TESS Asteroseismology of the Known Red-giant Host Stars HD 212771 and HD 203949

TESS observed HD 212771 and HD 203949 in 2 minutes cadence over 27.4 days during Sectors 2 and 1 of Cycle 1, respectively. Both targets were part of a larger cohort of 79 "fast-track" targets that were processed using a special version (Handberg & Lund 2018) of the TESS Asteroseismic Science Operations Center³⁶ (TASOC; Lund et al. 2017a) photometry pipeline.³⁷ Starting from calibrated target pixel files, aperture photometry was conducted following a procedure similar to the one adopted in the K2P² pipeline (Lund et al. 2015), originally developed to generate light curves from data collected by K2. The extracted light curves were subsequently corrected for systematic effects using the Kepler Asteroseismic Science Operations Center (KASOC) filter (Handberg & Lund 2014).

Figure 1 shows the light curves of HD 212771 (left panel) and HD 203949 (right panel) produced by the TASOC pipeline. Both light curves have high duty cycles (∼98% and ∼94%, respectively), displaying a gap midway through (due to the data downlink) that separates the two spacecraft orbits in each sector. A 2.5 days periodicity can be seen, especially in the bottom left subpanel, caused by the spacecraft's angular momentum dumping cycle. Moreover, a region of large jitter can be seen in the right panel toward the end of the sector, a feature common to Sector 1 pointings (Handberg & Lund 2018).

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We adopt the atmospheric parameters and elemental abundances obtained for HD 212771 by Campante et al. (2017), which are based on the analysis of a high-quality Fiber-fed Extended Range Optical Spectrograph (FEROS) spectrum (see Table 1).

Particular care must, however, be taken regarding HD 203949, because use of the model-independent scaling relation $g\propto {\nu }_{\max }\,{T}_{\mathrm{eff}}^{1/2}$ (Brown et al. 1991; Kjeldsen & Bedding 1995; Belkacem et al. 2011), where ν_max is the frequency of maximum oscillation amplitude (see Section 3.1), leads to an initial estimate of the surface gravity ($\mathrm{log}g\sim 2.4$) that is significantly lower than the spectroscopic value quoted in the discovery paper ($\mathrm{log}g=2.94\pm 0.20;$ Jones et al. 2011, 2014).

Therefore, we instead adopt the spectroscopic parameters listed for HD 203949 in the SWEET-Cat catalog³⁸ (Santos et al. 2013), whose $\mathrm{log}g$ is compatible with the one inferred from asteroseismology. These are based on the analysis of a high-resolution (R ∼ 100,000) Ultraviolet and Visual Échelle Spectrograph (UVES) spectrum (for details, see Sousa et al. 2018) and are listed in Table 2. Analysis of a lower-resolution (R ∼ 48,000) FEROS spectrum by the same authors, albeit considering a larger number of iron lines, led to fully consistent spectroscopic parameters.

Table 2.  Stellar Parameters for HD 203949

Parameter	Value	Source
Basic Properties
TIC	129649472	1
Hipparcos ID	105854	2
TESS Mag.	4.75	1
Sp. Type	K2 III	3
Spectroscopy
Teff (K)	4618 ± 113	4
[Fe/H] (dex)	0.17 ± 0.07	4
[α/Fe] (dex)	0.07 ± 0.09	5
$\mathrm{log}g$ (cgs)	2.36 ± 0.28	4
SED and Gaia DR2 Parallax
AV	0.13 ± 0.10	5
Fbol (erg s−1 cm−2)	(2.27 ± 0.22) × 10−7	5
R* (R⊙)	10.30 ± 0.51	5
L* (L⊙)	43.34 ± 4.27	5
π (mas)	12.77 ± 0.13a	6
SBCR
θ (mas)	1.284 ± 0.011	5
R* (R⊙)	10.8 ± 1.6	5
Asteroseismologyb
Δν (μHz)	4.10 ± 0.14	5
νmax (μHz)	31.6 ± 3.2	5
ΔΠ1 (s)	⋯	⋯
M* (M⊙)	1.23 ± 0.15/1.00 ± 0.16	5
R* (R⊙)	10.93 ± 0.54/10.34 ± 0.55	5
ρ* (gcc)	0.00134 ± 0.00010/0.00130 ± 0.00011	5
log g (cgs)	2.453 ± 0.027/2.415 ± 0.044	5
t (Gyr)	6.45 ± 2.79/7.29 ± 3.06	5

Notes.

