Detection of Solar-like Oscillations in Subgiant and Red Giant Stars Using 2 minute Cadence TESS Data

Based on all 2 minute cadence TESS light curves from Sector 1 to 60, we provide a catalog of 8651 solar-like oscillators, including frequency at maximum power ( νmax , with its median precision σ = 5.39%), large frequency separation (Δν, σ = 6.22%), and seismically derived masses, radii, and surface gravity values. In this sample, we have detected 2173 new oscillators and added 4373 new Δν measurements. Our seismic parameters are consistent with those from Kepler, K2, and previous TESS data. The median fractional residual in νmax is 1.63%, with a scatter of 14.75%, and in Δν it is 0.11%, with a scatter of 10.76%. We have detected 476 solar-like oscillators with νmax exceeding the Nyquist frequency of Kepler long-cadence data during the evolutionary phases of subgiants and the base of the red giant branch, which provide a valuable resource for understanding angular momentum transport.

The NASA Transiting Exoplanet Survey Satellite (TESS ) mission (Ricker et al. 2015) has provided an opportunity to study solar-like oscillations in stars across the entire sky.Previous studies had extensively used TESS data to characterize solar-like oscillators, with a primary focus on the Continuous Viewing Zones (CVZs) near the ecliptic pole due to longest observation duration (Silva Aguirre et al. 2020;Mackereth et al. 2021;Hon et al. 2022;Stello et al. 2022).Hon et al. (2021) initially used deep learning techniques to detect solar-like oscillations in red giants across the full sky on the first two years of TESS full-frame images (FFI, Sector 1 to 26), identifying about 158,000 giants with ν max .Hatt et al. (2023) detected 4,177 solar-like oscillators using both 2-minute and 20-second cadence data (Sector 1 to 46), reporting ν max and ∆ν estimates.
By the end of Sector 60, TESS had completed observations of both the north and south ecliptic hemispheres for the second time.More than half of targets with 2-minute data had been observed in at least two sectors.Longer photometric time series provide higher frequency resolution in the Fourier domain, leading to improved precision in asteroseismic measurements.In this work, we aim to perform a complete search for solar-like oscillators and provide their global seismic parameters using TESS 2-minute cadence data.In addition, by combining T eff from the Gaia DR3 Radial Velocity Spectrometer (RVS) survey (Recio-Blanco et al. 2023), we estimate stellar radii, masses and surface gravity using the seismic scaling relations.

Preliminary data selection
We download all available 2-minute cadence light curves spanning Sector 1 to 60 from the Mikulski Archive for Space Telescopes (MAST) 1 .These light curves were extracted and de-trended by the TESS Science Processing Operations Center (SPOC) pipeline (Twicken et al. 2016;Jenkins 2017).
A sample of stars selected for oscillation detection is based on the effective temperature (T eff ) and radius (R) values from the TESS Input Catalog version 8.2 (TICv8.2;Stassun et al. 2019) 1).This categorization results in 154,817 main sequence stars and subgiants, as well as 38,203 red giants.

