Spinning up the Surface: Evidence for Planetary Engulfment or Unexpected Angular Momentum Transport?

Stellar rotation rates are a sensitive tracer of stellar structure, magnetism, and internal transport of angular momentum. As single stars evolve, several physical processes are expected to act, including angular momentum loss via stellar winds, meridional circulation, internal waves, and magnetic instabilities, among others (see e.g., Maeder & Meynet 2000; Mathis 2013; Aerts et al. 2019). Unfortunately, their relative strength, effectiveness, and timescales have been challenging to constrain theoretically. Each mechanism is, however, generally expected to leave behind a characteristic radial rotation profile. For example, in radiative regions purely hydrodynamic mechanisms such as shear instabilities can act to reduce shear while advective currents can create it (e.g., Zahn 1992; Talon et al. 1997; Meynet & Maeder 2000; Palacios et al. 2003; Decressin et al. 2009; Mathis et al. 2018). Internal magnetic fields are often expected to lead to uniform rotation profiles in large stellar regions (e.g., Mestel & Weiss 1987; Spruit 2002; Eggenberger et al. 2005; Maeder & Meynet 2005; Cantiello et al. 2014; Fuller et al. 2019), while internal gravity waves can create complex and even counter-rotating zones (Kumar et al. 1999; Talon & Charbonnel 2005; Rogers 2015).

The existence of large databases of rotation rates, including spot modulations (e.g McQuillan et al. 2014; Ceillier et al. 2017; Santos et al. 2019; Gaulme et al. 2020; Santos et al. 2021) and spectroscopic $v\sin i$ measurements (e.g., Massarotti et al. 2008; Zorec & Royer 2012; Tayar et al. 2015) have significantly improved our theoretical predictions for the surface rotation rate evolution (Matt et al. 2015; van Saders et al. 2016; Tayar & Pinsonneault 2018). In addition, the ability to use asteroseismology, the study of stellar oscillations, to constrain the internal rotation rates (Beck et al. 2012; Deheuvels et al. 2012; Mosser et al. 2012; Deheuvels et al. 2014; Van Reeth et al. 2016; García & Ballot 2019; Aerts et al. 2019; Li et al. 2020b; Pedersen et al. 2021) of these stars have greatly constrained the rates and timescales of angular momentum transport (Tayar & Pinsonneault 2013; Cantiello et al. 2014) and led to significant theoretical work on the location of differential rotation and the mechanisms determining the rotation profile (Kissin & Thompson 2015; Fuller et al. 2019; Takahashi & Langer 2021).

Stars enter the pre-main sequence with a range of rotation rates inherited from their birth clouds. Interactions with their circumstellar disks as well as winds and outflows serve to regulate that angular momentum as they contract (e.g., Cieza & Baliber 2007), and leave behind a distribution of rotation rates that is likely correlated with the properties of these disks (Mamajek 2009; Rebull et al. 2018). At first, the core of these stars is decoupled from the angular momentum loss happening from the wind at the surface (Denissenkov et al. 2010), but the two zones recouple on mass-dependent timescales of order tens to hundreds of millions of years as these stars approach the main sequence (MacGregor & Brenner 1991; Gallet & Bouvier 2013; Lanzafame & Spada 2015; Somers & Pinsonneault 2016). The complexity of these processes (see also Curtis et al. 2020; Godoy-Rivera et al. 2021) makes it challenging to predict a priori what the rate of rotation or its radial or latitudinal profile should be for stars on the main sequence.

Empirically, it has been found that stars rotate approximately as solid bodies on the main sequence (Van Reeth et al. 2016, 2018; Li et al. 2019; Jermyn et al. 2020) and that seismic estimates of the envelope rotation rates in these stars are consistent with surface rotation measurements from spots or $v\sin i$ (Benomar et al. 2015; Nielsen et al. 2015; Beck et al. 2018; Hall et al. 2021). Once stars leave the main sequence, they seem to rotate close to a solid body for a short evolutionary interval (Deheuvels et al. 2020), then the core contracts and the envelope expands, leading to a rapidly rotating core and a slowly rotating envelope.

However, it has been noted by many authors that the cores do not spin up to the level expected of angular momentum conservation (see e.g., Tayar & Pinsonneault 2013), and so some mechanism must transport angular momentum from the core to the surface. Explorations of various hydrodynamic or magnetic mechanisms have thus far failed to match the necessary amount of angular momentum transport for all the observed stars (Eggenberger et al. 2012; Ceillier et al. 2013; Marques et al. 2013; Cantiello et al. 2014).

