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11institutetext: Department of Astronomy, University of Geneva, Chemin Pegasi
51, 1290 Versoix, Switzerland
11email<EMAIL_ADDRESS>22institutetext: Center for Astronomy,
Landessternwarte (ZAH/LSW), Heidelberg University, Königstuhl 12, 69117
Heidelberg, Germany 33institutetext: Heidelberg Institute for Theoretical
Studies (HITS), Schloss-Wolfsbrunnenweg 35, 69118 Heidelberg, Germany

# New red giants in NGC 6791 and NGC 6819 using _Kepler_ superstamps

A. Covelo-Paz 112233 N. Themeßl 2233 F. Espinoza-Rojas 2233 S. Hekker 2233

(Received XX; accepted YY)

###### Abstract

Context. Stars that are members of stellar clusters are assumed to be formed
at the same time and place from material with the same initial chemical
composition. These additional constraints on the ensemble of cluster stars
make these stars suitable as benchmarks.

Aims. We aimed 1) to identify previously unknown red giants in the open
clusters NGC 6791 and NGC 6819, 2) to extract their asteroseismic parameters,
and 3) to determine their cluster membership.

Methods. We followed a dedicated method based on difference imaging to extract
the light curves of potential red giants in NGC 6791 and NGC 6819 from
_Kepler_ superstamp data. We extracted the asteroseismic parameters of the
stars that showed solar-like oscillations. We performed an asteroseismic
membership study to identify which of these stars are likely to be cluster
members.

Results. We found 149 red giant stars within the _Kepler_ superstamps, 93 of
which are likely cluster members. We were able to find 29 red giants that are
not primary targets of _Kepler_ , and therefore, their light curves had not
been released previously. Five of these previously unknown red giants have a
cluster membership probability greater than 95%.

###### Key Words.:

asteroseismology – open clusters and associations: individual (NGC 6791, NGC
6819) – stars: solar-type – techniques: photometric

##  1 Introduction

Open clusters are remarkable features in the Milky Way. They contain up to a
few thousand stars that are thought to have formed at the same time from the
same molecular cloud. Hence, stars in clusters are assumed to have similar
properties, such as age, initial chemical composition, and distance. Due to
these shared initial conditions, studying the properties of cluster stars at
different evolutionary stages allows us to constrain and test theories of
stellar evolution and to gain insights into the formation and chemical
evolution of our own Galaxy (e.g. Vandenberg 1983; Salaris 2013; Cantat-Gaudin
& Anders 2020). In this study, we search for additional oscillating red giants
in the open clusters NGC 6791 and NGC 6819, which were observed by the
_Kepler_ space mission (Borucki et al. 2009; Gilliland et al. 2010).

_Kepler_ observed the same field in the sky for four years. From the $\sim
500\,000$ stars in the field that are brighter than the targeted threshold
(¡16 mag in the _Kepler_ passband; Batalha et al. 2010), $\sim$150 000 stars
were selected as primary targets for the mission. They are a subset of the
_Kepler_ Input Catalog (KIC; Brown et al. 2011). The _Kepler_ field of view
contains four open clusters: NGC 6791, NGC 6811, NGC 6819, and NGC 6866. Two
of them, NGC 6791 and NGC 6819 ($\sim$8.5 and $\sim$2.5 Gyr old, respectively;
Basu et al. 2011), were found to contain a substantial number of oscillating
red giant stars, and $\sim$120 have been targeted by the _Kepler_ mission and
were studied with asteroseismology based on these data. For these stars,
studies have determined asteroseismic parameters, stellar properties such as
mass and radii (Hekker et al. 2011a), evolutionary stage (Corsaro et al.
2012), mass loss (Miglio et al. 2012), helium content (McKeever et al. 2019),
core mixing (Bossini et al. 2017), stellar ages (Basu et al. 2011), and
cluster membership (Stello et al. 2011). However, these clusters are likely to
contain more oscillating stars that have not yet been analyzed.

Asteroseismology is a powerful technique that can probe the internal structure
of stars through the study of their global oscillations. This method can be
used to obtain global properties of red giant stars, such as stellar mass,
radius, and evolutionary stage. To perform an asteroseismic analysis, it is
necessary to obtain the light curve of the star. The mode of operation of
_Kepler_ was based on providing the light curves for only those stars that
were observed as primary targets of the mission, that is, a subset of the KIC
catalog. In addition to the target pixel files that were obtained for the
preselected stars, the mission collected photometric data of the whole central
regions of the open clusters NGC 6791 and NGC 6819. These data products are
so-called superstamps that comprise long-cadence ($\sim 30$ minutes)
photometric observations with a spatial size of $200\times 200$ pixels (13.3
arcminutes on one side). These data can be used to extract the light curve of
any resolved star within the superstamps. Most of the stars in the open
clusters NGC 6791 and NGC 6819 were not primarily targeted, and therefore, no
light curves were released. We aim to extract the light curves of oscillating
red giants from the superstamp data that were not primary targets of _Kepler_.

The light curve of a star can be extracted with different methods. The most
commonly used technique is aperture photometry, which was successfully applied
to the observed KIC stars and some superstamp stars (e.g. Handberg & Lund
2014; Lund et al. 2015). Aperture photometry is a reliable method for fairly
isolated stars, but has its limits in highly crowded fields, for instance,
central regions of open clusters or for saturated objects because it can
introduce background signal. In contrast, difference imaging is a preferred
technique for probing crowded fields because it removes all nonvariable signal
that neighboring stars might be introducing. A light-curve extraction method
based on difference imaging was implemented by Colman et al. (2022). They
successfully tested their _IRIS_ pipeline on KIC targets that are located
within the _Kepler_ superstamp data.