^aAdjusted for the systematic offset of Stassun & Torres (2018). ^bFundamental stellar properties are provided assuming that the star is either on the RGB or in the clump, respectively (see Section 5.2).

References. (1) Stassun et al. (2018b), (2) van Leeuwen (2007), (3) Houk (1982), (4) Sousa et al. (2018), (5) this work, (6) Gaia Collaboration et al. (2018).

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We conducted a detailed abundance analysis of HD 203949 based on both the UVES and FEROS spectra, following the methodology described by Adibekyan et al. (2012, 2015a). Abundances derived from the two spectra are consistent within 1σ, with UVES-based results being slightly more precise. Our analysis shows that HD 203949 has a chemical composition typical of a thin-disk, metal-rich K giant (e.g., Adibekyan et al. 2015b; Jofré et al. 2015). The star shows enhancement in Na and Al relative to iron ([Na/Fe] = 0.22 ± 0.13 dex and [Al/Fe]=0.25 ± 0.12 dex based on the UVES spectrum), typical of evolved stars (e.g., Adibekyan et al. 2015b). Finally, we computed the relative abundance of α elements as the unweighted mean of the Mg, Si, Ca, and Ti abundances derived from the UVES spectrum, resulting in [α/Fe] = 0.07 ± 0.09 dex.

We fitted the spectral energy distributions (SEDs) of both stars using broadband photometry to determine empirical constraints on the stellar radii and luminosities, following the method described in Stassun & Torres (2016) and Stassun et al. (2018a). The available broadband photometry in published all-sky catalogs (i.e., APASS, 2MASS and Wide-field Infrared Survey Explorer) provides coverage over the wavelength range ≈0.4–22 μm. For each star, we fitted a standard Kurucz (2013) stellar atmosphere model, selected according to the spectroscopically determined T_eff, $\mathrm{log}g$, and [Fe/H] (see Section 2.2). With these constraints fixed, the remaining free parameter in the fit was the extinction, A_V, which we limited to the maximum for the line of sight from the dust maps of Schlegel et al. (1998). Finally, we integrated the (non-reddened) SED to obtain the bolometric flux at Earth (F_bol) which, with the T_eff and the Gaia DR2 distance (adjusted for the systematic offset of Stassun & Torres 2018), gives the stellar radius.

The best-fit parameters for HD 212771, with reduced χ² = 4.7, are: A_V = 0.04 ± 0.04, F_bol = (3.06 ± 0.14) × 10⁻⁸ erg s⁻¹ cm⁻², resulting in R_⋆ = 4.44 ± 0.13 R_⊙ and L_⋆ = 11.67 ± 0.57 L_⊙. For HD 203949, the best-fit parameters, with reduced χ² = 3.7, are: A_V = 0.13 ± 0.10, F_bol = (2.27 ± 0.22) × 10⁻⁷ erg s⁻¹ cm⁻², resulting in R_⋆ = 10.30 ± 0.51 R_⊙ and L_⋆ = 43.34 ± 4.27 L_⊙. The derived luminosities will be used in Section 4 as input to the grid-based modeling.

Pietrzyński et al. (2019) derived the distance to the Large Magellanic Cloud with a 1% precision using eclipsing binaries as distance indicators. In order to achieve such precision, they used a dedicated SBCR based on the observation of 48 red-clump (RC) stars with the PIONIER/VLTI instrument (Gallenne et al. 2018). We used this relation to place empirical constraints on the angular diameters and linear radii of HD 212771 and HD 203949.

