. Saio et al. [155] showed that the most common g-mode patterns are sectoral modes, which means those with $\ell= m$ (e.g., $\ell= m = 1$ and $\ell= m = 2$). Here we use the convention that prograde modes have positive $m$ values. In addition, we measured the slopes of the period-spacing patterns and compared them with the results of G. Li et al. (2020b), since different modes form distinct groups in the diagram of pattern slope versus mean period. Both $\ell= 1$ and $\ell= 2$ sectoral modes show decreasing period spacing with increasing period. The most common modes are expected to be $\ell= 1$ and $m = 1$. When we found two period-spacing patterns where one had roughly half the mean period of the other, we identified the shorter-period pattern as $\ell= 2$, $m = 2$ g modes. In some stars, we also detected Rossby modes. These are pure inertial modes with the Coriolis force as the restoring force. In the observer’s reference frame, they appear at about 1.5 times the $\ell= 1$, $m = 1$ g-mode period, showing increasing period spacings and a distinctive amplitude profile (e.g. T. Van Reeth et al. [178]; H. Saio et al. [156]; G. Li et al. (2019b)).

After identifying each observed period-spacing pattern, we applied the TAR to fit the data. We refer to T. Van Reeth et al. [177], H. Saio et al. [155], and N. Z. Rui et al. [154] for summaries of the theory and its practical applications in asteroseismology. In short, the period spacing is calculated as

where $\lambda_{\ell,m,s}$ is the eigenvalue of Laplace’s tidal equation, and $s = 2f_{\rm rot}/f_{\rm co}$ is the spin parameter (twice the ratio of the near-core rotation rate to the co-rotating pulsation frequency). We fixed the g-mode phase $\alpha_g$ to 0.5. The asymptotic spacing $\Pi_0$ is defined as $\Pi_0 = 2\pi^2\left[\int_{\rm gc}(N\,dr/r)\right]^{-1}$, where $N$ is the Brunt–Väisälä frequency and the integral is taken over the g-mode cavity (gc). Since $\Pi_0$ generally decreases as the central hydrogen abundance decreases, it provides an asteroseismic constraint on the evolutionary stage; in combination with spectroscopic constraints, it can be used to estimate stellar ages ([122]). For a more detailed description, we refer to a series of related papers, such as T. Van Reeth et al. [179], G. Li et al. (2020b), and G. Li et al. (2026).

Using this TAR framework, we fitted the observed period-spacing patterns to infer the near-core rotation rate $f_{\rm rot}$ and asymptotic spacing $\Pi_0$ for each target; the resulting measurements are summarised in § 4.

Overview of the Seismic Measurements

Table 1 lists all g-mode pulsators with clear period-spacing patterns in our sample of 16 stellar groups. Figure 1 shows the CMDs of all 16 stellar groups in this work, highlighting the locations of the g-mode pulsators. In total, we identified 68 such pulsators. For the Kepler clusters, most targets were already reported in the 611-$\gamma$ Dor sample of G. Li et al. (2020b), demonstrating the completeness of that catalogue. By cross-matching the Kepler target list with the Gaia DR3 membership catalogues of newly identified clusters in the Kepler field, we added seven additional Kepler targets to our sample. For clusters observed by TESS, we incorporated our previous studies of NGC 2516 (G. Li et al. (2024)), the Pleiades (D. J. Fritzewski et al. [54]), UBC1 (D. J. Fritzewski et al. [55]), and NGC 3532 (G. Li et al. (2026)). In addition, we added g-mode pulsators in the Hululwa subgroups of Vela OB2 and the associations within Cep–Her, as well as in the open clusters NGC 1901 and NGC 2632 (the Beehive cluster).

Near-core Rotation Rates

The left panel of Figure 2 shows the distribution of near-core rotation rates for the stellar-group members in this work. This distribution is distinct from that of the Kepler field stars reported by G. Li et al. (2020b). The stellar-group members show three peaks: a high-rotation peak above $2.5\,\mathrm{d}^{-1}$, dominated by the Pleiades, NGC 2516, and NGC 3532; an intermediate peak between $1.5$ and $2.0\,\mathrm{d}^{-1}$; and a peak around $1.0\,\mathrm{d}^{-1}$, mainly populated by older stellar groups with ages comparable to or greater than that of NGC 6866. By comparison, the Kepler field stars show a dominant peak around $1.0\,\mathrm{d}^{-1}$ and a slow-rotation plateau below $0.5\,\mathrm{d}^{-1}$.

The fact that the Kepler field stars show slower near-core rotation rates than the stellar-group members in this work suggests that Kepler g-mode pulsators may, on average, be older than NGC 6866, implying that the excitation mechanism may preferentially operate in older main-sequence stars. However, we emphasise that this comparison is subject to observational biases. One source of observational bias arises from the TESS light curves. Due to their short time baselines, the frequency resolution $\delta f$ is limited; consequently, the observations are less sensitive to the long-period modes exhibited by slow rotators because the period resolution decreases as $\delta P = P^2\delta f$. Another observational bias is the incompleteness of the stellar-group sample. Our sample contains few stellar groups older than 1 Gyr, partly because of sample incompleteness and partly because unbound associations disperse while dynamical evolution preferentially dissolves low-mass open clusters over time. Open-cluster dissolution timescales depend strongly on cluster mass and environment, ranging from less than 1 Gyr for low-mass systems to several Gyr for more massive clusters ([96, 95]).