We used the method developed by Colman et al. (2022) to extract the light
curves of red giant stars from the _Kepler_ open cluster superstamp data of
NGC 6791 and NGC 6819. We selected $\sim 500$ stars in the superstamps that
are potential cluster red giants. We did this using colors and magnitudes from
Gaia data (eDR3; Gaia Collaboration et al. 2021), and distances derived by
Bailer-Jones et al. (2021). About half of the selected stars were not primary
targets of _Kepler_ , and their light curves were not previously extracted. We
downloaded the uncorrected light curves of the KIC targets in our sample,
extracted by Colman et al. (2022), and applied the _IRIS_ pipeline to the non-
KIC targets. We corrected the light curves using a modified version of the
KASOC correction filter (Handberg & Lund 2014). We performed an asteroseismic
analysis including cluster membership study of those stars that showed solar-
like oscillations.

##  2 Target selection

We focused on the open clusters NGC 6791 and NGC 6819, which are known to host
a substantial number of red giant stars. The _Kepler_ mission provided high-
quality photometric data for these clusters over a time span of four years.
These superstamp data enable an asteroseismic analysis of any resolved star
within the central regions of the clusters, including stars that were not
primary targets of the mission.

First, we computed the expected number of red giant stars in these clusters
that are observable with _Kepler_. Based on color-magnitude data from ground-
based cluster surveys (Stetson et al. 2003; Hole et al. 2009; Ak et al. 2016),
we selected the stars that are likely to be red giants according to their
location in the color-magnitude diagram. We only considered stars with a _V_
magnitude below 16.7, as we do not expect to find oscillations in fainter red
giants (Stello et al. 2011). We found $\sim 200$ and $\sim 150$ observable red
giants in NGC 6791 and NGC 6819, respectively. So far, asteroseismic studies
have focused on $\sim 120$ oscillating red giants in total in these clusters,
potentially leaving several dozen stars to be studied.

To find these cluster red giant stars, we selected all the stars in the
superstamps that are within the published color, magnitude, and distance
ranges of the confirmed cluster red giants (Stello et al. 2011). We obtained
the colors and magnitudes for these reference stars from _Gaia_ eDR3. We used
the _gaia-kepler.fun_ crossmatch database111https://gaia-kepler.fun/ to
determine their _Gaia_ identification numbers from the KIC numbers provided by
Stello et al. (2011). We took distance measurements provided by Bailer-Jones
et al. (2021) that were derived based on _Gaia_ eDR3 parallaxes. The intervals
of color, magnitude, and distance that we obtained for cluster red giants are
shown in table 1.

Table 1: Intervals applied to our target selection.

Cluster | Color $(bp-rp)$ |  _Gaia_ (mag) | Distance (pc)
---|---|---|---
NGC 6791 | 1 – 2.5 | 12 – 17 |  $2\,500$ – $5\,500$
NGC 6819 | 0.8 – 2.5 | 10 – 15 |  $1\,000$ – $4\,200$
222Color, magnitude, and distance ranges for the confirmed cluster red giants
in Stello et al. (2011).

We searched the _Gaia_ eDR3 catalog for stars that fulfilled these criteria
within the superstamp regions. We obtained a list of 281 candidate red giants
in NGC 6791 and 232 in NGC 6819. These are more than the $\sim 200$ and $\sim
150$ observable red giants that we expect in each cluster. Therefore, it is
likely that a subset of these candidates are not red giant stars. Figures 1
and 2 show the positions of these candidates within the superstamps. Out of
these stars, 225 are not primary targets of _Kepler_ , and their light curves
have not been released so far.

Figure 1: Cluster superstamp of NGC 6791. These data were released as 20
substamps. We selected 281 stars as red giant candidates (encircled). Figure
2: Same as Fig. 1, now for NGC 6819. We selected 232 stars as red giant
candidates (encircled).

##  3 Light-curve extraction

The _Kepler_ superstamps contain long-cadence ($\sim 30$ minutes; Jenkins et
al. 2010) photometric data for stars in NGC 6791 and NGC 6819, obtained during
the observing quarters 1-17 of the mission. This results in over four years of
data for both clusters. No observations are available for NGC 6819 during
quarters 6, 10, and 14, due to a broken CCD.

To extract the light curves of the selected stars from the superstamps, we
applied the _IRIS_ pipeline (Colman et al. 2022), which is based on a
difference-imaging method. The pipeline starts by cutting out a 5x5 pixel
postage stamp from the superstamp with the target star at the center. This
places the data in a format similar to a _Kepler_ target pixel file, that is,
a time series of pixel images that contains all the photometric data of the
star that were obtained during a given quarter. The code then estimates the
crowding of the region around the star by comparing the total magnitude of the
frame-averaged postage stamp to the known _Kepler_ magnitude of the star. If
the two magnitudes are similar, the star is fairly isolated. However, if the
postage magnitude is lower than the magnitude of the star (i.e., the postage-
stamp flux is higher than the flux of the star), it is likely that a nearby
star contaminates the data. Because _Kepler_ magnitudes are only available for
primary targets of the mission (Brown et al. 2011), we instead estimated the
crowding using Gaia magnitudes because the two missions used similar
passbands. Then, the 5×5 pixel postage stamp is resampled by a factor of 20 to
100×100 pixels using bilinear interpolation in order to create more precise
apertures for the stars (see Fig. 3). Next, an aperture mask is defined as a
2D Gaussian function with a width based on the crowding of the region.
Apertures for isolated stars have a larger width than those for stars with
crowded backgrounds. This reduces the contamination of nearby stars in crowded
regions. Difference imaging is then applied to the 100×100 pixel stamps by
subtracting the frame-averaged image from each frame in the stamps. This
removes all the flux sources that are not variable. Finally, the flux is
extracted from each frame by applying the aperture mask. The result is a light
curve for a single quarter that only accounts for variable sources.

Figure 3: Resampling of the pixel stamps with the _IRIS_ code. Left: $5\times
5$ pixel stamp of one of the target stars in NGC 6819. Right: $100\times 100$
pixel stamp of the same star, obtained after resampling the original stamp by
a factor of 20 using bilinear interpolation.