For HD 212771, considering V = 7.60 ± 0.01 (Høg et al. 2000), K = 5.50 ± 0.02 (Cutri et al. 2003), A_V = 0.005 (using the Stilism dust map; Lallement et al. 2014; Capitanio et al. 2017), and A_K = 0.089A_V (Nishiyama et al. 2009), we obtained (using Equation (2) of Pietrzyński et al. 2019) a limb-darkened angular diameter of θ = 0.375 ± 0.003 mas. The quoted uncertainty (0.8%) arises from the rms scatter (0.018 mag) of the SBCR in Pietrzyński et al. (2019). Using the Gaia DR2 parallax, we then derived a stellar radius of R_* = 4.45 ± 0.04 R_⊙. We must, however, also consider the source of uncertainty associated with the 2MASS infrared photometry (0.02 mag), which corresponds to an additional uncertainty in the radius of 0.05 R_⊙. We thus finally obtained R_* = 4.45 ± 0.07 R_⊙. Applying the same procedure to HD 203949 (V = 5.62 ± 0.01, K = 2.99 ± 0.24, and A_V = 0.004), we obtained a limb-darkened angular diameter of θ = 1.284 ± 0.011 mas and a stellar radius of R_* = 10.8 ± 1.6 R_⊙ (after taking into account the exceptionally large uncertainty of 0.24 mag in the infrared photometry). The derived stellar radii are consistent with those obtained from the SED analysis.

The large frequency separation, Δν, and frequency of maximum oscillation amplitude, ν_max, were measured based on the analysis of the above power spectra. A range of well-tested and complementary automated methods were used in the analysis (Huber et al. 2009, 2011; Mosser & Appourchaux 2009; Mathur et al. 2010; Mosser et al. 2011; Corsaro & De Ridder 2014; Corsaro et al. 2015; Davies & Miglio 2016; Campante 2018; Yu et al. 2018), which have previously been extensively applied to data from Kepler/K2 (e.g., Hekker et al. 2011; Verner et al. 2011). Returned values were subject to a preliminary step which involved the rejection of outliers following Peirce's criterion (Peirce 1852; Gould 1855). For each star, we finally adopted the values of Δν and ν_max corresponding to the smallest normalized rms deviation about the median, considering both parameters simultaneously (i.e., both parameters originate from the same source/method). Uncertainties were recalculated by adding in quadrature the corresponding formal uncertainty and the standard deviation of the parameter estimates returned by all methods. Consolidated values for Δν and ν_max are given in Tables 1 and 2.

Mixed modes in HD 212771 were analyzed following the method of Mosser et al. (2015), which revealed the signature of the period spacing, ΔΠ₁. Its value, computed as in Vrard et al. (2016), is ΔΠ₁ = 84.3 ± 1.6 s. A fit of the mixed-mode pattern provides a more refined value of the period spacing, ΔΠ₁ = 85.3 ± 0.3 s, and a coupling factor q = 0.19 ± 0.03. Such values are in agreement with the general trends found in Kepler data for stars on the red-giant branch (RGB; Mosser et al. 2017). This is supported by the star's location in a ΔΠ₁–Δν diagram (see Figure 1 of Mosser et al. 2014). We thus reclassify HD 212771 as a low-luminosity RGB star based on asteroseismology.

Since the mixed-mode pattern also revealed rotational multiplets, we next performed an analysis of the rotational splittings of dipole mixed modes (based on a power spectrum oversampled by a factor of 4). In a preliminary step, rotational splittings were identified using an asymptotic mixed-mode pattern modulated by a core rotation rate of 400 nHz. Comparison of the spectrum with the asymptotic fit revealed 13 mixed modes with a height-to-background ratio larger than 5, among which 8 are forming rotational doublets, corresponding to the mixed-mode orders −40, −38, −35, and −34 (see Figure 4 and Table 3). The remaining components were identified as being $| m| =1$ modes. The absence of any significant dipole mode with azimuthal order m = 0 is in favor of a star seen edge-on. As shown by Kamiaka et al. (2018), deriving a reliable and precise value of the stellar inclination is difficult when the height-to-background ratio of the modes is small. Based on the observed height-to-background ratio of the rotational doublets, an inclination angle larger than 75° is to be expected, consistent with a potentially aligned transiting system.

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To derive the mean core rotation, rotational splittings were expressed as a function of ζ, which describes the relative contribution of the inner radiative region to the mode inertia (Goupil et al. 2013; Deheuvels et al. 2014; Mosser et al. 2018). This method allowed us to derive the individual splitting of each component of the multiplet, with the total rotational splitting between the m = −1 and m = +1 components being split according to the respective ζ coefficients of each mode. We further assumed that the uncertainties of the unresolved dipole mixed modes cannot be less than half the frequency resolution. The method then returns a nominal, albeit imprecise, mean core rotation of δν_rot = 354 ± 151 nHz.