We do not see a slow-rotation plateau in our stellar-group sample comparable to that found in the Kepler data ($f_{\rm rot} < 0.5\,\mathrm{d}^{-1}$, G. Li et al. 2020b, see also Figure 2).

Binary interactions are a possible pathway for producing slowly rotating g-mode pulsators, through mechanisms such as inverse tides [56, 51] (G. Li et al. 2020a) or Cassini-state trapping [57]. In bound-cluster environments, dynamical encounters preferentially disrupt wide binaries, whereas tightly bound (or “hard”) binaries tend to become even more tightly bound [73, 77]. This process could in principle enhance the role of close binaries in producing slow rotators. The paucity of slow rotators in our sample is therefore more plausibly explained by observational selection effects: the shorter TESS time baselines provide poorer frequency and period resolution than the four-year Kepler data, making slowly rotating g-mode patterns harder to identify.

The right panel of Figure 2 shows the evolution of near-core rotation rates with host-group age. Although the rotation rates are broadly distributed, the upper envelope shows an increasing trend up to $\sim100$ Myr, followed by a gradual decline at older ages. The young stars in Huluwa, CWNU 1183, and Cep–Her have rotation rates ranging from $\sim0.5\,\mathrm{d}^{-1}$ to $\sim2.5\,\mathrm{d}^{-1}$. Around $\sim100$ Myr, the stars show the fastest rotation rates, reaching $\sim3.0\,\mathrm{d}^{-1}$ in NGC 2516 and the Pleiades. Thereafter, the maximum rotation rate decreases with age, dropping to $\sim2.0\,\mathrm{d}^{-1}$ at 1 Gyr in NGC 6811. As stated above, our observations are more sensitive to fast rotators; therefore, the upper envelope should be observationally complete. Observed surface-rotation distributions of solar-like stars in young clusters also show a qualitatively similar spin-up, which F. Gallet & J. Bouvier [60] attributed to PMS contraction following disk dispersal (see their Fig. 1).

Mass-dependent Evolution of Near-core Rotation Rates

In this section, we compare our observed near-core rotation rates, $f_{\mathrm{rot}}$, with stellar evolution models. Because these stars are members of coeval stellar groups, their ages are known and their masses can be estimated from their locations in the CMDs, enabling a direct comparison with theoretical models. We used the g-mode asteroseismic models of J. S. G. Mombarg et al. [119]. We refer to previous papers for a more detailed description of the input physics of these models, including the treatments of helium enrichment (K. Verma et al. [182]), metallicity (M. F. Nieva & N. Przybilla [129]), overshooting, rotational effects on stellar structure (B. Paxton et al. [138, 139]), angular-momentum transport (J. S. G. Mombarg [117]), and element mixing in radiative layers.

We briefly summarize the rotation treatment used by J. S. G. Mombarg et al. [119]. Rotation is turned off during the pre-main-sequence phase and is switched on when the model reaches the zero-age main sequence, defined by the criterion that the nuclear luminosity exceeds 90% of the total luminosity. At this stage, the model is assigned an initial rotation rate (we use 5% or 55% of the critical rotation rate $\Omega_{\mathrm{crit}}$ in Figure 3) and is allowed to relax to equilibrium. This explains the sudden rise in the model rotation rate in panels (a) and (d) of Figure 3. It also explains why, in § 5 and Figure 9, we needed to recalculate some models when discussing rotational effects during the pre-main-sequence phase. The centrifugal correction to the stellar structure is applied using the shellular approximation (e.g. A. S. Endal & S. Sofia [49]; G. Meynet & A. Maeder [115]; B. Paxton et al. [138]). AM transport is implemented in a fully diffusive framework by assuming a constant viscosity of $\nu= 10^{7}\,\mathrm{cm}^{2}\,\mathrm{s}^{-1}$, calibrated using several slowly rotating $\gamma$ Dor stars (J. S. G. Mombarg [117]). This prescription does not enforce rigid rotation, but the relatively high viscosity leads to efficient AM transport and suppresses strong radial differential rotation. F. D. Moyano et al. [124] suggested that combining near-core rotation rates with reliable projected surface rotation velocities ($v\sin i$) would provide a stronger test of the internal AM-transport efficiency.

Figure 3 displays the near-core rotation rates, $f_{\mathrm{rot}}$, as a function of stellar age in different mass bins. We also overplot the theoretical rotation curves for multiple choices of stellar-model input parameters, as described in the caption. From Figure 3, we find that the observed rotation-rate distribution depends strongly on stellar mass. For stars with masses below $1.6\,M_{\odot}$ (panel (a) of Figure 3), most targets lie well below the rotation rates predicted by the models with 55% $\Omega_{\mathrm{crit}}$, indicating that they are moderate rather than rapid rotators. For stars between 1.6 and $1.8\,M_{\odot}$ (panel (b) of Figure 3), the fraction of slow rotators decreases. At masses above $1.8\,M_{\odot}$, most stars rotate rapidly, with $f_{\mathrm{rot}}$ following the 55% $\Omega_{\mathrm{crit}}$ curve or lying even higher.

