To Grow Old and Peculiar: A Survey of Anomalous Variable Stars in M80 and Age Determination using K2 and Gaia

Despite the interest generated by T Sco, no further variable stars were identified in M80 until Pickering & Bailey (1898) and Bailey (1902) reported the first two discoveries, followed by five more by Sawyer (1942) and Sawyer Hogg (1955). The first extensive work was published by Wehlau et al. (1990), based on decades of photographic data. Their work included ten variables, although two of those, R Sco and S Sco, initially labeled as V6 and V7, turned out to be nearby Mira stars that are not associated with the cluster. More recently, Shara et al. (2005) discovered two more variables, and then Kopacki (2013) carried out a thorough photometric survey and discovered twenty new variables, thirteen of which are pulsating stars. Light variations were detected in three stars in far-ultraviolet photometry, two of which were known RR Lyrae stars, while the third turned out to be a new SX Phe-type pulsator (Thomson et al. 2010). Salinas et al. (2016) confirmed previous uncertain variable star identifications with adaptive optics imaging photometry. Finally, Figuera Jaimes et al. (2016) identified six further variable stars in the core of the cluster, all of which show slow, low-amplitude brightness changes.

The two brightest variable stars, which were also identified first, are red giants: M80-V1 is a W Vir-type Cepheid variable, and V2 is a possible semiregular star with uncertain periodicity. Of the two, V1 has been studied more extensively: based on the 16.0 d pulsation period of the star, Sawyer (1942) estimated a distance of 16 kpc to M80, and Plachy et al. (2017) identified cycle-to-cycle variations in the star from the continuous photometry obtained during the K2 mission of the Kepler space telescope.

The majority of the other variables in the cluster are pulsating stars, with 15 RR Lyrae and four SX Phoenicis stars identified so far. These identified variables have been cataloged by Clement et al. (2001)¹¹1https://www.astro.utoronto.ca/~cclement/read.html, and we follow their V–numerical variable notation here. The number of RRab and RRc stars are nearly the same, with seven RRab and eight RRc stars identified, which is typical for Oosterhoff II-type clusters (Bono et al. 1994).

The Kepler space telescope observed multiple globular clusters during the K2 mission (Howell et al. 2014; Borucki 2016). This was the first time that extended high-precision photometry was obtained for these objects: earlier observations with the Hubble space telescope, for example, only collected multicolor snapshots to study the color-magnitude distributions of the cluster members instead (Sarajedini et al. 2007; Piotto et al. 2015). Moreover, earlier space photometry missions were limited in resolution and depth due to smaller telescope apertures, and in the number of target stars due to processing power and data storage constraints.

The necessity to repurpose Kepler into the K2 mission opened up the possibility to observe a wide variety of targets, and to experiment with new applications. Stellar clusters were covered by larger continuous pixel mosaics, including eight globular clusters over the mission (M4, M9, M19, M80, NGC5897, NGC6293, NGC6355 and Terzan 5), even though the limited resolution of the telescope, at 4”/px, was a clear deficit when observing stellar fields as dense as the insides of globular clusters (Cody et al. 2018).

Before our study, K2 light curves have been studied in depth only for M4, the closest and loosest of these eight clusters ²²2Results on the oscillating red giants and mass loss in M80 were published after the completion of this paper by Howell et al. (2023).. Miglio et al. (2016) investigated the asteroseismic properties of bright red giants in the cluster, and found excellent agreement with independent distance moduli and stellar masses based on isochrone fitting. Howell et al. (2022) and Tailo et al. (2022) both estimated the integrated mass loss between the late stages of stellar evolution, based on asteroseismic mass estimates for several cluster members. The light curves of the stellar population of the cluster were searched for variable stars and exoplanets (Wallace et al. 2019a, 2020). Moreover, stars with millimagnitude amplitude variations were identified on the horizontal branch, labeled as ultra-low amplitude RR Lyrae stars (Wallace et al. 2019b). Additional modes in some overtone RR Lyrae stars were reported by Kuehn et al. (2017). In contrast, only a single W Vir-type variable at the outskirts of M80 has been studied so far from all the other clusters that were observed in the K2 mission (Plachy et al. 2017).

M80 was observed during Campaign 2 of the K2 mission. This campaign collected data from the vicinity of the Galactic center and the Upper Scorpius star-forming region in late 2014 for 77.1 d. The campaign was rather uneventful, save for brief periods of scattered light caused by Mars passing through the field-of-view of the telescope. A few frames were also discarded at the beginning of the campaign due to poor pointing performance.

M80 was covered with a $100\times 100$ px continuous pixel mask, which translates to a field-of-view of $400"\times 400"$. Given the compactness of M80, with a half-light radius of only $r_{h}=37"$, this easily encompasses most of the cluster, even though the Jacobi radius of M80 is considerably larger at $r_{J}=20.9^{\prime}$ (Harris 1996 (2010 edition); de Boer et al. 2019). Images were collected in long cadence mode, with an integration time of 29.4 min per frame.

