TESS observations of the Pleiades cluster: a nursery for $\delta$ Scuti stars

Explaining the details of excitation and mode selection in $\delta$ 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 do only a subset of stars in the instability strip show $\delta$ 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 $\kappa$ (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 $\delta$ 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 $\delta$ 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 $\delta$ 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-$\Sigma$ 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-$\Sigma$ 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 7. V1229 Tau (HD 23642) is a well-studied eclipsing and spectroscopic binary 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 Sec. 4.1 for details).

Ten stars in Table 7 are named variables (column 1). These include the six $\delta$ 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 $\gamma$ 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 7 (columns 5–7) is based on magnitudes and parallaxes from Gaia DR3 (Gaia Collaboration et al., 2021; Lindegren et al., 2021; Riello et al., 2021). In Fig. 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 $E(\mbox{$G_{BP}-G_{RP}$})=0.055$ (Andrae et al., 2018).

Some of the spread in the cluster main sequence is from binarity. The twelve red circular outlines in Fig 1a mark known spectroscopic binaries from the list compiled by Torres et al. (2021), and some of these clearly lie above the cluster sequence. Figure1a also shows several stars above the main sequence with values of Gaia RUWE (renormalised 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 the next section.

We have measured $v\sin i$ for 49 stars in our sample using spectra collected by the Center for Astrophysics (CfA) survey (Torres, 2020; Torres et al., 2021). These were gathered with the Tillinghast Reflector Échelle Spectrograph (TRES), a high-resolution ($R=44,000$) fiber-fed échelle mounted on the 1.5m 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 non-rotating 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 (Gray, 2005). The resulting $v\sin i$ values are listed in column 10 of Table 7 and are indicated as source 1 in column 11. For an additional 10 stars, we used $v\sin i$ measurements from Gaia RVS 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 color-magnitude diagram in Figure 1b 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., 2022; Malofeeva et al., 2023). This is at least partly responsible for the extended main-sequence turn-offs 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; Chen et al., 2022a; He et al., 2022). Rotation does not only affect the turn-off, but also broadens the main sequence itself, and we are seeing good evidence for this in the Pleiades in Fig. 1b.

Observations with TESS are made in 27-d sectors (Ricker et al., 2015). The Pleiades were observed in the fourth year of the mission, in Sectors 42–44 (2021 August 20 to 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 PDCSAP¹¹1Pre-search Data Conditioning Simple Aperture Photometry light curves that were provided by the SPOC (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-min cadence), which showed no evidence for $\delta$ Scuti pulsations.²²2The light curve for HD 23479 was contaminated by oscillations from HD 23463 (separation 39 arcsec), which is a red giant whose parallax and proper motion show it to be currently passing through the Pleiades cluster. 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-min) observations show pulsations and we have included it as a $\delta$ Scuti star in the table and figures (apart from Fig. 2).

In total, we detected $\delta$ Scuti pulsations in 36 of the stars in our sample, as flagged in Table 7 (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 non-detections showed no significant peaks above about 4 times the noise. The last two columns of Table 7 show the frequency and amplitude of the strongest mode in each $\delta$ Scuti star (measured in the range 10 to 80 d^-1).

The amplitude spectra for the 35 $\delta$ Scuti stars observed by TESS are shown in Fig. 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.

Figure 3 shows the $\delta$ 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 (Fig. 3a) and the accompanying histogram (Fig. 3b) 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 ($72\pm 6\%$), and in the middle of the instability strip (0.20–0.40) it is 21/25 ($84\pm 7\%$). This pulsator fraction is significantly higher than the 50–60% found in the Kepler $\delta$ Scuti sample by Murphy et al. (2019).

Although the Pleiades cluster is unusually rich in $\delta$ 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 7). 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 $\delta$ Scuti instability strip, and five of these are pulsating. The conclusion is that chemical peculiarity can only account for two of the non-pulsators 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 de-reddened $G_{BP}-G_{RP}$ colors using an updated version of Table 5 of Pecaut & Mamajek (2013)³³3http://www.pas.rochester.edu/~emamajek/EEM_dwarf_UBVIJHK_colors_Teff.txt. We estimated approximate stellar luminosities from $G$ magnitudes and Gaia DR3 parallaxes, using $V$ bolometric corrections and $G-V$ colors from the same source.

The solid blue lines in Fig. 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 $\alpha_{\rm ov}=0.2$, and a solar-calibrated value for the mixing length parameter ($\mbox{$\alpha_{\rm MLT}$}=1.8$). With the caveat that $\alpha_{\rm MLT}$ could have a different value for the Pleiades, we conclude that the observed $\delta$ Scuti strip for our sample is quite well matched to the theoretical calculations.

The dashed purple lines in Fig. 4 mark the instability strip for $\delta$ Scuti stars observed with Kepler (Murphy et al., 2019). The offset with respect to the Pleiades might come from a combination of: (1) different $T_{\rm eff}$ 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 $\delta$ 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 $\delta$ 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 degrees 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 magnitudes for every kpc in distance. We also show the sample of $\gamma$ Doradus stars in the Kepler field studied by Li et al. (2020), again restricted to $b>10^{\circ}$ (orange points). Overall, Fig. 5 displays very nicely the effect of interstellar reddening on the pulsational instability strips. Note that we have not given a list of $\gamma$ 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.

The quantity $\nu_{\rm max}$ 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 $\nu_{\rm max}$. It was suggested by Brown et al. (1991) that when scaling from the Sun to other stars, $\nu_{\rm max}$ 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 $g/\sqrt{\mbox{$T_{\rm eff}$}}$. That line of reasoning underlies the scaling relation

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 $\nu_{\rm max}$ is a useful observable for $\delta$ Scuti stars, given that it shows a correlation with $T_{\rm eff}$ (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 $\delta$ Scuti stars in the Pleiades (see Fig. 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 $T_{\rm eff}$, 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 $\delta$ 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 $\nu_{\rm max}$ in $\delta$ 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 $\delta$ Scuti stars, on the other hand, the distribution of amplitudes is much less ordered (see Fig. 2). Therefore, even defining what is meant by $\nu_{\rm max}$ in $\delta$ Scuti stars is not straightforward. One approach is to use the frequency of the strongest mode, $f_{1}$, which we have listed in Column 14 of Table 7. Given that many stars in Fig. 2 have several modes with similar amplitudes, this is clearly not an ideal metric. Not surprisingly, given the diversity in Fig. 2, we found that plots of $f_{1}$ versus various stellar parameters (such as $T_{\rm eff}$ and $v\sin i$) did not show any obvious correlations.

The variety of oscillation spectra in Fig. 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 8 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, $\Delta\nu$) scale as the square root of stellar density (e.g., Aerts et al., 2010). Hence, we might expect $\Delta\nu$ to vary substantially among the Pleiades $\delta$ Scuti stars, given their range of masses. However, theoretical models of young main-sequence $\delta$ Scuti stars show that for fixed metallicity, $\Delta\nu$ is remarkably constant across a wide range of masses (see Fig.4a of Murphy et al. 2021 and Murphy et al., in preparation). This makes the vertical lines in Fig. 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 Sec. 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 $\delta$ 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 color-magnitude diagram (Fig. 1b). Using time-series photometry from NASA’s TESS Mission (plus one star observed by Kepler/K2), we detected $\delta$ 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 (Fig. 4). On the other hand, the characteristics of the pulsation spectra are very varied and do not correlate very strongly with stellar temperature (Fig. 2), calling into question the existence of a useful $\nu_{\rm max}$ relation for $\delta$ Scutis, at least for young stars. By including $\delta$ Scuti stars observed in the Kepler field (Fig. 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.