11institutetext: School of Physics and Astronomy, University of Birmingham,
Birmingham B15 2TT, UK
11email<EMAIL_ADDRESS>22institutetext: Stellar Astrophysics
Centre (SAC), Department of Physics and Astronomy, Aarhus University, Ny
Munkegade 120, DK-8000 Aarhus C, Denmark 33institutetext: Center for Space
Science, NYUAD Institute, New York University Abu Dhabi, PO Box 129188, Abu
Dhabi, United Arab Emirates 44institutetext: Sydney Institute for Astronomy
(SIfA), School of Physics, University of Sydney, Camperdown, NSW 2006,
Australia. 55institutetext: Department of Chemistry and Physics, Florida Gulf
Coast University, Fort Myers, FL 33965 66institutetext: Institute for
Astronomy, University of Hawai‘i, 2680 Woodlawn Drive, Honolulu, HI 96822, USA
77institutetext: Department of Astronomy and Space Sciences, Science Faculty,
Erciyes University, 38030 Melikgazi, Kayseri, Turkey 88institutetext: Research
School of Astronomy and Astrophysics, Mount Stromlo Observatory, The
Australian National University, Canberra, Australian Capital Territory,
Australia. 99institutetext: White Dwarf Research Corporation, 9020 Brumm
Trail, Golden, CO 80403, USA 1010institutetext: School of Physics, University
of NSW, 2052, Australia

# A Catalogue of Solar-Like Oscillators Observed by TESS in 120-second and
20-second Cadence

Emily Hatt E-mail<EMAIL_ADDRESS>Martin B. Nielsen 11 2 2 3 3
William J. Chaplin 11 2 2 Warrick H. Ball 11 2 2 Guy R. Davies 11 Timothy R.
Bedding 22 4 4 Derek L. Buzasi 55 Ashley Chontos 66 Daniel Huber 66 Cenk
Kayhan 77 Yaguang Li 22 4 4 Timothy R. White 22 4 4 8 8 Chen Cheng 44 Travis
S. Metcalfe 99 Dennis Stello 1010

###### Abstract

Context. The Transiting Exoplanet Survey Satellite (TESS) mission has provided
photometric light curves for stars across nearly the entire sky. This allows
for the application of asteroseismology to a pool of potential solar-like
oscillators that is unprecedented in size.

Aims. We aim to produce a catalogue of solar-like oscillators observed by TESS
in the 120-second and 20-second cadence modes. The catalogue is intended to
highlight stars oscillating at frequencies above the TESS 30-minute cadence
Nyquist frequency with the purpose of encompassing the main sequence and sub-
giant evolutionary phases. We aim to provide estimates for the global
asteroseismic parameters $\nu_{\mathrm{max}}$ and $\Delta\nu$.

Methods. We apply a new probabilistic detection algorithm to the 120-second
and 20-second light curves of over 250,000 stars. This algorithm flags targets
that show characteristic signatures of solar-like oscillations. We manually
vet the resulting list of targets to confirm the presence of solar-like
oscillations. Using the probability densities computed by the algorithm, we
measure the global asteroseismic parameters $\nu_{\mathrm{max}}$ and
$\Delta\nu$.

Results. We produce a catalogue of 4,177 solar-like oscillators, reporting
$\Delta\nu$ and $\nu_{\mathrm{max}}$ for 98% of the total star count. The
asteroseismic data reveals vast coverage of the HR diagram, populating the red
giant branch, the subgiant regime and extending toward the main-sequence.

Conclusions. A crossmatch with external catalogs shows that 25 of the detected
solar-like oscillators are a component of a spectroscopic binary, and 28 are
confirmed planet host stars. These results provide the potential for precise,
independent asteroseismic constraints on these and any additional TESS targets
of interest.

###### Key Words.:

Asteroseismology – Catalogs – Stars: oscillations – Methods: data analysis

##  1 Introduction

Asteroseismology, the study of the intrinsic oscillations of stars, has
revealed the physical properties of thousands of stars to high precision (e.g.
Metcalfe et al., 2014; Lebreton & Goupil, 2014; Lagarde et al., 2015;
Serenelli et al., 2017; Yu et al., 2018; Yıldız et al., 2019). Solar-like
oscillators, where-in modes are excited and damped by the turbulent motion of
gas in the outer convection zone, have been of particular interest due to the
host of identifiable overtones present in their oscillation power spectra. The
spectra of such stars can be characterized via two global parameters, the
large frequency separation ($\Delta\nu$) and the frequency at maximum power
($\nu_{\mathrm{max}}$). The former describes the regular frequency interval
separating overtone modes of a given angular degree. The latter refers to the
central frequency of the Gaussian-like envelope describing the visible power
excess caused by the modes. These two parameters are the most readily
available in the spectrum of a solar-like oscillator and, when combined with
an independent measure of effective surface temperature ($T_{\mathrm{eff}}$),
can be exploited to determine the mass and radius of a star to within a few
percent (Silva Aguirre et al., 2012; Huber et al., 2012; Guggenberger et al.,
2016; Gaulme et al., 2016; Yıldız et al., 2016; Li et al., 2021; Mathur et
al., 2022).

With the only requirement for the excitation of modes being the presence of an
outer convection zone, solar-like oscillations have been observed in stars on
the main sequence (e.g. Chaplin et al., 2014), in the subgiant phase (e.g.
Appourchaux et al., 2012b; Mathur et al., 2022), and on the red giant branch
(e.g. Bedding et al., 2010; Yu et al., 2018; Çelik Orhan et al., 2021). As a
given star evolves through these phases, structural changes will affect the
properties of the oscillations. The least evolved stars oscillate at a few
thousand $\mu$Hz. This decreases as the star evolves off the main-sequence,
dropping to below $\sim$100 $\mu$Hz on the red giant branch. Despite the large
coverage of the Hertzprung-Russell (HR) diagram, current catalogues are
disjoint in evolutionary state. Detections are dominated by a large number of
red giants and a much smaller set of main-sequence stars, with the subgiant
phase only sparsely sampled. Although a decrease in numbers is expected during
this phase, given their rapid evolution, observational constraints have
magnified the discrepancy.