For the data reduction, we used the versatile and tested differential-image photometry method based on the FITSH software package (Pál 2012). Most other photometry methods rely on pixel photometry, i.e., summing the flux from a discrete set of pixels and then correcting for image motions afterward. However, pixel photometry can be difficult to achieve for very dense stellar fields that also move about in the images. We, therefore, followed the more conventional method of registering the images to the same reference frame and then applying classical aperture photometry to differential images. This method was used already to collect photometry for a variety of moving objects in the Solar System (Farkas-Takács et al. 2017; Molnár et al. 2018a; Marton et al. 2020; Szabó et al. 2020; Kalup et al. 2021), but also for stellar, stationary targets (Plachy et al. 2017; Vida et al. 2017), and the details have been presented in the works referenced.

In brief, we collected the K2 target pixel files containing the images of the cluster and a few nearby stars and combined them into a larger image. We then calculated the astrometric solutions for all the frames of the campaign, anchoring the astrometry to the brighter stars on these mosaic images, based on an initial solution for the Full Field Images acquired during the campaign. These steps were necessary to transform the images into the same reference frame and to correct for the attitude changes of the telescope. Since only two reaction wheels were operable during the K2 mission, the telescope was freely rotating about the optical axis due to torque generated by solar radiation pressure. The drifting attitude was reset to the unstable equilibrium point with thrusters every six hours, causing a quasi-periodic instrumental signals in the photometry.

We then enlarged each frame linearly in both the RA and Dec dimensions by 3.1 times, distributing the flux levels from the original pixels among the new ones. We employ this step to lessen the effects of low pixel resolution and sharp stellar PSFs (point spread functions) which may lead to strong fringing caused by the sub-pixel position differences between the aligned images. This is especially important to ensure smoother images after subtracting the master frame in the next step. Smaller pixels also allow us finer control over the aperture sizes.

With the aligned frames at hand, we created a master frame from a subset of images and then subtracted that from every individual image. Aperture photometry was carried out on the differential images. We then used the Gaia EDR3 G magnitudes as reference brightness since the two missions use very similar bandpasses, and their magnitude values have been found to correlate well (see, e.g., Molnár et al. 2018b), and shifted the differential light curves to the calculated median flux levels, using the Kepler flux calibration of Lund et al. (2015).

One limitation of our method is that it affects the measured amplitudes. We tested apertures between 3–5 px in the enlarged images (the former equalling $\approx 1$ px in the original images) to limit contamination from neighboring stars. While these tight apertures led to cleaner light curves, they come at the cost of cutting off the outer parts of the PSFs and thus underestimating the variation amplitudes.

The very dense stellar field meant that the raw light curves from the aperture photometry often contained various systematics and instrumental signals, especially those close to the core or other bright stars. The main source of these systematics were the attitude changes of the telescope, causing characteristic six-hour changes in the light curves. As the Sun was moving closer to the field-of-view, two further, slower changes occurred: the amount of zodiacal light increased in the background, and the sizes of the stellar images also increased due to temperature-induced focus changes. Therefore, the light curves required further processing to remove these to the best possible extent.

However, RR Lyrae light curves can be notoriously hard to correct as they include a high-amplitude signal with timescales similar to the frequency of the attitude corrections (Plachy et al. 2021). One post-processing method we found to work exceptionally well with RR Lyrae light curves is the K2 Systematics Correction algorithm (K2SC, Aigrain et al. 2016). This method uses Gaussian Processes to simultaneously fit two signals in the data, with the intrinsic variation assumed to be (quasi-)periodic in time, whereas the systematics assumed to correlate with the pixel positions of the source.

While K2SC is an excellent tool to remove the fast systematics related to the attitude changes, it preserves most of the slow trends in the data. This is beneficial if the slow trends are intrinsic to the targets, but the trends present in the RR Lyrae light curves are of instrumental origin. We removed these with a polynomial-fitting algorithm, where we first determined the pulsation period, then optimized the coefficients of the polynomial by minimizing the phase dispersion of the phase-folded light curve (Bódi et al. 2022). This way we ensured that the pulsation cycles overlap not only in phase but in flux as well, and the polynomial follows the average brightness of the star much more closely than a simple least-squares fit to the light curve would, even for polynomial orders in the 10-20 range. We present one particularly difficult case in Fig. 2.

In a few cases, we opted to scale the light curve with the calculated trend instead of subtracting it. Scaling is equivalent to correcting any sensitivity changes in the photometry, such as changes to the PSF size or shape compared to the aperture, which might introduce flux loss.

The final step of the photometric post-processing was the removal of clear outlier points via sigma clipping the light curve. We then proceeded with the frequency analysis, as described in Sect. 4, where we identified cross-contamination between some of the light curves. In the final light curves presented in Table 5 in Appendix A, contamination coming from nearby known variable stars have been prewithened, so that the light curves contain variations intrinsic to the targeted variable star to the highest extent possible.

We obtained spectra from two telescopes for selected targets. Observations were collected with the LDSS3 (Low Dispersion Survey Spectrograph) instrument installed on the 6.5 m Magellan Clay telescope at Las Campanas Observatory. Five RRc stars (V3, V4, V13, V14, V16) were observed on May 20, 2017. One spectrum per star was recorded with 450 or 600 s exposure times, using the VPH-All grism that covers the whole visible spectrum (425–1000 nm) and has a resolution of R = 860.

We carried out observations with the Dual Imaging Spectrograph (DIS) on the 3.5 m ARC (Astrophysics Research Consortium) telescope at Apache Point Observarory in New Mexico. Observations were collected on multiple occasions, but were challenging given the low altitude of the cluster and the faintness of the targets. Although the resolution of these spectra were higher than the LDSS3 ones, their SNR turned out to be too low to be useful to us.