In order to properly fit the background power spectral density (PSD) of HD 203949, three Harvey-like profiles were required, as determined from a Bayesian model comparison using DIAMONDS (Corsaro & De Ridder 2014). One of the profiles in this preferred model has, however, a timescale and amplitude that do not conform with expectations based on the measured ν_max (e.g., Kallinger et al. 2014), with a "knee"³⁹ at $\sim 300\ \mu \mathrm{Hz}$ (see right panel of Figure 2). We suspect that this second power hump is caused by jitter in the TESS data that remains after applying the KASOC filter, which is particularly pronounced during the 1347–1350 days period of poor spacecraft tracking (see right panel of Figure 1). We note that the power hump is also evident from the simple aperture photometry (SAP) delivered by the TESS Science Processing Operations Center (SPOC; Jenkins et al. 2016), while it is largely removed in the co-trended Presearch Data Conditioning SAP (PDCSAP)—the oscillation signal in the PDCSAP data is, however, of lower quality than the one present in the TASOC data.

Support for the hypothesis of jitter causing the second power hump comes from the MOM_CENTR2 data delivered by SPOC, which gives the flux-centroid along rows on the charge-coupled device (CCD). The PSD of this centroid time series shows a clear excess at ∼300 μHz. Jitter at this frequency would cause a variation in the flux from inter/intra pixel sensitivity and from flux exiting/entering the aperture. We found that adopting a larger aperture than the one set by the TASOC pipeline made the power hump disappear, but at the cost of a degraded oscillation signal. Furthermore, the hypothesis that this feature is instrumental in nature is reinforced by noting that the power hump nearly vanishes if the 1347–1350 days data are omitted from the PSD calculation, and that the short-cadence light curve for the nearby star TIC 129679884 shows the same effect.

Since the power hump is well separated in frequency from the power excess due to oscillations, we could account for it in the fitted background without affecting the analysis of the oscillations.

HD 212771 was observed by K2 in short cadence (Campante et al. 2017; North et al. 2017), which enabled its asteroseismic investigation. Here, we compare the asteroseismic performances of K2 and TESS by assessing the ratio of the observed maximum oscillation amplitudes for this star, i.e., ${A}_{\max }^{{TESS}}/{A}_{\max }^{K2}$.

The absolute calibration of the oscillation amplitudes depends on the instrument's bandpass. TESS has a redder bandpass than Kepler/K2, meaning observed amplitudes are expected to be lower in the TESS data by a factor of ∼0.85 (Campante et al. 2016b). Based on a blackbody approximation, Lund (2019) finds this factor to be slightly lower, i.e., ∼0.83–0.84 on average within the T_eff range considered in that study. We measured the maximum oscillation amplitude per radial mode, A_max, following the method introduced by Kjeldsen et al. (2005, 2008), which involves determining the peak of the heavily smoothed, background-corrected amplitude oscillation envelope having accounted for the (bandpass-dependent) effective number of modes per radial order.⁴¹ This yielded ${A}_{\max }^{{TESS}}=12.8\pm 2.3\ \mathrm{ppm}$ and ${A}_{\max }^{K2}=17.1\pm 0.9\ \mathrm{ppm}$, resulting in a ratio ${A}_{\max }^{{TESS}}/{A}_{\max }^{K2}=0.75\pm 0.14$, consistent with the expected ratio.

We caution the reader that the estimated ${A}_{\max }^{{TESS}}/{A}_{\max }^{K2}$ is prone to unaccounted biases due to the stochastic nature of the oscillations (e.g., Arentoft et al. 2019), especially when considering the short time coverage compared to the lifetime of the modes as well as the non-contemporaneity of the TESS and K2 data sets. Moreover, the absolute values of ${A}_{\max }^{{TESS}}$ and ${A}_{\max }^{K2}$, taken individually, are also subject to biases arising from the choice of background model. Their ratio, however, can be more accurately estimated if both values are computed assuming the same functional form for the background model, which has been done here. Despite the above, this preliminary, single-point estimate of ${A}_{\max }^{{TESS}}/{A}_{\max }^{K2}$ provides support for the predicted yield of solar-like oscillators using TESS's 2 minutes cadence observations (Schofield et al. 2019).