Relying predominantly on space-based photometry means observations of solar-
like oscillators are mostly limited to data collected by a handful of
missions. Of these, the Kepler (Borucki et al., 2010) mission provides the
longest time series for a large number of available targets. Observing the
same patch of sky for four years, the mission monitored approximately 196,000
targets (e.g. Huber et al., 2014). Data were collected in two modes - long and
short-cadence, with the associated sampling rates corresponding to Nyquist
frequency limits of 283 $\mu$Hz and 8496 $\mu$Hz, respectively. The short-
cadence data spans the full range in frequency where solar-like oscillations
are located. However, due to telemetry constraints, the number of targets
observed in the longer cadence greatly outnumbered those in short. Indeed, of
the total observed targets only a few thousand were selected for short-cadence
(Thompson et al., 2016). Therefore, of the tens of thousands of solar-like
oscillators detected using Kepler data, the vast majority are more evolved
stars (Stello et al., 2013; Hekker et al., 2011; Yu et al., 2018).

Although sparse in comparison, detections of solar-like oscillators were made
in the short-cadence data (Chaplin et al., 2011b). Due to the reduced capacity
for such observations, these slots were reserved for targets most suited to
the main aims of the mission: the detection of exoplanets via the transit
method. This led to the preferential selection of cool main sequence stars
(Batalha et al., 2010). The combination of the selection criteria for the
short-cadence observations and the Nyquist frequency in the long cadence data
resulted in the asteroseismic yield lacking a significant number of subgiant
stars. The largest list of such stars was constructed by Li et al. (2020) and
numbers only 50 subgiants.

The TESS mission (Ricker et al., 2014) launched in 2018 and has been surveying
the majority of the sky, providing an extensive database of potential solar-
like oscillators. The nominal mission lasted two years and observations
continue during the first extended mission, which will finish observing in
September of 2022. To maximise the sky coverage, observations are made in
sectors with an average length of 27.4 days. Most targets are captured in one
or two sectors, while a small number of stars are located where the sectors
overlap at the ecliptic poles (known as the continuous viewing zones).
Similarly to Kepler, the majority of the stars monitored by TESS in the
nominal mission were observed at 30-minute cadence (referred to as Full Frame
Images, or FFIs), corresponding to a Nyquist frequency of 278 $\mu$Hz.
Currently the largest systematic searches for solar-like oscillators have been
performed with observations at this cadence, and therefore restricted to the
more evolved stars (Silva Aguirre et al., 2020; Hon et al., 2021; Mackereth et
al., 2021; Stello et al., 2022). Shorter cadences are available for a smaller
set of targets, with the nominal mission including a 120-second integration
time (double the Kepler short-cadence). The extended mission introduced
20-second data for a reduced target list while the FFI cadence was shortened
to 10-minutes. With Nyquist frequencies of 4167 $\mu$Hz and 25000 $\mu$Hz
respectively, the 120-second and 20-second cadence data allow us to detect
solar-like oscillations in less evolved solar-like oscillators.

To that end, we used 120-second and 20-second TESS data to search for
oscillations in stars observed during Sectors 1 to 46. Starting with a smaller
set of targets that were identified as the most likely to oscillate above the
30-minute FFI Nyquist frequency (Schofield et al., 2019), we have identified
400 candidate solar-like oscillators by eye. These were used to optimise a
detection algorithm presented in Nielsen et al. (2022) (henceforth referred to
as N22). We then passed the remaining stars observed during the aforementioned
sectors to this tuned pipeline. Although the main aim of this work is to
construct a list of solar-like oscillators, we found we could exploit the
probability distributions calculated by the algorithm to measure the global
properties ($\nu_{\mathrm{max}}$ and $\Delta\nu$). Therefore, we provide these
values for the majority of the detected solar-like oscillators.

##  2 Target selection

The full list of targets observed in 120-second cadence by TESS exceeds
300,000. The Asteroseismic Target List (ATL, Schofield et al., 2019) gives
some indication of which stars are most likely to be solar-like oscillators
prior to running the algorithm. By separating this sample from the full set of
120-second cadence targets we can loosen detection constraints whilst keeping
the required manual validation to manageable levels. To distinguish the stars
in the ATL from the remaining targets observed in 120-second cadence we will
refer to the latter sample as ‘the Large Sample’.

The ATL was constructed prior to the launch of TESS to provide a prioritised
list of targets most likely to yield detections of solar-like oscillations
(Schofield et al., 2019; see also Fausnaugh et al., 2021; Godoy-Rivera et al.,
2021). Aimed at 120-second cadence data, the list was restricted to stars
which would oscillate above the 30-minute FFI Nyquist frequency. To select
targets the authors employed asteroseismic scaling relations for
$\nu_{\mathrm{max}}$ (Campante et al., 2016). This allowed them to locate
stars in the TESS field-of-view predicted to have $\nu_{\mathrm{max}}$ ¿ 240
$\mu$Hz. Calculating the expected power excess caused by the modes, the
authors estimated the probability that the oscillations would be detectable.
Only those targets with at least a 5% probability of making a detection were
retained, which constituted $\approx$ 25,000 targets. Of these, 11,220 had
been observed at the time of this work. In the following analysis, values of
parallax and $T_{\mathrm{eff}}$ (required by the detection algorithm) were
taken from the ATL. The ATL used parallaxes from Gaia data release 2 (GDR2,
Gaia Collaboration et al., 2018), supplemented at bright magnitudes with
values from the eXtended Hipparcos Catalogue (XHIP, Anderson & Francis, 2012).
Effective temperatures in the ATL were computed from a polynomial in
dereddened (B-V) colour, using coefficients according to Torres (2010).

The Large Sample consists of the remaining 120-second cadence targets. We
selected stars brighter than 11th magnitude in 2MASS $\,K_{\mathrm{S}}$
magnitude, and used $T_{\mathrm{eff}}$ from the TESS Input Catalogue (TIC,
Stassun et al., 2019) to restrict to the range 4500K ¡ $\,T_{\mathrm{eff}}$ ¡
6500K. This includes the typical ranges in $T_{\mathrm{eff}}$ of stars from
the main sequence to the red giant branch, and removes stars that are likely
too faint for modes to be visible (Stello et al., 2017). In this set we
analysed light curves for 255,089 stars. We applied the same cuts to all of
the targets observed in 20-second cadence, which yielded light curves for 6157
stars. Parallaxes for both sets were again drawn from GDR2.