The identity of this mechanism has remained unclear, as no current theories perfectly match all the observations (e.g., Eggenberger et al. 2019; den Hartogh et al. 2020). In addition, the radial location of the differential rotation is unclear, and various authors have argued that it could be in the surface convection zone (Kissin & Thompson 2015; Tayar & Pinsonneault 2018; Takahashi & Langer 2021) although others expect it to be concentrated in radiative regions (Fuller et al. 2019; Fellay et al. 2021). For most stars, getting measurements of the rotation rate at more than two locations—usually a "core" and a "surface"—has been challenging because of the limitations of the measurable oscillation modes, and thus this conflict has remained unresolved.

In addition, it is known that orbital angular momentum can be exchanged with rotational angular momentum through tidal interactions (Zahn 1977). Work has suggested that binary synchronization (Song et al. 2013), mass transfer (Packet 1981; Renzo & Götberg 2021), and planet engulfment (Privitera et al. 2016a, 2016b; Bolmont & Mathis 2016; Ahuir et al. 2021) can all affect the rotation of a star. However, the impact of these sorts of interactions on the stellar rotation profile, including the rate at which various regions of the star are spun up, is poorly constrained.

In this paper, we present observations of KIC 9267654 that suggest it has a nonmonotonic radial rotation profile (see Figure 1). Asteroseismology, spectroscopy, and photometry agree that the star is a lower red giant branch (RGB) star (T_eff = 4792 ± 75 K, $\mathrm{log}g$ = 2.98 ± 0.007) of 1.138 ± 0.039 (random) ± 0.035 (systematic) M_⊙ (Pinsonneault et al. 2018). It was observed by the Kepler mission (Borucki et al. 2010) for its full duration. Its seismic oscillations were first characterized by Mosser et al. (2012) and detailed modeling of its oscillation frequencies and rotational splittings were carried out by Corsaro et al. (2015); Pérez Hernández et al. (2016), and Triana et al. (2017). In particular, these works noted a well-constrained core rotation rate of Ω_g = 908–939 nHz (P ${}_{\mathrm{core}}\sim 12.6$ days), slightly higher than average for stars in this regime (Gehan et al. 2018). Several methods of estimation suggested an envelope rotation rate of Ω_p = 20.8–65.0 nHz (P_env ∼ 178–556 days), with most closer to the faster end of that estimate, although a linear fit to the approximate trapping parameter suggested a potentially counter-rotating envelope (see Triana et al. 2017, for more discussion of the various methods used to estimate the envelope rotation and their relative precision). We note that these results are consistent with the ensemble of core rotation rates available for similar stars (Gehan et al. 2018), other estimates of the core rotation rate of this star (Ω_g = 920 ± 10.06 nHz; Gehan et al. 2018), and also simple theoretical models of the surface rotational evolution. The oscillation pattern was used to estimate an inclination angle of ${72.4}_{-6.0}^{+17.6}$ degrees for this star (Gehan et al. 2021), its modes, including the ℓ = 1 modes, looked to have normal visibility, and there was no evidence of surface spots or activity (Ceillier et al. 2017; Gaulme et al. 2020). This star was observed for two sectors by the Transiting Exoplanet Survey Satellite (TESS; Ricker et al. 2015), and designated TIC 164832220, but it is too faint for oscillation modes to be easily detected in those data (see Stello et al. 2022).

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Very recently, Daher et al. (2022) estimated surface rotation velocities for a large number of stars with spectroscopic data from the Sloan Digital Sky Survey (Blanton et al. 2017) Apache Point Galactic Evolution Experiment (APOGEE; Majewski et al. 2017). These stars have moderate resolution (R ∼ 22,000) spectra taken in the H-band on the du Pont and Sloan Foundation (Gunn et al. 2006) telescopes and reduced automatically using the APOGEE Stellar Parameters and Chemical Abundances Pipeline (ASPCAP; Holtzman et al. 2015; Nidever et al. 2015; Zamora et al. 2015; García Pérez et al. 2016; Holtzman et al. 2018; Jönsson et al. 2020) to obtain spectroscopic parameters. For red giant stars, the Daher et al. (2022) analysis ran an additional search for rotational broadening using cross-correlation methods to artificially broadened template spectra (Tayar et al. 2015; Dixon et al. 2020). In their analysis, they suggested a relatively rapid rotation velocity of 6.25 km s⁻¹ for this star, much faster than the (<1 km s⁻¹) rotation velocity suggested by the seismic envelope rotation and inclination constraints. They also found no strong evidence of a close binary companion in the APOGEE radial velocity measurements (ΔRV_max = 0.3 km s⁻¹, v_scatter = 0.18 km s⁻¹), consistent with previous work by Price-Whelan et al. (2020).