RC stars, i.e., cool He-core burning stars, occupy a confined parameter space in the ΔΠ₁–Δν diagram around 300 s and 4.1 μHz (Mosser et al. 2012). Although the Δν value measured for HD 203949 is consistent with it being an RC star, the low-frequency resolution of the power spectrum hinders a measurement of ΔΠ₁. This in turn prevents a definitive classification of its evolutionary state from being made based on the ΔΠ₁–Δν diagram, due to the underlying degeneracy for Δν ⪅ 10 μHz (e.g., Mosser et al. 2014). In an attempt to assess the evolutionary state of HD 203949, we have thus conducted a number of analyses, which we summarize below.

Machine learning classification. We employed the deep learning method of Hon et al. (2017, 2018), which efficiently classifies the evolutionary state of oscillating red giants by recognizing visual features in their asteroseismic power spectra. A test set accuracy of 93.2% has been reported when applying the classifier to a 27 days photometric time series (Hon et al. 2018). Application of this method to the power spectrum of HD 203949 returns a probability of it being an RC star of p ∼ 0.6, having taken into account the effect of detection bias in the training set.

Alternatively, we have made use of Clumpiness (J. Kuszlewicz et al. 2019, in preparation). Clumpiness uses a handful of well-engineered features and a gradient boosting algorithm (xgboost; Chen & Guestrin 2016) to classify stars as RGB or RC (or even as possible main-sequence stars observed in long cadence) in the time domain. These features include the median absolute deviation (MAD) from the median of the time series flux, the number of zero crossings, a measure of the stochasticity following Kedem & Slud (1981, 1982) and Bae et al. (1996), the MAD of the first differences, and, to complement the time series features, the K-band absolute magnitude is also included, which is computed using distances from Bailer-Jones et al. (2018) and a 3D dust map from Green et al. (2015). Across a range of time series lengths, from 27 days up to 4 years, the classifier maintains an accuracy of approximately 92%. Computing the features for HD 203949, the classifier returns a probability of 0.6 of it being in the RC.

Grid-based modeling. For a given set of seismic and spectroscopic observational constraints, the evolutionary state of HD 203949 can also be assessed from the results of grid-based modeling. We have thus performed two separate analyses, each assuming as prior information a specific evolutionary state, i.e., RGB or RC. We found that the probability of HD 203949 being an RC star is 75 times greater than it being an RGB star (or p = 0.99), as determined by the ratio of the overall posterior probabilities of both scenarios. Interpreting this in terms of a Bayes' factor provides very strong evidence in support of the RC scenario given the adopted set of seismic and spectroscopic constraints. We looked into which observational constraints are driving this result by analyzing their posterior distributions. RC stellar models reproduce all constraints very well, while RGB models cannot simultaneously fit the effective temperature and metallicity for stellar masses that are compatible with the seismic data. RGB models with 1 M_⊙ are too cool for [Fe/H] = 0.17 by about 200 K or, conversely, too metal-rich for the observed effective temperature by about 0.35 dex. The temperature difference between the RC and the RGB at fixed log g is smaller for tracks of larger masses, as the effective temperature of the clump does not change while that of the RGB gets higher. Our grid-based modeling for the RGB scenario reflects this, yielding a higher mass, around 1.2 M_⊙. This higher mass is obtained at the expense of a posterior ν_max higher than, and in tension with, the observed value. Finally, it is worth mentioning that this conclusion is robust against the temperature scale defined by the choice of mixing length, α_MLT, in the stellar models. We tested models with α_MLT ranging from 1.8 (solar-calibrated value with an Eddington atmosphere) to 2.1 (solar-calibrated value with a Krishna Swamy atmosphere), with almost no impact on the Bayes' factor, which varied from 75 for α_MLT = 1.8 down to 70 for α_MLT = 2.1.

We have also employed the Bayesian inference method of Stock et al. (2018). This method compares the position of a star in the Hertzsprung–Russell diagram with those of the latest PARSEC evolutionary models (Bressan et al. 2012). The spectroscopically determined metallicity, B − V color, and astrometry-based luminosity (Arenou & Luri 1999), computed from the adjusted Gaia parallax in Table 2, were used as constraints. Moreover, the initial mass function and the evolutionary timescale at each model position were used as priors in the Bayesian inference. The outcomes are probability density functions for the stellar parameters as well as probabilities of the star being either on the RGB or the horizontal branch. The method was carefully tested by Stock et al. (2018) against reference samples with accurate stellar parameters determined using different methods, and was found to deliver very reliable results. In particular, its reliability was tested against a sample of evolved stars with evolutionary states determined from asteroseismology, resulting in an accuracy of 86%. Application of this method returns a probability of HD 203949 being an RC star of p = 0.93.