Three stars, V03, V14 and V16 were observed with the GIRAFFE instrument on the VLT U2 (Kueyen) telescope in 2004 as part of a larger program targeting HB stars in the cluster (Recio-Blanco et al. 2004). We downloaded the wavelength-calibrated spectra from the ESO archive and analyzed them along with the others. These are high-resolution (R $\sim$ 20,000) but low SNR ($\sim$ 20) spectra, but we were still able to estimate some atmospheric parameters from them.

Variables V10 and V15 are about 1.1 mag brighter than the rest of the RR Lyrae stars and the horizontal branch of the cluster, suggesting that they are either not members of M80 or are some other, more luminous variables in the cluster (see Sect. 6.2 for a detailed discussion of the cluster CMD). Unfortunately, Gaia did not acquire useful parallaxes for either of the stars, so we could not decide their membership based on distances alone. The Gaia data put both stars above the HB, but the overtone star, V10, which we would expect to be hotter, appears to be the redder of the two. V10 is not present in the Pan-STARRS observations, but V15 is, and it appears to be 2 mag brighter and significantly bluer than the normal RR Lyrae stars.

The relative Fourier parameters of both V10 and V15 agree with the K2 RRab and RRc distributions, respectively, suggesting that they are indeed RR Lyrae variables. We know from models that He-enhanced RR Lyrae stars are more luminous than those with canonical abundances, but even a significant excess can only lead to a 0.2–0.5 mag increase in brightness, considerably less than the measured 1.1 mag value (Marconi et al. 2018). Furthermore, we do not expect strong differences in the He content within the population of a globular cluster. Therefore, we conclude that V10 and V15 must be foreground objects.

M80 includes six RRab stars as confirmed members of the cluster. All have rather long periods, between 0.60 and 0.82 d. Two of the stars, V19 and V20, are close to the center of the cluster, which degrades the quality of their K2 photometry. We were able to collect precise photometry for the other four stars.

We investigated the light curves for signs of modulation and/or extra modes. We identified additional frequencies in multiple stars, but those turned out to be cross-contamination between the pulsators. After we removed these signals from the light curves, we did not detect any signs of modulation or extra modes in the member RRab stars.

We detected a slight amplitude decrease in the assumed foreground star V10, but without any associated phase change. Slow amplitude changes can be caused either by instrumental effects or intrinsic amplitude variation, but in this case its origin remains ambiguous.

The most striking result from our photometry was the discovery of multiple peculiar overtone stars with very unusual light curve shapes and strong amplitude and phase modulations. The distribution of peculiar and more regular RRc stars is roughly half and half. Two of the four regular RRc stars, V03 and V04 (as well as the foreground star, V15) appear to be classic overtone stars, with asymmetric light curves and prominent humps ob the rising branches. Two further stars, V17 and V18, have more symmetric light curves with no detectable shockwave features, but this is to be expected from long-period RRc stars, above 0.4 d period. V17 is near the center, and thus its light curve suffers from strong systematics. The light curve of V18 is noisy too, but modulation is clearly detectable in it, especially in the pulsation phase: it is reminiscent of many other Blazhko RRc stars with strong phase modulation.

The four remaining stars, V13, V14, V16 and the newly discovered M80 15470, however, appear to be drastically different. Each varies with low amplitude and have strongly variable light curves, and they remain almost sinusoidal even at maximum amplitude. To test the modulation properties, we first computed the temporal variation of the pulsation amplitude and phase by cutting the light curve into short segments and fitting the $A_{1}$ and $\phi_{1}$ parameters of the same $f_{1}$ pulsation frequency in each segment independently. The results, along with V18, the other modulated RRc star, are shown in Fig. 5.

We found that the modulation is strictly periodic in only one of the stars, V13, in which the amplitude variation is moderate as well. In contrast, the modulation in V16 appears to be quasi-periodic, and the pulsation amplitude drops almost to zero in some instances. Finally, in V14 and M80 15470, we find a shorter and a longer modulation cycle operating simultaneously. To test this, we calculated the temporal variations of the fast modulation by segmenting and fitting the $A_{1}(t)$ data sets in the same way as we did with the light curves (the red points in Fig. 5). While the amplitude of the fast modulation stayed almost constant in both stars, their phases followed the slow changes present in the $\phi_{1}(t)$ data. We also detect complete rotations of the pulsation phase in both stars.

We find that the second, longer modulation is present differently in the amplitude and phase variations of V14 and M80 15470. The amplitude modulation appears to be a simple addition of the short and long cycles. But since the phase variations are also added together, the longer cycle can also be detected in the amplitude modulation as a phase modulation of the shorter cycle. In contrast, the phase modulation includes both cycles, but the amplitude of the shorter cycle appears to be also variable, with the cycle jump happening at pulsation amplitude minimum (or amplitude modulation minimum).

The four strongly modulated stars have very asymmetric sidepeak amplitudes. We show the structures of sidepeaks around the first overtone frequency in Fig. 6. We mirrored the spectra around the position of the main pulsation frequency (in gray) to show how, even if sidepeaks appear both below and above, they do not form symmetric structures, and no significant frequency counterparts can be found that would from a triplet structure with the pulsation frequency. The only sign of a symmetric sidepeak pair can be found in V18, the foreground star, and it corresponds to the slow decrease of the pulsation amplitude on timescales longer than the observations. This can be either a long modulation cycle or a side effect of data processing.