This mass-dependent rotation distribution has also been reported in NGC 2516 and NGC 3532 (G. Li et al. 2024; G. Li et al. 2026). In these two clusters, with ages of $\sim100$ and $\sim300\,\mathrm{Myr}$, respectively, g-mode pulsators with masses below $1.6\,M_{\odot}$ also rotate more slowly than the more massive pulsators in the same clusters. The mass-dependent rotation rate matches the surface rotation rates reported previously for stars in the same mass range (F. Royer et al. [153]). Our larger sample also suggests that an additional mechanism may contribute to the spin-down of stars in this mass range. One possible explanation is residual magnetic braking near the Kraft-break transition, where the presence of surface convective envelopes may allow magnetised winds to remove AM, although the efficiency is expected to decrease as these envelopes become thinner (e.g. R. P. Kraft [93]; A. C. Beyer & R. J. White [24]; X.-Y. Wang et al. (2026)). Stars around $1.6\,M_{\odot}$ are expected to have shallow convective envelopes, which are also important for the excitation of $\gamma$ Dor g modes (M. A. Dupret et al. [48]), so some level of magnetic braking may still operate. We note, however, that A. C. Beyer & R. J. White [24] placed the transition between slow and fast rotators at $1.32$–$1.41\,M_{\odot}$. The lower-mass pulsators discussed in this work are therefore not slow rotators in an absolute sense; rather, they rotate more slowly relative to the more massive stars above $1.6\,M_{\odot}$ in our sample.

Asymptotic Spacing

The left panel of Figure 4 shows the distribution of the asymptotic spacing $\Pi_{0}$ for the stellar-group members. We also compare our results with those for Kepler field stars from G. Li et al. (2020b). We find that the stellar-group members have larger $\Pi_{0}$ values than the field stars. Compared with the Kepler sample, our stellar-group sample shows an excess of pulsators with $\Pi_{0}$ values from $\sim4500\,\mathrm{s}$ to $\sim5500\,\mathrm{s}$, mainly due to stellar groups younger than 300 Myr, and a paucity of pulsators with $\Pi_0$ values below $\sim3800$ s. As $\Pi_0$ decreases slightly with evolution, it is often used as an age indicator, implying that our stellar-group sample is younger than the field-star sample, probably because older stellar groups are underrepresented in our sample.

The right panel of Figure 4 shows the evolution of $\Pi_0$ with host-group age. First, we find that most stars have $\Pi_0 \lesssim6000$ s. Based on their locations on the CMDs, these stars typically have masses below $2.0\,M_\odot$ and therefore fall within the typical parameter range of $\gamma$ Dor stars. We also find that $\Pi_0$ increases slightly near the beginning of the main sequence up to an age of $\sim300$ Myr and then declines slightly at older ages. The models of G. Li et al. (2025) indicate that $\Pi_0$ can also increase during the early main-sequence evolution of stars with masses above approximately $2\,M_\odot$. However, we note that differences in metallicity and initial stellar mass can also affect $\Pi_0$ (R. M. Ouazzani et al. [132]).

Pre-main-sequence stars or very young main-sequence stars may still undergo rapid structural changes, which could lead to a fluctuation in $\Pi_0$. We provide a brief discussion of pre-main-sequence g-mode pulsators in § 5. In addition, we find five stars with much larger $\Pi_0$ values. Two of them, located in Cep–Her and NGC 2516, have larger masses inferred from their CMD positions and are therefore classified as SPB stars. We identify the remaining three stars as blue stragglers in NGC 6866, NGC 6819, and NGC 6791, and discuss them in § 6.

Mass-dependent Evolution of Asymptotic Spacing

$\Pi_0$

Analogous to Section 4.2 and Figure 3, we examine the evolution of $\Pi_0$ in different mass bins. Figure 5 shows the observed $\Pi_0$ as a function of age for four mass ranges: $1.4$–$1.6$, $1.6$–$1.8$, $1.8$–$2.1$, and $2.1$–$4.0\,M_\odot$. We also overplot the theoretical $\Pi_0$ values computed from the same model grid of J. S. G. Mombarg et al. [119].

In each panel of Figure 5, we show two sets of theoretical models: one at the lower boundary of the mass range (black curves) and one at the upper boundary (blue curves). Because $\Pi_0$ generally increases with mass for stars that are not too close to the terminal-age main sequence, the observed $\Pi_0$ values are expected to lie between these two sets of theoretical curves.

In panel (a) of Figure 5 (the $1.4$–$1.6\,M_\odot$ mass range), the theoretical curves reproduce the observed trend well. In this mass range, excluding the pre-main-sequence stars and the blue straggler, $\Pi_0$ decreases from $\sim4500$ s near the beginning of the main sequence to $\sim4000$ s near the terminal-age main sequence. Therefore, $\Pi_0$ can be considered as a good age indicator in this mass range. As mentioned in § 2.2, the two g-mode pulsators in NGC 1901, shown as hexagons, have masses around $1.6\,M_\odot$ and $\Pi_0$ values below 4000 s. If we adopt an age of 820 Myr for this cluster, as suggested by the gyrochronological result of M. Bernizzoni et al. [22], the observed $\Pi_0$ values agree with the theoretical predictions. By contrast, adopting an age of $\sim400$ Myr or younger [79, 40] would place the two stars in clear disagreement with the models, which predict $\Pi_0$ values larger than those observed at such ages.