The APOGEE survey also provided chemical abundance information for this star (see Section 6), and characterized it as a relatively common evolved solar-like object with a metallicity [Fe/H] = −0.02 ± 0.03 dex and an alpha-element enhancement [α/Fe] = 0.00 ± 0.01, suggesting that it should be comparable to the ensemble of well-studied stars in the Kepler field. This star has also been observed by Gaia. Identified by the Gaia DR3 ID 2107170676942345088, its photometry is consistent with being a red giant (G = 11.97 and BP-RP = 1.193; Gaia Collaboration et al. 2021) relatively nearby (parallax = 0.8444 mas; distance 1151 pc; Bailer-Jones et al. 2021). It follows a disk-like orbit with a low eccentricity (0.18), and it is currently about one thin disk scale height above the Galactic plane (z ${}_{\max }=408$ pc). The Renormalized Unit Weight Error for this star is 0.969, which indicates that it is well fit as a single point source.

The Gaia radial velocity analysis published as part of the Gaia DR3 data release (Gaia Collaboration et al. 2022) indicates a linear trend in the 24 radial velocities of KIC 9267654 of −7.5 ± 3.8 m s⁻¹ day⁻¹, significant at the 2σ level. The star is denoted as an SB1, meaning there are no indications for a second set of lines and implying that the secondary must be fainter than the primary. It need not be much less massive than the primary though since the primary is evolved already, while the secondary might still be on the main sequence. In the following, we derive limits on the mass of the secondary given the radial velocity trend and the primary mass. The 24 radial velocities measurements, which are not available yet individually, have been taken over a time interval of 931.915 days. The mean radial velocity of all measurements taken in that time frame is −28.8 ± 1.1 km s⁻¹.

Assuming that a linear trend without notable deviations can be maintained over at most half of the period of an orbit, the minimum period of the system would be twice as long, i.e., 1864 days or about 5.1 yr. For periods upwards of this limit, we have derived the constraint on the minimum companion mass (companion mass times the sine of the unknown orbital inclination) that would be compatible with a radial velocity semiamplitude consistent with a linear trend of the given value over half of the assumed period under the assumption of a circular orbit. The blue line in Figure 2 illustrates this constraint, while the blue area indicates its 1σ confidence region. The red line indicates the primary mass; the secondary, assuming it is not only less massive but also less luminous than the primary, should have a somewhat smaller mass. As can be seen, orbital periods between 5.1 yr and about 12 yr are all compatible with the nominal observed radial velocity trend, and would generate minimum secondary masses between about 0.3 and 1.0 M_⊙. If the error on the radial velocity trend is taken into account, the minimum masses could be even smaller (down to about 0.1 M_⊙) and the orbital periods somewhat larger (up to about 21 yr). Ground-based radial velocity measurements from APOGEE and the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST; Cui et al. 2012) are sparse and uncertain enough that while they are consistent with the presence of such a trend at about the same order of magnitude, they do not add significant additional constraints. The minimum astrometric signature of all of these orbits is too small (at maximum of the order of 20 μas for the widest orbits) to be detected by Gaia, so this is consistent with the star not having been identified as an astrometric binary already. Depending on the inclination, the astrometric signature could in theory be larger than this limit, and the astrometric excess noise of 63 μas observed for this star could in principle be due to the spectroscopic companion. However, since the Gaia astrometric residuals also suffer from systematics, we refrain from modeling the orbit further based on the astrometric jitter.

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We conclude that it is highly likely that KIC 9267654 is orbited by a low-mass stellar companion with a period of the order of 5 to 20 yr. However, it is complicated to use such a companion to directly explain the surface rotation period. In general, tidal forces (see Section 7.1 for more discussion) work toward synchronizing the orbital and rotational motion, so in the case of a circular orbit, a companion with a 5 yr period would be both too far away to be strongly interacting and would be forcing the surface toward a 5 yr rotation period, not the 42 day period observed. In eccentric orbits, the rotation rate is spun up toward the pseudosynchronous rotation rate, although it does not always reach that value on short timescales (Zimmerman et al. 2017). In order for the likely companion inferred from Gaia to be pseudosynchronized with the observed surface rotation would require an orbital eccentricity greater than 0.98. While highly eccentric binaries including giants do exist (e.g., Heeren et al. 2021), the system properties require careful tuning to survive the main-sequence phase, so we work under the assumption that the wide companion is not directly responsible for the observed rotation. There are also orbital configurations that lead to more complex dynamics where a wide companion can tighten the orbit of an inner pair (e.g., the eccentric Kozai–Lidov effect; Naoz 2016), and it is the unidentified inner body that is causing the anomalous surface rotation. Such a scenario is not inconsistent with our observations, but we do not have sufficient data to confirm the presence of any inner companion directly.

