Benchmarking the spectroscopic masses of 249 evolved stars using asteroseismology with TESS

ABSTRACT

One way to understand planet formation is through studying the correlations between planet occurrence rates and stellar mass. However, measuring stellar mass in the red giant regime is very difficult. In particular, the spectroscopic masses of certain evolved stars, often referred to as ‘retired A-stars’, have been questioned in the literature. Efforts to resolve this mass controversy using spectroscopy, interferometry, and asteroseismology have so far been inconclusive. A recent ensemble study found a mass-dependent mass offset, but the result was based on only 16 stars. With NASA’s Transiting Exoplanet SurveySatellite (TESS), we expand the investigation of the mass discrepancy to a total of 92 low-luminosity stars, synonymous with the retired A-stars. We measure their characteristic oscillation frequency, |$\mathrm{\nu }_{\mathrm{max}}$|⁠, and the large frequency separation, |$\mathrm{\Delta \nu }$|⁠, from their TESS photometric time series. Using these measurements and asteroseismic scaling relations, we derive asteroseismic masses and compare them with spectroscopic masses from five surveys, to comprehensively study the alleged mass-dependent mass offset. We find a mass offset between spectroscopy and seismology that increases with stellar mass. However, we note that adopting the seismic mass scale does not have a significant effect on the planet occurrence-mass-metallicity correlation for the so-called retired A-stars. We also report seismic measurements and masses for 157 higher luminosity giants (mostly helium-core-burning) from the spectroscopic surveys.

1 INTRODUCTION

Correlations between the planet occurrence rate and host star properties, in particular stellar mass, can inform us about planet formation (e.g. see Fischer & Valenti 2005; Johnson et al. 2010; Dawson & Johnson 2018; Ghezzi, Montet & Johnson 2018; Yang, Xie & Zhou 2020; and Wolthoff et al. 2022). For this, it is important to sample stars across a large range of masses, including those significantly more massive than the Sun. However, the main-sequence A- and hot F-type stars have broad spectral lines making radial velocity measurements less precise. Hence, radial velocity planet searches have been biased against intermediate-mass A- and hot F- type stars. To circumvent this difficulty in finding planets around the intermediate-mass A- and hot F-type stars, Johnson et al. (2006) set out to find planets around their cooler, more evolved counterparts in the subgiant and red giant regimes. They referred to these stars as ‘retired A’-stars. However, A- and F-progenitors that ascend the red giant branch become difficult to distinguish from their G- and K- counterparts because of their similar temperatures (⁠|$T_{\mathrm{eff}}$|⁠) and luminosities (L), leaving stellar mass as the only way to differentiate between these stars. Thus, accurately determining the stellar mass of these evolved stars is important.

Traditionally, stellar masses are determined using spectroscopy and grid-based modelling via isochrone fitting. Lloyd (2011) compared the masses of a selection of evolved planet-hosting stars from the Exoplanet Orbit Data base¹ (Wright et al. 2011) with a sample of field stars with similar mass (M) and surface gravity (⁠|$\log g$|⁠) from the catalogues by Allende Prieto & Lambert (1999) and Glebocki & Gnacinski (2005). Lloyd (2011) discovered a discrepancy between the mass distributions for the samples of evolved planet-hosting stars from the Exoplanet Orbit Data base and the field stars and suggested the masses of these evolved planet-hosting stars were overestimated by up to 50 per cent. They attributed the deficit of massive evolved planet-hosting stars in their sample to the differences in evolution speeds of stars with different stellar masses. Massive stars evolve faster than less-massive stars and are hence less common, and the failure to account for this difference in evolution speeds of stars in grid-based modelling may lead to erroneous determination of the stellar mass.

Later, Johnson, Morton & Wright (2013) benchmarked their apparent-magnitude-limited subgiant sample against Galactic stellar population models by Girardi et al. (2005) and found no such overestimation in spectroscopic masses. Johnson et al. (2013) argued that their imposed apparent magnitude limit partially counteracted the lower number of massive stars expected from their differential evolution by increasing the relative number of massive stars. However, Lloyd (2013) used apparent magnitude-limited weights for the isochrone integration in his 2011 calculations and argued that irrespective of such limit used in target selection, there was a deficit of massive stars in the subgiant and red giant regime compared to what was reported in the literature. Supporting this argument by Lloyd (2013) and Schlaufman & Winn (2013) found consistency between the velocity dispersions for their subgiant sample and their main-sequence F5-G5 sample, but not with their main-sequence A0-F5 sample. This consistency led them to conclude that their subgiants are less-massive than main-sequence A0-F5 stars.