The light curves of the KIC targets in our sample have already been extracted
using the IRIS method by Colman et al. (2022). Thus, we downloaded the
uncorrected light curves of the KIC stars and used the IRIS pipeline to
extract those of the non-KIC targets. After extracting each light curve, we
applied a number of corrections to remove systematics introduced by the
instrument and the mission. We applied the KASOC filter (Handberg & Lund
2014), which was designed to correct _Kepler_ light curves obtained with
aperture photometry. This pipeline uses the quality flags released by the
mission and removes data points that are flagged as desaturation events,
manual exclusions, and argabrightening. Furthermore, it corrects for the jumps
in the light curve that are produced by attitude tweaks. Other quality flags
are ignored. However, we realized that safe modes and Earth points produced
significant jumps in our light curves. Therefore, we extended the jump
corrections to data points showing these quality flags. Then, the pipeline
filtered the light curve for long-term trends (i.e., instrumental drifts and
stellar activity) and short-term trends (i.e., transit features and
instrumental effects, e.g., sudden jumps after safe modes), giving each filter
a different weight depending on the relative standard deviation of the signal.
Last, we performed sigma clipping to remove all data points that deviated by
more than $5\sigma$ from the average. The resulting light curves showed
significantly diminished systematic effects.

After we obtained the corrected light curves of the star for every observed
quarter, we normalized the flux to be shown in parts per million. Last, we
appended the normalized light curves of each quarter to produce the final
light curve.

The resulting light curves of the red giants in our catalog that show
oscillations are available on GitHub333https://github.com/astroalba/kepler-
red-giants-lc.

##  4 Asteroseismic analysis

We computed a power density spectrum for each star from the extracted light
curves with the aim of detecting solar-like oscillations. The power density
spectrum of a red giant star shows a distinct power excess that comprises the
oscillation modes. To identify this potential power excess, we first
implemented the automated CV method following Bell et al. (2019). This method
is based on the coefficients of variation (CV), that is, the ratio of the
standard deviation of the power to its mean. This ratio should be equal to 1
in the presence of $\chi^{2}_{2}$ noise statistics as expected for the power
density spectrum of solar-like oscillators. Any signal that is not caused by
stochastic noise will present higher CV values. An expected width of the
oscillatory signal in the CV method as a function of the frequency of maximum
oscillation power ($\nu_{\rm max}$) was introduced based on the analysis of
the stars in the APOKASC-DR2 (Pinsonneault et al. 2018). We found 59 solar-
like oscillators and 44 stars with ambiguous results. After visual inspection
of the latter, we confirmed 46 oscillations that the CV method could not
clearly detect, probably due to changes in the statistics of the power density
spectrum due to contamination of neighboring stars. Combining this with
oscillating red giants from the literature and a final visual inspection, we
identified a final sample of 149 oscillating red giants, (91 in NGC 6791 and
58 in NGC 6819) in our set of 513 stars.

For these 149 oscillating stars, we performed an asteroseismic analysis and
extracted the frequency of their maximum oscillation power
($\nu_{\textrm{max}}$) using the code called tools for the automated
characterization of oscillations (TACO) (Hekker et al. in prep.). We obtained
$\nu_{\textrm{max}}$ from a global fit to the power density spectrum through a
Bayesian Markov chain Monte Carlo framework. The model consists of three
granulation components, one white-noise term, and a Gaussian fit to the power
excess comprising $\nu_{\textrm{max}}$. We took the 50th percentile from the
posterior $\nu_{\textrm{max}}$ distribution as the final parameter estimate
and the 16th and 84th percentiles as its uncertainties. In Figure 4 we show a
power density spectrum with the global fit. We report the _Gaia_ eDR3 $G$
magnitudes and the measured $\nu_{\textrm{max}}$ values for the oscillating
red giant stars in the field of view of NGC 6791 and NGC 6819 in tables
LABEL:6791 and LABEL:6819.

Figure 4: Power density spectrum (in black) of one of the target stars in NGC
6791 (star 39 in table 1). The solid red line shows the global model fit
computed by TACO, which includes three granulation components (dashed blue
lines), one white-noise component (horizontal dotted magenta line), and a
Gaussian fit to the oscillation power excess (dashed yellow line).

Out of the 149 oscillating red giants, 83 were previously analyzed by Corsaro
et al. (2012). They obtained asteroseismic parameters, including
$\nu_{\textrm{max}}$, for 115 oscillating red giant stars in the _Kepler_ open
clusters. At the time, only seven quarters of _Kepler_ data were available,
which corresponds to a time stamp of $\sim 19$ months (less than half of the
data that are currently available). A comparison between our results and
theirs is shown in figure 5. Although the two results agree for most stars
(with a sigma-clipped scatter of 4, in line with earlier works; e.g. Hekker et
al. 2011b), there are a few stars with very different values of
$\nu_{\textrm{max}}$ as a result of the two methods. These outliers seem to
have picked up an entirely different signal on the power density spectrum.
This might be due to differences in the methods used for light-curve
extraction and correction.

Figure 5: Comparisons of the frequencies of maximum oscillation
($\nu_{\textrm{max}}$) that we obtained to those released by Corsaro et al.
(2012).

##  5 Cluster membership study

We performed an asteroseismic cluster membership study to identify the
oscillating stars that belong to NGC 6791 and NGC 6819. Following the approach
introduced by Stello et al. (2010), we used the $\nu_{\rm max}$ measurements
together with the Gaia $G$ magnitudes to determine the most likely cluster
members. We note here that the $G$ passband covers a wavelength range of about
330 – 1050 nm, which is similar to the 2MASS passbands used by Stello et al.
(2010).

For red giant stars, the asteroseismic parameter $\nu_{\textrm{max}}$ is
related to the global properties of the star through a scaling relation (Brown
et al. 1991; Kjeldsen & Bedding 1995),

$\nu_{\textrm{max}}\simeq\frac{M/{\rm
M}_{\odot}(T_{\textrm{eff}}/{T_{\textrm{eff,}}}_{\odot})^{3.5}}{L/\rm
L_{\odot}}\nu_{\textrm{max,\sun}},$ (1)

where $M$, $T_{\textrm{eff}}$, and $L$ are the mass, effective temperature,
and luminosity of the star. The nominal effective temperature of the Sun is
$T_{\textrm{eff,}\odot}=5\,772\,K$ (Prša et al. 2016), and
$\nu_{\textrm{max,\sun}}=3\,100\,\mu\textrm{Hz}$ (Basu et al. 2010) is a
reference value that scales the relation to the Sun.