We also note that given we do not detect a second set of oscillations or an anomalous convective background (see Section 5) it is almost impossible for any additional evolved giant stars to be present in the system. Since our primary star is a giant, and therefore quite bright, any main-sequence companion would be significantly fainter. If we assume single star evolution, the less-evolved secondary would be less massive than the primary and therefore at brightest a G star, contributing at most a few percent of the light of the system and therefore unlikely to affect any spectroscopic results derived from deep lines or many lines (Halbwachs et al. 2014), although there is a possibility that some of the abundances derived only from weak lines could be affected. If we allow for the possibility of mass transfer during the main sequence, following the work of Sun et al. (2021), we expect the star we currently see as the primary to have gained mass during its main sequence. This would have reset the rotation rate, but it would likely have spun down to a normal rotation rate relatively quickly (Leiner et al. 2018), and thus would still require an additional interaction much closer to the current time.

Given this evidence, we therefore conclude that the companion identified in the Gaia data should be well separated from and significantly fainter than the star of interest, so it should not substantially impact the detailed seismic or spectroscopic analyses discussed in the following sections. We also do not expect it to be directly related to the unusual rotation profile we observe, but suggest that further study could prove interesting in a dynamical sense.

Given the highly unusual detection of a surface rotation faster than the bulk envelope rate, it seemed necessary to confirm the surface rotation velocity. In particular, the APOGEE resolution is only R ∼ 22000, which has a formal $v\sin i$ detection limit of 13.1 km s⁻¹. While cross-correlation analysis has suggested that it is possible to distinguish slower rotation velocities, values below 10 km s⁻¹ are still difficult, and most authors are highly skeptical of constraints below ∼5–8 km s⁻¹ (Tayar et al. 2015; Dixon et al. 2020; Simonian et al. 2020).

We therefore obtained a higher resolution spectrum using the High-Efficiency and high-Resolution Mercator Echelle Spectrograph (HERMES; Raskin et al. 2011) instrument on the 1.2 m Mercator telescope on La Palma. The star was observed on 2021 October 28 for two observations of 45 minutes, each with a signal-to-noise ratio (S/N) of ≈20 at 618 nm and with a resolution of R ≃ 85,000. Data were reduced using the dedicated HERMES reduction pipeline, which includes flat-fielding and wavelength calibration (Raskin et al. 2011). In order to infer the spectroscopic parameters, the HERMES spectra were first normalized by fitting a second-order spline to the continuum following the method described in Abdul-Masih et al. (2021). Then the two spectra were coadded and compared to a large grid of model atmospheres using the spectral analysis code Grid Search in Stellar Parameters (GSSP; Tkachenko 2015). GSSP uses a grid of atmosphere models precomputed with LLmodels (Shulyak et al. 2004) and computes synthetic spectra on the fly using the SynthV (Tsymbal 1996) spectrum synthesis code. The HERMES spectral range covers from 400 to 900 nm, but only the region from 450 to 700 was used for the stellar parameter search. This analysis was done independently of the APOGEE parameters.

The resulting fits (see Figure 3) were very similar to the APOGEE values with ${T}_{\mathrm{eff}}={4750}_{-210}^{+220}$ K, $\mathrm{log}g$ = 3.16 ± 0.46 dex, and $[{\rm{M}}/{\rm{H}}]=-{0.05}_{-0.20}^{+0.18}$ dex, suggesting that the published spectroscopic parameters are likely to be reliable. In addition, this analysis gave an estimate for the surface rotation velocity of $v\sin i={5.96}_{-0.97}^{+0.91}$ km s⁻¹, consistent with the APOGEE constraint, and significantly inconsistent with the seismic envelope rotation rate.

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In addition, the cross-correlation function of the individual HERMES spectra show no evidence for a second set of lines that would indicate a spectroscopic binary companion, nor do they show any strong radial velocity shifts that may have been expected in a tidally locked system with a stellar mass secondary component, although we cannot confirm or further constrain the sort of wide companion suggested by the Gaia data. We also report the nondetection of lithium features at around 670 nm in our optical spectrum. Given the measurement constraints, this rules out a lithium abundance at or above solar ([Li/Fe] < 0, A(Li) < 1.1). Such abundances would be consistent with previous observations of the lithium abundance for a star of this mass, metallicity, and surface gravity, as for most giants the lithium line is not detectable, although the detectability does scale with temperature (Martell et al. 2021). However, given that we only measure an upper limit, we cannot rule out this star being depleted in lithium, which has been suggested to occur in some cases where planetary engulfment drives mixing through the thermohaline instability (Deal et al. 2015).