For reference, we also identified targets with a published detection of solar-
like oscillations and some measure of the global asteroseismic parameters. A
set of 13 such stars was produced, which is shown in Table 1 and referred to
in the following as the ‘literature sample’. We prioritized targets
oscillating at frequencies above the Kepler long-cadence Nyquist as per the
main aim of the catalogue. Parallaxes and effective temperatures were drawn
from GDR2.

Table 1: Global asteroseismic parameters of stars in the literature sample.

Name | TIC |  $\nu_{\mathrm{max}}$ ($\mu$Hz) |  $\Delta\nu$ ($\mu$Hz) | Source
---|---|---|---|---
HD 19916 | 200723869 | 1188 $\pm$ 40 | 61.4 $\pm$ 1.5 | TESS 120-second 1
HD 222416 | 441462736 | 430 $\pm$ 18 | 28.94 $\pm$ 0.15 | TESS 120-second 2
$\lambda^{2}$ For | 122555698 |  $\approx$ 1280 | 69.76 $\pm$ 0.23 | TESS 120-second 3
HD 212771 | 12723961 | 226.6 $\pm$ 9.4 | 16.25 $\pm$ 0.19 | TESS 30-minute FFI 4
HD 222076 | 325178933 | 203.0 $\pm$ 3.6 | 15.60 $\pm$ 0.13 | TESS 120-second 5
94 Aqr | 214664574 | 875 $\pm$ 12 | 50.2 $\pm$ 0.4 | TESS 120-second 6
$\gamma$ Pav | 265488188 | 2693 $\pm$ 95 | 119.9 $\pm$ 1.0 | TESS 20-second 7
$\pi$ Men | 261136679 | 2599 $\pm$69 | 116.7 $\pm$ 1.1 | TESS 20-second 7
$\nu$ Ind | 317019578 |  | 25.08 ± 0.10 | TESS 120-second 8
$\beta$ Hyi | 267211065 |  $\approx$ 1000 | 57.24 $\pm$ 0.16 | HARPS and UCLES, WIRE 9
$\mu$ Ara | 362661163 |  $\approx$ 2000 | 89.68 $\pm$ 0.19 | HARPS 10
$\mu$ Her | 460067868 | 1216 $\pm$ 11 | 64.2 $\pm$ 0.2 | SONG 11
$\alpha$ Men | 141810080 | 3134 $\pm$ 440 | 140 $\pm$ 2 | TESS 20-second 12

  * References.

  * 1

Addison et al. (2021)

  * 2

Huber et al. (2019)

  * 3

Nielsen et al. (2020)

  * 4

Campante et al. (2019)

  * 5

Jiang et al. (2020)

  * 6

Metcalfe et al. (2020)

  * 7

Huber et al. (2022)

  * 8

Chaplin et al. (2020)

  * 9

Bedding et al. (2007), Karoff et al. (2007)

  * 10

Bouchy et al. (2005)

  * 11

Grundahl et al. (2017)

  * 12

Chontos et al. (2021)

##  3 Data selection

We used detrended light curves produced by the TESS Science Processing
Operations Center (SPOC) pipeline (Jenkins et al., 2016), which carries out
the simple aperture photometry and removes instrumental trends. We used light
curves recorded in 120-second cadence, except when 20-second data were
available. In the literature sample, we used 120-second cadence light curves
for all but three stars ($\gamma$ Pav, $\pi$ Men and $\alpha$ Men), where we
used 20-second cadence light curves. We used the open source package
Lightkurve (Lightkurve Collaboration et al., 2018) to stitch sectors together,
and remove flux values exceeding 5$\sigma$.

As TESS observes in 27.4 day sectors, there are gaps present in the light
curves. During the nominal mission the northern and southern hemispheres were
observed for 13 sectors respectively, amounting to a year in each. The
extended mission returned to the southern hemisphere, meaning the light curves
of some targets contain year-long gaps. Both leaving the gaps and methods to
fill the gaps (such as linear interpolation, Stello et al. (2015)) introduce
strong correlations between frequency bins. Assuming mode lifetimes follow the
relation given by Appourchaux et al. (2012a) (see also Lund et al., 2017), at
$\,T_{\mathrm{eff}}$ = 5000K, we expect mode lifetimes on the order of weeks.
Therefore, if a star is observed in the nominal mission and then a year later
in the extended, we expect the modes have been re-excited so that the
variability in the time series is no longer correlated. Hence we removed the
gap in the data by shifting the timestamps. As in N22, gaps larger than 50
days were treated this way. Gap closing in this manner is not the optimal
approach and does alter the line profiles, which would impact measurements of
individual frequencies, as was discussed in Bedding & Kjeldsen (2022).
However, as noted in N22, the inclusion of gaps significantly increased the
false positive rate (see N22 Fig. A.1) necessitating closing the gaps for our
detection tests. Furthermore we report only the global seismic parameters, and
do not measure individual frequencies.

We then used the Lightkurve package to produce a power density spectrum via
the ‘fast’ Lomb-Scargle method (Lomb, 1976; Scargle, 1982; Press & Rybicki,
1989).

##  4 Detection of solar-like oscillators

In the following section we briefly review the methods used in the detection
algorithm of N22, before discussing the detections made in each set of
targets. The detection test consists of two modules, which exploit different
properties of solar-like oscillators:

  1. 1.

Power excess test: The first module uses the power spectral density of the
time series. Given the assumption that the noise in each frequency bin follows
a $\chi^{2}$ distribution with 2 degrees of freedom, the probability that only
noise is present in a given bin is calculated (the H0 probability). The
probability that an envelope is present is then computed via a prediction of
the expected power in a hypothetical envelope centered on each frequency bin
(the H1 probability). The prediction is calculated via the methods of Chaplin
et al. (2011a) and Schofield et al. (2019), requiring $\,T_{\mathrm{eff}}$.
Prior information on $\nu_{\mathrm{max}}$ is used, guided by parallax and
2MASS $\,K_{\mathrm{S}}$-band magnitude.

  2. 2.

