TESS Observations of the Pleiades Cluster: A Nursery for δ Scuti Stars

Explaining the details of excitation and mode selection in δ Scuti stars is one of the major unsolved challenges in stellar pulsations (see reviews by Goupil et al. 2005; Handler 2009; Lenz 2011; Guzik 2021; Kurtz 2022). Why does only a subset of stars in the instability strip show δ Scuti pulsations? And how can two stars occupy essentially the same position in the H–R diagram but only one show pulsations?

One obvious explanation is that some stars have pulsations too weak to be detected. However, CoRoT and Kepler pushed the detection threshold down to extremely low levels (Balona et al. 2015; Michel et al. 2017; Bowman & Kurtz 2018; Guzik 2021), and it is still the case that only about half the stars in the central part of the instability strip are pulsating (Murphy et al. 2019).

Another possible factor is chemical composition. Stars with different metallicities can pass through a given location in the H–R diagram at different ages and with different opacities in the driving zone. This will affect pulsations driven by the κ (opacity) mechanism (Guzik et al. 2018) and even more so for chemically peculiar stars (Murphy et al. 2015; Guzik et al. 2021), so it is likely that chemical composition is part of the explanation. But even in open clusters, which are assumed to have a uniform metallicity (De Silva et al. 2006; Sestito et al. 2007; Bovy 2016), the pulsator fraction is much less than 1. In the Pleiades, for example, Breger (1972) found four δ Scuti stars, and three decades later, that number still only stood at six (Koen et al. 1999; Li et al. 2002; Fox Machado et al. 2006). Kepler/K2 observed five of these in short-cadence (1 minute) mode (Murphy et al. 2022), and the long-cadence (30 minutes) data hinted at more variables (Rebull et al. 2016).

NASA's TESS Mission (Ricker et al. 2015) is producing high-precision, rapid-cadence light curves over most of the sky, opening up new possibilities for studying large samples of δ Scuti stars (e.g., Antoci et al. 2019; Balona & Ozuyar 2020; Barceló Forteza et al. 2020; Bedding et al. 2020; Murphy et al. 2020). In this Letter, we use data from Gaia and TESS to perform the most detailed search to date for δ Scuti pulsators in the Pleiades open cluster (Messier 45).

We selected an initial list of likely Pleiades members using Gaia DR2 astrometry and the BANYAN-Σ code (Gagné et al. 2018). We used the default Pleiades parameters and did not include any radial velocity information (to avoid biasing against binaries). We selected all stars with BANYAN membership probabilities above 90% and Gaia colors 0.0 < G_BP − G_RP < 0.7, which correspond approximately to spectral types in the range A0 V to F8 V. This gave a list of 83 stars. We note that our membership selection was not altered by updating to Gaia DR3.

We also included five stars listed by Heyl et al. (2022) as escaped Pleiades members (HD 17962, HD 20655, HD 21062, HD 23323, and HD 34027). These stars are too distant from the Pleiades core to have been included in our BANYAN-Σ selection. We note that a cross-check of the G and early K dwarfs in the Heyl et al. (2022) sample with TESS indicated most of the suggested escapees have <10 day rotation periods, which is consistent with expectations for Pleiades membership (Curtis et al. 2019).

Our final sample of 89 stars is listed in Table 1. V1229 Tau (HD 23642) is a well-studied eclipsing and spectroscopic binary (SB) that consists of two A-type stars with an orbital period of 2.4611 days (see Groenewegen et al. 2007 and references therein). Both components are A-type stars, so we have listed them separately in the table (see Section 4.1 for details).