In addition to the spectroscopy-based mass determinations, the retired A-star mass controversy has been explored using other methods like asteroseismology and interferometry. Asteroseismology, in particular, can provide us with precise model-independent stellar masses (Stello et al. 2008; Kallinger et al. 2010; Chaplin & Miglio 2013; Gaulme et al. 2016; Huber et al. 2017; Yu et al. 2018) while long-baseline interferometry provides better constraints on effective temperatures and radii, thus reducing systematic errors in model-dependent stellar mass determinations (White et al. 2018). Johnson et al. (2014) made the first attempt to use asteroseismology to test the spectroscopic mass of HD 185351 – the only known intermediate-mass evolved planet-hosting star observed by Kepler (Borucki et al. 2010). However, they could not reconcile their stellar mass measurements from spectroscopy, asteroseismology and interferometry. The reconciliation was later achieved by Hjørringgaard et al. (2017) with a more comprehensive asteroseismic modelling. They found an overestimation of about |$\sim$|15 per cent in the spectroscopic mass of HD 185351. Similarly, for seven of the eight evolved planet-hosting stars observed using the ground-based Stellar Observations Network Group (SONG; Andersen et al. 2016) telescope, Stello et al. (2017) found an overestimation of 15–20 per cent in spectroscopic masses compared to the corresponding seismic masses. Additionally, using interferometry for five evolved planet-hosting stars, White et al. (2018) found the spectroscopic masses from the literature to be 15 per cent larger than their interferometry-based values. On the other hand, contrary to the above evidence suggesting the presence of a mass offset, Campante et al. (2017, 1 star) and North et al. (2017, 7 stars) found no apparent difference between the spectroscopic and seismic masses in their samples of stars, of which not all were hosting planets. Ghezzi & Johnson (2015) investigated the presence of a mass offset with 59 evolved stars using model-independent masses from binary systems (26 stars) and asteroseismology (33 stars) and found no significant evidence for it. Later, Ghezzi et al. (2018, 245 stars) arrived at the same conclusion from their spectroscopic and kinematic analyses.

Malla et al. (2020) performed an ensemble study to understand why some seismic studies found a discrepancy between the spectroscopic and seismic mass scales while others did not. They combined their seismic results for four evolved planet-hosting stars with 12 other stars studied by Stello et al. (2017) and North et al. (2017). From three different spectroscopic sources (Mortier et al. 2013; Jofré et al. 2015; Stock, Reffert & Quirrenbach 2018), they found that stars above a mass threshold of 1.6 M|$_\mathrm{\odot }$| had a significant mass offset, while those below the threshold did not. This result is consistent with the findings by Stello et al. (2017) and North et al. (2017). The transition mass of |$\sim$|1.6 M|$_\mathrm{\odot }$| is the same as the one that separates fast and slow-moving evolving stars in the subgiant regime where most of the retired A-stars lie. However, the Malla et al. (2020) ensemble study only had relatively few stars with masses below 1.0 M|$_\mathrm{\odot }$| and above 1.6 M|$_\mathrm{\odot }$|⁠, leading to an inconclusive result. More stars across a wider mass range would be required to make firmer conclusions about such mass-dependent offset. Fortunately, with the launch of the Transiting Exoplanet Survey Satellite (TESS; Ricker et al. 2016), we now have high-cadence time-resolved data for many more stars with spectroscopically derived masses. Hence, we can use TESS to measure the asteroseismic-based masses of these stars.

In this paper, we expand the sample of evolved stars for which we can test the previous spectroscopic mass determinations against seismically determined masses, and to provide more stars in the mass range poorly covered by Malla et al. (2020). For this purpose, we use the photometric data from the first three years of the TESS mission and asteroseismic scaling relations to determine the seismic masses of these stars. With this large data set, we further expand the scope of the mass offset found by Malla et al. (2020) towards up to five different spectroscopic sources. In Section 2, we discuss the selection criteria for our targets. We measure our global seismic parameters in Section 3 and our seismic masses in Section 4. In Section 5, we discuss the mass discrepancy between spectroscopic and seismic mass scales guided by our results. In Section 6, we draw conclusions based on our findings.