Seismic data detection
We transform all the light curves (PDCSAP data) of our pre-selected stars (Section 2.1) into power density spectra using the Lomb-Scargle periodogram method (VanderPlas 2018).We apply a 5 σ-clipping to remove outliers, and divide the light curves by a 10-day median filter to eliminate low-frequency signals in each sector, and concatenate the light curves of all available sectors (García et al. 2011).
We detect the oscillation power excess in each power density spectrum using the collapsed autocorrelation function (collapsed ACF) method (Huber et al. 2009).First, we divide the power spectrum in equally logarithmic bins and smooth the result using an empirical 40% percentile filter to obtain a crude estimate of the back-1 Data can be found in MAST: 10.17909/t9-nmc8-f686 ground.Second, the residual power spectrum, obtained from dividing the power density spectrum by the estimated background, is segmented into overlapping subsets.The width of each subset is approximately 4∆ν exp around its central frequency (ν center ), where ∆ν exp is estimated as 0.263 × ν 0.772 center (Stello et al. 2009).For each subset, we calculate the absolute ACF and then collapse the ACF by its referring ν center .Finally, we smooth the collapsed ACFs with an empirical 7 µHz filter and fit them with a Gaussian profile centered on their maximum peak, along with constant noise.
We retain stars with a signal-to-noise ratio(SNR) greater than 1.5, and identify 7,870 solar-like oscillators.For stars with 1.2 ≤ SNR ≤ 1.5, we carefully visually inspect their power density spectra for the presence of power excess, and confirm 209 oscillators.The 8,080 solar-like oscillators are shown in Figure 1 (blue dots), including 61 main sequence stars and subgiants, and 8,019 red giants.This indicates a solar-like oscilla- tion detection rate of approximately 20% in red giants.Furthermore, we repeat the same procedure for stars not presented in TICv8.2 and identify an additional 571 oscillators.In total, we have identified an asteroseismic sample of 8,651 stars.
Figure 2 illustrates the distribution of the sample across the ecliptic celestial sphere, covering nearly the entire sky.TESS focused on a specific segment of the ecliptic during the fourth year, spanning from Sector 42 to 46, to coincide with the portion of the K2 observation zones.Consequently, some stars (green dots) were observed for 2-3 sectors near the ecliptic.In order to minimize the contamination from stray Earth-and moonlight, TESS boresights toward a latitude of +85 • in some sectors, which leads to an incomplete coverage of the northern hemisphere at low latitudes.The black dashed circles within 20 • of the northern and southern ecliptic poles represent the CVZs.

Measuring the frequency at maximum power
We use the center of the fitted Gaussian profile to the collapsed ACF (Section 2.2) as the initial ν max,guess .To fit the power density spectrum, we employ a model that consists of a Gaussian envelope, three background Har- (1) where η(v) = sinc (πν/2ν nyq ) accounts for the frequency-dependent attenuation resulted from the observational signal discretization, and ν nyq is the Nyquist frequency (e.g., Chaplin et al. 2011b;Kallinger et al. 2014).For other parameters, a i and b i represent the root-mean-square (rms) and the characteristic frequency of the ith Harvey component, respectively.H g , ν max , and σ are the height, the central frequency, and the width of the Gaussian envelope, respectively.W n corresponds to the contribution of white noise.

Measuring the large frequency separation
We use the ACF method to measure ∆ν values (Huber et al. 2009;Chontos et al. 2022), shown in Figure 4. Figure 4(a) displays the échelle diagram of the oscillation modes.To prepare for the ∆ν measurement, we first normalize the power density spectrum by dividing it by the MCMC-fitted background (Gaussian component excluded).Then, we restrict the normalized power density spectrum to the frequency range of ν max ±3∆ν exp , as shown in Figure 4 (b).Within this frequency range, we calculate the ACF and apply a boxcar filter with an empirical width of 0.2∆ν exp .Finally, ∆ν is measured as the maximum value within the range of 0.7-1.3∆ν exp in the smoothed ACF, as depicted in Figure 4(c).
To evaluate the significance of the ∆ν measurements, we calculate SNR through dividing the maximum value of normalized Fourier transforms (FT) on the ACF by the noise, corresponding to the half of ∆ν or ∆ν.The noise is represented by the rms of the normalized FT on the ACF, as shown in Figure 4(d).Consequently, we obtain a sample of 7,509 stars with valid ∆ν measurements, adopting only ∆ν measurements with SNR ≥ 3.
Following Huber et al. ( 2011), the uncertainties of ∆ν are estimated by conducting 500 perturbations on the power-density spectrum using a χ 2 distribution with two degrees of freedom.For each perturbation, the fitting procedure is repeated, and the standard deviation of 500 measurements is considered as the uncertainty.