Barium is an element often used to identify stars that have been polluted by AGB companions. We have examined our HERMES spectrum for regions sensitive to barium and found no evidence of barium overabundance in this giant.

The original asteroseismic estimates of the core and envelope rotation rates come from the work of Triana et al. (2017), which analyzed a sample of 13 stars on the lower red giant branch using a variety of methods to try to separate the information from the core region from the envelope region. Their core rotation estimate was later shown to be consistent with an entirely independent analysis published in Gehan et al. (2018), emphasizing that this result, which is much simpler to measure, is likely to be robust. However, the envelope rotation rate can be more challenging to estimate, and so they applied six different methods including models, inversions, inferences, and fits (see Triana et al. 2017, for a more detailed discussion of each method). For KIC 9267654, four of the rotation rates measured by these methods agreed to within the uncertainties.

For this paper, we have taken a careful look at the available Kepler data, using the KEPSEISMIC ²⁵ light curves (García et al. 2011, 2014; Pires et al. 2015), where the data systematics, gaps, and instrumental effects have been carefully treated, and compare the results to the ensemble of Kepler data that have been homogeneously analyzed in the time since the original papers on this star were published. In our analysis, we have searched for any indication that would suggest that any of the properties might be unusual or mismeasured in a way that could impact the conclusions of this paper. We have found no such evidence.

Specifically, we find that the convective background for this star (see the top panel in Figure 4) is entirely consistent with the relations found for the Kepler red giants (Mathur et al. 2011; Kallinger et al. 2014), in agreement with what was found for this star in Sayeed et al. (2021). This also makes it hard to imagine that the spectroscopic broadening we are interpreting as rotation is caused by unusual atmospheric macroturbulence, which should also correlate with the stellar surface convection and thus the granulation. We also find that the mode amplitudes and widths for this star are fully consistent with the expectations for a star of this type (e.g., Mosser et al. 2011; Corsaro et al. 2017), with no obvious indications of e.g., strong magnetic fields (Fuller et al. 2015; Loi 2020; Bugnet et al. 2021). All of these properties are measured at extremely high S/N (see the bottom panel in Figure 4) using the Markov Chain Monte Carlo (MCMC) Bayesian fitting code apollinaire ²⁶ (Breton et al. 2022). By doing so, we ensured that the new results were not dependent on the Bayesian fitting scheme used (i.e., MCMC with apollinaire versus a nested sampling tool in DIAMONDS; Corsaro & De Ridder 2014).

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Because the signal-to-noise in the seismic modes is so high, estimating rotational splittings for this star is much less challenging than usual. The g-mode dominated ℓ = 1 mixed modes are significantly narrower and offset from the usual ℓ = 1 ridge; their splitting is clear and consistent with previous estimates of the core rotation rate.

We have also looked at the available ℓ = 2 and ℓ = 3 modes for potential detection of rotational splittings from the envelope region. Using apollinaire, we fit five orders of ℓ = 0, 2 modes and three ℓ = 3 modes between 95 and 136 μHz. We allow the splitting, ν_s , to vary between 0.01 and 0.6 μHz, and allow the amplitude ratios between the different degree modes to vary freely. Our MCMC chain had 500 walkers and between 20,000 and 55,000 steps. We tested a variety of different constraints on the inclination angle. We concluded that it is not possible with the current data to effectively constrain the inclination angle of the star using only the p modes. It was only possible to constrain a combination of the projected splitting and the inclination angle (Ballot et al. 2006). For this reason, we used the inclination angle derived from the mixed modes by Gehan et al. (2018) to run a final fit of the p modes; the result is shown in Figure 5. This requires assuming that the inclination of the envelope is the same as the inclination of the core, which may or may not be true depending on what has happened to this star. Nevertheless, this seems the most reasonable starting assumption, and it produces a posterior probability of the inclination angle is rather flat with a median value of ${78.1}_{-8.0}^{+8.1}$ degrees and a rather Gaussian posterior probability for the rotational splitting centered at 0.021 ± 0.006 μHz (corresponding to rotation periods between 445 and 825 days). It is worth noting that for all of the fits using only p modes that we have tried, the envelope rotation periods obtained were longer than 200 days, regardless of the chosen inclination constraint. They were also generally slower than the rotation constraints published in Triana et al. (2017), but for our purposes that only makes the detected rapid rotation of the surface more significant.