Table 1. Sample of A and F Stars in the Pleiades

Name	HD	HIP	TIC	G	MG	GBP − GRP	Esc.	SB	$v\sin i$		δ Sct	Am	f1	a1
									(km s−1)	(src)			(day−1)	(parts per thousand)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)	(13)	(14)	(15)
	22578	17000	113956708	6.70	1.04	0.00	0	0	242 ± 22	1	0	0	⋯	⋯
24 Tau	23629		405484171	6.30	0.59	0.01	0	0	184 ± 15	1	0	0	⋯	⋯
V1229 Tau A	23642	17704	125754991	7.32	1.61	0.01	0	1			0	0	⋯	⋯
	23410	17572	67830155	6.90	1.25	0.02	0	0	180 ± 9	1	0	0	⋯	⋯
	23950	17921	440695282	6.04	0.39	0.02	0	0	133 ± 7	1	0	0	⋯	⋯
	24899	18559	149980785	7.20	1.43	0.03	0	1	67 ± 2	1	0	0	⋯	⋯
	23568	17664	405484416	6.80	1.11	0.03	0	0	188 ± 5	2	0	0	⋯	⋯
	22614	17034	427545204	7.10	1.54	0.04	0	0	114 ± 2	1	0	0	⋯	⋯
	23631		440681316	7.29	1.58	0.04	0	1	13 ± 5	1	0	1	⋯	⋯
	23632	17692	440681358	7.00	1.32	0.04	0	0	194 ± 3	2	0	0	⋯	⋯
	23913	17892	440691760	7.00	1.32	0.04	0	0	205 ± 21	1	0	0	⋯	⋯
	23964	17923	440695975	6.81	1.15	0.06	0	1	5 ± 1	1	0	0	⋯	⋯
	23948		35159593	7.55	1.87	0.09	0	0	115 ± 1	2	0	0	⋯	⋯
	22637	17043	113981021	7.27	1.56	0.11	0	1	131 ± 10	1	0	0	⋯	⋯
	23872		346626001	7.53	1.76	0.13	0	0	246 ± 5	2	1	0	62.01	0.09
	23489		125736946	7.35	1.68	0.13	0	0	124 ± 2	1	1	0	22.64	0.08
	24076	17999	35205647	6.93	1.09	0.14	0	0			0	0	⋯	⋯
	21062	15902	29058513	7.11	2.05	0.15	1	0	118 ± 1	2	1	0	47.64	1.05
	23336	17547	385554826	7.40	1.92	0.17	0	0	243 ± 3	2	1	0	31.33	0.67
	23763	17791	35156298	6.94	1.13	0.18	0	0	116 ± 2	1	1	0	33.28	0.10
	23155	17403	405483425	7.51	2.06	0.18	0	0	205 ± 5	1	1	0	32.92	1.05
	24178		84336172	7.65	1.98	0.20	0	0	214 ± 13	1	0	0	⋯	⋯
V650 Tau	23643		440681425	7.75	2.11	0.22	0	0	238 ± 7	1	1	0	32.64	2.97
	23886		346626099	7.96	2.32	0.23	0	0	125 ± 2	2	1	0	56.62	1.94
	23852		440691730	7.71	2.07	0.23	0	0	148 ± 4	1	1	0	17.77	1.59
	23388	17552	67828699	7.73	2.17	0.24	0	0	204 ± 7	1	1	0	14.14	0.51
	23402		67830321	7.80	2.11	0.25	0	0	248 ± 6	1	1	0	40.86	0.42
V1187 Tau	23194		405483707	8.04	2.39	0.27	0	0	37 ± 1	1	1	1	53.18	1.46
	23924		440695768	8.09	2.42	0.27	0	0			0	1	⋯	⋯
	23409		385589694	7.83	2.15	0.27	0	0	213 ± 5	1	1	0	32.31	1.95
	23430	17583	385558439	8.02	2.37	0.28	0	0	130 ± 3	1	1	0	44.99	0.86
	23863		346626294	8.10	2.45	0.30	0	0	163 ± 6	1	1	0	41.47	1.28
	17962	13522	77568727	8.15	2.45	0.30	1	0	152 ± 2	2	1	0	39.35	0.57
	20655	15552	402366726	7.55	2.47	0.31	1	0	146 ± 2	2	1	0	34.88	1.38
	23361		385552144	8.02	2.38	0.31	0	0	219 ± 8	1	1	0	32.66	0.97
V1228 Tau	23628		125754823	7.63	2.10	0.31	0	0			1	0	32.54	0.74
	21744	16407	46476992	8.09	2.50	0.32	0	0	130 ± 3	1	1	0	41.78	0.81
	23664	17729	125754460	8.27	2.56	0.34	0	0	96 ± 2	1	0	0	⋯	⋯
	23610	17694	440681752	8.12	2.60	0.34	0	1	26 ± 1	1	0	1	⋯	⋯
V624 Tau	23156		405483817	8.20	2.55	0.35	0	0			1	0	39.03	1.67