For red giant stars, the stellar masses and effective temperatures vary only
marginally compared to the luminosities, which have a wider range of values
when these stars evolve. Thus, there is a tight correlation between
$\nu_{\textrm{max}}$ and the stellar luminosity. For cluster red giants, this
translates into a correlation between $\nu_{\textrm{max}}$ and the apparent
stellar magnitude because all the stars are assumed to be located at a similar
distance. By plotting the apparent magnitude versus $\nu_{\textrm{max}}$,
cluster red giants line up, while fore- and background stars deviate from the
correlation.

In Figure 6 we show the measured asteroseismic $\nu_{\textrm{max}}$ values
versus the published Gaia $G$ magnitudes for our stars with detected solar-
like oscillations in NGC 6791 (top) and NGC 6819 (bottom). In each diagram, we
indicate the confidence region (dashed lines) hosting stars with a 95%
confidence to be part of the cluster population. The confidence intervals for
each cluster were computed around a linear regression line based on
$\nu_{\textrm{max}}$ values, $G$ magnitudes, and their respective
uncertainties for a set of preselected KIC open cluster red giants that were
studied by Stello et al. (2010). Their cluster memberships were independently
confirmed through asteroseismic, radial velocity, and proper motion studies.
The cluster membership probabilities of stars outside the 95% confidence
intervals decrease with increasing distance to the confidence region.

Figure 6: _Gaia_ G magnitude vs. frequency of the maximum oscillation power
$\nu_{\rm max}$ for red giants in NGC 6791 and NGC 6819. Dots are KIC stars,
and star symbols are newly detected stars. Filled symbols are likely to be
cluster members, and open symbols are nonmembers. The axes are oriented to
make the plot similar to a color-magnitude diagram. The dashed lines show the
regions in which cluster stars tend to line up in these diagrams and their 95%
confidence intervals.

Using this method, we found that 93 red giants have an asteroseismic cluster
membership probability of more than 95% (61 in NGC 6791 and 32 in NGC 6819).
Of these, 5 stars are not primary targets of _Kepler_ , and they are confirmed
to be cluster members using an asteroseismic analysis for the first time here.
Figure 7 shows the positions of these oscillating cluster red giants within
their respective clusters.

Figure 7: Sky positions of the oscillating red giants that we found to be
likely cluster members. Dots are KIC stars, and star symbols are newly
detected stars. The large circles represent the approximate location of the
clusters (Cantat-Gaudin & Anders 2020), and the central cross represents the
cluster center.

Because we expect these clusters to host $\sim 200$ and $\sim 150$ observable
red giant stars, respectively (see section 2), it is likely that we missed
about three-quarters of the cluster red giants. This could be due to our
restrictive selection in color, magnitude, and distance (see table 1), or due
to limitations of our method for extracting the oscillations in the most
crowded regions of the cluster, where the aperture masks are narrow in order
to prevent contamination. It is also possible that we missed some oscillating
stars due to a high level of noise in the power density spectrum, which would
partially hide the oscillations.

An alternative method for determining cluster membership that does not rely on
asteroseismology was presented by Cantat-Gaudin & Anders (2020). This method
applies an unsupervised classification scheme using Gaia DR2 proper motions
and parallaxes to compute membership probabilities. The authors studied
$1\,481$ stellar clusters in the Galactic disk, including NGC 6791 and NGC
6819, and provided a list of cluster stars and their membership probability.
We added the membership determination from Cantat-Gaudin & Anders (2020) to
tables LABEL:6791 and LABEL:6819 of our oscillating stars. Out of the 149
oscillating red giants that we detected, 113 are considered cluster members
with a probability of 100% in their work, while our method retrieved 93
members with a probability of 95%. Thus, the two methods agree for most of the
stars in our sample, except for $\sim 10\%$ of them. It seems that our method
is much more restrictive in determining cluster membership, and we might be
missing some members due to this.

##  6 Summary and conclusions

We have successfully extracted the light curves of 513 red giant candidates in
the open clusters NGC 6791 and NGC 6819 using the superstamp data from
_Kepler_. We were able to confirm that 149 of these stars are oscillating red
giants, and we measured their frequency of maximum oscillation power
($\nu_{\textrm{max}}$). By performing an asteroseismic membership study, we
found that 93 of these red giants are likely to be cluster members. 75 of
these were previously reported to be cluster members by Stello et al. (2011)
based on a similar membership determination method. 11 nonmember red giants in
our sample were reported to be cluster members by Stello et al. (2011). This
is probably because our membership determination method is based on the
correlation between the _Gaia_ magnitude of each star and its
$\nu_{\textrm{max}}$, while they used the _K_ magnitude against $\Delta\nu$.
Although both strategies are based on the same principle, it is possible that
there is some scatter between the two methods, which would explain the
disagreement for the 11 stars. It is also worth noting that at the time, only
four quarters of Kepler data were available, making their light curves four
times shorter than those we extracted.

Out of the 149 oscillating red giants that we found, 29 are not primary
targets of _Kepler_ , and their light curves have not been released
previously. We found that 5 of these red giants are asteroseismic cluster
members.

The method that we followed to extract the light curves from the _Kepler_
superstamps allowed us to obtain the asteroseismic parameters of stars that
are very close to the cluster center, which would be very challenging for
aperture photometry. This method cannot only be applied to solar-like
oscillators, but also to any other star within the superstamp data. Moreover,
it can be used to extract the light curves in any moderately crowded region as
long as high-precision long-term photometric data are available.