The situation becomes more complex in the higher-mass bins. Starting from $1.6\,M_{\odot}$ (panels (b), (c), and (d) of Figure 5), we find more outliers: several stars have $\Pi_0$ values that lie outside of the theoretical predictions. A straightforward explanation for this $\Pi_0$ discrepancy is that the mass estimates for higher-mass stars are too crude. These stars rotate rapidly, so gravity darkening is non-negligible and can shift their positions significantly in the CMD [e.g. 50, 28, 127]. However, S. J. Murphy et al. [127] suggests a mass uncertainty of only $\sim0.1\,M_{\odot}$, which is insufficient to explain the observed $\Pi_0$ discrepancy. Differences between the metallicities adopted in the models and those of the observed stars could also contribute to this discrepancy. Nevertheless, most clusters in our sample with available spectroscopic metallicity measurements have approximately solar metallicities. Alternatively, the discrepancy may point to missing physics in the models, such that the surface parameters ($T_{\mathrm{eff}}$ and $L$) cannot be fully reconciled with the internal seismic diagnostic $\Pi_0$.

We also find that all three blue stragglers appear as outliers in the $\Pi_0$–age diagrams in Figure 5. We discuss these pulsating blue stragglers in detail in § 6.

Inferring Initial Rotation Distributions from Evolved Populations

The known ages of the stellar groups allow us to infer the initial rotation distributions through forward population modelling. Following J. S. G. Mombarg & S. Mathis [120], we grouped the stellar groups listed in Table 1 into four age bins, excluding the blue stragglers. The bins were chosen to include as many stars as possible while retaining a relatively narrow age range. For each bin, we generated synthetic populations of 1000 stars at both the youngest and oldest ages of the bin. We drew stellar masses from the observed mass distribution and adopted the probability density function (PDF) of the core-boundary mixing scale ($f_{\mathrm{CBM}}$) from ?. The initial rotation rate at the zero-age main sequence, expressed as a fraction of the critical rotation frequency, was drawn from a normal distribution with mean $\mu_{\omega_{0}}$ and standard deviation $\sigma_{\omega_{0}}$. We then evolved the sampled models to the selected ages and constructed the predicted distributions of near-core rotation frequency and $\Pi_{0}$. Thus, the distributions shown below represent the evolved populations at the boundaries of each age bin, rather than the initial rotation distributions themselves.

For each age bin, we optimized the free parameters $\mu_{\omega_{0}}$ and $\sigma_{\omega_{0}}$ by maximizing the likelihood. To compute this likelihood, we first obtained a kernel density estimate (KDE) from the rotation frequencies of the simulated population. The log-likelihood, $\mathcal{L}$, was then given by

where $f_{\mathrm{rot},i}$ are the observed rotation frequencies. We divided the stellar groups into four age bins: 45–135 Myr (22 stars), 200–350 Myr (12 stars), 590–800 Myr (21 stars), and 900–1300 Myr (11 stars). Figure 6 compares the observed near-core rotation-frequency distributions with the simulated distributions corresponding to the maximum-likelihood values of $(\mu_{\omega_{0}}, \sigma_{\omega_{0}})$. Because the model near-core rotation rates generally decrease over most of the main-sequence evolution (Figure 3), the predicted distributions shift towards lower rotation frequencies with increasing age, producing a larger fraction of slow rotators in the older populations. In general, the observed distributions agree with our predictions. However, for the two youngest bins, the large number of stars with rotation frequencies around $3\,\mathrm{d}^{-1}$ would require initial rotation rates above the upper limit of the grid, namely 55% of the critical rotation rate. The synthetic populations therefore do not fully represent the rapidly rotating end of these young samples, and the inferred initial-rotation parameters are limited by the boundary of the model grid. With the treatment of rotation adopted in our models, most stars above this threshold reach critical rotation on the main sequence. The mismatch may therefore indicate either substantial differential rotation or limitations in the adopted rotational-evolution prescription. For the two older bins, we inferred mean initial rotation rates of 20–30% of the critical rotation rate, in agreement with the results of J. S. G. Mombarg et al. [118] and J. S. G. Mombarg & S. Mathis [120]. J. S. G. Mombarg & S. Mathis [120] applied this population-modelling approach to the field-star sample analysed by C. Aerts [2], using the normalized central hydrogen mass fraction, $X_\mathrm{c}/X_\mathrm{ini}$, as a proxy for age. Here, we group the cluster stars by the independently determined ages of their host clusters. Despite this difference in binning, the observed near-core rotation frequencies show a qualitatively similar decline with age in the field and cluster samples. We also note that the g-mode pulsators in the younger stellar groups have a higher average mass than those in the older stellar groups. This difference partly reflects the shorter main-sequence lifetimes of higher-mass stars, which have already evolved off the main sequence in the older groups.

Similarly, Figure 7 shows the predicted and observed distributions of $\Pi_0$. We find good agreement for the two youngest bins, whereas for the two older bins, the observed $\Pi_0$ values are lower than predicted by approximately 200 s on average. Less efficient chemical mixing in the radiative envelope could reduce $\Pi_0$ at a given age. However, our models already assume low levels of mixing, making this explanation unlikely. The oldest bin contains only NGC 6811, so the discrepancy may partly reflect an underestimated age for this cluster.