V647 Tau	23607		405484188	8.24	2.55	0.35	0	0	19 ± 1	1	1	1	38.38	1.47
	23323		385553714	8.55	2.63	0.36	1	0	123 ± 1	2	1	0	20.81	2.49
	24711	18431	14111056	8.30	2.64	0.37	0	0	138 ± 3	1	1	0	42.82	0.79
V1229 Tau B	23642	17704	125754991	8.20	2.49	0.37	0	1			1	1	21.89	0.15
	23246		348639016	8.12	2.64	0.38	0	0			1	0	23.31	0.19
	23791		440690782	8.34	2.66	0.38	0	0			1	1	20.89	0.38
V1210 Tau	23585		405484093	8.33	2.68	0.41	0	0	108 ± 3	1	0	0	⋯	⋯
	21510	16217	405461432	8.33	2.76	0.42	0	0			1	0	21.75	0.45
	23479		385589599	8.23	2.57	0.44	0	0			0	0	⋯	⋯
	23028	17325	114083179	8.36	2.72	0.44	0	0	68 ± 1	1	1	0	⋯	⋯
	23325		385509282	8.55	2.72	0.47	0	0	85 ± 1	2	1	1	23.22	0.64
	23157	17401	67768222	7.86	2.32	0.49	0	0	58 ± 1	1	1	0	32.46	0.55
V1225 Tau	22702		427580304	8.75	2.98	0.49	0	0	137 ± 6	1	0	0	⋯	⋯
	23488	17625	125736216	8.65	2.99	0.49	0	1	18 ± 1	1	1	0	22.04	0.88
	34027	24808	82969878	8.85	2.77	0.49	1	0			0	0	⋯	⋯
	23375		385552372	8.55	2.88	0.50	0	0			0	0	⋯	⋯
V534 Tau	23567		405484574	8.48	3.11	0.50	0	0			1	0	38.71	1.06
	23733		35155873	8.21	2.56	0.50	0	1	166 ± 25	1	1	0	18.26	0.16
	22146		26126738	8.79	3.04	0.50	0	0			1	0	11.13	0.05
	23290	17481	67788829	8.63	2.96	0.51	0	0			0	0	⋯	⋯
	24132	18050	84331341	8.77	3.07	0.53	0	0			0	0	⋯	⋯
	23326		67829720	8.89	3.26	0.54	0	0	19 ± 1	1	0	0	⋯	⋯
	23512		61139371	8.04	2.37	0.54	0	0	170 ± 8	1	1	0	53.64	0.05
	23792		440690206	8.31	3.10	0.55	0	1	164 ± 11	1	0	0	⋯	⋯
	23289	17497	67787772	8.89	3.23	0.55	0	0	26 ± 1	1	0	0	⋯	⋯
		16423	26078071	8.78	3.24	0.56	0	0			0	0	⋯	⋯
	24655		14109779	8.98	3.54	0.59	0	0	22 ± 1	1	0	0	⋯	⋯
	23912		440691379	9.03	3.33	0.59	0	0	151 ± 4	1	0	0	⋯	⋯
	22887	17225	114060256	9.07	3.44	0.60	0	0			0	0	⋯	⋯
	23133		114166637	8.89	3.27	0.60	0	0	122 ± 22	1	0	0	⋯	⋯
	23351		385552643	8.90	3.22	0.62	0	1			0	0	⋯	⋯
	23511		125736995	9.20	3.53	0.62	0	0	30 ± 1	1	0	0	⋯	⋯
	24086		84331854	9.01	3.33	0.62	0	0			0	0	⋯	⋯
	22977	17289	114084434	9.06	3.42	0.63	0	0			0	0	⋯	⋯
	24302	18154	427735820	9.34	3.67	0.64	0	0			0	0	⋯	⋯
	23513		61145701	9.30	3.64	0.64	0	0	32 ± 1	1	0	0	⋯	⋯
	23584		405484278	9.38	3.71	0.65	0	0	82 ± 2	1	0	0	⋯	⋯
	23312	17511	67788288	9.36	3.63	0.66	0	0			0	0	⋯	⋯
		17125	353928999	9.50	3.78	0.66	0	0	85 ± 2	1	0	0	⋯	⋯
	23514		61145611	9.31	3.58	0.66	0	0			0	0	⋯	⋯
		18544	14177821	9.29	3.78	0.66	0	0	72 ± 2	1	0	0	⋯	⋯
	23732		35155396	9.12	3.45	0.66	0	0	23 ± 1	1	0	0	⋯	⋯
	23061		258067594	9.37	3.68	0.66	0	0			0	0	⋯	⋯
SAO 93581			67789284	9.30	3.65	0.68	0	0			0	0	⋯	⋯
	23975		35204900	9.52	3.82	0.68	0	0			0	0	⋯	⋯
		16639	46538779	9.43	3.77	0.68	0	0			0	0	⋯	⋯
	23352		385552619	9.57	3.91	0.68	0	0	34 ± 1	1	0	0	⋯	⋯
	23158		67768242	9.43	3.77	0.69	0	1	40 ± 1	1	0	0	⋯	⋯
	24463		348769726	9.60	3.94	0.70	0	0			0	0	⋯	⋯