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Further explorations of this star might consider imposing a nonmonotonic rotation profile ad hoc on top of a stellar structure model whose fundamental parameters reproduce those of KIC 9267654. The imposed rotation profile should match the inferred estimates at the core-envelope boundary, subsurface convection zone, and surface, respectively. From here, one could determine that model's theoretical pulsation spectrum using the GYRE stellar oscillation program (Townsend & Teitler 2013), including the rotation kernels of each oscillation mode observed in the spectrum, and compare this to the observations to determine whether additional constraints can be placed on the stellar latitudinal or radial rotation profile (García et al. 2008; Davies et al. 2015). However, given the challenges of such an exercise (Gizon & Solanki 2003), we consider it beyond the scope of this study.

It has been shown that much of the variance in the elemental abundances of dwarf stars in the Galactic disk is confined to a small number of independent chemical vectors that can be mapped to various Galactic enrichment processes (Price-Jones & Bovy 2018; Weinberg et al. 2019; Griffith et al. 2021; Joyce et al. 2022). This provides us with fairly strong expectations for the abundance patterns of stars as a function of age, mass, and metallicity, making it possible to identify outliers from the expected pattern in a fairly straightforward manner. If the unusual rotation profile of KIC 9267654 is due to some kind of mass transfer or collision with a companion or a planet, enrichment by an AGB star, or the result of formation in an unusual environment, it is conceivable that such an event could have resulted in a deviation of its surface abundances from this expected pattern. Again, we find no strong evidence of such a deviation.

To explore this possibility, we selected a comparison sample from the APOKASC-2 catalog of stars with measured asteroseismic gravities, ages, and masses (Pinsonneault et al. 2018) and many elemental abundances determined in APOGEE DR16 (Ahumada et al. 2020). We kept all stars with valid results for seismic $\mathrm{log}g$, age, and mass, and with T_eff within 50 K, $\mathrm{log}g$ within 0.3 dex, and mass within 0.1 M_⊙ of KIC 9267654. Figure 6 compares these 176 RGB stars to KIC 9267654 in α-enhancement versus metallicity and mass versus age, to give a sense of the properties of this star as well as the range of the comparison sample, and they are all quite similar in these fundamental quantities. As one might expect when looking at a restricted metallicity range in the Kepler field, most of these stars are α-poor disk members with α-element abundances that correlate slightly with metallicity, and masses that are strongly correlated with their inferred ages.

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In Figures 6, 7, and 8 the blue crosses in the lower left of each panel show the median uncertainties in the comparison set, and we have increased the reported uncertainties in the fundamental parameters [M/H] and [α/Fe] by a factor of 5 to make them more visible. While we note that the reported uncertainties seem rather small, investigating their reasonableness is outside the scope of the present investigation.

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Figures 7 and 8 show individual elemental abundances versus metallicity for the comparison stars as well as KIC 9267654. Figure 7 focuses on carbon, nitrogen, and oxygen, which are produced and destroyed in CNO cycle fusion, and serve as sensitive indicators of dredge-up and internal mixing in red giant stars. The value of the carbon-to-nitrogen ratio [C/N], which is set by the depth and temperature of the first dredge-up in giants, is strongly correlated with stellar mass for stars low on the red giant branch, as this star is (Martig et al. 2016; Ness et al. 2016). The gain of a large amount of mass from a stellar or substellar companion could potentially alter the surface abundances and move a star off of this correlation. We show in the lower panel of Figure 7 that this star is only slightly discrepant with the comparison sample, and as such has likely not gained more than a few hundredths of a solar mass since its first dredge-up. The middle right panel in Figure 7 also shows [C/N] versus [M/H]. The ratio for KIC 9267654 is well within the distribution of the APOKASC comparison sample, which similarly does not seem to require significant abundance changes or mass gain from a companion after the first dredge-up.

In Figure 8 elements from the different nucleosynthetic groups are labeled in red (light odd-Z), green (alpha), magenta (iron peak), and purple (neutron capture). KIC 9267654 is clearly depleted in aluminum and enhanced in copper relative to the comparison set, mildly enhanced in carbon, manganese, and cerium, and depleted in silicon and potassium. These are not known signals of any common internal mixing, binary mass transfer, or planetary engulfment process. We are aware that some of the abundances presented in this Figure could shift with the inclusion of NLTE effects. However, since the comparison stars are of similar temperatures, surface gravities, and metallicities, we expect the whole sample to be shifted in similar ways and thus we do not expect NLTE effects to significantly change which abundances in our star are anomalous relative to the comparison sample.

We also explore whether the lack of detected lithium enhancement can place constraints on the accretion of material from a stellar or substellar companion. Using the Galactic Archaeology with HERMES DR2 data set (GALAH; Buder et al. 2018), merged with effective temperature and luminosity measurements from Gaia DR2, we investigated a population of 26,183 stars with lithium abundance signatures and [Fe/H] = 0 ± 1 dex. Following the procedure outlined in Soares-Furtado et al. (2021), we binned these signatures by the stellar effective temperature and luminosity, calculating the median lithium baseline for each bin, as well as the median absolute deviation of the median lithium baseline. Using a postprocessing approach that is also outlined in Soares-Furtado et al. (2021), we then determined the lithium enrichment signature accompanying the ingestion of a 1 M _Jup substellar companion.