Large separation test: The second module looks for the signature of the
regularly spaced overtones. This is achieved using the methods described in
Mosser & Appourchaux (2009), who used the autocorrelation function (ACF) of
the time series. A band-pass filter is placed on the power spectrum at a test
frequency and the ACF of this filtered time series is calculated via an
inverse Fourier transform. Repeating this for other test frequencies, we
produce a 2D ACF in test frequency (a proxy for $\nu_{\mathrm{max}}$) and lag
(related to the large frequency separation via $\tau=1/\Delta\nu$). This
2-dimensional map is collapsed along the lag axis to produce a 1-dimensional
distribution in frequency. To evaluate whether the probability the observed
collapsed ACF is inconsistent with noise, N22 approximate the response due to
noise by a $\Gamma$ distribution.

Using 400 solar-like oscillators and non-detections manually identified from
the ATL, N22 established the performance of the pipeline for a range of
detection thresholds. They found the pipeline was able to attain a true
positive rate of 94.7% and a false positive rate of 8.2% when asking for a
response at least one of the two modules111This is achieved when taking a
threshold of 0.77 on the power excess module and 0.73 on the frequency spacing
module..

In the following sections we discuss the detections made in the four samples
via this algorithm (see Table 4). All of the reported solar-like oscillators
have been manually vetted to check for false positives. We retain only targets
in which we are confident we can identify the presence of oscillations,
prioritizing a reduced false positive rate over maximising the yield. This may
cause an under-representation of targets with very low signal-to-noise. A
break down of the total counts, and which sample they belong to, can be seen
in Table 3. Cross referencing with NASA’s Exoplanet Archive
222https://exoplanetarchive.ipac.caltech.edu, we found 28 of the stars in our
catalogue are confirmed planet hosts. The majority of these stars have not yet
been studied asteroseismically. Asteroseismic inferences on these targets are
reserved for an upcoming work. We also cross-referenced with the Ninth
Catalogue of Spectroscopic Binary Orbits Pourbaix et al. (SB9, 2004)
discovering a further 25 stars are components in spectroscopic binary systems.

Fig. 1 shows the value of 2MASS $K_{\mathrm{S}}$ magnitude against the
predicted value of $\nu_{\mathrm{max}}$. In grey we show targets observed in
120-second cadence with a detection probability greater than 10% using the
methods described by Chaplin et al. (2011a) and Schofield et al. (2019). The
gap in the grey population starting at K${}_{\mathrm{S}}\approx 4$ is present
in the full sample of short cadence targets and not enforced by the
probability cut, which only puts upper limits on $\nu_{\mathrm{max}}$ and
magnitude. It is likely the result of the TESS target selection process, which
consists of selecting stars from a number of lists including cool dwarfs,
known planet hosts, bright stars, hot subdwarfs and guest investigator targets
(Stassun et al., 2018, 2019). We did not detect solar-like oscillations in any
targets with $\nu_{\mathrm{max}}$ ¡ 5 $\mu$Hz, regardless of magnitude. As
discussed in N22, the predicted mode amplitude used in the power excess module
included the observed decrease near the red edge of the $\delta$ Scuti
instability strip. This was done via a factor which depends on
$\nu_{\mathrm{max}}$ and $T_{\mathrm{eff}}$, so that at a given temperature
amplitudes decrease as a function of frequency (Chaplin et al., 2011a). The
correction was calibrated using main-sequence stars and therefore may not be
appropriate for the most evolved targets. Indeed, at $T_{\mathrm{eff}}=4800$K
the factor decreases to approximately zero at frequencies below 5 $\mu$Hz,
which suppresses detections in the power excess module. In addition, from the
approximate relation between $\nu_{\mathrm{max}}$ and $\Delta\nu$ (Stello et
al., 2009, see Eq. 1) at a $\nu_{\mathrm{max}}$ of 5 $\mu$Hz we would expect
$\Delta\nu$ to be below 1 $\mu$Hz. This is approaching the resolution in a
single sector of TESS data (0.4 $\mu$Hz). Therefore, detections in the
repeating pattern module are also increasingly unlikely.

Figure 1: 2MASS $K_{\mathrm{S}}$ Magnitude and predicted $\nu_{\mathrm{max}}$
for stars observed in 120-second cadence with a detection probability
exceeding 10% (grey). The targets which we identified as solar-like
oscillators are marked in blue. Table 2: Seismic parameters

[table head = TICID No. Sectors RP PE $\nu_{\mathrm{max}}$ ($\mu$Hz)
$\sigma(\nu_{\mathrm{max}})$ ($\mu$Hz) $\Delta\nu$ ($\mu$Hz)
$\sigma(\Delta\nu)$ ($\mu$Hz) sample Flag
]example_of_submission.csv 333Catalogue of seismic parameters for detected
solar-like oscillators. The full table is available in online materials.
Quantities RP and PE track which modules the target produced a detection in.
Flag is ‘SB9’ for targets in the Ninth Catalogue of Spectroscopic Binary
Orbits (Pourbaix et al., 2004) and ‘PH’ for targets which are confirmed planet
hosts according to NASA’s Exoplanet Archive.

###  4.1 Literature Sample

Of the 13 solar-like oscillators drawn from the literature, the algorithm
flagged a detection in both modules for 11 stars. $\mu$ Ara produced a
response in the power excess module, but not the repeating pattern.
Oscillations in this star have thus far only been detected in Doppler velocity
(Bouchy et al., 2005). As the signal from granulation is lower relative to the
modes in velocity measurements than in photometry (Basu & Chaplin, 2017), the
single module response is likely just an effect of the decreased signal-to-
noise. The remaining star, HD19916, did not produce a flag in either module.
Although oscillations in HD19916 have been detected in TESS 120-second cadence
data the authors note that a custom aperture had to be used, expanding to
include more of the stellar flux (Addison et al., 2021). To maintain
consistency with the rest of our catalogue, we did not mimic this approach. We
note that the stars with detections reported in 20-second data ($\gamma$ Pav,
$\pi$ Men and $\alpha$ Men) produced flags in both modules. However, if we use
the available 120-second data for the same stars, one is not detected at all
($\pi$ Men) and the others are only detected in the power excess module,
despite oscillating at frequencies well below the corresponding Nyquist
frequency limit. The improvement made by the 20-second data was highlighted by
Huber et al. (2022).