2 TARGET SELECTION AND OBSERVATIONS

We selected 451 evolved stars that had spectroscopic masses previously studied by either Mortier et al. (2013, M13), Jofré et al. (2015, J15), Wittenmyer et al. (2016, W16), Ghezzi et al. (2018, G18), or by Stock et al. (2018, S18) and that were observed in 2-min cadence during the first three years of the TESS mission. Table 1 (column 2) shows the total number of unique stars in our sample, along with thenumber of stars analysed from each spectroscopic survey. All five spectroscopic sources derived their masses by fitting isochrones or evolutionary tracks, with J15 and S18,² utilizing Bayesian inference. We note here that S18 incorporated evolutionary speeds into their spectroscopic mass determinations. Fig. 1 shows the colour–magnitude diagram for the 451 stars in our sample along with solar–metallicity BaSTI tracks³ (Pietrinferni et al. 2004) to guide the eye. Of the five chosen spectroscopic sources, M13, J15, and S18 studied evolved stars and were previously used to study the mass offset by Malla et al. (2020). G18 studied evolved stars (both planet-hosting and non-planet-hosting) to derive a planet occurrence-mass-metallicity correlation, while W16 studied the retired A-stars as observed from the Southern hemisphere. In Table 2, we list the spectroscopic mass range covered by our sample from each source and in Table 3, we list the spectroscopic masses of the stars for each spectroscopic source. From Fig. 2 and also Table 3 (columns 6–10), we can see that 66 stars are studied by multiple spectroscopic sources. Such stars are plotted multiple times in Fig. 1.

To distinguish between what can be viewed as subgiants/early red giant branch stars (low-luminosity sample), akin to the retired A-star sample, and the more evolved red giant branch and red clump stars (high-luminosity sample), we define the stars with absolute magnitude |$M_{V} \ \lt $| 1.25 and colour |$B-V \ \gt $| 0.8 to be high-luminosity stars (represented by the dashed black line in Fig. 1). The remaining stars are considered low-luminosity stars. Of the 451 stars in our sample, we find 283 high-luminosity and 168 low-luminosity stars based on the criteria above. A spectroscopic-source-wise breakdown of the low- and high-luminosity stars is provided in Table 1. We also mark individual stars as a low- or high-luminosity stars in Table 3 (column 11).

The selected targets had at least |$\sim$|27 d (one sector) of TESS data available.⁴ The targets were observed in a 2-min cadence, and the data was downloaded from the TESS Asteroseismic Science Operations Center (TASOC) website.⁵ For our analysis, we used the corrected light curves (PDCMAP) provided by the TESS Science Processing Operations Center (SPOC; Jenkins et al. 2016), which uses a pipeline similar to the Kepler Science Operations Center pipeline. Table 3 (columns 4 and 5) lists the TESS magnitudes and the observing coverage of our targets.

We first excluded any known anomalies (e.g. due to cosmic rays or stray light) by only using data with a zero pixel-quality flag as marked by the SPOC pipeline. The resulting light curves were subjected to a highpass filter of |$\sim$|3 |$\mathrm{\mu }$|Hz (⁠|$\sim$|4 d) to remove any slow trends. For stars 24 Sex and HD 185351, the quality of the time series was poor and showed trends with periods less than |$\sim$|4 d, which interfered with the detection of oscillations. Hence, we used a |$\sim$|50 |$\mathrm{\mu }$|Hz highpass filter for these two stars. We then performed a 4-|$\sigma$| clipping to remove significant outliers from the light curves. For seven stars, we also removed any strong features (e.g. dips, flares) to prevent interference with the oscillation detection before applying a highpass filter. To do so, we removed any sudden changes in the mean with amplitudes larger than 4-|$\sigma$| of the light curve and of duration |$\sim$|0.1–2.5 d. Lastly, we combined the light curves from different sectors by normalizing the flux by dividing out the median on a per-sector basis with the timestamps preserved.