Asteroseismic Sample
We present an asteroseismic sample of 8,651 solar-like oscillators with ν max , including 7,509 stars with ∆ν.Notably, 2,173 stars from this sample are new oscillators that were not previously detected (Hon et al. 2021(Hon et al. , 2022;;Hatt et al. 2023).Compared to Hatt et al. ( 2023), we add 4,373 new ∆ν of stars.Additionally, we flag 781 binaries and 85 exoplanet host stars by cross-matching the sample with Spectroscopic Binary Orbits Ninth Catalog3 , NASA Exoplanet Archive4 , the TESS Eclipsing Binary Catalog5 , and Gaia DR3 nss two body orbit Catalog, respectively (Pourbaix et al. 2004;Howard et al. 2022;Prša et al. 2022;Gaia Collaboration 2022).The results are listed in Table 1.
Figure 5 shows the histogram of relative uncertainties for ν max and ∆ν.The number of sectors (N sectors ) marks the observation duration, with longer duration corresponding to lower uncertainties.This indicates that longer duration significantly improves measurement precision.
Figure 6 shows the well-established power-law relation of ν max and ∆ν (Stello et al. 2009;Hekker et al. 2009).The black dotted line is expressed as ∆ν = α • (ν max ) β .It is fitted by an MCMC method, and consequently, we obtain α = 0.236 ± 0.001 and β = 0.789 ± 0.001 .The ν max and ∆ν exhibit a linear relation in logarithmic coordinates, especially for stars with σ(∆ν)/∆ν ≤ 0.1.The stars having ∆ν precision worse than 0.1 and ν max ∼ 20-100µHz, may correspond to red clump (RC), as they exhibit complex power spectra (Hon et al. 2017).The number of our sample increases with Tmag at Tmag < 5, which is consistent with the overall sample.However, for Tmag > 9, the number of oscillators significantly decreases with increasing TESS magnitude.This suggests an optimal magnitude range of 6 ≤ Tmag ≤ 9 for observing solar-like oscillations.Additionally, there is a gap around Tmag = 7, consisting with Hatt et al. ( 2023).The gap exists in both all 2-minute cadence targets and our sample.We examined the histogram of TESS magnitude for each sector from Sector 1 to 60 and found the gap in each of them.It possibly results from the inhomogeneous selection for TESS observations of 2-minute cadence data.

Comparison of ν max and ∆ν Measurements
In Figure 8, we compare our global seismic parameters with those of common stars from literature.The results demonstrate good agreement, despite the differences in the methods and data.The median fractional residual in ν max is 1.63% with a scatter of 14.75%, while the median fractional residual in ∆ν is 0.11% with a scatter of 10.76%, as shown in Table 2.
Figure 9 shows the distribution in ν max -ν 0.75 max /∆ν for our sample and stars in Kepler /K2 long-cadence data and TESS 2-minute data from Hatt et al. ( 2023).Compared to Kepler /K2 sample, on the one hand, there are fewer high-luminosity red giants in our sample, because our oscillators were observed within shorter duration.On the other hand, near the Nyquist frequency, it is possible to measure ∆ν with long-cadence data but challenging to measure ν max , because the granulation background fitting could be biased and Nyquist aliases may occur (Yu et al. 2016(Yu et al. , 2018)).In this context, TESS 2minute cadence data prove valuable.
Notably, we have detected 401 solar-like oscillators with ν max exceeding the Nyquist frequency of Kepler /K2 long-cadence data.These oscillators are moreevolved subgiants or low-luminosity red giants, whose solar-like oscillation were seldom detected by either longor short-cadence observation of the previous Kepler /K2 mission.Such stars transform from nearly-uniform rotation to differential rotation, helping us to understand angular momentum transport (e.g., Aerts et al. 2019;Deheuvels et al. 2020;Kuszlewicz et al. 2023;Wilson et al. 2023).

Fundamental stellar parameters
By cross-matching our sample to Gaia DR3 RVS spectra data, we obtain 7,173 stars with asteroseismic parameters and T eff .We estimate radius (R seismic ), mass  (M seismic ), and surface gravity (log g) of these stars by the scaling relations (Ulrich 1986;Brown et al. 1991;Kjeldsen & Bedding 1995;Belkacem et al. 2011): where ν max,⊙ = 3090 µHz, ∆ν ⊙ = 135.1 µHz, and T eff,⊙ = 5777 K adopted from Huber et al. (2013).The estimates of M seismic , R seismic , and log g are listed in Table 3, with their median uncertainties of 9.20%, 6.24% and 0.01 dex (0.79%), respectively.To validate our asteroseimic radii, we use another independent method to derive radii and luminosities for these stars.We employ the SEDEX pipeline (Yu et al. 2021(Yu et al. , 2023) ) alongside MARCS model spectra for performing the spectral energy distribution (SED) fitting.Our approach adopts spectroscopic T eff , log g, and [M/H] priors (from Gaia DR3 RVS spectra) and com- Note-Catalog of fundamental stellar parameters for 7,173 stars.T eff are collected from Gaia DR3 RVS spectra, the stellar Mseismic,Rseismic and log g are provided by scaling relations, RSED and LSED obtained through the SED fitting.The machine-readable table is fully accessible.bines them with apparent magnitudes from 32 band passes across nine photometric databases (Yu et al. 2023) to derive both extinction and bolometric fluxes.
Leveraging Gaia DR3 parallaxes, we then compute luminosities and deduce stellar radii in conjunction with the spectroscopic T eff .The uncertainties in bolometric fluxes are assessed through a Bayesian framework, and the uncertainties in luminosities and radii were determined via error propagation given T eff uncertainties.It is noted that the above two methods adopt the same effective temperature, implying that the measurements in both approaches may be subject to potential systematic effects related to T eff .Figure 10 shows the comparison between R seimic and R SED .The result reveals a good agreement, with a median fractional residual of −0.79% and a standard deviation of 16.60%.This consistency is partly attributed to employing the same effective temperature in both measurements.The estimates of R SED and L SED are also listed in Table 3.