Pre-main-sequence g-mode pulsators

Pre-main-sequence g-mode pulsators have long been predicted to exist. M.-P. Bouabid et al. [27] found that the instability strip of pre-main-sequence $\gamma$ Dor stars spans nearly the same temperature range as that of main-sequence $\gamma$ Dor stars. T. Steindl et al. [169] used an accretion model and found that an appropriate choice of the mass accretion rate and the fraction of injected accretion energy can reproduce the observed instability strip of pre-main-sequence pulsators.

Pre-main-sequence g-mode pulsators have been discovered by the CoRoT and TESS missions, but period spacings have generally not been reported (e.g. [190, 169]). Owing to the different internal chemical stratification (e.g. the lack of a strong chemical gradient), the period-spacing pat-

terns of pre-main-sequence g-mode stars are expected to be smoother than those of main-sequence g-mode pulsators. One PMS pulsator with a period-spacing pattern detected in K2 data was reported by L. Ketzer & K. Zwintz [90]. Meanwhile, KIC 9850387 was initially proposed to be a PMS g-mode pulsator with a clear period-spacing pattern [189], but subsequent studies disagreed [165, 164]. Recently, Wadhwa et al. (in prep.) discovered the g-mode pulsator TIC 26532226, which shows a clear period-spacing pattern, in the Perseus complex; this star is included in Table 1.

In this work, we investigated two additional young stellar complexes: the Vela OB2 complex [134] and the Cep–Her complex [87]. As listed in Table 1, we found one g-mode pulsator with a clear period-spacing pattern in Vela OB2 (TIC 56640851, shown in Figure 8) and five in Cep–Her. In addition, CWNU 1183, a newly identified young cluster in the Kepler field of view with an age of around 46 Myr, hosts one clear g-mode pulsator.

For the period-spacing pattern of the Vela OB2 complex member TIC 56640851 shown in Figure 8, we find that the period spacings are small, approaching the period resolution of the two-consecutive-sector TESS light curve. Nevertheless, we are still able to identify the g-mode periods owing to the high amplitudes of the mode (top panel of Figure 8) and obtain a linearly decreasing period-spacing pattern (bottom panel of Figure 8). We infer a relatively fast near-core rotation rate of $2.634 \pm0.007\ \mathrm{d}^{-1}$ and an asymptotic spacing $\Pi_0$ of $4302^{+70}_{-60}\ \mathrm{s}$. The mass given by X. Pang et al. [134] is $\sim2.19\,M_\odot$; at this mass, a much higher $\Pi_0$ of around $6000\ \mathrm{s}$ would be expected for a main-sequence star compared with the observed value.

To investigate how $\Pi_0$ evolves with age, Figure 9 displays the observed asymptotic spacing $\Pi_0$ versus stellar age for stars in young stellar groups. We also show representative theoretical evolutionary tracks computed from the pre-main-sequence models of A. Gautam et al. [64]. The displayed tracks use models with initial metal mass fraction $Z = 0.015$, corresponding to a near-solar composition relative to the solar bulk metallicity $Z_{\odot,\mathrm{bulk}} = 0.0142$ adopted from M. Asplund et al. [7]. Rotation was included from the beginning of the pre-main-sequence evolution, with the tracks shown here initiated with solid-body equatorial rotation of $8\ \mathrm{km}\,\mathrm{s}^{-1}$. We find that $\Pi_0$ changes rapidly during the pre-main-sequence phase, whereas it evolves slowly with age after the zero-age main sequence. For stars with $M \sim1.6\,M_\odot$, $\Pi_0$ remains around $4700\ \mathrm{s}$, and, in general, $\Pi_0$ increases with stellar mass. Similar rapid evolution of $\Pi_0$ during the pre-main-sequence phase was also reported by M.-P. Bouabid et al. [27], who used the stellar-evolution code CLES [163] rather than MESA.

From Figure 9, we infer that the stars from Cep–Her and CWNU 1183 should have already entered their main-sequence phases. For the stars with mass around $1.6\,M_\odot$, we find that their $\Pi_0$ are slightly smaller than predicted (shown by the dotted line). This difference can be explained by adjusting stellar parameters, e.g., decreasing stellar mass or increasing initial velocity would decrease the theoretical $\Pi_0$ values.

We find two stars for which the theoretical $\Pi_0$ values do not match the observations. First, TIC 303754397 ($\sim1.59\,M_\odot$), a member of the Cupavo association in the Cep–Her complex, has an anomalously small $\Pi_0$. This discrepancy may arise from an insecurely identified period-spacing pattern due to short TESS observation, or from uncertainties in the isochrone-derived stellar mass or evolutionary stage. Alternatively, if the star has undergone binary mass transfer, its internal chemical stratification and hence its g-mode period spacings may differ from those predicted by single-star models [69] (T. Wu et al. 2026). Second, TIC 277570969 ($\sim3.42\,M_\odot$), a member of the Cynar­as association in the Cep–Her complex, shows an extremely large $\Pi_0$. Previous studies have revealed similar $\Pi_0$ discrepancies, which are more significant in the high-mass range. The physics behind such discrepancies remains unclear. Rotation may play a role, because gravity darkening can shift the position of a star in the CMD and therefore bias the mass estimate from isochrone fitting. However, we obtain a relatively low rotation rate for this star ($0.750\,\mathrm{d}^{-1}$), so the purely observational effect of rotation should be marginal.