Stars with a single modulation sidepeak next to the pulsation frequency (also known as doublets) are also called BL1 stars. In the OGLE sample, Netzel et al. (2018) found that 24% of modulated RRc stars belong to the BL1 group. While it is possible that ground-based observations might not reveal low-amplitude sidepeaks that belong to triplets with very different amplitudes, high-precision space-based observations also revealed several BL1 RRc stars (Netzel et al. 2023). Apparently, the RR Lyrae population of M80 is also peculiar in the way of having only BL1 RRc stars in the cluster. Two very similar stars were discovered by Netzel & Smolec (2019) in the OGLE Bulge data, both having low amplitudes, short periods and two close-by frequency peaks. We discuss the occurences of similar stars further in Section 7.1.

We determined the modulation periods from the $A_{1}(t)$ amplitude variation data for each star. This method was considerably more accurate than relying on the sidepeak distances in the frequency spectrum alone for all stars except V13, where results agreed for both methods. In V14 and M80 15470 we were able to determine the periods of the long and short cycles separately. In V16, the modulation appears to be quasi-periodic, and we identified two characteristic timescales based on the frequency spectrum of the amplitude variation.

We now know, thanks to high-precision photometric measurements, that many RR Lyrae stars, and specifically, the majority of RRc stars, are not pure single-mode pulsators. We did not find any extra modes in RRab stars in M80, therefore we focus on the overtone stars here. Additional low-amplitude modes have been identified in large numbers in the OGLE bulge RRc light curves (Netzel et al. 2015b, a; Netzel & Smolec 2019). Similar modes have been observed in a few RRc stars by the space-based CoRoT and Kepler prime missions (Szabó et al. 2014; Moskalik et al. 2015; Sódor et al. 2017). Recently, systematic studies of RRc stars observed by TESS and K2 concluded that 81–83% of first-overtone stars exhibit extra modes (Molnár et al. 2022; Benkő et al. 2023).

M80 includes a multitude of different variables beyond the RR Lyrae stars, including bright red giants and various faint stars.

In order to determine the basic physical parameters, we matched the observed spectra with the synthetic spectra using the FERRE code (Allende Prieto et al. 2006). For the grid of synthetic spectra we used the BOSZ models (Bohlin et al. 2017) and convolved new grids that matched the same resolution as the observed spectra covering the wavelength range 4200–7000 Å. The custom-made grid of model spectra were covering –2.5 ¡ [Fe/H] ¡ –1.0 in steps of 0.25 dex, 3.0 ¡ $\log{g}$ ¡ 5.0 in steps of 0.5 dex, and 6000 K ¡ T_eff ¡ 10000 K, in steps of 250 K.

In our analysis we fixed the microturbulent velocity and the value of $\alpha$-elements to 2 km s^-1 and 0.25, respectively, which are reasonable for stars of this spectral type and the low resolution does not enable us to determine these parameters properly from the fit. We shifted the observed spectra to rest wavelengths and used the FERRE code to quantitatively compare them to each spectrum within the grid of synthetic spectra by minimizing the corresponding $\chi^{2}$ function. We excluded the following telluric line regions from the fit: 5883–5961 Å, 6275–6325 Å, 6475–6523 Å.

Fig. 13 shows the observed (black lines) and the best matching synthetic spectra (red lines) of each star. The resulting basic parameters and the estimated random uncertainties are listed in Table 3. For determining the uncertainty of the fit, we multiplied the observed spectra by ${\rm 1}+\sigma$ and, ${\rm 1}-\sigma$ which simulates two spectra slightly different from the original spectrum. Then, the fit of each line is repeated while keeping all other parameters unchanged. The average difference between these two new fits and the original best-fit spectrum was the defined uncertainty associated with the fit itself. The low resolution of the spectra and the lack of strong metal lines allows only poor constrains for $\log{g}$ and the metallicity, but the resulting parameters for the latest are in good agreement with the [Fe/H] value of the cluster.

The VLT spectra include a much narrower wavelength range (434–458.9 nm) than the LDSS3 spectra. The stellar atmosphere parameters were estimated via a comparison with a grid of synthetic stellar spectra downloaded from the POLLUX database (Palacios et al. 2010). The grid included all $\alpha$-enhanced ([$\alpha$/Fe] = $+$0.4) model spectra in the database with 5500 $<$ T_eff $<$ 8000 K, 1.0 $<$ log(g) $<$ 4.0, and -3.0 $<$ [Fe/H] $<$ 0.0. The synthetic models were then smoothed and resampled to match the resolution and binning of the observed spectra. In preparation for analysis, the observed spectra were iteratively continuum normalized using a low order Chebyshev function and then shifted in wavelength space to match the synthetic spectra via cross correlation. Intensity residuals in each wavelength bin were recorded for all synthetic and observed spectrum pairs, and then analyzed to determine the best-fit models.

We were able to get rough parameter estimates for two out of the three observed stars (V03, V14, V16). For V03, we found $T_{\rm eff}$ to be around 6750–7000 K and [Fe/H] of about -2. The former is in agreement with the temperature range of RR Lyrae stars, while the latter matches the [Fe/H] value of the cluster.