For a star of 1.1 M_⊙, T_eff = 4792 K, and L = 15.4 L_⊙, we calculated that a lithium baseline of A(Li) = 1.03 ± 0.18 dex would be expected on average, although a large range of lithium abundances is observed in the population. For such a host, the ingestion of a 1 M _Jup companion would result in a lithium abundance signature of 1.1 dex, which would only represent a statistically insignificant 0.5σ increase in the expected lithium abundance.

To produce a statistically significant (5σ) lithium enrichment signature, a star of this mass and evolutionary state would be required to consume a companion of 33 M _Jup—a massive brown dwarf or tens of gas giants. We illustrate the minimum-mass companion required to produce an ingestion-derived lithium enrichment signature with a 5σ statistical significance in Figure 9, where KIC 9267654 is illustrated in the H-R diagram as a red star. Also depicted are the location of the main-sequence turnoff (gray-hued cross) and luminosity bump (salmon-hued diamond) corresponding to this stellar track. Given the large mass that would need to be ingested to create a significant lithium enhancement, we determine that an observable lithium enrichment signature is extremely unlikely to be present in a star of this mass and evolutionary state, and therefore the lack of a lithium detection in this star is not sufficient evidence to rule out a significant interaction event. Similarly, the upper limit we are able to place on the lithium abundance is not low enough to argue for mixing-driven lithium depletion (Deal et al. 2015) and so the observed lithium constraint argues neither for nor against any particular formation scenario. For consistency with Soares-Furtado et al. (2021), we have used the GALAH DR2 data set for this analysis and comparison. While the GALAH DR3 data set is now available (Buder et al. 2021), we do not expect that changing to the newer measurements would substantially change our conclusion that significant mass would have to be accreted to create a noticeable change in the lithium abundance for a star with this deep of a surface convection zone.

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Given that our further investigations of the rotation of KIC 9267654 seem to indicate that the inferred nonmonotonic rotation profile is robust, it is interesting to consider how the star ended up in this unusual configuration. There are several potential explanations that must be considered in our endeavor to understand the unusual rotation profile of KIC 9267654.

7.1. Tidal Waves

7.2. Turbulent Convection

7.3. Internal Gravity Waves

We have presented evidence to support the existence of a nonmonotonic radial rotation profile for KIC 9267654, with a rapidly rotating core (P_core = 12.6 days), a slowly rotating envelope (P_env ≳ 178 days), and a moderately rotating surface (P_surf = 42 days), inferred using a combination of spectroscopic and asteroseismic data. We have collected this evidence from two entirely independent spectroscopic investigations, as well as several asteroseismic analyses. The data seem to consistently indicate that KIC 9267654 is a relatively normal lower red giant branch star, whose only glaringly unusual feature is its odd rotation profile, and possibly a few offset abundances. While Gaia suggests a companion in an orbit much longer than the rotation period, we find no evidence for the existence of a tidally synchronized stellar companion or significant ongoing mass transfer in this system, although we cannot exclude such scenarios entirely.

We note that this star is not the only giant with an unusual surface rotation rate. Other stars have been noted whose claimed surface rotation rates are faster than their core rotation rate (e.g., Kurtz et al. 2014; Ceillier et al. 2017; Aerts et al. 2019; Tayar et al. 2019), or significantly faster than single stellar evolution would predict (e.g., Ceillier et al. 2017; Tayar & Pinsonneault 2018). However, in most of these cases, the unusual surface rotation is presumed to be linked to tidal interactions with another star (Tayar et al. 2015; Li et al. 2020a; Daher et al. 2022) or a much earlier planetary engulfment (Carlberg et al. 2012; Privitera et al. 2016c; Bolmont & Mathis 2016; Ahuir et al. 2021). In other cases, these stars come from ensemble analyses, where a few percent of stars are often affected by measurement errors or target contamination (Aigrain et al. 2015), and envelope rotation rates are rarely available. Finally, in other well-studied red giants including e.g., KIC 3744043, the envelope rotation rate estimated with asteroseismic techniques (P_env ∼ 104–159 days; Triana et al. 2017) may come out slightly slower than the surface rotation rate measured from the broadening of spectroscopic lines ($v\sin i$ = 2.5 ± 1.0 km s⁻¹, P_rot ∼ 94.5 ± 45.9 days; Thygesen et al. 2012; Gehan et al. 2021). Nonetheless, the disagreement is within the properly propagated measurement uncertainties and its core is rotating significantly faster than both its envelope and surface, over a period of ${{P}}_{\mathrm{core}}\sim 21.6$ days (Triana et al. 2017; Gehan et al. 2018), which makes it hard to draw strong conclusions. What makes KIC 9267654 so interesting is the existence of a well-measured three-point rotation profile where all three measurements have been verified by multiple teams and independent analyses, and the surface and envelope rotation rates disagree with each other at a significant level given the small measurement uncertainties.