In the upcoming PLATO mission, the provisional fields that are expected to be
observed (LOPS2 and LOPN1) contain about 300 open clusters (Nascimbeni et al.
2022). Our method can be used to extract the light curves of cluster stars
observed by PLATO and provides an opportunity of performing asteroseismic
analyses on these clusters. These analyses would allow us to obtain the
parameters of more clusters in the Milky Way, which in turn would bring us
closer to understanding the nature of these objects in our Galaxy.

###### Acknowledgements.

We acknowledge funding from the ERC Consolidator Grant DipolarSound (grant
agreement # 101000296). This work was funded by the Deutsche
Forschungsgemeinschaft (DFG, German Research Foundation) – Project-ID
138713538 – SFB 881 (“The Milky Way System”, subproject P02)

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##  Appendix A Tables

Table 2:  Oscillating red giants in NGC 6791. ID | KIC | RA (°) | DEC (°) |  _Gaia_ (mag) |  $\nu_{\mathrm{max}}$ ($\mu\mathrm{Hz}$) | Member (this work) | S11 member | C20 member
---|---|---|---|---|---|---|---|---
1 | - | 290.1856 | 37.6687 | 16.93 | $20.4_{-0.6}^{+0.4}$ | No | - | -
2 | - | 290.3508 | 37.7717 | 16.27 | $10.1_{-0.3}^{+0.6}$ | No | - | Yes
3 | - | 290.2810 | 37.7486 | 16.89 | $23.5_{-1.9}^{+10.2}$ | No | - | Yes
4 | - | 290.2403 | 37.7394 | 16.38 | $30.2_{-0.5}^{+0.4}$ | No | - | -
5 | - | 290.2641 | 37.7722 | 16.06 | $30.2_{-1.0}^{+8.7}$ | No | - | Yes
6 | - | 290.2548 | 37.7754 | 16.56 | $23.8_{-0.2}^{+0.4}$ | No | - | Yes
7 | - | 290.2796 | 37.7958 | 16.22 | $31.2_{-0.7}^{+0.5}$ | No | - | Yes
8 | - | 290.2794 | 37.7974 | 16.78 | $21.1_{-0.04}^{+0.1}$ | No | - | Yes
9 | - | 290.1708 | 37.7726 | 15.85 | $27.8_{-11.0}^{+1.7}$ | No | - | Yes
10 | - | 290.0669 | 37.8447 | 17.00 | $38.3_{-1.4}^{+1.4}$ | No | - | -
11 | - | 290.2177 | 37.7681 | 14.85 | $47.1_{-1.5}^{+1.3}$ | Yes | - | -
12 | - | 290.2525 | 37.7804 | 16.64 | $29.3_{-1.3}^{+1.2}$ | No | - | Yes
13 | - | 290.2031 | 37.7875 | 15.99 | $28.5_{-4.7}^{+0.6}$ | No | - | Yes
14 | - | 290.2500 | 37.8004 | 16.81 | $74.6_{-1.9}^{+1.4}$ | No | - | Yes
15 | - | 290.2836 | 37.8190 | 15.12 | $79.1_{-2.5}^{+1.0}$ | Yes | - | Yes
16 | - | 290.2318 | 37.8126 | 16.58 | $81.3_{-13.1}^{+0.8}$ | No | - | Yes
17 | - | 290.1668 | 37.8011 | 16.08 | $18.5_{-2.1}^{+0.8}$ | No | - | -
18 | 2297384 | 290.1899 | 37.6641 | 14.21 | $20.4_{-0.3}^{+0.3}$ | Yes | Yes | Yes
19 | 2435987 | 290.0822 | 37.7819 | 14.53 | $38.1_{-0.4}^{+0.4}$ | Yes | Yes | Yes
20 | 2436097 | 290.1020 | 37.7705 | 14.66 | $42.3_{-5.8}^{+0.6}$ | Yes | Yes | Yes
21 | 2436209 | 290.1196 | 37.7214 | 14.80 | $58.2_{-1.0}^{+0.7}$ | Yes | Yes | Yes
22 | 2436332 | 290.1361 | 37.7728 | 14.30 | $27.6_{-0.5}^{+0.7}$ | Yes | Yes | Yes
23 | 2436334 | 290.1365 | 37.7006 | 14.78 | $63.5_{-7.3}^{+3.1}$ | Yes | - | Yes
24 | 2436417 | 290.1452 | 37.7750 | 14.10 | $25.9_{-0.4}^{+0.5}$ | Yes | Yes | Yes
25 | 2436458 | 290.1494 | 37.7811 | 14.53 | $35.4_{-0.3}^{+0.7}$ | Yes | Yes | Yes
26 | 2436540 | 290.1577 | 37.7569 | 14.86 | $52.8_{-4.3}^{+2.0}$ | Yes | Yes | Yes
27 | 2436543 | 290.1579 | 37.7470 | 14.12 | $23.4_{-0.7}^{+0.7}$ | Yes | - | Yes
28 | 2436593 | 290.1618 | 37.7430 | 15.40 | $21.9_{-1.1}^{+10.8}$ | No | Yes | Yes
29 | 2436608 | 290.1634 | 37.7437 | 14.45 | $23.5_{-0.4}^{+0.4}$ | No | - | Yes
30 | 2436682 | 290.1702 | 37.7727 | 14.14 | $27.1_{-0.5}^{+0.5}$ | Yes | - | Yes
31 | 2436688 | 290.1709 | 37.7174 | 15.09 | $79.2_{-1.0}^{+1.1}$ | Yes | Yes | Yes