V16 is also consistent with a low metallicity and appears to be a bit warmer than V03 at 7000–7250 K and with comparable gravity or slightly higher. These differences, however, can also be attributed to differences in pulsation phases during the observations.

V14 apprears to have been in a more unstable atmospheric phase of pulsation when the spectrum was taken than the other two stars. This makes the parameters we determined even more uncertain, but the data suggests that it was warmer and had a higher gravity than V03 during observations.

We compared the derived $T_{\rm eff}$ and $log\,g$ values to other RR Lyrae stars, using the parameters published by Nemec et al. (2013) and Crestani et al. (2021) in Fig. 14. The plot shows that although we have high uncertainties, especially in $\log\,g$, our results fit into the distribution of field RRc stars well. The presence of pulsation and the unknown pulsation phases also affect our results, and may explain, at least partially, the differences for stars where we have observations from both telescopes (connected with the dashed lines). Overall, the spectroscopic observations confirm that the parameters of the normal and peculiar RRc stars are similar and that all of them are metal-poor horizontal-branch stars and part of the cluster.

The $\phi_{31}$ relative amplitude parameter, together with the period, can be used to estimate the photometric [Fe/H] parameter of the stars (Jurcsik & Kovács 1996). One drawback of the relative Fourier parameters—and therefore of the photometric [Fe/H] relations—is that the shape of the light curve is wavelength-dependent. We calculated the photometric [Fe/H] indices for the stars, where we were able to determine the $\phi_{31}$ parameter of the light curve. We used both the relations derived by (Nemec et al. 2013) and that were calibrated for the Kepler passband, although only for a small sample from the original Kepler mission. We also used the original photometric [Fe/H] relations of Jurcsik & Kovács (1996) and Morgan et al. (2007) who first determined them for RRab and RRc stars, respectively, where we corrected for the passband-dependent phase differences following the methods described by Nemec et al. (2013). Results are listed in Table 8 in the Appendix. Here we assume an uncertainty of 0.15 dex uniformly, based on the

Figure 15 shows how the various [Fe/H] indices compare to each other. Our spectroscopic values are in good agreement with the values we mentioned in Sect. 1, such as with the results of Carretta et al. (2015), which we highlight in the plot with the gray line. For RRc stars, spectroscopic and photometric values agree in most cases except for the peculiar star V13, where the photometric relations overestimate the [Fe/H] index. For RRab stars, however, the spread is quite noticeable. The Jurcsik & Kovács (1996) relation is known to overestimate [Fe/H] for metal-poor stars. The relation of Nemec et al. (2013) can correct for this for short-period stars, but that relation was not calibrated for stars with periods over 0.7 d. As a result, the extrapolated relation starts to deviate steeply towards higher indices for the long-period stars, as Fig.  15 illustrates.

The Gaia mission provides invaluable observations of Milky Way stars and subsystems. We downloaded photometry and parallax data from the Early Data Release 3 (EDR3) for the rectangular area covered by the K2 image mosaic (Gaia Collaboration et al. 2021). We then identified the variable stars studied in this paper from the collection of 11230 stars. Since M80 is very dense, not all stars have measurements in the $G_{\rm BP}$ and $G_{\rm RP}$ bands or valid parallax values. Unfortunately this is true for the variables as well: V17, V20, V21, V24 and V27 have no color information.

We first plotted the parallaxes of the stars to see if any have large values that might indicate a foreground star. We filtered out stars where the RUWE (Renormalised Unit Weight Error) parameter exceeded 1.4, which could indicate either binarity or other issues with fitting a single-star parallax solution. We then corrected for the parallax zero-point offsets with the gaiadr3_zeropoint³³3https://gitlab.com/icc-ub/public/gaiadr3_zeropoint code (Lindegren et al. 2021).

We were especially interested in the two overluminous RR Lyrae stars V10 and V15, but unfortunately neither of them have useful parallax measurements. V15 have no calculated parallax at all, while for V10 both the parallax uncertainty and the calculated RUWE parameters are exceedingly high.

As Fig. 16 illustrates, the parallaxes of the brighter stars, red giants and RR Lyrae stars, agree with the parallax of the cluster itself. Individual parallaxes become rather uncertain at $G>15$ mag, evident by the spread of the RR Lyrae stars. However, the mean parallax of the nine RR Lyrae stars that have useful measurements is $\overline{\varpi_{RRL}}=0.075\pm 0.085$ mas, which agrees with that of the cluster.

The rest of the stars are fainter and thus fall into the quickly expanding spread of parallaxes. Of the five further stars for which parallax data are available, two positive and two negative values fall into the general spread of points. Only one star, V22, deviates significantly, with a corrected parallax of $2.51\pm 0.31$, which would suggest a distance of only $\sim 400$ pc. However, that distance would lead to an absolute brightness of $M_{G}\approx 10.5$ mag, and would put the star well below the main sequence but above the white dwarf region on the Hertzsprung–Russell diagram, which is almost entirely unpopulated. On the other hand, the variation of the star and its position on the color-magnitude diagram (see next section) of the cluster both suggest that it is an SX Phe star within the cluster. We therefore conclude that it is more likely that its parallax has been measured erroneously.