Figs 3 a1 and a2 show the final light curves for 57 Vir and 36 Dor, representative of short and long time series, which were observed by TESS for 1 and 22 sectors, respectively. We use these stars as examples in the following sections.

3 EXTRACTION OF GLOBAL SEISMIC PARAMETERS

Similar to Malla et al. (2020), we computed the power density spectra of each light curve using a discrete Fourier transform. Figs 3 b1 and b2 show the power density spectra for 57 Vir and 36 Dor. To measure the frequency of maximum acoustic power |$\mathrm{\nu }_{\mathrm{max}}$| and the large frequency of separation |$\mathrm{\Delta \nu }$|⁠, we used the SYD pipeline⁶ (Huber et al. 2009). The SYD pipeline corrects for the granulation background, locates |$\mathrm{\nu }_{\mathrm{max}}$| and measures |$\mathrm{\Delta \nu }$| from the autocorrelation of the power spectrum. Figs 3 c1 and c2 show the residual power spectra after the granulation background is divided out. The |$\mathrm{\nu }_{\mathrm{max}}$| and |$\mathrm{\Delta \nu }$| values are tabulated in Table 4 (columns 5 and 6).

Of the 451 stars analysed with SYD, we found 249 stars that exhibit solar-like oscillations – 92 low- and 157 high-luminosity stars. Table 1 (columns 3, 5, and 7, i.e. N|$_\mathrm{osc}$|⁠, N|$_\mathrm{low, osc}$|⁠, and N|$_\mathrm{high, osc}$|⁠) provides a spectroscopic-source-wise breakdown of the solar-like oscillators in our sample. Here we note that we only have a tentative detection of |$\mathrm{\nu }_{\mathrm{max}}$| for four stars, as marked in Table 4 (column 5).

To verify, and possibly correct, the |$\mathrm{\Delta \nu }$| measurements by SYD, we used échelle diagrams. The échelle diagrams are obtained by dividing the power density spectrum into segments of length equal to a trial |$\mathrm{\Delta \nu }$| and then stacking these segments vertically. The acoustic modes of the same degree form vertical ridges when the trial |$\mathrm{\Delta \nu }$| corresponds to the correct large frequency separation. We use the SYD |$\mathrm{\Delta \nu }$| as an initial guess. Figs 3 d1 and d2 depict the échelle diagrams for 57 Vir and 36 Dor, respectively. However, the SYD |$\mathrm{\Delta \nu }$| did not provide good vertical alignment for nine stars (marked in Table 4, column 6). For these stars, we use the echelle⁷ module (Hey 2019) to adjust the trial |$\mathrm{\Delta \nu }$| to the final adopted value guided by the |$\mathrm{\Delta \nu }$|–|$\epsilon$| relation by Corsaro et al. (2012). In such a case, we take as our uncertainty the minimum shift in |$\mathrm{\Delta \nu }$| needed to move the vertical ridges clearly out of alignment (an illustration of this can be seen in Fig. 5 of Stello et al. 2011). We find an average uncertainty of 0.165 |$\mathrm{\mu }$|Hz for these nine stars. Table 4 (column 6) lists the final |$\mathrm{\Delta \nu }$| observed for our targets. Despite our attempts to achieve a good vertical mode alignment using SYD pipeline and/or echelle module, we could only make a tentative detection of |$\mathrm{\Delta \nu }$| for 28 stars. Further, we could not measure |$\mathrm{\Delta \nu }$| for seven stars. Such stars are also marked in Table 4 (column 6).

4 DETERMINING STELLAR MASS

We use two asteroseismic scaling relations to determine three seismic masses: one based on |$\mathrm{\nu }_{\mathrm{max}}$|⁠, one based on |$\mathrm{\Delta \nu }$|⁠, and one based on |$\mathrm{\nu }_{\mathrm{max}}$| and |$\mathrm{\Delta \nu }$|⁠. The |$\mathrm{\nu }_{\mathrm{max}}$|-based mass uses the relation between |$\mathrm{\nu }_{\mathrm{max}}$| and the acoustic cutoff frequency (Brown et al. 1991; Kjeldsen & Bedding 1995). Following Stello et al. (2008), this leads to the following relation for mass:

To be consistent with Stello et al. (2017) and Malla et al. (2020), we use |$\mathrm{\nu }_\mathrm{max,\odot }$| = 3090 |$\mathrm{\mu }$|Hz and T|$_\mathrm{eff,\odot }$|  = 5777 K (Huber et al. 2009).