CONCLUSIONS
We have presented a sample of 8,651 solar-like oscillators with ν max measurements, including 7,509 stars with ∆ν using TESS 2-min cadence light curves.Comparing with literature, we have newly detected 2,173 oscillators and added 4,373 ∆ν measurements.Our seismic parameters demonstrate good consistency with those from previous studies.The median fractional residual for ν max is 1.63% with a scatter of 14.75%, and the median fractional residual for ∆ν is 0.11% with a scatter of 10.76%.
We have detected 476 solar-like oscillators that exhibit ν max values exceeding the Nyquist frequency of Kepler /K2 long-cadence data, which increases the sample size of more-evolved subgiants and low-luminosity red giants.Such oscillators may provide observational constraints on the stellar internal rotation profiles, which potentially contributes to our understanding of angular momentum transport.
We have estimated asteroseismic masses (with a median precision of 9.21%), radii (with a median precision of 6.24%), and log g for a subset of 7,173 stars crossmatched from Gaia DR3 RVS spectra data.Our asteroseismic radii are in good agreement with the radii from the SED fitting.
Our sample covers the entire sky, showing the advantage of the TESS mission to detect solar-like oscillators.With further observations by TESS , a greater number and diversity of potential solar-like oscillators are expected to be detected.This will provide valuable observational targets for future missions, such as PLATO (to be launched in 2026; Rauer et al. 2014) , which will significantly improve observations of stars with detectable solar-like oscillations.A higher-precision sample of solar-like oscillators spanning from main sequence stars to red giants, will provide new perspectives on stellar structure and evolution.
, with criteria of 1R ⊙ ≤ R ≤ 40 R ⊙ and 3700K ≤ T eff ≤ 7000K.This resulted in the identification of 193,020 candidates, depicted as gray dots in Figure 1.To categorize the stars into dwarfs and giants, we employ the relation R = 10 p R ⊙ , with p = T eff (K.(2019) as the boundary (indicated by the red dashed line in Figure

Figure 1 .
Figure 1.R versus T eff for 2-minute cadence targets and seismic targets.The T eff and radii are sourced from TICv8.2.Light gray dots show the 2-minute cadence targets, blue dots show the seismic targets, and the red dashed line, reference from Hon et al. (2019), shows the boundary used to distinguish early sub-giant stars from those ascending the red giant branch.

Figure 2 .
Figure 2. The distribution of detected solar-like oscillators across the celestial sphere.The color bar corresponds to the observation duration, denoted by the number of sectors.Some stars (green dots) are observed for 2-3 sectors near the ecliptic because TESS focused on a specific segment of the ecliptic from Sector 42 to 46 coinciding with the portion of the K2 observation zones.The northern ecliptic hemisphere contains gaps to avoid excessive contamination from stray Earth-and moonlight, and the corresponding region appears at low latitudes close to the ecliptic.The black dashed circles represent the CVZs.

Figure 3 .
Figure 3. Representative power spectra of TESS 2-min cadence light curves.In each panel, the gray line shows the real data, and the black line shows the data smoothed by a boxcar filter of 3 µHz wide.The solid blue line shows the MCMC fitting result, with the red dashed line for the fitted Gaussian envelope, the green dashed curve for the three Harvey components, and the brown straight line for the white noise.The inset figure shows the power spectrum near νmax divided by the background.