With the Gaia EDR3 photometry at hand, we constructed a color-magnitude diagram (CMD) for the cluster. First, we simply queried the area of the K2 mosaic image, in order to contain all stars, including variables that might not be part of the cluster. Here we only excluded stars where $G_{BP}$ and/or $G_{RP}$ data were not available or their flux-over-error ratio was below five in those passbands. We then also created a clean CMD to show where the population of the cluster really lies. For this, we first filtered stars by proper motion, removing those that have no data or differ from the proper motion of the cluster by more than 2.2 mas/yr. This limit was chosen based on the radial profile of the cluster in proper motion space. We then filtered the CMD further based on the Gaia corrected color excess factor parameter, $C^{*}$. This factor indicates when there is an imbalance between the three different fluxes measured by Gaia, but a high score does not necessarily indicate poor data quality (Riello et al. 2021). A higher $C^{*}$ cutoff results in higher completeness at the cost of lower purity. Here chose a limit of $\pm 10\sigma_{C^{*}}$ to obtain a clean but still adequately populated CMD for the cluster, following Eq. 18 of Riello et al. (2021), to take the increasing photometric scatter towards fainter stars into account.The final filtering step was the exclusion of stars where $G_{BP}\geq 20.3$ mag. This is needed because towards the faint end of the Gaia dataset, the $G_{BP}$ fluxes tend to be overestimated, which can cause systematic bias for red sources (Riello et al. 2021). These filters removed most of the faint stars on the Main Sequence, and some of the strongly variable stars as brightness changes also elevate the $C^{*}$ scores.

To transform the apparent Gaia brightnesses to absolute magnitudes, we used the distance modulus provided by Baumgardt & Vasiliev (2021) calculated the interstellar extinction with the mwdust code for each Gaia passband (Bovy et al. 2016). The extinction values are: $A_{\rm G}=0.599\pm 0.020$ mag; $A_{\rm BP}=0.715\pm 0.025$ mag; $A_{\rm RP}=0.414\pm 0.025$ mag. The absolute CMD for the cluster, with the variable stars indicated, can be seen in Fig. 17.

As comparison, we also downloaded the mean photometry of sources up to 4’ distance from the center of the cluster from the second release of the Pan-STARRS $3\pi$ survey (Chambers et al. 2016). The Pan-STARRS photometry is affected by crowding and saturation towards the core: this can be seen in the left-hand image of Fig. 1, but also in the distribution of detections in sky coordinates, which includes multiple string-like features which do not correspond to real stars. While such spurious detections can be filtered out, these issues lead to poor coverage of the core. Furthermore, Pan-STARRS photometry saturates around 13–14 mag, which effectively cuts off the brightest red giants from the CMD: we mark the $g$-band saturation limit with the dashed line on the right side of Fig. 17. The saturation limit clearly affects the variable red giants in the sample as well, with V01 and [CBG2015] 16162 appearing much redder than in the Gaia CMD. For this CMD, we used the averages from the Schlegel et al. (1998) and Schlafly & Finkbeiner (2011) dust and reddening maps⁴⁴4NASA/IPAC Infrared Science Archive, https://irsa.ipac.caltech.edu/: $A_{g}=0.75\pm 0.05$ mag and $A_{i}=0.40\pm 0.04$ mag.

We highlighted the positions of the RR Lyrae stars in the HB from both CMDs in the lower panels of Fig. 17. These clearly show that the RRab stars, the normal RRc stars and the strongly modulated RRc stars form a continuous group in the HB. This confirms that the modulated stars are indeed RR Lyrae stars, despite the unexpected light curve shapes.

In fact, the spread of RR Lyrae stars is very narrow, only about 0.1 mag in absolute brightness, indicating extremely similar luminosities for the entire RR Lyrae population. In contrast, the CMD of about a hundred field stars presented by Molnár et al. (2022) and the CMD of the entire Gaia DR3 sample published by Clementini et al. (2023) both span more than 1.0 magnitude in $M_{\rm G}$ brightness.

With the Gaia CMD, we can also confirm the positions and thus evolutionary stages of two out of the three SX Phe stars. V22 and V23 are indeed blue stragglers above the MS turnoff point.

The newly identified binary EPIC 204270257 appears to lie redward both from the MS and the RGB. It is very likely that this is a foreground star, which is intrinsically fainter than our CMD would suggest. A look at the single- and binary-star main sequences on the Gaia HRD indicates that a binary with identical components at the same $G_{\rm BP}-G_{\rm RP}$ color would be about three magnitudes fainter at $M_{G}\sim 6$ mag. That difference would put it to about the quarter of the distance of M80 (Gaia Collaboration et al. 2018).

A notable star in the CMDs is V28, which appears to be an intrinsically very blue but not very luminous object. Assuming that it is a cluster member, then it is a hot subdwarf star along the EHB, the blue, downward extension of the HB, as we mentioned in Sect. 4.5.4 (Culpan et al. 2022). The observed rotational variation rules out the possibility of it being a foreground white dwarf, as those do not have star spots and thus would not produce such light curves (Kawaler 2004). EHB stars, on the other hand, have been recently found to show chemical spots, as we mentioned earlier: therefore we classify V28 as a rotational or $\alpha^{2}$ CVn-type variable within the cluster.