We also know that |$\mathrm{\Delta \nu }$| scales with the square root of stellar mean density (Ulrich 1986). Hence, we compute a |$\mathrm{\Delta \nu }$|-based seismic mass as follows:

Here |$f_\mathrm{\Delta \nu }$| is a necessary correction factor applied to the scaling relation linking |$\mathrm{\Delta \nu }$| and density. We use the software asfgrid⁸ by Sharma et al. (2016) to obtain the correction factor.

By combining equation (2) with equation (1), we measure a seismic mass using both |$\mathrm{\nu }_{\mathrm{max}}$| and |$\mathrm{\Delta \nu }$| with very little dependence on |$T_{\mathrm{eff}}$| and eliminating the need for a luminosity determination, which for data with good |$\mathrm{\Delta \nu }$| measurements, like those from Kepler, has been the most common way to determine seismic masses on large ensembles (see Kallinger et al. 2010; Pinsonneault et al. 2014, 2018; Serenelli et al. 2017; and Yu et al. 2018):

To perform a like-for-like comparison between the spectroscopic-based isochrone masses from the literature and our seismic masses, we adopt the spectroscopic parameters (⁠|$T_{\mathrm{eff}}$| and [Fe/H]) determined from each spectroscopic survey to derive the seismic masses using the seismic scaling relations (equations 1, 2, and 3).

We used isoclassify⁹ (Huber et al. 2017; Berger et al. 2020) to compute luminosities for the solar-like oscillators in our sample. We used the spectroscopic parameters (⁠|$T_{\mathrm{eff}}$| and [Fe/H]) from the corresponding spectroscopic source (M13, J15, W16, G18, or S18). We also adopted Gaia eDR3 parallaxes (Gaia Collaboration 2016, 2022a) for stars in the magnitude range 6 < G < 21 (57 stars), Gaia DR2 parallaxes (Gaia Collaboration 2018) for stars with 5 |$\le$|G|$\le$| 6 (97 stars), and Hipparcos parallaxes for the rest (van Leeuwen 2007, 95 stars). The source of parallax used for each star is marked in Table 4 (column 7). We discuss our choice of parallaxes in more detail in Appendix  A. We also used the Tycho V|$_\mathrm{T}$| photometry as an input. For three stars (NGC 4349 127, BD+20 274, and BD−13 2130), the Tycho V|$_\mathrm{T}$| magnitudes were unavailable and hence, we used the 2MASS K|$_s$| magnitudes. We set the dustmap parameter to ‘allsky’ to use a combination of reddening maps (Drimmel, Cabrera-Lavers & López-Corredoira 2003; Marshall et al. 2006; Green et al. 2015; and Bovy et al. 2016) to provide full sky coverage as implemented in the mwdust package by Bovy et al. (2016). Table 5 (column 4) shows the resulting luminosities using the spectroscopic parameters from each spectroscopic source.

Now, with all the input for the scaling relations at hand, we derived the three seismic masses |$M_\mathrm{1}$|⁠, |$M_\mathrm{2}$|⁠, and |$M_\mathrm{3}$| from equations 1, 2, and 3 using the spectroscopic parameters from M13, J15, W16, G18, and S18. We list the seismic masses in Table 5 (columns 5–7) for each spectroscopic source. We will compare these seismic masses to their corresponding spectroscopic masses in Section 5.

5 MASS COMPARISON

5.1 Mass-dependent mass offset in low-luminosity stars

There is clear evidence in the literature that the different seismic masses based on the scaling relations in equations 1, 2, and 3 do not perform equally well. Based on analyses of nearly equal-mass cluster red giants, both Miglio et al. (2016) and Howell et al. (2022) found that the |$\mathrm{\nu }_{\mathrm{max}}$|-based relation (equation 1) provides results that are more in line with astrophysical expectations and that show the least scatter (among equal-mass stars). We therefore expect equation (1) to be the best seismic mass to use for our comparison with the spectroscopic results. However, we first wished to check for our sample that equation (1) provides the most robust results. Because our sample is comprised of field stars, we do not have an astrophysical ‘true’ mass for each star to serve as a reference. However, we can still compare our three different seismic masses to the spectroscopic mass, which we can use as our reference mass even if it has a suspected offset from the true mass. This is because the potential offset is expected to change smoothly with mass in an ensemble sense. Hence, the scatter in the differences between each seismic mass scale and the spectroscopic one, for a given reference mass, still gives an indication of the overall precisions of the different seismic mass scales.