###  4.2 Asteroseismic Target List

To construct the set of stars used to establish the performance of the
detection algorithm in N22, a manual inspection of the 11,220 spectra
discussed in Sect. 2 was performed. On the construction of the the sets of 400
oscillators and 400 ‘non-oscillators’, several stars fell into the category of
targets where, although some excess power was present in the spectrum, we were
unable to unambiguously classify the target as a solar-like oscillator. Since
that work was done, new sectors of data had become available, which could
facilitate unambiguous classification. We therefore re-ran the algorithm on
the full set of 11,220 spectra. With the testing set of oscillators from N22
removed, 2651 stars were flagged in just one module and 490 in two. Of the
single module detections, the vast majority were false positives presenting
some large non-solar type signal rather than solar-like oscillations (such as
periodic dips caused by a transit, eclipse, or classical oscillations). Such
stars were not included in the metrics stated in N22. Including these stars in
the false-positive metric for a single module response increases the
percentage to $\approx$20%. In total (with the testing set included) we
detected 494 solar-like oscillators with responses in both modules, and
another 258 with a single module response.

###  4.3 Large Sample

For the 255,089 stars for which we analysed light curves, we expect a false
positive rate of 8.2%. Assuming the majority are not solar-like oscillators,
this would equate to false positives in the range of $\approx$20,000. We found
37,250 flagged in at least one module, therefore we took the more conservative
approach and performed a manual inspection of stars that produced a flag in
both modules. Of the 5,781 stars which produced flags in both modules, we
found 2,927 clear solar-like oscillators. We have retained the list of single-
module responses, but reserve releasing it until they have been manually
vetted, to avoid confusion. Unlike the ATL sample, we have relaxed the
requirement that $\nu_{\mathrm{max}}$ exceeds 240 $\mu$Hz. This gives a set of
targets which are cooler on average, and more strongly peaked in magnitude
(see Fig. 11 and 10).

###  4.4 20-second cadence

Of the 6157 stars in this set, the algorithm produced a single module response
for 1585, and a double module response for 421. Upon visual inspection of
these targets, we were able to clearly identify 490 solar-like oscillators.

Table 3: Detection counts in each sample. ‘Double’ refers to cases where the star flagged a detection in both the power excess and repeating pattern modules. ‘Single’ refers to cases where the star flagged in one module only. Sample |  Double |  Single |  Total
---|---|---|---
Literature |  11 |  1 |  12
ATL |  494 |  258 |  752
Large |  2927 |  - |  2927
20-sec |  288 |  198 |  486
Total |  3720 |  457 |  4177
Figure 2: Top panel: Mean simulated collapsed ACF as a function of $\Delta\nu$
for filtered white noise. Colours represent time series of different lengths,
with one sector in black, four in blue, nine in green and twelve in magenta.
Pale lines show the predictions for each length according to Eq. 2. Bottom
panel: Variance on the simulated collapsed ACF presented in the top panel.
Figure 3: Main panel shows an asteroseismic HR diagram for stars in all
samples (orange circles). Effective temperatures have been drawn from the TIC
in all cases, to maintain consistency. Contour lines represent measurements
from Kepler data reported in Yu et al. (2018), Lund et al. (2017) and
Serenelli et al. (2017), with effective temperatures from GDR2. The horizontal
dashed line represents the Kepler long cadence Nyquist frequency. Three
stellar tracks at masses 1.0, 1.5 and 2.0 M⊙ generated by MIST (Choi et al.,
2016) are shown in grey. The distributions in $\,T_{\mathrm{eff}}$ and
$\nu_{\mathrm{max}}$ are shown in the bottom and right panels, respectively.
Here, the catalogue is split into the ATL set in turquoise and the Large
Sample in pink (dashed) with the Kepler distribution shown in black. Figure 4:
A comparison of the global asteroseismic parameters measured by our algorithm
to those reported in the literature. Stars are coloured by the number of
modules in which they produce a flag; pink for a single module, brown for two
modules and an open grey marker for none. Triangles represent stars for which
no uncertainty on $\nu_{\mathrm{max}}$ was reported in the literature. Targets
$\lambda^{2}$ For, $\nu$ Ind and HD212771 which are discussed in the text are
marked with a diamond, circle and square respectively. The left and right
panels show the fractional difference between the values of
$\nu_{\mathrm{max}}$ and $\Delta\nu$ as measured by the algorithm versus
literature value respectively.

Figure 5: The main panel shows $\Delta\nu$ as a function of
$\nu_{\mathrm{max}}$ measured by the algorithm for validated solar-like
oscillators from the ATL set. Stars producing flags in only one module are
shown in pink, those producing flags in both modules are shown in brown.
Triangles mark stars that were likely misclassified as solar-like oscillators.
Targets TIC381975502 and TIC271701447 which are discussed in the text have
been marked with a diamond and circle. The black dotted line shows Eq. 1.
Additional panels show the fractional uncertainties on $\Delta\nu$ and
$\nu_{\mathrm{max}}$.

.

##  5 Global asteroseismic parameters

Table 4: Parameters for Eq. 2 and 3. Parameter | Value
---|---
$B$ | 1.54
$\alpha$ | 0.65
$\beta$ | 0.36
$c$ | 0.34

Alongside enabling detection, the probability distributions calculated in the
detection process allow us to measure the global asteroseismic parameters
$\Delta\nu$ and $\nu_{\mathrm{max}}$. There are already a number of pipelines
dedicated to measuring these parameters via different methods (Huber et al.,
2009; Hekker et al., 2010; Kallinger et al., 2010; Mathur et al., 2010; García
et al., 2014; Elsworth et al., 2017; Zinn et al., 2019). However, as the main
aim of this work is the construction of a list of solar-like oscillators, a
full comparison between our method and such alternatives is reserved for
future work.

The probability distribution as a function of frequency calculated by the
frequency spacing method (see Sect. 4) was normalized to unit integral over
the spectrum, producing a probability density. The 50th percentile of this was
used to measure $\nu_{\mathrm{max}}$, with the 16th and 84th percentiles
giving the confidence interval.