We use the publicly available MIST database (Choi et al. 2016) to generate non-rotating isochrones spanning ages 10 to 17 Gyr. These are transformed to the magnitudes and colors of the relevant photometric systems corresponding to three sources considered: Bessell UBVRI (Bessell 1990), reproducing the Johnson-Cousins system, to accompany photometry from Alcaino et al. (1998), Pan-STARRS grizy passbands for the PS1 data, and Gaia G, $G_{\rm BP}$, $G_{\rm RP}$ passbands for EDR3 to accompany data queried in the present analysis. In determining the best-fitting age and metallicity for M80, we consider isochrones with [Fe/H] values of $-1.2$ to $-2.1$ dex in increments of $0.1$ dex.

We first re-fit the data presented by Alcaino et al. (1998) using the much more recent MIST models. In their analysis, Alcaino et al. (1998) combine inferences of 16 Gyr and 18 Gyr using two different sets of isochrones—those of Bergbusch & Vandenberg (1992) and McClure et al. (1987), respectively—to report a best-fitting composite age and metallicity of $17\pm 2$ Gyr and [Fe/H]$=-1.70\pm 0.15$.

Presently, we find that MIST isochrones with a metallicity of [Fe/H]$=-1.7\pm+0.1$, under the assumption of no $\alpha$–element enhancement ([$\alpha$/Fe]$=0$), still fit Alcaino et al. (1998)’s data well, particularly along the red giant branch. However, models with ages in the range of 12 to 13 Gyr show a level of consistency similar to that of 17 Gyr models. We also find that for any combination of age and metallicity considered, some adjustment to the distance modulus and reddening is required to achieve alignment between the data and models—this cannot be accomplished by varying the isochrone input parameters alone. The first panel of Figure 18shows a set of MIST isochrones with [Fe/H]$=-1.7$ and ages as indicated overlaid on the data of Alcaino et al. (1998). To provide the best visual fit, V-band and I-band extinction values of $A_{V}=0.568$ and $A_{I}=0.334$, respectively, and a distance modulus of $(m-M)=14.96$ are adopted.

Though there is some tension between our results and those of Alcaino et al. (1998), we note that both sets of models used in their analysis are 30 (or more) years old. In addition to this, the isochrones of Bergbusch & Vandenberg (1992) were oxygen-enhanced, but Alcaino et al. (1998)’s results were derived prior to the revision of solar abundances in 2009 (Asplund et al. 2009). Likewise, the helium contents adopted in the models of McClure et al. (1987) were known to be inappropriate by the time of Bergbusch & Vandenberg (1992)’s publication. That estimations of the fundamental parameters of stellar populations can shift so much on the basis of abundances underscores the importance of treating these quantities carefully in stellar modeling.

More recent literature fits of isochrones to M80 include those of Barker & Paust (2018), who report best-fitting metallicities and ages of M80 according to three different sets of isochrones:

• –

  [Fe/H]$=-1.65$ dex, $12.5$ Gyr using DSEP (the Dartmouth Stellar Evolution Program, Dotter et al. 2008);

• –

  [Fe/H]$=-1.68$ dex, $13.5$ Gyr using PARSEC (the PAdova and TRiest Stellar Evolution Code, Bressan et al. 2012); and

• –

  [Fe/H]$=-1.90$ dex. $14.0$ Gyr using MIST.

We now fit MIST isochrones, computed over the same parameter ranges, to two new data sources. The center and right-hand panels of Figure 18 show the best-fitting models to M80 data from (1) PanSTARRS DR2 mean photometry and (2) Gaia EDR3, respectively. Table 5 summarizes the age and metallicity determinations for each data set. We note that in three cases (including Alcaino et al. 1998), the model-derived metallicities are reported under the assumption that [$\alpha$/Fe]$=0$. We note that these can be rescaled to an $\alpha$-enhanced basis (e.g., [$\alpha$/Fe]$=+0.3$) as needed. For example, the combination [Fe/H]$=-1.8$, [$\alpha$/Fe]$=0.3$ is roughly equivalent to [Fe/H]$=-1.59$, [$\alpha$/Fe]$=0$, and so forth (see Table 1 of Joyce et al. 2023 and related discussion on how to account for $\alpha$-enhancement in MIST). We find that the age and metallicity determinations for M80 based on modern data are consistent with the MIST results presented in Barker & Paust (2018) and broadly consistent with each other.

The fact that there is some variance among best-fitting ages and metallicities for the same targets, using the same models, perhaps calls into question consistency between the extinction maps used to distance-correct the three different observational data sets. However, this also demonstrates that astronomers should proceed with caution when using isochrones–which are themselves interpolated models subject to their own complex network of uncertainties–to perform age determinations. The global precision with which isochrone-based ages can be stated, realistically, is at the 2-3 Gyr level (including considerations for modeling uncertainties and variations in physical assumptions; see Joyce et al. 2023; Joyce & Tayar 2023). By this metric, our age determinations according to Gaia and PanSTARRS are formally consistent, and the age determinations according to Alcaino et al. (1998) are approximately $1\leavevmode\nobreak\ \sigma$ older.

Beyond the extra modes, the light curve shapes of RRc stars present an interesting dichotomy as well, with some stars (especially V03 and V04) appearing as normal overtone variables with clear hump features, whereas others showing very sinusoidal variations with strong modulation(s) (V13, V14, V16 and M80 15470). Our photometric and spectroscopic results confirm that these stars are members of the cluster and hence are in the same position as the regular RRc stars.