Note. HIP and TIC refer to the Hipparcos Catalog and the TESS Input Catalog, respectively. Column 8: a value of 1 for Esc. indicates an escaped member (Heyl et al. 2022). Column 9: 1 indicates a spectroscopic binary (SB; Torres et al. 2021). Column 11: source for $v\sin i$ is 1 (this work) or 2 (Gaia DR3). Column 12: 1 indicates δ Scuti star. Column 13: 1 indicates Am star (metallic-lined A star; Renson & Manfroid 2009). Columns 14 and 15: frequency (in cycles per day) and amplitude (in parts per thousand) of the strongest δ Scuti mode. For V1229 Tau A & B, the magnitudes and colors (columns 5–7) are estimates (see Section 4.1).

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Ten stars in Table 1 are named variables (column 1). These include the six δ Scuti stars previously known from ground-based observations (V534 Tau, V624 Tau, V647 Tau, V650 Tau, V1187 Tau, and V1228 Tau; Breger 1972; Koen et al. 1999; Li et al. 2002), together with two γ Doradus stars (V1210 Tau and V1225 Tau; Martín & Rodríguez 2000) and both members of the eclipsing binary V1229 Tau (HD 23642).

The photometry in Table 1 (columns 5–7) is based on magnitudes and parallaxes from Gaia DR3 (Gaia Collaboration 2021; Lindegren et al. 2021; Riello et al. 2021). In Figure 1 we show the color–magnitude diagram (CMD) of the sample. No correction for extinction or reddening was made. We have included a PARSEC isochrone (Marigo et al. 2017), with a metallicity of Z = 0.017 and an age of 110 Myr, which are appropriate for the Pleiades (Gaia Collaboration et al. 2018). We shifted the isochrone to account for extinction and reddening, using values of A_G = 0.11 and E(G_BP − G_RP) = 0.055 (Andrae et al. 2018).

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Some of the spread in the cluster main sequence is from binarity. The 12 red circular outlines in Figure 1(a) mark known spectroscopic binaries from the list compiled by Torres et al. (2021), and some of these clearly lie above the cluster sequence. Figure 1(a) also shows several stars above the main sequence with values of Gaia RUWE (renormalized unit weight error) significantly greater than 1.0, indicating they are likely to be binaries (Evans 2018; Belokurov et al. 2020). Note that stars with high RUWE values can still provide useful parallaxes, although generally with larger uncertainties (e.g., El-Badry et al. 2021; Lindegren et al. 2021; Maíz Apellániz et al. 2021). As a check, we examined the fidelity_v2 diagnostic calculated by Rybizki et al. (2022) and found it to have a value of 1.0 for all stars in our sample, indicating the astrometric solutions are reliable.

We conclude that stars well above the cluster sequence have high RUWE, are spectroscopic binaries, or both. The remaining spread in the observed sequence can be attributed to the presence of rapid rotators, as discussed in Section 3.