N22 only required the ACF collapsed along the lag ($\tau$) axis to perform a
detection. To determine $\Delta\nu$ we instead collapsed along test frequency.
Rather than summing the ACF for all test frequencies at a given lag, we
exploited the approximate relation between $\nu_{\mathrm{max}}$ and
$\Delta\nu$ (Stello et al., 2009),

$\frac{\tilde{\nu}_{\mathrm{max}}}{\nu_{\mathrm{max,\odot}}}=\bigg{(}\frac{\Delta\nu}{\Delta\nu_{\odot}}\bigg{)}^{a},$
(1)

where we took the value $a$ = 0.791 as in N22. This estimate of
$\nu_{\mathrm{max}}$ at a given $\Delta\nu$ ($\tilde{\nu}_{\mathrm{max}}$)
allowed us to restrict the range of frequencies summed. Accordingly, we only
summed bins in the range
$|\nu_{\mathrm{max}}-\tilde{\nu}_{\mathrm{max}}|<0.2\tilde{\nu}_{\mathrm{max}}$.

To calculate the expectation from a spectrum devoid of oscillations we
utilized 103 white noise realizations. Similarly to N22 we found that, for
filtered white noise, the noise statistics can be well approximated by a
$\Gamma$ distribution in lag. The mean of this distribution can be described
by the empirical relation

$\mu(\tau)=A(B+\tau^{\alpha}/N_{\nu}^{\beta}),$ (2)

where $N_{\nu}$ is the number of frequency bins included in the calculation of
the ACF at a given $\tau$. Utilizing the emcee package (Foreman-Mackey et al.,
2013) we fitted for the parameters $B$, $\alpha$ and $\beta$, the results of
which can be found in Table 4. The parameter $A$ is a calibration constant
which depends on the time series length and was determined on a star-by-star
basis. Using Eq. 1 to estimate the value of $\Delta\nu$
($\widetilde{\Delta\nu}$) given the measured value of $\nu_{\mathrm{max}}$, we
masked the ACF in the range 0.7$\widetilde{\Delta\nu}$ ¡ $\Delta\nu$ ¡
1.3$\widetilde{\Delta\nu}$. The calibration factor $A$ was then estimated by
the ratio of the modelled to observed ACF in the first 5 $\mu$Hz and final 50
$\mu$Hz (with the latter range accounting for the decrease in frequency
resolution at small lag).

We found that the variance in the collapsed ACF can be approximated by,

$\sigma(\tau)^{2}=c\mu(\tau)^{2},$ (3)

with the value of $c$ determined by a fit to the white noise simulations (see
Table 4). A comparison of the predictions from Eq. 2 and 3 to simulations of
different time series length can be seen in Fig. 2. We also tested the model
on data binned to different effective lengths. The net effect of the binning
is an additional multiplicative factor, which is accounted for in the
calibration.

We used Eq. 2 and 3 to establish the probability ($P_{\Delta\nu}$) that the
collapsed ACF ($r$) at a given value of $\tau$ is inconsistent with noise.
Logarithmic probabilities were used for numerical stability. Given that the
envelope will cause an excess above the mean, we can label any divergences
below the mean as noise. Therefore the natural choice is the survival
function,

$\log
P_{\Delta\nu}=-\log\left(\int_{r}^{\infty}\frac{\beta^{\alpha}}{\gamma(\alpha)}r^{\prime,\alpha-1}\mathrm{exp}(-\beta
r^{\prime})dr^{\prime}\right),$ (4)

where the shape parameter is $\alpha(\tau)=(\mu(\tau)/\sigma(\tau))^{2}$ and
the scale parameter $\beta(\tau)=\mu(\tau)/\sigma(\tau)^{2}$. Normalizing
$P_{\Delta\nu}$ to unit integral over the $\Delta\nu$ axis produces a
probability density. The 50th percentile of this was used to measure
$\Delta\nu$, with the 16th and 84th percentiles giving the confidence
interval.

In the following sections we discuss the values of $\Delta\nu$ and
$\nu_{\mathrm{max}}$ in each of our samples. We utilize our literature sample
to briefly comment on the robustness of our methods in TESS data compared to
results produced largely from bespoke analysis of individual stars. We then go
on to discuss the results in the remaining new detections. A summary of the
catalogue can be seen in Fig. 3. We note that in some targets, values of
$\Delta\nu$ may be reported despite the star not producing a flag in the
repeating pattern module. To report a detection we require that the repeating
pattern merit function exceeds a threshold that was chosen as the best balance
between the false positives and false negatives. Therefore, a star could
produce a measurable response in the collapsed ACF, while the merit function
peaks just below the selected threshold. Accordingly, we only removed
measurements from the final catalogue that were manually identified as clear
outliers in the $\nu_{\mathrm{max}}$-$\Delta\nu$ plane. The values that have
been removed shown in Fig 9 of the appendix.

###  5.1 Literature Sample

Of the 13 targets making up the sample, 9 have published $\nu_{\mathrm{max}}$
values with uncertainties. In the remaining stars, the authors focussed on
determining individual frequencies rather than global parameters, and so
estimates of $\nu_{\mathrm{max}}$ without uncertainties were published. A
comparison of the literature values to those measured by our method can be
seen in Fig. 4. On average, the measured values of $\nu_{\mathrm{max}}$ are
larger than those reported in the literature by $\approx$ $2.5\%$. The star
with largest fractional difference is HD 212771, where our value of
$\nu_{\mathrm{max}}$ is larger by $\approx$ $9\%$. The literature value was
measured using FFI data processed by the TESS Asteroseismic Science Operations
Center (TASOC) pipeline (Handberg et al., 2021). From visual inspection of the
signal-to-noise spectrum of HD 212717 we found the envelope extended beyond
the FFI Nyquist frequency. The attenuation caused by the sampling integration
causes a decrease in power near the Nyquist frequency, which could have caused
an underestimate on $\nu_{\mathrm{max}}$ in Silva Aguirre et al. (2020).
Visual inspection of the power spectra confirms our higher value is more
accurate.

In total 11 stars have measurements of $\Delta\nu$ in the literature. In the
case of $\nu$ Ind, the most recent asteroseismic study was made in Chaplin et
al. (2020), where the authors used a single sector of TESS data to fit
individual modes. We measured $\Delta\nu$ from the gradient of a linear fit to
the radial mode frequencies as a function of order (White et al., 2011). We
took the same approach for $\lambda^{2}$ For where the authors also did not
provide estimates of $\Delta\nu$ (Nielsen et al., 2020). A comparison of the
values with those from the algorithm can be seen in the right panel of Fig. 4.
The agreement is better than for $\nu_{\mathrm{max}}$, with a mean fractional
difference on $\Delta\nu$ of $0.24\%$.