Of the 168 low-luminosity stars, 92 show solar-like oscillations (Table 1, columns 4 and 5). We plot the difference between the seismic and spectroscopic mass scales as a function of the spectroscopic mass in Fig. 4 (Panels a1, b1, and c1, with a panel for each seismic scale). Here, we use all five different spectroscopic sources. The 22 low-luminosity stars listed in Table 3 appear in more than one of our spectroscopic sources and are plotted multiple times. Stars with tentative detections are also included in this analysis. In agreement with Miglio et al. (2016) and Howell et al. (2022), we indeed see the smallest scatter (at fixed reference mass) for the |$\mathrm{\nu }_{\mathrm{max}}$|-based seismic mass (equation 1), supporting its use. In addition, we note that the three seismic mass scales have different zero-points relative to the spectroscopic reference, but interestingly, that difference is largely proportional to the exponent of |$T_{\mathrm{eff}}$| in the three mass scaling relations. Hence, it seems this is not dominated by an intrinsic zero-point difference between the seismic scales, but more likely pointing to a systematic offset in the adopted |$T_{\mathrm{eff}}$| scale. If we adjust the |$T_{\mathrm{eff}}$| scale by −120 K, we can bring all three seismic mass scales to a similar zero-point¹⁰ (Fig. 4 a2, b2, and c2). We note that this |$T_{\mathrm{eff}}$| shift is comparable to our adopted |$T_{\mathrm{eff}}$| uncertainty (100 K; Thygesen et al. 2012).¹¹

For our main comparison between seismic and spectroscopic masses, we adopted the |$\mathrm{\nu }_{\mathrm{max}}$|-based seismic scale. However, we did not apply the 120 K |$T_{\mathrm{eff}}$| shift in the following as we do not claim to know what the true mass scale of our sample is. In Fig. 5, we show this comparison for each spectroscopic source. By plotting our results together with the ensemble study results by Malla et al. (2020) for M13, J15, and S18 (black dots), we find our results are consistent with their findings. Further, from Fig. 5, we find that the mass offset is the smallest for the S18 subsample in which evolutionary speeds were taken into account.

5.1.1 Fitting the mass-dependent mass offset

It is clear from Fig. 5 that there is a mass-dependent mass offset. To quantify this offset, we fitted polynomials of varying orders and a step function (following a suggestion by Malla et al. 2020) to the mass offset without |$T_{\mathrm{eff}}$|-correction and computed the Bayesian Information Criterion (BIC). Schwarz (1978) first proposed BIC as a way to choose between alternate models in regression where the model with the lowest BIC is the preferred. We used the weighted least squares (WLS) method from the statsmodel module in python to fit polynomials of order 0–7 and the step function. We found the BIC to be minimum for a first-order polynomial fit (BIC = −82.89) of the following form:

However, a second-order polynomial fit had a BIC of −78.58, with the difference in BIC (⁠|$\Delta$|BIC) being 4.31. This value of |$\Delta$|BIC implies that the first-order polynomial is a good fit to our mass offset (Raftery 1995; Fabozzi et al. 2014). However, we cannot completely rule out a second-order polynomial. Future work is needed to expand beyond the limits of the current study and comprehensively model the offset to potentially rule one out. Fig. 6 shows how well the first order polynomial model fits the mass offsets. We advise caution on the use of equation (4) because it is only applicable to stars with spectroscopic masses 0.91–2.90 M|$_\mathrm{\odot }$|⁠, as can be inferred from Table 2 (column 5).