Based on the measured $\Pi_0$ values and isochrone-constrained ages, only two stars, TIC 26532226 in the Alcaeus group of the Perseus star-forming complex and TIC 56640851 in Vela OB2, are clearly pre-main-sequence g-mode pulsators. Both stars show small $\Pi_0$ values that can only be explained by the oscillatory $\Pi_0$ track during the pre-main-sequence phase. Within the membership and age framework of X. Pang et al. [134], TIC 56640851 is assigned to Huluiwa 5, the youngest subgroup of Vela OB2, with an age of 7.5–14.5 Myr. Our seismic model with $2.2\,M_\odot$ (the dashed line in Figure 9) reaches a $\Pi_0$ minimum at an age of 5 Myr, suggesting that this star is extremely young. We also find that, although the current minimum value of $\Pi_0$ is still larger than the observed value, increasing the initial velocity in the model would lower the minimum $\Pi_0$ and could explain the observed $\Pi_0$.

Blue stragglers

We identify three pulsating blue stragglers with clear period-spacing patterns: KIC 8264293 in NGC 6866, KIC 5024455 in NGC 6819, and KIC 2438249 in NGC 6791. We exhibit their amplitude spectra and period-spacing patterns in Figure 10, Figure 11a, and Figure 11b.

Among the cluster members, we manually identified stars lying above the cluster main sequence in the CMDs as blue-straggler candidates. Cross-matching these candidates with the catalogue of blue stragglers in open clusters by M. J. Rain et al. [144] shows that KIC 8264293 and KIC 2438249 are included, whereas KIC 5024455 is not. The latter is nevertheless listed as a member of NGC 6819 in the catalogue of E. L. Hunt & S. Reffert [79].

We find that the mass of KIC 2438249 given by E. L. Hunt & S. Reffert [79] is too small, falling below the typical lower boundary of $\sim1.5\,M_\odot$ for $\gamma$ Dor stars. We therefore redetermined the masses of the three pulsating blue stragglers. For KIC 5024455 and KIC 2438249, we manually searched for the best-fitting MIST isochrones around the literature values, then shifted the ages younger until the main sequence extended to the locations of the blue stragglers. We adopted the mass of the isochrone point with the same $G$-band magnitude as the blue straggler as the mass listed in Table 1. We assigned typical uncertainties of $\pm0.1\,M_\odot$, slightly larger than the usual uncertainties reported by E. L. Hunt & S. Reffert [79]. We obtained $1.48 \pm0.10\,M_\odot$ for KIC 5024455 and $1.73 \pm0.10\,M_\odot$ for KIC 2438249. We note that the mass estimates for the blue stragglers are preliminary; for example, they do not account for their merger or mass-transfer histories or adequately consider reddening. We therefore expect the estimated masses of the blue stragglers to have substantial systematic uncertainties.

For KIC 8264293, we adopted a spectroscopic mass estimate of $3.18^{+0.17}_{-0.10}\,M_\odot$ based on HERMES spectroscopy, Gaia astrometry, extinction corrections, and bolometric corrections. A more detailed description of the spectroscopic analysis will be given by Wang et al. (in prep.).

Figure 4 shows that all three pulsating blue stragglers have higher $\Pi_0$ values than normal $\gamma$ Dor stars. This is expected for KIC 8264293, as it lies in the mass range of SPB stars, but it is unusual for KIC 5024455 and KIC 2438249 because they have typical $\gamma$ Dor-star masses ($< 2.0\,M_\odot$). Their unusually large $\Pi_0$ values may reflect an interesting mass-transfer or merger formation history.

Several recent studies have investigated how the formation processes of blue stragglers reshape their internal structures and how these changes are reflected in g-mode period-spacing patterns. J. Henneco et al. [75] studied merger products involving massive stars near the Hertzsprung Gap and found that their g-mode period-spacing patterns can exhibit pronounced deep dips caused by strong chemical gradients. J. Henneco et al. [76] further investigated the merger of two main-sequence stars using three-dimensional magnetohydrodynamic simulations. They found that the merger process can generate a double-peaked Brunt–Väisälä frequency profile owing to the formation and subsequent recession of a new convective core, leading to period-spacing patterns that differ significantly from those of single stars. Z. Guo (2026) showed that the periodicity of the period-spacing modulation, measured in radial order, is directly related to the location of sharp features in the Brunt–Väisälä frequency profile. This provides a new diagnostic of the internal chemical structure and evolutionary state of a star, and has recently been applied to a sample of 26 SPB stars (Z. Guo & C. Aerts [68]). Blue stragglers are expected to retain these unusual chemical stratification profiles, producing additional modulations in their g-mode period-spacing patterns that preserve information about their formation history, as demonstrated by collision models (L. Briganti et al. [34]) and mass-transfer models (T. Wu et al. 2026).