32 | 2436732 | 290.1749 | 37.7984 | 14.14 | $28.8_{-1.8}^{+0.5}$ | Yes | Yes | Yes
33 | 2436814 | 290.1815 | 37.7839 | 14.21 | $24.0_{-0.4}^{+0.8}$ | Yes | Yes | Yes
34 | 2436824 | 290.1820 | 37.7782 | 14.48 | $33.9_{-0.3}^{+0.3}$ | Yes | Yes | Yes
35 | 2436900 | 290.1882 | 37.7428 | 14.46 | $35.7_{-0.4}^{+0.3}$ | Yes | Yes | Yes
36 | 2436912 | 290.1889 | 37.7883 | 14.18 | $30.0_{-1.0}^{+1.0}$ | Yes | Yes | Yes
37 | 2436935 | 290.1905 | 37.7406 | 15.65 | $34.7_{-3.9}^{+1.1}$ | No | - | Yes
38 | 2436944 | 290.1917 | 37.7986 | 14.17 | $28.5_{-0.5}^{+0.5}$ | Yes | Yes | -
39 | 2437040 | 290.1986 | 37.7923 | 14.16 | $25.7_{-0.3}^{+0.3}$ | Yes | Yes | Yes
40 | 2437103 | 290.2031 | 37.7867 | 14.38 | $38.3_{-1.4}^{+1.4}$ | Yes | Yes | Yes
41 | 2437164 | 290.2069 | 37.7355 | 14.16 | $30.1_{-0.7}^{+0.5}$ | Yes | - | Yes
42 | 2437240 | 290.2118 | 37.7248 | 14.65 | $45.9_{-1.0}^{+0.5}$ | Yes | Yes | Yes
43 | 2437267 | 290.2141 | 37.7751 | 13.81 | $38.0_{-1.5}^{+2.0}$ | No | - | Yes
44 | 2437296 | 290.2159 | 37.7800 | 16.02 | $71.4_{-0.7}^{+0.7}$ | No | - | Yes
45 | 2437325 | 290.2185 | 37.7876 | 15.29 | $84.8_{-2.7}^{+2.1}$ | Yes | Yes | Yes
46 | 2437327 | 290.2188 | 37.7679 | 14.85 | $59.4_{-0.9}^{+1.0}$ | Yes | - | Yes
47 | 2437353 | 290.2203 | 37.7592 | 14.14 | $28.8_{-0.5}^{+0.4}$ | Yes | Yes | Yes
48 | 2437402 | 290.2233 | 37.7886 | 14.66 | $46.4_{-0.6}^{+0.6}$ | Yes | Yes | Yes
49 | 2437444 | 290.2258 | 37.7746 | 14.00 | $18.9_{-0.3}^{+0.2}$ | Yes | Yes | Yes
50 | 2437488 | 290.2291 | 37.7614 | 14.95 | $65.4_{-4.2}^{+1.3}$ | Yes | Yes | Yes
51 | 2437507 | 290.2304 | 37.7209 | 14.03 | $19.8_{-0.3}^{+0.4}$ | Yes | Yes | Yes
52 | 2437539 | 290.2326 | 37.7085 | 14.54 | $47.2_{-12.7}^{+0.8}$ | Yes | - | Yes
53 | 2437564 | 290.2346 | 37.7426 | 14.23 | $28.07_{-0.6}^{+0.7}$ | Yes | Yes | Yes
54 | 2437589 | 290.2363 | 37.7187 | 14.25 | $47.8_{-0.6}^{+0.6}$ | No | Yes | Yes
55 | 2437653 | 290.2410 | 37.7852 | 15.09 | $70.9_{-1.0}^{+1.0}$ | Yes | Yes | Yes
56 | 2437698 | 290.2448 | 37.7203 | 14.19 | $27.7_{-0.7}^{+1.1}$ | Yes | Yes | Yes
57 | 2437781 | 290.2518 | 37.7878 | 15.21 | $82.5_{-1.4}^{+1.6}$ | Yes | Yes | Yes
58 | 2437805 | 290.2536 | 37.7777 | 14.15 | $29.7_{-0.6}^{+0.6}$ | Yes | Yes | Yes
59 | 2437901 | 290.2621 | 37.7677 | 14.25 | $30.2_{-0.4}^{+0.4}$ | Yes | - | Yes
60 | 2437933 | 290.2645 | 37.7771 | 15.39 | $92.7_{-7.0}^{+13.5}$ | Yes | Yes | Yes
61 | 2437957 | 290.2674 | 37.7730 | 15.25 | $91.0_{-2.0}^{+1.8}$ | Yes | Yes | Yes
62 | 2437972 | 290.2684 | 37.7694 | 15.15 | $80.7_{-0.9}^{+0.8}$ | Yes | Yes | Yes
63 | 2437976 | 290.2690 | 37.7815 | 15.24 | $83.1_{-1.7}^{+1.5}$ | Yes | Yes | Yes
64 | 2437987 | 290.2697 | 37.7656 | 14.18 | $31.4_{-0.6}^{+0.6}$ | Yes | Yes | Yes
65 | 2438038 | 290.2748 | 37.7994 | 14.94 | $63.6_{-0.6}^{+0.6}$ | Yes | Yes | Yes
66 | 2438051 | 290.2762 | 37.7499 | 14.09 | $27.1_{-0.6}^{+0.5}$ | Yes | Yes | Yes
67 | 2438069 | 290.2777 | 37.7176 | 14.00 | $31.4_{-1.0}^{+1.1}$ | No | - | -
68 | 2438139 | 290.2836 | 37.7971 | 13.55 | $33.9_{-2.2}^{+1.0}$ | No | - | No (70%)
69 | 2438140 | 290.2838 | 37.7589 | 15.00 | $67.9_{-6.9}^{+2.7}$ | Yes | Yes | Yes
70 | 2438191 | 290.2894 | 37.7531 | 15.21 | $90.8_{-1.9}^{+1.9}$ | Yes | - | Yes
71 | 2438333 | 290.3042 | 37.7168 | 14.90 | $60.9_{-1.2}^{+0.9}$ | Yes | Yes | Yes
72 | 2438470 | 290.3230 | 37.7904 | 14.90 | $65.9_{-1.7}^{+0.6}$ | Yes | - | Yes
73 | 2568575 | 290.0295 | 37.8334 | 13.41 | $29.5_{-1.0}^{+3.6}$ | No | - | -