###  5.2 Asteroseismic Target List

Of the 752 validated solar-like oscillators, we report both $\Delta\nu$ and
$\nu_{\mathrm{max}}$ for 739. In the majority of cases the determination of
the two goes hand-in-hand, with both coming from the autocorrelation function
collapsed along the relevant axis. However it is possible to detect the
envelope without a signal from the frequency spacing.

In order to assess the quality of the measured $\nu_{\mathrm{max}}$ and
$\Delta\nu$ values, we exploit the approximate scaling relation between the
two (Eq. 1). Although there is a slight mass dependence in the exponent $a$
(Stello et al., 2009), the general trend remains such that stars disagreeing
significantly with the rest of the population may indicate an error in one (or
both) of the measured values.

Fig. 5 shows the relation between the values of $\nu_{\mathrm{max}}$ and
$\Delta\nu$ for the targets in the ATL sample. The majority of the stars with
detections in both modules follow Eq. 1. The star with smallest $\Delta\nu$ is
TIC 381975502 (CD-56 1110). Here, a background eclipsing binary introduced
several harmonic peaks in the power spectral density at low frequency. These
appear in the ACF as a large response at a test frequency corresponding to the
frequency of the orbital harmonics, resulting in the algorithm incorrectly
assigning both $\Delta\nu$ and $\nu_{\mathrm{max}}$. This is also the case for
TIC 271701447 (HR 4749; HD 108570). The values of $\nu_{\mathrm{max}}$ and
$\Delta\nu$ for these targets have been removed from the final catalogue,
while IDs have been retained.

For targets detected in just one module there is a larger scatter about the
scaling relation as shown on Fig. 5. Using an exponent on Eq. 1 of $a=0.791$
as calculated in N22, $\Delta\nu$ for 13 targets differs by more than 30% from
the value predicted by the scaling relation and measured value of
$\nu_{\mathrm{max}}$. We performed a manual inspection of these stars and
found four are likely misclassifications. A further two passed the detection
threshold, both at the envelope and at a much lower frequency, biasing the
resulting parameters. In three stars, the estimated $\nu_{\mathrm{max}}$ used
in the prior was significantly higher than the observed value, being
overestimated by factors of three, five and two. In these cases, the
parallaxes reported in the ATL were drawn from XHIP rather than GDR2. The
$\nu_{\mathrm{max}}$ predicted using GDR2 parallaxes produced a prior more
consistent with the measured $\nu_{\mathrm{max}}$. The remaining stars could
be divided into two sets: Targets with less than one full sector of data and
high-$\nu_{\mathrm{max}}$ targets with low mode amplitudes. The resulting low
signal-to-noise could impact the determination of $\Delta\nu$. Values of
$\nu_{\mathrm{max}}$ and $\Delta\nu$ for these outliers have been removed.

In Fig. 3 the stars in the ATL sample cluster about the base of the red giant
branch and extend toward the main sequence. The peak of the distribution falls
just above the Kepler long cadence Nyquist frequency, populating the
previously sparsely sampled region. The density falls off toward higher
$\nu_{\mathrm{max}}$, which is likely a result of the decreasing mode
amplitude.

###  5.3 Large Sample

Here, we report both $\nu_{\mathrm{max}}$ and $\Delta\nu$ for all but 62
stars. For these outliers, we found similar issues to those discussed in the
ATL. Additionally, we noted 16 stars where the probability distributions in
$\nu_{\mathrm{max}}$ were multi-modal. The remaining targets vastly outnumber
those from the ATL, and span the red giant branch (as seen on Fig. 3). The
density increases with decreasing $\nu_{\mathrm{max}}$ until it peaks at
$\approx 49\mu$Hz. At the high-$\nu_{\mathrm{max}}$ tail, we note an overlap
between the ATL and Large Sample. There are 119 stars that did not appear in
the ATL, despite showing oscillations at frequencies above 240 $\mu$Hz. Of
these, just under half lie near the ATL cutoff, with
$240<\nu_{\mathrm{max}}<300\mu$Hz. A total of 63 stars, however, are above 300
$\mu$Hz in a region that should be included in the ATL. There are several
reasons why these targets could have been omitted. The estimate of
$\nu_{\mathrm{max}}$ in the ATL was a function of $T_{\mathrm{eff}}$, such
that a significant underestimate on the latter could have pushed the former
beyond the enforced 240 $\mu$Hz cut. Calculating Teff for the additional
targets using the methods stated in the ATL, we did not find a systematic
underestimate compared to GDR2, with values agreeing to within 10% in over 90%
of the targets. The other possibility is that the detection probabilities for
these targets were underestimated. This could be the result of an
overestimated noise level caused by, for example, underestimating the size of
the predicted pixel mask or a greater degree of contamination from background
sources. A full comparison between the predictions in the ATL and the observed
yield is reserved for future work.

According to the main aim of the TESS mission (Ricker et al., 2014), we
expected targets proposed for 120-second cadence would be less evolved than
the giants presented here. Although targets were also selected if they were
brighter than $T_{\mathrm{mag}}$ = 6 (where Tmag is magnitude of the star for
the TESS instrument response), which would preferentially select bright
giants, we found that $\approx$ 80% of the giants in which we detected solar-
like oscillations were fainter than this limiting magnitude. We therefore
checked that the oscillations occur in the star associated with the TIC number
being searched, rather than another star in the mask, by comparing the
$\nu_{\mathrm{max}}$ value predicted by the prior to the detected value (see
Fig. 7). In general, the ratio of the two was close to unity, indicating the
detected envelope belongs to the target in question.

Figure 6: Distribution in $\,K_{\mathrm{S}}$-band magnitude for the detections
from the Large Sample which have values of $\nu_{\mathrm{max}}>240\mu$Hz, and
those made from targets included in the ATL. Figure 7: Prior
$\nu_{\mathrm{max}}$ ($\nu_{\mathrm{max,prior}}$) versus measured values in
short cadence targets. Blue dashed line represents the 1-1 line.