From Fig. 5 (panels a–e), we note that fitting the first order polynomial to individual spectroscopic sources yields intercepts between −0.7 and −0.06 M|$_\mathrm{\odot }$| and slopes between 0.26 and 0.67. We find that the slopes for individual fits of M13 (0.67 |$\pm$| 0.18), J15 (0.48 |$\pm$| 0.05) and S18 (0.51 |$\pm$| 0.33) are consistent with each other. G18 has the least slope of 0.26 |$\pm$| 0.1 owing to the larger scatter in its mass offsets. The W16 sample has the most precise fit with a slope of 0.64 |$\pm$| 0.08 while S18 has the least precise fit because of only five data points.¹²

Despite the larger ensemble size used in this work, our study still suffers from a deficit of low-luminosity stars with spectroscopic masses below 1 M|$_\mathrm{\odot }$| and above 1.8 M|$_\mathrm{\odot }$|¹³ From Table 2 (column 5), we note that our low-luminosity solar-like oscillators covers a spectroscopic mass range of 0.91–2.19 M|$_\mathrm{\odot }$|⁠. As a result, we are unable to define how the mass offset behaves at masses well below 1 and well above 2 M|$_\mathrm{\odot }$|⁠. With TESS observing more evolved stars in the late subgiant/early red giant branch regime, future work might be able to explore the mass-dependent mass offset at sub-solar masses and masses above 2 M|$_\mathrm{\odot }$|⁠.

5.2 The high-luminosity stars

Of the 451 stars, we have 283 high-luminosity stars, according to the criteria listed in Section 2 (also marked individually in Table 3, column 11). The most luminous stars in this sample oscillate at frequencies too low to resolve with the length of our current TESS data and our highpass filter of 3 |$\mathrm{\mu }$|Hz. The most luminous star in our sample oscillates at 0.3 |$\mathrm{\mu }$|Hz. We need at least 15 sectors of TESS data (i.e. more than a full year’s coverage) to detect oscillations at this |$\mathrm{\nu }_{\mathrm{max}}$|⁠. However, we find no such stars with multisector TESS data oscillating at such small frequencies in our sample. To be conservative, we do not report any seismic detections below a |$\mathrm{\nu }_{\mathrm{max}}$| of 8 |$\mathrm{\mu }$|Hz. Taking this hard detection limit into account, we have 157 solar-like oscillators, a spectroscopic source-wise breakdown of which is provided in Table 1 (columns 6–7). Similar to our low-luminosity sample, we compare our seismic masses to the spectroscopic masses by plotting the difference between the two as a function of spectroscopic mass in Fig. 7. We do not have a statistically significant high-luminosity star sample size for the spectroscopic sources M13, W16, and G18. Hence, these sources have been excluded from the figure and any discussion concerning the high-luminosity stars.

From Fig. 7, we see a rather complicated mass offset. This observed offset is non-trivial to understand from a stellar evolution point, unlike the arguments used on the low-luminosity sample, where stellar tracks are well separated and non-overlapping. The high-luminosity stars are mostly in the region of the colour–magnitude diagram where the tracks clump together, making it harder to determine stellar mass using stellar models. Therefore, determining the stellar masses using a more model-independent method like asteroseismology might provide more robust stellar masses for these stars. However, the |$\mathrm{\nu }_{\mathrm{max}}$|-based seismic relation (equation 1) seems to break down for stars with radius larger than about 30–50 R|$_\mathrm{\odot }$| (Zinn et al. 2019b, 2023), which affects up to six stars¹⁴ in our sample.

6 CONCLUSIONS

We constructed a sample of 451 evolved stars from five different spectroscopic sources: M13, J15, W16, G18, and S18. Of the 451 stars, we found 249 solar-like oscillators from 2-min cadence TESS data and measured their |$\mathrm{\nu }_{\mathrm{max}}$| and |$\mathrm{\Delta \nu }$|⁠.