Figure 4 .
Figure 4.An example of measuring ∆ν for TIC 38828538 : (a) the échelle diagram, the red dashed line represents the value of νmax; (b) the residual power spectrum; (c) the autocorrelation function, the two red dashed lines represent the positions of ∆ν and twice ∆ν from left to right; (d) the Fourier transforms of ACF, the two red dashed lines represent the positions of half of ∆ν and ∆ν in period from left to right, the blue dashed line shows noise.vey components, and white noise (Chaplin et al. 2014): We estimate ν max and its uncertainty by Bayesian inference using Monte Carlo Markov Chain (MCMC) simulations(Foreman-Mackey et al. 2013).The initial fitting parameters for MCMC are from the Maximum Likelihood Estimation (MLE) method 2 (Huber et al. 2009;Kallinger et al. 2010).The minimum number of steps for the MCMC estimation is 3000 and the maximum number of steps is 5000.The ν max is estimated as the median of the posterior probability distribution, and the uncertainties are approximated as the 16 th /84 th percentiles.Representative examples of the background fitting are shown in Figure3.

Figure 5 .
Figure 5. Histogram of relative uncertainties for νmax and ∆ν.Nsectors shows the number of sectors.The gray line represents the entire sample, while the purple, blue, yellow, and red lines represent stars observed for 1 to 2 sectors, 3 to 4 sectors, 5 to 13 sectors, and stars observed for more than 14 sectors, respectively.

Figure 7 .
Figure 7. Histogram of TESS magnitude (Tmag) for all 2-minute cadence targets and the seismic stars.The gray color shows all 2-min cadence targets, the blue color shows oscillators with νmax, and the red color shows stars with ∆ν.

Figure 7
Figure7shows the histogram of TESS magnitude (Tmag) for all 2-minute cadence stars and our sample.The number of our sample increases with Tmag at Tmag < 5, which is consistent with the overall sample.However, for Tmag > 9, the number of oscillators significantly decreases with increasing TESS magnitude.This suggests an optimal magnitude range of 6 ≤ Tmag ≤ 9 for observing solar-like oscillations.Additionally, there is a gap around Tmag = 7, consisting with Hatt et al. (2023).The gap exists in both all 2-minute cadence targets and our sample.We examined the histogram of TESS magnitude for each sector from Sector 1 to 60 and found the gap in each of them.It possibly results from the inhomogeneous selection for TESS observations of 2-minute cadence data.

Figure 8 .
Figure 8.Comparison between global seismic parameters measured in this work and those from previous literature.The black dashed lines in the top panel show the one-to-one relation between the two parameters.The bottom left panel shows the fractional residuals of νmax, calculated as (ν max,literature − ν max,this work ) /ν max,this work .Similarly, the bottom right panel displays the fractional residuals of ∆ν, calculated as (∆ν literature − ∆ν this work ) /∆ν this work .

Figure 9 .
Figure 9. νmax vs. ν 0.75 max /∆ν diagram.The horizontal axis shows νmax, while the vertical axis shows ν 0.75 max /∆ν, which is a mass proxy related to temperature.The gray triangles and crosses represent samples from Kepler and K2 long-cadence data, respectively.Blue dots show sample from previous TESS 2-minute data as presented by Hatt et al. (2023) and yellow dots show our sample.

Figure 10 .
Figure 10.Comparisons of radii from the asteroseismic scaling relations with radii from the SED fitting.The color bar represents the relative error of ∆ν.The bottom panel displays fractional residuals between radius estimates, denoted as ∆R = RSED − Rseismic.

Table 1 .
Stellar Global Oscillation Parameters Note-The source of the adopted stellar types for each star is indicated by the following: (1) Spectroscopic Binary Orbits Ninth Catalog, (2) the TESS eclipsing binary catalog, (3) NASA's Exoplanet Archive, (4) Gaia DR3 nss two body orbit Catalog.SNR indicates the signal-to-noise ratio of ∆ν.The machine-readable table is fully accessible.

Table 2 .
Comparison of Global Seismic Parameters with Previous Literature

Table 3 .
Fundamental stellar parameters