74 | 2569055 | 290.1252 | 37.8386 | 14.17 | $31.2_{-0.6}^{+1.1}$ | Yes | Yes | Yes
75 | 2569078 | 290.1288 | 37.8125 | 13.65 | $24.2_{-3.6}^{+0.3}$ | No | - | -
76 | 2569360 | 290.1639 | 37.8013 | 14.09 | $20.8_{-0.3}^{+0.3}$ | Yes | Yes | Yes
77 | 2569390 | 290.1670 | 37.8514 | 15.01 | $60.7_{-1.2}^{+1.1}$ | Yes | - | Yes
78 | 2569426 | 290.1703 | 37.8538 | 14.56 | $60.7_{-0.9}^{+2.7}$ | Yes | - | -
79 | 2569618 | 290.1927 | 37.8196 | 14.80 | $55.6_{-0.5}^{+0.5}$ | Yes | Yes | Yes
80 | 2570094 | 290.2405 | 37.8170 | 15.00 | $69.9_{-1.4}^{+4.2}$ | Yes | Yes | Yes
81 | 2570172 | 290.2483 | 37.8030 | 15.08 | $74.2_{-1.2}^{+0.7}$ | Yes | Yes | Yes
82 | 2570214 | 290.2522 | 37.8386 | 14.11 | $26.1_{-0.9}^{+1.1}$ | Yes | Yes | Yes
83 | 2570244 | 290.2560 | 37.8014 | 15.37 | $97.3_{-3.1}^{+2.6}$ | Yes | Yes | Yes
84 | 2570384 | 290.2752 | 37.8681 | 14.96 | $48.5_{-1.7}^{+1.8}$ | No | Yes | Yes
85 | 2570518 | 290.2920 | 37.8336 | 14.68 | $46.1_{-8.4}^{+0.6}$ | Yes | Yes | Yes
86 | 2570575 | 290.2985 | 37.8467 | 15.14 | $77.4_{-1.0}^{+1.0}$ | Yes | - | Yes
87 | 2570578 | 290.2990 | 37.8794 | 13.98 | $32.5_{-1.8}^{+0.6}$ | No | - | -
88 | 2570652 | 290.3113 | 37.8854 | 14.43 | $84.2_{-0.8}^{+0.8}$ | No | - | No (60%)
89 | 2570696 | 290.3180 | 37.8709 | 13.62 | $15.3_{-0.2}^{+0.2}$ | Yes | - | -
90 | 2570924 | 290.3587 | 37.8256 | 14.75 | $53.4_{-0.5}^{+0.5}$ | Yes | - | Yes
91 | 2707716 | 290.1904 | 37.9098 | 14.36 | $29.2_{-1.3}^{+1.1}$ | Yes | - | Yes
Table 2: continued. 444We report whether they are cluster members following our method (this work), and whether they were determined to be cluster members in Stello et al. 2011 (S11) and Cantat-Gaudin & Anders 2020 (C20; only when their membership probability is 100%). Table 3:  Oscillating red giants in NGC 6819. ID | KIC | RA (°) | DEC (°) |  _Gaia_ (mag) |  $\nu_{\mathrm{max}}$ ($\mu\mathrm{Hz}$) | Member (this work) | S11 member | C20 member
---|---|---|---|---|---|---|---|---
92 | - | 295.2984 | 40.0901 | 13.60 | $25.8_{-1.2}^{+1.0}$ | No | - | -
93 | - | 295.2936 | 40.1458 | 14.06 | $62.1_{-1.6}^{+1.5}$ | No | - | -
94 | - | 295.2583 | 40.1445 | 14.24 | $40.6_{-0.9}^{+0.9}$ | No | - | -
95 | - | 295.2676 | 40.1656 | 13.61 | $27.6_{-0.6}^{+1.1}$ | No | - | -
96 | - | 295.3279 | 40.1953 | 12.26 | $20.8_{-0.5}^{+0.4}$ | Yes | - | No (60%)
97 | - | 295.2844 | 40.1772 | 13.29 | $14.0_{-0.2}^{+0.2}$ | No | - | -
98 | - | 295.3115 | 40.1835 | 12.52 | $39.6_{-0.4}^{+0.7}$ | Yes | - | Yes
99 | - | 295.4381 | 40.1639 | 14.69 | $52.2_{-0.4}^{+0.4}$ | No | - | -
100 | - | 295.4468 | 40.2657 | 14.45 | $52.9_{-13.4}^{+2.3}$ | No | - | -
101 | - | 295.3954 | 40.3276 | 13.06 | $63.1_{-1.1}^{+1.0}$ | Yes | - | -
102 | - | 295.3926 | 40.3291 | 13.12 | $31.3_{-0.9}^{+15.0}$ | No | - | -
103 | - | 295.3621 | 40.3200 | 13.91 | $22.4_{-0.03}^{+0.2}$ | No | - | -
104 | 4936825 | 295.2691 | 40.0808 | 13.14 | $29.5_{-0.8}^{+2.9}$ | No | - | -
105 | 5023953 | 295.2415 | 40.1382 | 12.59 | $41.9_{-2.1}^{+1.8}$ | Yes | Yes | Yes
106 | 5024043 | 295.2585 | 40.1078 | 12.78 | $56.7_{-1.9}^{+1.6}$ | Yes | Yes | -
107 | 5024268 | 295.2959 | 40.1866 | 11.31 | $19.5_{-1.5}^{+6.0}$ | No | No | Yes
108 | 5024297 | 295.3010 | 40.1927 | 12.90 | $34.1_{-1.0}^{+13.02}$ | No | Yes | Yes
109 | 5024312 | 295.3034 | 40.1915 | 13.54 | $83.9_{-3.0}^{+2.7}$ | Yes | Yes | Yes
110 | 5024322 | 295.3049 | 40.1116 | 13.09 | $64.2_{-21.0}^{+1.4}$ | Yes | - | No (60%)
111 | 5024327 | 295.3060 | 40.1989 | 12.75 | $46.6_{-0.6}^{+0.6}$ | Yes | Yes | Yes