The peculiar RRc stars are characterized by (at least) two close frequencies with similar amplitudes that are within an order of magnitude to each other, and a light curve that lacks the characteristic hump features just before maximum light. They might be a subtype of BL1 stars, i.e., RRc stars where we observe only one side-peak next to the pulsation frequency instead of modulation triplets. Examples of such stars exist elsewhere, too, but we know little else about them. The most prominent examples are V701 Pup (Antipin & Jurcsik 2005), the two Bulge stars identified by Netzel & Smolec (2019), and V37 in the globular cluster NGC6362 (Smolec et al. 2017). We searched for more such stars in the literature, but light curves are often sampled too sparsely for clear classification. We identified the variable star KT–26 in M22 (Rozyczka et al. 2017), V12 in NGC6401 (Tsapras et al. 2017), V8, V13 and V16 in NGC4147 (Arellano Ferro et al. 2018) as further examples of peculiar, strongly phase- and amplitude-modulated RRc stars with sine-like light curves.

One reason for the relative obscurity of these stars might be that classification pipelines easily miss these or assign them to different classes (e.g., rotational variables) since their light curves are unlike regular RR Lyrae stars. As such, it is unclear how frequent they might be among RR Lyrae stars, and if they warrant a separate subcategory or not. This could be answered by combining the capabilities of the TESS and Gaia missions, where absolute CMD positions can help to find more RR Lyrae stars with unusual light curves.

Our results highlight the rich landscape of RR Lyrae pulsations, especially that of RRc stars. These stars feature not only an abundance of extra modes, but various types of modulations as well: the classical Blazhko-type in BL2 stars with symmetric side-peaks in the frequency spectra; the beating-like variation in BL1 stars between distinct, close-by frequencies; and the third group of phase-modulated RRc stars (not represented in M80) that cannot be explained with simple light-time effects (see, e.g., Derekas et al. 2004; Sódor et al. 2017).

We identified one new RRc star and one new long-period red giant variable star in the cluster. The RRc star is a new member of the low-amplitude, strongly modulated group present in the cluster.

Regarding the other variables, the K2 campaign unfortunately was too short to determine periodicities in red giant variables. On the other hand, we confirm that the variables V25 and V27 are eclipsing binaries. Finally, V28 turned out to be an interesting case: its position in the cluster CMD and its variation indicates that it is an EHB star exhibiting rotational variation. The star likely features chemically peculiar spots on its surface, similar to other EHB variables (Momany et al. 2020).

Few asteroseismic studies focused on globular clusters so far. This is understandable given their large distances and compact nature, and the corresponding resolution and sensitivity limitations of space missions like Kepler and TESS. However, as both our study and the works of Wallace et al. (2019a, b), Howell et al. (2022, 2023), or Tailo et al. (2022) show, continuous and high-precision photometry can reveal a wealth of information about the clusters and their constituent stars. The analysis of clusters was identified as one of the important topics where archival K2 data can deliver new discoveries (Barentsen et al. 2018). Analysis of further clusters observed by K2 is under way (e.g., Kalup et al., in prep., Howell et al., in prep.)

Globular clusters are not well-suited targets for photometry missions like TESS and PLATO that work with small telescopes that have large fields of view at the cost of low angular resolution (21 and 15 ”/px, respectively). Therefore, any observations of even the closest and loosest clusters like M4 will provide only limited scientific results. There are, however, larger missions in development as well.

The European HAYDN (High-precision AsteroseismologY in DeNse stellar fields) project is an ESA Voyage 2050 mission proposal, and the only one that is being designed specifically for asteroseismic purposes (Miglio et al. 2019). The prospective space telescope is designed to survey dense stellar fields like the bulge, as well as open and globular clusters. It is planned to have an optical system similar to Kepler in size, but with a much higher angular resolution (0.25”/px). This mission is expected to detect oscillations down to the base of the red giant branch for multiple clusters.

Another proposed mission, the Chinese Earth 2.0 (or ET) project that is planned to have one 30 cm telescope pointed towards Baade’s window in the Bulge in order to search for microlensing events (Ge et al. 2022). This microlensing telescope will have sub-arcsecond pixel resolution but only over a 4 deg² field of view. Hopefully this will still include the two globular clusters within Baade’s window, NGC 6522 and NGC 6528.

The largest telescope that is planned to aim towards the Bulge repeatedly is the American Nancy Grace Roman Space Telescope, funded by NASA. A significant amount of telescope time will be dedicated to the Galactic Bulge Time Domain Survey, which will be carried out in a way that is very similar to the K2 campaigns and thus offers many comparisons (Akeson et al. 2019; Gaudi 2022). Roman will observe the selected 2 deg² Bulge fields continuously for 62 days in each run with 15 min cadence, but at a considerably better resolution and depth (0.1 ”/px and down to 22–24 mag, respectively) in red and near-infrared wavelengths. Although the survey is currently optimized for microlensing, the inclusion of any globular cluster within or near the Bulge would be highly desirable, as they can provide a huge variety of stellar and galactic science cases (see the white papers of Molnár et al. 2023; Grunblatt et al. 2023).

These future capabilities would allow us to study more clusters and in much more detail than what we were able to achieve with Kepler.