Asymptotic Acoustic-Mode Offset. Kallinger et al. (2012) found an empirical relation between the asymptotic offset, _c, of radial modes in red giants and the evolutionary state, separating H-shell (RGB) from He-core burning stars. Christensen-Dalsgaard et al. (2014) provided a theoretical interpretation of this relation, which was found to derive from differences in the thermodynamic state of the convective envelope. Both works acknowledge the potential of this relation for distinguishing RGB and clump stars when faced with observations that are too short to allow such a distinction based on the determination of ΔΠ₁. We extracted frequencies⁴² from the PSD of HD 203949 using the multi-modal approach described in Corsaro (2019). The value of _c was then constrained from an échelle diagram and found to be 1.24 ± 0.05. The quoted uncertainty corresponds to the width of the expected ℓ = 0 ridge in the échelle diagram and reflects the lack of resolving power to properly disentangle radial modes from adjacent quadrupole modes. We note, however, that this uncertainty is not consistent with the one in Δν and should thus be considered as a lower limit. An uncertainty of 0.05 in _c translates into a relative uncertainty in Δν of about 0.05/n_max < 1% (e.g., Mosser et al. 2013), with n_max the radial order at ν_max. Table 2 nevertheless quotes a relative uncertainty in Δν of 3.4%. Once the uncertainty in _c has been calibrated, the measured value of _c = 1.2 ± 0.2 then allows for both evolutionary states (within 1.5σ) in the top panel of Figure 4 of Kallinger et al. (2012).

Spectroscopic evolutionary state. We made an attempt at inferring the spectroscopic evolutionary state of HD 203949 as described in Holtzman et al. (2018). The basic idea behind this approach is to use a ridgeline in the T_eff–$\mathrm{log}g$ plane that is a function of metallicity, and supplement this with a measurement of the surface [C/N] ratio, as the latter is expected (and observed) to further separate the RGB and RC. This approach was devised to separate RGB and RC stars in the (asteroseismic) APOKASC sample (Pinsonneault et al. 2018) and has an accuracy of approximately 95%. In the absence of a [C/N] measurement, we estimated the range of possible values from the stellar mass, taking as reference the APOKASC sample. This led to the star being most likely in the RC. However, we also have to account for the fact that the above relations are defined in the APOKASC sample only and that there could be a systematic offset between the T_eff and/or metallicity scales. To test this, we computed the photometric temperature by means of the infrared flux method (González Hernández & Bonifacio 2009), leading to a temperature cooler than the spectroscopic one (at the 1.5σ level). Adopting the photometric temperature, one instead arrived at the RGB classification. The issue of evolutionary state hence seems to rely sensitively on the effective temperature, given that the error on the spectroscopic T_eff is large enough to encompass both scenarios.

In summary, all but one approach give an ambiguous answer. The spectroscopic evolutionary state is unresolved due to the possibility of a systematic offset between the T_eff scales. The asymptotic acoustic-mode offset, _c, whose uncalibrated uncertainty is a poorly constrained lower limit, allows for both evolutionary states. Despite its inconclusiveness in this particular instance, machine-learning classification still exhibits a high degree of accuracy, thus holding great promise for large ensemble studies with TESS (e.g., Galactic archaeology). Finally, the two applications of grid-based modeling provide very strong evidence in support of the RC scenario given the adopted set of seismic and spectroscopic constraints. Although the balance of evidence seems to favor the RC scenario, there are two points worth noting. First, there has been rising concern that standard RC models might suffer from important underlying systematic errors (e.g., An et al. 2019), which could undermine results coming out from the grid-based modeling approach. Second, there is no direct observational evidence decisively pointing to either scenario. In light of the above, we thus refrain from providing a definitive classification of the evolutionary state of HD 203949.

The history, evolution and fate of the planet orbiting HD 203949 change significantly depending on whether the star is an RGB or a RC star. The more straightforward scenario is that HD 203949 is in the process of ascending the RGB and will eventually engulf the orbiting planet. The alternative scenario, in which HD 203949 is in the RC, calls for a more detailed examination. We now go on to discuss this scenario.