112 | 5024404 | 295.3152 | 40.1696 | 12.86 | $47.4_{-10.9}^{+1.7}$ | Yes | Yes | Yes
113 | 5024414 | 295.3164 | 40.1865 | 12.65 | $76.4_{-0.2}^{+0.2}$ | No | Yes | Yes
114 | 5024456 | 295.3210 | 40.1811 | 11.08 | $142.6_{-0.4}^{+0.4}$ | No | Yes | Yes
115 | 5024476 | 295.3240 | 40.1544 | 12.51 | $52.2_{-1.5}^{+1.6}$ | No | Yes | Yes
116 | 5024512 | 295.3281 | 40.1985 | 13.29 | $60.5_{-5.8}^{+13.8}$ | Yes | Yes | Yes
117 | 5024517 | 295.3288 | 40.1947 | 13.00 | $38.8_{-2.8}^{+5.3}$ | No | Yes | Yes
118 | 5024582 | 295.3389 | 40.1992 | 12.67 | $47.2_{-0.6}^{+0.6}$ | Yes | Yes | No (30%)
119 | 5024583 | 295.3390 | 40.1834 | 12.73 | $32.3_{-3.5}^{+5.4}$ | Yes | Yes | Yes
120 | 5024601 | 295.3411 | 40.1968 | 12.46 | $29.0_{-3.2}^{+12.3}$ | Yes | Yes | Yes
121 | 5024750 | 295.3608 | 40.1949 | 11.81 | $11.4_{-0.2}^{+0.4}$ | Yes | Yes | Yes
122 | 5024967 | 295.3935 | 40.1461 | 12.79 | $48.7_{-3.0}^{+3.6}$ | Yes | Yes | Yes
123 | 5025021 | 295.4035 | 40.1508 | 12.84 | $47.4_{-0.6}^{+0.5}$ | Yes | - | -
124 | 5025101 | 295.4205 | 40.1867 | 13.00 | $23.0_{-0.5}^{+0.2}$ | No | - | -
125 | 5111718 | 295.1535 | 40.2548 | 13.80 | $111.4_{-3.2}^{+3.1}$ | Yes | Yes | Yes
126 | 5111767 | 295.1655 | 40.2312 | 13.64 | $28.3_{-0.9}^{+2.2}$ | No | - | -
127 | 5111940 | 295.2069 | 40.2420 | 13.00 | $55.1_{-2.1}^{+6.4}$ | Yes | Yes | Yes
128 | 5111949 | 295.2092 | 40.2197 | 12.76 | $39.6_{-1.7}^{+1.5}$ | Yes | Yes | Yes
129 | 5111987 | 295.2166 | 40.2600 | 14.95 | $87.9_{-11.8}^{+2.1}$ | No | - | -
130 | 5112072 | 295.2333 | 40.2276 | 13.74 | $123.8_{-20.9}^{+6.3}$ | Yes | Yes | Yes
131 | 5112118 | 295.2411 | 40.2314 | 12.59 | $26.3_{-1.3}^{+0.9}$ | Yes | - | -
132 | 5112281 | 295.2695 | 40.2476 | 12.18 | $71.9_{-0.6}^{+0.6}$ | No | - | -
133 | 5112361 | 295.2841 | 40.2524 | 13.05 | $74.4_{-1.1}^{+1.1}$ | Yes | No | -
134 | 5112373 | 295.2858 | 40.2250 | 12.76 | $43.4_{-12.1}^{+0.8}$ | Yes | Yes | Yes
135 | 5112387 | 295.2886 | 40.2454 | 12.78 | $40.6_{{}_{5}.1}^{+1.3}$ | Yes | Yes | Yes
136 | 5112401 | 295.2913 | 40.2637 | 12.56 | $39.0_{-0.4}^{+0.4}$ | Yes | Yes | Yes
137 | 5112403 | 295.2919 | 40.2190 | 13.89 | $20.1_{-1.0}^{+1.1}$ | No | Yes | Yes
138 | 5112467 | 295.3033 | 40.2066 | 12.76 | $36.1_{-0.8}^{+8.1}$ | Yes | Yes | Yes
139 | 5112491 | 295.3064 | 40.2057 | 12.71 | $45.2_{-0.5}^{+0.5}$ | Yes | Yes | Yes
140 | 5112730 | 295.3395 | 40.2326 | 12.72 | $44.0_{-7.3}^{+1.3}$ | Yes | Yes | Yes
141 | 5112734 | 295.3407 | 40.2031 | 12.80 | $30.9_{-1.2}^{+1.4}$ | No | Yes | Yes
142 | 5112744 | 295.3426 | 40.2789 | 12.89 | $43.0_{-0.6}^{+0.5}$ | Yes | Yes | Yes
143 | 5112880 | 295.3628 | 40.2079 | 12.23 | $22.5_{-1.5}^{+1.8}$ | Yes | Yes | Yes
144 | 5112938 | 295.3714 | 40.2178 | 12.76 | $44.9_{-16.0}^{+2.3}$ | Yes | Yes | Yes
145 | 5112948 | 295.3726 | 40.2389 | 12.83 | $32.7_{-0.6}^{+9.9}$ | No | Yes | Yes
146 | 5112950 | 295.3731 | 40.2058 | 12.71 | $38.6_{-1.2}^{+1.0}$ | Yes | Yes | Yes
147 | 5112974 | 295.3761 | 40.2560 | 12.64 | $33.6_{-2.4}^{+4.1}$ | Yes | Yes | Yes
148 | 5113041 | 295.3888 | 40.2097 | 12.79 | $37.1_{-6.7}^{+1.1}$ | Yes | Yes | Yes
149 | 5200152 | 295.3494 | 40.3623 | 12.67 | $45.5_{-1.8}^{+1.0}$ | Yes | Yes | Yes
Table 3: continued. 555We report whether they are cluster members following
our method (this work), and whether they were determined to be cluster members
in Stello et al. 2011 (S11) and Cantat-Gaudin & Anders 2020 (C20; only when
their membership probability is 100%).