W. Szewczuk et al. [172] conducted detailed seismic modelling of KIC 8264293, treating it as a normal single-star evolutionary object and arguing that its parallax was inconsistent with membership in NGC 6866. They derived a mass of 3.54 $M_\odot$, an age of 6 Myr, and a central hydrogen abundance of $X_{\mathrm{c}} \sim0.71$. However, the membership probability of this star in NGC 6866 is 70% according to T. Cantat-Gaudin et al. [39], 81% according to L. Hunt & S. Reffert [79], and 99.8% according to H. Wang et al. (2026). We therefore consider this star to be a member of NGC 6866.

As shown in Figure 10, we identified two period-spacing patterns in KIC 8264293: one corresponding to prograde sectoral modes with $(\ell,m)=(1,1)$ (Figure 10a), and the other to prograde sectoral modes with $(\ell,m)=(2,2)$ (Figure 10b). For the $\ell= 1$, $m = 1$ pattern, we detected an overall smooth period-spacing pattern with a very deep dip at $P \sim0.326$ d. The dip is primarily caused by a mode with a small amplitude at $P = 0.327219(4)$ d. Its SNR is 7.75, with an amplitude of 3.8 $\pm$ 0.4 ppm, higher than the well-accepted SNR $> 4$ criterion (M. Breger et al. [32]). This mode also passed the criterion implemented in the code STAR SHADOW (L. W. IJspeert et al. [82]. In the analysis of W. Szewczuk et al. [172], this low-amplitude mode was not reported; instead, they found a local fluctuation in the period-spacing pattern around 0.326 d. However, such a strong fluctuation is not expected for an extremely young star with $X_{\mathrm{c}} \sim0.71$, because stars near the zero-age main sequence have not yet developed strong chemical gradients outside their convective cores. Additionally, the deep dip detected here does not resemble the dips caused by the coupling between g modes in the near-core regions and inertial modes in the convective cores predicted by R. M. Ouazzani et al. [131] and H. Saio et al. [157], as those features are generally broader and shallower. Changing the parameters in the coupling process or including magnetic fields may produce a deeper dip (L. Barrault et al. [16]), but this has not yet been investigated. Alternatively, the deep dip may be related to unusual internal chemical gradients associated with the formation of the blue straggler, as predicted by J. Henneco et al. [75]. If so, this deep dip provides valuable constraints on the internal structure of the star. Combining this information with the CMD of NGC 6866 may allow us to trace the formation history of the blue straggler.

For KIC 5024455 (Figure 11a), we detected two period-spacing patterns, both with $\ell= 1$: one with $m = 1$ and the other with $m = 0$. The $m = 0$ pattern is smooth, whereas the $m = 1$ pattern exhibits some variations. The presence of $m = 0$ modes in this rapid rotator indicates that the inclination of the star’s rotation axis should be small (H. Saio et al. [155]). For KIC 2438249 (Figure 11b), we detected a long period-spacing pattern with numerous fluctuations.

Conclusions

In this work, we performed a survey of g-mode pulsators with clear period-spacing patterns in coeval stellar populations using Gaia astrometry together with Kepler and TESS photometry. Reliable membership identification from Gaia DR3 allows us to estimate masses and ages that are difficult to determine for isolated field stars. The four-year high-precision Kepler photometry provides light curves with sufficient frequency resolution to resolve g-mode period-spacing patterns. Building on prior knowledge from hundreds of Kepler g-mode pulsators, we can also identify such patterns in TESS data, despite its lower frequency resolution.

We used the traditional approximation of rotation (TAR) to fit the g-mode period-spacing patterns and derived two asteroseismic quantities: the near-core rotation rate $f_{\mathrm{rot}}$ and the asymptotic spacing $\Pi_{0}$. These quantities trace AM transport and near-core evolution in early-type main-sequence stars. In total, we collected 68 g-mode pulsators with clear period-spacing patterns from 16 stellar groups.

For the near-core rotation rates, we find that the stellar-group members in our sample generally rotate faster than the Kepler field stars studied by G. Li et al. (2020b). This difference is probably caused by a combination of observational selection effects from the shorter TESS light curves and the relatively young age distribution of the stellar groups in our sample. We also find a paucity of slow rotators ($f_{\rm rot} < 0.5\,\mathrm{d}^{-1}$) compared with the Kepler sample, which is probably due, at least in part, to the lower frequency resolution of the TESS light curves.

The near-core rotation rates show a clear evolutionary trend. The fastest rotators occur at ages around $\sim100$ Myr, beyond which the upper envelope of $f_{\rm rot}$ gradually decreases with age. By subdividing the stars into different mass ranges, we find that stars with masses between 1.4 and $1.6\,M_\odot$ rotate more slowly than higher-mass stars. This may indicate that stars below $1.6\,M_\odot$ retain some residual magnetic braking associated with their surface convective envelopes, leading to angular-momentum loss through magnetised winds.

For the asymptotic spacing, $\Pi_0$, the stellar-group members show larger values than the Kepler field sample, indicating that they are generally younger. We find that $\Pi_0$ does not follow a strictly monotonic relation with age; instead, it increases slightly near the beginning of the main sequence and then decreases (Figure 4), consistent with stellar-model calculations.