We have measured $v\sin i$ for 49 stars in our sample using spectra collected by the Center for Astrophysics survey (Torres 2020; Torres et al. 2021). These were gathered with the Tillinghast Reflector Échelle Spectrograph, a high-resolution (R = 44,000) fiber-fed échelle mounted on the 1.5 m reflector at the Fred Lawrence Whipple Observatory, Arizona. Following Zhou et al. (2018), we extracted line profiles from each spectrum via a least-squares deconvolution (Donati et al. 1997) against a synthetic nonrotating ATLAS9 template (Castelli & Kurucz 2003). The broadening profile was then modeled as a combination of kernels describing the effects of rotational, macroturbulent, and instrumental broadening (Gray2005). The resulting $v\sin i$ values are listed in column 10 of Table 1 and are indicated as source 1 in column 11. For an additional 10 stars, we used $v\sin i$ measurements from Gaia Radial Velocity Spectrometer spectra (Creevey et al. 2022), which are indicated as source 2 in the table. By way of validation, we note there is good consistency for 15 stars with $v\sin i$ measurements from both sources. We also note that the distribution of our $v\sin i$ measurements is similar to that of A-type stars in general (e.g., Royer et al. 2007; Zorec & Royer 2012), so that we can consider the Pleiades to be representative of the broader population.

The CMD in Figure 1(b) is color coded by $v\sin i$. It is well known that rotation causes stars to move in the CMD (Pérez Hernández et al. 1999; Fox Machado et al. 2006; Espinosa Lara & Rieutord 2011; Lipatov & Brandt 2020; Wang et al. 2023; Malofeeva et al. 2023). This is at least partly responsible for the extended main-sequence turnoffs seen in the CMDs of young- and intermediate-age clusters (Bastian & de Mink 2009; Yang et al. 2013; Brandt & Huang 2015; Goudfrooij et al. 2017; Gossage et al. 2019; Sun et al. 2019; de Juan Ovelar et al. 2020; Kamann et al. 2020; J. Chen et al. 2022; He et al. 2022). Rotation does not only affect the turnoff but also broadens the main sequence itself, and we are seeing good evidence for this in the Pleiades in Figure 1(b).

Observations with TESS are made in 27 day sectors (Ricker et al. 2015). The Pleiades were observed in the fourth year of the mission, in Sectors 42–44 (2021 August 20–November 6). Most Pleiades stars have TESS data in all three sectors, and a few were also observed in Sectors 18 or 19. All the stars in our sample except two have TESS observations with 120 s cadence, and we used the lightkurve package (Lightkurve Collaboration et al. 2018) to download the PDCSAP ⁷  light curves that were provided by the Science Processing Operations Center. The first exception was HD 23479. For this star we extracted a light curve from the TESS full-frame images (10 minute cadence), which showed no evidence for δ Scuti pulsations. ⁸  The second exception was HD 23028, which fell just off the edge of the detector and is the only star in our sample with no TESS observations. For this star, Kepler/K2 long-cadence (30 minutes) observations show pulsations, and we have included it as a δ Scuti star in the table and figures (apart from Figure 2).

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In total, we detected δ Scuti pulsations in 36 of the stars in our sample, as flagged in Table 1 (column 12). These include the six previously known from ground-based observations (V534 Tau, V624 Tau, V647 Tau, V650 Tau, V1187 Tau, and V1228 Tau), plus 30 additional detections. For all detections, the amplitude spectrum showed several clear peaks at least 10 times the mean noise level (and often much higher), while the nondetections showed no significant peaks above about 4 times the noise. The last two columns of Table 1 show the frequency and amplitude of the strongest mode in each δ Scuti star (measured in the range 10–80 day⁻¹).

The amplitude spectra for the 35 δ Scuti stars observed by TESS are shown in Figure 2, ordered according to Gaia G_BP − G_RP. The detections include four of the five escaped members (Heyl et al. 2022), and the similarity of those oscillation spectra to confirmed members of the Pleiades lends support to their status as escaped members.

4.1. V1229 Tau (HD 23642)

V1229 Tau is a well-studied eclipsing and SB, with a period of 2.4611 days (see Groenewegen et al. 2007 and references therein). Both components are A-type stars, and so we have treated them separately.