###  5.4 20-Second cadence

The measured values of $\Delta\nu$ and $\nu_{\mathrm{max}}$ can be seen in
Fig. 8. A total of 16 stars were removed by manual identification. We note
that the uncertainties on $\Delta\nu$ presented in Fig. 8 appear larger than
those presented in Fig. 5 (the ATL sample), which is likely due to the
population of targets at $\nu_{\mathrm{max}}$ $<$ 100 $\mu$Hz. The mean
fractional uncertainty on the measured $\Delta\nu$ in the 20-second cadence
sample is 2.1%, approximately consistent with 1.9% in the ATL sample. Again,
we find the population is dominated by evolved stars, with the distribution
peaking at a $\nu_{\mathrm{max}}$ value of 50 $\mu$Hz.

We note the presence of a detection in an oscillator observed by Kepler (KIC
6106415; HD 177153; ”Perky”), which is a clear outlier in Fig. 8. The
algorithm reports a $\Delta\nu$ of 131 $\mu$Hz despite measuring a
$\nu_{\mathrm{max}}$ of 127 $\mu$Hz. Using Kepler data oscillations were
identified at $\nu_{\mathrm{max}}$ = 2249 $\mu$Hz (Lund et al., 2017). The
envelope we detected at 127 $\mu$Hz (which can be visually identified) appears
to be on another red giant in the pixel mask. Therefore the prior has caused
an erroneous measurement of $\Delta\nu$.

Figure 8: $\Delta\nu$ versus $\nu_{\mathrm{max}}$ for validated solar-like
oscillators from the 20-second cadence set. Stars producing flags in only one
module in pink, those producing flags in both are in brown.

##  6 Conclusions

Applying the algorithm introduced by Nielsen et al. (2022) to 120-second and
20-second cadence observations from the TESS mission spanning Sectors 1 to 46,
we have detected solar-like oscillations in a total of 4177 targets. Of these,
12 belong to a set of previously reported solar-like oscillators, 752 to stars
that appeared in the ATL and 486 were detected using 20-second cadence data.
The remaining are targets brighter than 11th magnitude in 2MASS
$K_{\mathrm{S}}$, with temperatures in the range 4500K ¡ $\,T_{\mathrm{eff}}$
¡ 6500K, observed in 120-second cadence. Since Sector 46, data for additional
sectors have been released. We leave the analysis of these and the data
collected in upcoming sectors as we approach the end of the first extended
mission for future work.

All catalogued targets have been manually vetted to confirm the presence of
oscillations. We note that signals from eclipsing binaries, classical
pulsators, or transiting planetary bodies can cause false positive detections.
Therefore, we highlight that when using the algorithm presented in N22 with
very large data sets, the more conservative approach (asking for responses in
both modules) is the most effective at reducing the amount of manual vetting
required.

We have extended the work of N22 to include methods to measure the global
asteroseismic parameters, $\nu_{\mathrm{max}}$ and $\Delta\nu$. We introduced
a new model to parameterize the collapsed ACF to produce a probability density
for $\Delta\nu$. Applying this technique to the catalogue of detections, we
measured the global asteroseismic parameters for 98% of the targets.
Overlaying these stars on the asteroseismic HR diagram ($\nu_{\mathrm{max}}$
and $\,T_{\mathrm{eff}}$) allowed us to confirm the ATL successfully
identified the least evolved stars, with little overlap in the remaining
detections. The small set of stars that appear to have been missed by the ATL
cluster about $K_{\mathrm{S}}$ = 6 mag, a region where the GDR2 astrometric
solutions are known to have inferior astrometry (Lindegren et al., 2018),
suggesting an issue in the parallaxes.

This catalogue has demonstrates the significant contribution the TESS mission
can make to the field of asteroseismology. Isolating targets from the ATL, the
increase in the number of detections between the 280 $\mu$Hz cut-off enforced
by the 30-minute FFI observations and the upper edge of our catalogue at
around 1000 $\mu$Hz is at least 2-fold on the detections made in Kepler data.
With the inclusion of the stars detected in 120-second cadence that did not
appear in the ATL, we were able to use a homogeneous data set to measure
asteroseismic values in solar-like oscillators from the subgiant regime
through the red giant branch.

###### Acknowledgements.

Funding for the TESS mission is provided by the NASA’s Science Mission
Directorate. E.J.H., W.J.B. and G.R.D. acknowledge the support of Science and
Technology Facilities Council. T.R.B. acknowledges support from the Australian
Research Council (Discovery Project DP210103119). M.B.N. acknowledges support
from the UK Space Agency. C.K. is supported by Erciyes University Scientific
Research Projects Coordination Unit under grant number DOSAP MAP-2020-9749.
D.B. acknowledges support from NASA through the Living With A Star Program
(NNX16AB76G) and from the TESS GI Program under awards 80NSSC18K1585 and
80NSSC19K0385. D.H. acknowledges support from the Alfred P. Sloan Foundation
and the National Aeronautics and Space Administration (80NSSC21K0652). T.S.M.
acknowledges support from NASA grant 80NSSC22K0475. The authors acknowledge
use of the Blue-BEAR HPC service at the University of Birmingham. This paper
includes data collected by the Kepler mission and obtained from the MAST data
archive at the Space Telescope Science Institute (STScI). Funding for the
Kepler mission is provided by the NASA Science Mission Directorate. This work
has made use of data from the European Space Agency (ESA) mission Gaia
(https://www.cosmos.esa.int/web/gaia), processed by the Gaia Data Processing
and Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, in particular the institutions
participating in the Gaia Multilateral Agreement. This publication makes use
of data products from the Two Micron All Sky Survey, which is a joint project
of the University of Massachusetts and the Infrared Processing and Analysis
Center/California Institute of Technology, funded by the National Aeronautics
and Space Administration and the National Science Foundation.

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##  Appendix A Additional Plots

Figure 9: $\Delta\nu$ as a function of $\nu_{\mathrm{max}}$ for targets in the
final catalogue in brown. Values that were removed after manual identification
are shown as open circles. Figure 10: Distribution of Teff for targets used in
the testing set of 400 oscillators from N22 compared to those in the catalogue
reported here. Figure 11: As in figure 10 with 2MASS KS magnitude