The theoretical $\Pi_0$ values reproduce the observed trend for stars between 1.4 and $1.6\,M_\odot$, suggesting that $\Pi_0$ can provide useful asteroseismic age constraints for stars and clusters in this mass range. For example, the low $\Pi_0$ values ($< 4000$ s) of the two g-mode pulsators in NGC 1901 support the older age inferred from gyrochronology and disfavour the substantially younger ages inferred from isochrone fitting. However, above $1.6\,M_\odot$, there is an increasing discrepancy between the observed and theoretical $\Pi_0$ values. This discrepancy may reflect uncertainties in CMD-based mass estimates or missing physics that prevents the stellar surface parameters from being fully reconciled with the internal seismic diagnostic. Future work should address this issue through spectroscopic follow-up of surface rotation ($v\sin i$), detailed corrections for gravity darkening, and seismic modelling beyond $\Pi_0$, such as fitting each identified mode, as in J. S. G. Mombarg et al. [121] and G. Li et al. (2025).

Because these stars belong to coeval stellar groups, we can more reliably identify their evolutionary stages and distinguish pre-main-sequence pulsators from pulsating blue stragglers. We report a new pre-main-sequence g-mode pulsator with clear period-spacing patterns, TIC 56640851, in Vela OB2. Adopting the membership and age scale of X. Pang et al. [134], the star is assigned to the Hulluwa 5 subgroup. Our new rotating pre-main-sequence evolutionary model at this star’s mass shows that the star happens to lie near the minimum of the oscillating $\Pi_0$ curve, making it an excellent age diagnostic. The asteroseismic age inferred from $\Pi_0$ is consistent with Hulluwa 5 being the youngest subgroup.

We report three pulsating blue stragglers with clear period-spacing patterns: KIC 8264293 in NGC 6866, KIC 5024455 in NGC 6819, and KIC 2438249 in NGC 6791. Their $\Pi_0$ values are outliers compared with single-star evolutionary models in Figure 5. We also detect a deep dip in the period-spacing pattern of KIC 8264293, suggesting that a recent formation event may have left a detectable signature in its internal structure. Detailed modelling of these pulsating blue stragglers, combined with constraints from their host clusters, may help reveal their progenitors, formation epochs, and formation pathways.

Overall, this work provides a homogeneous sample of g-mode pulsators in coeval stellar populations, highlighting the strong synergy between stellar physics and studies of stellar groups. For stellar physics, our uniformly derived measurements of $f_{\rm rot}$ and $\Pi_0$ offer a valuable benchmark for future asteroseismic modelling of internal processes, including AM transport, chemical mixing, and the calibration of 1D and 2D models for early-type main-sequence stars. For studies of stellar groups, our asteroseismic age constraints provide an independent perspective on age dating, while peculiar objects such as pre-main-sequence pulsators and pulsating blue stragglers offer an interior view of star-formation sequences in stellar complexes (e.g. S. Ratzenböck et al. [146]) and of stellar interactions in bound clusters.

Beyond the Kepler and TESS missions, future space-based photometric missions, including PLATO (H. Rauer et al. [147]) and ET2.0 (J. Ge et al. (2022)), will continue to advance the synergy between asteroseismology and research on stellar groups. Their longer time span, higher cadence, and wider coverage will provide unparalleled opportunities for ensemble asteroseismic studies of well-characterised stellar populations.

Acknowledgments

GL acknowledges the support of the Australian Research Council through the DECRA project DE250100773. SJM was supported by the Australian Research Council cil through Future Fellowship FT210100485. FDM acknowledges support by the National Natural Science Foundation of China (NSFC, Nos. 12288102, 12125303), the Strategic Priority Research Program of the Chinese Academy of Sciences (grant Nos. XDB1160303, XDB1160300, XDB1160000, XDB1160200, XDB1160201), the CAS Project for Young Scientists in Basic Research (YSBR-148), the Yunnan Revitalization Talent Support Program “Yun-Ling Scholar” project, International Centre of Supernovae (ICESUN), Yunnan Key Laboratory of Supernova Research (No. 202505AV340004), the New Cornerstone Science Foundation through the XPLORER PRIZE, and the Yunnan Revitalization Talent Support Program-Science & Technology Champion Project (No. 202305AB350003). The research leading to these results has received funding from the Flemish Government under the long-term structural Methusalem funding program by means of the project SOUL: Stellar evolution in full glory, grant METH/24/012 at KU Leuven, as well as from the European Research Council (ERC) under the Horizon Europe programme (Synergy Grant agreement N° 101071505: 4D-STAR). While partially funded by the European Union, views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council. Neither the European

Union nor the granting authority can be held responsible for them. TRB acknowledges support from the Australian Research Council through Laureate Fellowship FL220100117. GL received travel support from the National Natural Science Foundation of China (NSFC) through grant 12273002. CYL is supported by the NSFC (grant No. 12233013) and by the CSST project CMS-CSST-2025-A13.

This work made use of Lightkurve (Lightkurve Collaboration et al. 2018) to download the Kepler light curves and TESSUTILS² [62] to extract and process the TESS light curves. We used NumPy [70] and Astropy [8, 10] (Astropy Collaboration et al. 2018) for numerical calculations, Matplotlib [80] for plotting, and emcee [52] for Markov chain Monte Carlo sampling.

GL used ChatGPT (OpenAI; https://chatgpt.com/) to assist with programming, figure preparation, and language editing of an English-language draft originally written by GL. Prism (OpenAI; https://openai.com/prism/) was used to assist with LaTeX editing and formatting. All AI-assisted content was reviewed and revised by the authors.

Author Contributions