The Gaia photometry (G = 6.82 and G_BP − G_RP = 0.10) measures the combined light of the system. In order to plot both components separately, we have estimated values in the table using the published effective temperatures (9750 ± 250 K and 7600 ± 400 K; Southworth et al. 2005) and a luminosity ratio of 0.355 ± 0.035 (David et al. 2016). The photometry given in columns 5–7 of Table 1 are estimates if the two components were measured separately, also taking into account the reddening and extinction of the cluster. In Figure 3(a), the black circular outlines show (from left to right) the A component, the combined system, and the B component.

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In addition to the eclipses, the TESS light curve shows high-frequency δ Scuti pulsations. The amplitude spectrum in Figure 2 was made after fitting and subtracting an eclipse model. Given the colors of the components (see Figure 3(a)), it is reasonable to conclude that the pulsations occur in the B component. To verify this, we examined the scatter in the time series after fitting and removing the five highest peaks in the amplitude spectrum. We found the scatter to be reduced everywhere in this prewhitened light curve, but the reduction was less during secondary eclipses because the five-peak fit is a poorer fit when part of the pulsating star is being eclipsed (note that the inclination of the system is about 78°, and the eclipses are not total; David et al. 2016). We can therefore confirm that it is the secondary component (V1229 Tau B) that is undergoing pulsations.

X. Chen et al. (2022) noted pulsations in V1229 Tau (which they referred to as TIC 125754991) and suggested that it is hotter than typical δ Scuti stars because they assumed the primary is the pulsator. Once we accept that the secondary is the pulsating component, this star becomes typical. A more detailed study of the pulsations of V1229 Tau (HD 23642) using the TESS light curve has been made by Southworth et al. (2023).

Figure 3 shows the δ Scuti detections as a function of Gaia G_BP − G_RP color index (without correcting for the reddening of the Pleiades, which is about 0.055; Andrae et al. 2018). We see in the CMD (Figure 3(a)) and the accompanying histogram (Figure 3(b)) that the pulsators lie within a strip that spans from about 0.10 to 0.55 in G_BP − G_RP. In this color range, the fraction of stars that pulsate is 36/50 (72% ± 6%), and in the middle of the instability strip (0.20–0.40) it is 21/25 (84% ± 7%). This pulsator fraction is significantly higher than the 50%–60% found in the Kepler δ Scuti sample by Murphy et al. (2019).

Although the Pleiades cluster is unusually rich in δ Scutis (with peak amplitudes in the range 50–3000 ppm, depending on the star), there are still several stars within the instability strip that are not pulsating (down to a sensitivity limit of 10–20 ppm). One possible explanation is chemical peculiarity, which typically occurs in slow rotators because helium sinks out of the He ii driving zone (Baglin et al. 1973; Deal et al. 2020). Slow rotation can be caused by tidal interactions with a binary companion (e.g., Fuller et al. 2017 and references therein), which is thought to be responsible for the Am stars ("m" for "metallic-lined"; e.g., Abt 1967; North et al. 1998; Debernardi et al. 2000; Stateva et al. 2012).

Eight stars in our sample were listed by Renson & Manfroid (2009) as being Am stars (see column 13 in Table 1). One of these is the eclipsing binary V1229 Tau, for which Abt & Levato (1978) gave the spectral type as A0 Vp(Si) + Am, indicating that the B component is an Am star. Overall, seven of the Am stars in our sample have colors that place them within the δ Scuti instability strip, and five of these are pulsating. The conclusion is that chemical peculiarity can only account for two of the nonpulsators in the Pleiades.

Figure 4 shows our sample in an H–R diagram. To construct this, we first corrected the observed Gaia photometry for extinction and reddening using the values given above. We estimated effective temperatures from the dereddened G_BP − G_RP colors using an updated version of Table 5 of Pecaut & Mamajek (2013). ⁹  We estimated approximate stellar luminosities from G magnitudes and Gaia DR3 parallaxes, using V bolometric corrections and G − V colors from the same source.