The variations in radius, luminosity, and mass of giant-branch stars often have destructive consequences for planetary systems (Veras 2016). Most important for HD 203949 b is the radius variation of the host star, which could incite star–planet tides that might engulf the planet (Villaver & Livio 2009; Kunitomo et al. 2011; Mustill & Villaver 2012; Adams & Bloch 2013; Nordhaus & Spiegel 2013; Valsecchi & Rasio 2014; Villaver et al. 2014; Madappatt et al. 2016; Staff et al. 2016; Gallet et al. 2017; Rao et al. 2018). The asteroseismic stellar mass of 1.00 ± 0.16 M_⊙ (under the clump assumption) would tidally influence and probably lead to the engulfment and destruction of a Jovian planet on a 184 days orbit at the tip of the RGB.

A planet which is engulfed in the low-density atmosphere of a giant-branch star usually decays quickly enough for it to be considered destroyed. Figure 4 of MacLeod et al. (2018) estimates decay times of engulfed Jovian planets across the Hertzsprung–Russell diagram, and finds that the spiral-in process lasts 10⁰–10⁴ orbits. The upper bound of this range (corresponding to about 5000 yr in our case) is much less than the timescale (about 2 Myr) in which this star's radius would exceed a (0.63 au) during the RGB phase. Hence, HD 203949 b would unlikely have survived being engulfed.

Now let us assume that the planet would avoid being engulfed. In general, there are two outcomes: (1) the outward expansion of the planet's orbit due to stellar mass loss dominates over tidal effects, and the planet's final semimajor axis increases, or (2) tidal effects dominate over mass loss, but only for a short enough time to prevent engulfment, leading to a decrease in the final semimajor axis. Outcome (2) is expected to be rare because the engulfment timescale is so small. Nevertheless, this outcome may explain the current orbit of HD 203949 b under the clump assumption.

We explored this possibility by performing numerical simulations of star–planet tides, with the intention of providing rough estimates.⁴³ We used four different stellar tracks with different values of the Reimers' mass-loss coefficient, η, metallicity and atmospheric type (Krishna Swamy and Eddington, which lead to different model T_eff scales on the RGB and hence different stellar radii), which fit the currently measured stellar observables. In all cases, a planetary semimajor axis corresponding to a 184 days period (0.63 au) is well within the maximal radial extent of the star, which is attained at the tip of the RGB and ranges from 0.85 to 0.99 au across the four tracks. Therefore, outcome (2) from above would apply to this system.

The extent to which the planet would be dragged inward changes depending on the details of the tidal formalism adopted. We used a basic formulation of dynamical tides from Zahn (1977), as implemented in Villaver et al. (2014), by (i) including frictional forces from the stellar envelope, (ii) adopting velocity and density prescriptions from Equations (53) and (54) of Veras et al. (2015), (iii) assuming zero eccentricity throughout the simulation, (iv) assuming a planetary radius of 1.0 R_J, and (v) assuming adiabatic stellar mass loss, which is a robust approximation for this system (Veras et al. 2011).

In order for the planet to achieve an orbit with a semimajor axis of 0.6–1.0 au, we hence find that the main-sequence semimajor axis of the planet would have resided within an extremely narrow range (an interval much smaller than 10⁻² au) centered on a specific value within the interval 3.1–3.5 au (which is set by the stellar model adopted and details of the tidal prescription). This result makes sense in the context of, for example, Figures 1, 4, and 6 of Villaver et al. (2014).

A different, but also viable explanation for the current 0.63 au orbit would be for the planet to have been gravitationally scattered into its current position after the host star had reached the tip of the RGB.⁴⁴ Although RGB mass loss might have triggered the instability leading to this scenario (Debes & Sigurdsson 2002; Veras et al. 2013), more recent suites of simulations of multiple giant-planet systems demonstrate that post-mass-loss scattering events—at least for single stars⁴⁵ —are usually delayed until the white dwarf phase (Mustill et al. 2014, 2018; Veras & Gänsicke 2015; Veras et al. 2016, 2018). Increasing the feasibility of gravitational scattering is that those studies adopted more massive stars than HD 203949, and hence would harbor shorter giant-branch lifetimes in which scattering could occur.