To explore the mass-dependent mass offset between the spectroscopic and seismic masses for subgiants and red giants, we determined the seismic masses from three different scaling relations (equations 1, 2, and 3) using spectroscopic parameters from M13, J15, W16, G18, and S18. We divided our initial sample into two subsets: 168 low- and 283 high-luminosity stars, such that the low-luminosity stars are synonymous with the previously studied retired A-stars (as defined by G18). Of these, we found 92 low- and 157 high-luminosity stars with solar-like oscillations. Comparing the spectroscopic and seismic masses for low-luminosity stars (mostly late subgiants and early red giants) reveals an increasing mass offset with mass between the two stellar mass scales. However, we found that the planet occurrence-mass-metallicity correlation does not significantly change when adopting the seismic masses. Despite our efforts to expand our ensemble size and to include more stars in the mass ranges not previously covered by Malla et al. (2020), our study is deficient in low-luminosity stars with spectroscopic masses well below 1 M|$_\mathrm{\odot }$| and above 2 M|$_\mathrm{\odot }$|⁠. A further study exploring these mass ranges may be needed to explore further the nature of the mass-dependent mass offset we observe.

We also found a mass offset between the spectroscopic and seismic masses for high-luminosity stars (primarily consisting of the red clump and more luminous stars). A possible explanation for the observed offset is the error-prone mass determination using isochrones due to the clumping together of evolutionary tracks in this region of interest.

ACKNOWLEDGEMENTS

Dennis Stello is supported by the Australian Research Council (DP190100666). Timothy R. Bedding acknowledges support from the Australian Research Council through Laureate Fellowship FL220100117. This paper includes data collected by the Transiting Exoplanet Survey Satellite (TESS) mission, which are publicly available from the Mikulski Archive for Space Telescopes (MAST). Funding for the TESS mission is provided by NASA’s Science Mission directorate. Sai Prathyusha Malla thanks Joel C. Zinn for helping with parallax correction.

DATA AVAILABILITY

The TESS data used in this article can be downloaded from TASOC (www.tasoc.dk). All the tables in this paper are available on CDS in a machine-readable format.

Footnotes

REFERENCES

APPENDIX A: A NOTE ON USE OF PARALLAXES

For computing luminosities using isoclassify in Section 4, we used parallaxes from three different sources: Gaia eDR3, DR2, and Hipparcos.

The Gaia eDR3 catalogue¹⁵, improves the precision by a factor of 1.5, compared to Gaia DR2 (Lindegren et al. 2021). So we prefer Gaia eDR3 parallaxes for our targets if they are available. However, despite the precision improvement, the Gaia eDR3 parallaxes suffer from systematic offsets and must be corrected for a zero-point offset. For our Gaia eDR3 parallaxes, we use the python code¹⁶ by Lindegren et al. (2021) to compute the zero-point offset based on the position, colour, and magnitude of the star. The zero-point offsets are then subtracted from the Gaia eDR3 parallaxes. However, these corrections can only be applied to stars with |$6 \ \lt\ G \ \lt\ 21$|⁠. To overcome these limitations, we only use the Gaia eDR3 parallaxes for stars with |$6 \ \lt\ G \ \lt\ 21$| and Gaia DR2 parallaxes for stars with |$G \ \lt\ 6$|⁠. We corrected our Gaia DR2 parallaxes using an |${\tt astrometric_pseudocolor}$|- and magnitude-based relation given by Zinn et al. (2019a).

We know that Gaia DR2 parallaxes are prone to calibration issues for stars brighter than G = 5 (Drimmel, Bucciarelli & Inno 2019). Hence, we used Hipparcos parallaxes for stars with G < 5. Also, we do not have any Gaia eDR3/DR2 measurement available for 66 stars. For these 66 stars, we use Hipparcos parallaxes instead. We also use Hipparcos parallaxes for three stars that have a larger fractional error in Gaia parallaxes than in Hipparcos.

By comparing the corrected eDR3 parallaxes to the DR2 ones for the stars that have both measurements (107 stars, where 58 stars are solar-like oscillators and 49 stars are not), we obtain a median fractional difference of about 0.8 per cent between the two parallaxes measurements. For seven stars¹⁷, we find the fractional difference to be more than 5 per cent, but less than 32 per cent. A possible reason for a larger fractional difference for these stars is due to the improvement in parallaxes from Gaia DR2 to eDR3. In conclusion, we find that the parallaxes from Gaia eDR3 corrected using the code by Lindegren et al. (2021) and from Gaia DR2 corrected using the relation by Zinn et al. (2019a) are consistent with each other.

Table A1 summarizes our discussion on the use of parallaxes in this paper. We also provide the source of parallax for each solar-like oscillator in Table 4 (column 7).