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The solid blue lines in Figure 4 show the theoretical instability strip calculated by Dupret et al. (2005), which used a typical solar composition (X = 0.7, Z = 0.02), a convective core overshooting parameter of α_ov = 0.2, and a solar-calibrated value for the mixing length parameter (α_MLT = 1.8). With the caveat that α_MLT could have a different value for the Pleiades, we conclude that the observed δ Scuti strip for our sample is quite well matched to the theoretical calculations.

The dashed purple lines in Figure 4 mark the instability strip for δ Scuti stars observed with Kepler (Murphy et al. 2019). The offset with respect to the Pleiades might come from a combination of (1) different T_eff scales being used; (2) having a homogeneous composition among Pleiades members, rather than the heterogeneous Kepler sample; (3) perhaps from having a slightly higher overall metallicity in the Pleiades; (4) from the Pleiades being young, as opposed to the Kepler sample where some stars that appeared near the ZAMS may be older stars of lower metallicity; and (5) the larger Kepler sample may give rise to more outliers at the hotter end of the distribution.

Figure 5 shows the effect of reddening on the δ Scuti instability strip by plotting the distance to each star versus its Gaia color index. The red points at the bottom show the Pleiades, and the blue points show δ Scuti stars detected by Kepler (Murphy et al. 2019). As expected, the observed instability strip shifts to the red with increasing distance. Note that we have restricted the Kepler sample to stars more than 10° from the Galactic plane in order to see the dependence on distance more clearly. We see that the reddening in G_BP − G_RP is approximately 0.15 mag for every kiloparsec in distance. We also show the sample of γ Doradus stars in the Kepler field studied by Li et al. (2020), again restricted to b > 10° (orange points). Overall, Figure 5 displays very nicely the effect of interstellar reddening on the pulsational instability strips. Note that we have not given a list of γ Doradus stars in the Pleiades although many are certainly present because having only a few TESS sectors often makes it difficult to distinguish unambiguously between gravity-mode pulsations and rotational modulation.

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The quantity ${\nu }_{\max }$ is defined for solar-like oscillations as the centroid of the power envelope (Kjeldsen & Bedding 1995). Solar-like oscillations are excited stochastically by near-surface convection, and the observed modes cover a broad range of frequencies centered at ${\nu }_{\max }$. It was suggested by Brown et al. (1991) that when scaling from the Sun to other stars, ${\nu }_{\max }$ should be a fixed fraction of the acoustic cutoff frequency. The latter is the frequency above which waves are no longer reflected at the surface and is expected from simple arguments to scale as $g/\sqrt{{T}_{\mathrm{eff}}}$. That line of reasoning underlies the scaling relation

$$\begin{eqnarray}&&{\nu }_{\max }\propto g/\sqrt{{T}_{\mathrm{eff}}},\end{eqnarray} \tag{ 1 }$$

which is widely used in the study of solar-like oscillations although its physical basis is not well understood (Belkacem et al. 2011; Kjeldsen & Bedding 2011; Chaplin & Miglio 2013; Hekker 2020; Zhou et al. 2020).

There have been suggestions that ${\nu }_{\max }$ is a useful observable for δ Scuti stars, given that it shows a correlation with T_eff (Balona & Dziembowski 2011; Barceló Forteza et al. 2018; Bowman & Kurtz 2018; Barceló Forteza et al. 2020; Hasanzadeh et al. 2021). However, the oscillation spectra of δ Scuti stars in the Pleiades (see Figure 2, which is ordered by color index) show the correlation to be weak or nonexistent for this sample of young main-sequence stars. In particular, we do not see a shift to higher radial orders with increasing T_eff, as predicted by theoretical models. Different theoretical treatments give slightly different predictions, but they all agree that we expect the excitation of higher radial order modes in δ Scuti stars as we move to higher temperatures within the instability strip (Dziembowski 1997; Houdek et al. 1999; Pamyatnykh 2000; Dupret et al. 2005; Houdek & Dupret 2015; Xiong et al. 2016; Xiong 2021).

It is also worth noting that there is no unambiguous definition for ${\nu }_{\max }$ in δ Scuti stars. In a star with solar-like oscillations, the stochastic nature of the excitation and damping from convection leads to a power envelope of modes that is roughly Gaussian, with a well-defined maximum. In many δ Scuti stars, on the other hand, the distribution of amplitudes is much less ordered (see Figure 2). Therefore, even defining what is meant by ${\nu }_{\max }$ in δ Scuti stars is not straightforward. One approach is to use the frequency of the strongest mode, f₁, which we have listed in Column 14 of Table 1. Given that many stars in Figure 2 have several modes with similar amplitudes, this is clearly not an ideal metric. Not surprisingly, given the diversity in Figure 2, we found that plots of f₁ versus various stellar parameters (such as T_eff and $v\sin i$) did not show any obvious correlations.

The variety of oscillation spectra in Figure 2 is quite remarkable although there is also similarity between some stars. To help guide the eye, the vertical dotted lines in the figure show the approximate locations of the first eight radial modes. These are based on the observed frequencies in the star V647 Tau, which has a particularly regular spectrum (Murphy et al. 2022, Table 4).

It is well established that oscillation frequencies (and therefore also the large separation, Δν) scale as the square root of stellar density (e.g., Aerts et al. 2010). Hence, we might expect Δν to vary substantially among the Pleiades δ Scuti stars, given their range of masses. However, theoretical models of young main-sequence δ Scuti stars show that for fixed metallicity, Δν is remarkably constant across a wide range of masses (see Figure 4(a) of Murphy et al. 2021 and Murphy et al. 2023, in preparation). This makes the vertical lines in Figure 2 quite useful for comparing the oscillation spectra.

Some of the variations between stars could be attributed to differences in rotation, but it is difficult to see much in the way of systematic trends. Furthermore, the distribution of $v\sin i$ values in the Pleiades, as noted in Section 3, is similar to that of A-type stars in general. On balance, our results seem to raise more questions than they answer. On the one hand, the very high fraction of pulsators in the Pleiades means we are not left wondering why some pulsate and others do not. On the other hand, we cannot explain why stars with similar properties have such different pulsation spectra although rotation presumably plays a role. An explanation for mode selection in δ Scuti stars remains as elusive as ever.

Using Gaia photometry and astrometry, we constructed a list of 89 probable members of the Pleiades with spectral types A and F. We measured projected rotational velocities ($v\sin i$) for 49 stars and confirmed that stellar rotation is a significant cause of the broadening of the main sequence in the CMD (Figure 1(b)). Using time-series photometry from NASA's TESS Mission (plus one star observed by Kepler/K2), we detected δ Scuti pulsations in 36 stars. Some stars suggested as being escaped members of the Pleiades by Heyl et al. (2022) have similar pulsation properties to confirmed members, which supports their identification as former members.

The fraction of Pleiades stars in the middle of the instability strip that pulsate is unusually high (over 80%), and their range of effective temperatures agrees well with theoretical models (Figure 4). On the other hand, the characteristics of the pulsation spectra are very varied and do not correlate very strongly with stellar temperature (Figure 2), calling into question the existence of a useful ${\nu }_{\max }$ relation for δ Scutis, at least for young stars. By including δ Scuti stars observed in the Kepler field (Figure 5), we show that the instability strip is shifted to the red with increasing distance by interstellar reddening. In summary, this work demonstrates the power of combining observations with Gaia and TESS for studying pulsating stars in open clusters.

We thank the TESS team for making this research possible. The TESS data used in this paper can be found in MAST. ¹⁰  We gratefully acknowledge support from the Australian Research Council through Discovery Project DP210103119, Future Fellowship FT210100485 and Laureate Fellowship FL220100117, and from the Danish National Research Foundation (Grant DNRF106) through its funding for the Stellar Astrophysics Centre (SAC). D.H. acknowledges support from the Alfred P. Sloan Foundation and the National Aeronautics and Space Administration (80NSSC21K0784). This research made use of Lightkurve, a Python package for Kepler and TESS data analysis (Lightkurve Collaboration et al. 2018). This work made use of several publicly available python packages: astropy (Astropy Collaboration 2013, 2018), lightkurve (Lightkurve Collaboration et al. 2018), matplotlib (Hunter2007), numpy (Harris et al. 2020), and scipy (Virtanen et al.2020).

This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC; https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement. We thank Konstanze Zwintz, Dennis Stello and the referee for useful comments on the paper.

Facility: TESS. -