Given the exciting possible explanations of the unusual rotation profile detected in KIC 9267654, and their impact on our understanding either of planetary engulfment and tidal theory or some unexplained physics in low-mass stellar interiors, we encourage further observational and theoretical work on this exciting system. In particular, a more detailed observational analysis of the surface rotational and chemical properties including r-process and s-process abundances could be interesting, as would longer-term searches for spot modulation as well as searches for surviving planetary companions in the system. Theoretical modeling of both tidal theory in general, as well as specific companions and orbital configurations that could produce the characteristics observed for KIC 9267654 might prove quite illuminating. More generally, the ability to not only identify planets in stable configurations similar to our own solar system, but also to trace out their changes as their stars evolve (Grunblatt et al. 2017; Rizzuto et al. 2017; Chontos et al. 2019; Gänsicke et al. 2019) has opened and is likely to continue to open interesting windows toward understanding planetary formation, evolution, and long-term habitability, while simultaneously constraining the physics of stellar surfaces and interiors.

We thank the referee for an efficient and helpful report. We thank Carles Badenes, Christine Daher, Daniel Huber, Anne Hedlund, and Lisa Bugnet for the helpful discussions that contributed to this paper. We also thank the members of the rotation working group at the KITP Transport in Stars 2021 program for input on this paper, and therefore acknowledge that this research was supported in part by the National Science Foundation under grant No. NSF PHY-1748958.

Support for this work was provided by NASA through the NASA Hubble Fellowship grant No. 51424 awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS5-26555. S.K. acknowledges funding from the European Union H2020-MSCA-ITN-2019 under grant agreement No. 860470 (CHAMELEON).

D.M.B. and T.V.R. gratefully acknowledge funding from the Research Foundation Flanders (FWO) by means of senior and junior postdoctoral fellowships with grant agreements 1286521N and 12ZB620N, respectively, and FWO long stay travel grants V411621N and V414021N, respectively.

M.S.F. gratefully acknowledges the support provided by NASA through Hubble Fellowship grant HST-HF2-51493.001-A awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, In., for NASA, under the contract NAS5-26555.

R.A.G., S.N.B, and S.M. acknowledge the support from GOLF and PLATO CNES grants at CEA Paris-Saclay.

S.L.M. acknowledges the support of the Australian Research Council through Discovery Project grant DP180101791.

S.R. gratefully acknowledges the support of the DFG priority program SPP 1992 "Exploring the Diversity of Extrasolar Planets" (RE 2694/7-1).

Based on observations obtained with the HERMES spectrograph, which is supported by the Research Foundation Flanders (FWO), Belgium, the Research Council of KU Leuven, Belgium, the Fonds National de la Recherche Scientifique (F.R.S.-FNRS), Belgium, the Royal Observatory of Belgium, the Observatoire de Genève, Switzerland and the Thüringer Landessternwarte Tautenburg, Germany.

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. STScI is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555.

This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/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 research has made use of NASA's Astrophysics Data System Bibliographic Services.

Funding for the Sloan Digital Sky Survey IV has been provided by the Alfred P. Sloan Foundation, the U.S. Department of Energy Office of Science, and the Participating Institutions.

SDSS-IV acknowledges support and resources from the Center for High Performance Computing at the University of Utah. The SDSS website is www.sdss.org.

SDSS-IV is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS Collaboration including the Brazilian Participation Group, the Carnegie Institution for Science, Carnegie Mellon University, Center for Astrophysics ∣ Harvard & Smithsonian, the Chilean Participation Group, the French Participation Group, Instituto de Astrofísica de Canarias, The Johns Hopkins University, Kavli Institute for the Physics and Mathematics of the Universe (IPMU)/University of Tokyo, the Korean Participation Group, Lawrence Berkeley National Laboratory, Leibniz Institut für Astrophysik Potsdam (AIP), Max-Planck-Institut für Astronomie (MPIA Heidelberg), Max-Planck-Institut für Astrophysik (MPA Garching), Max-Planck-Institut für Extraterrestrische Physik (MPE), National Astronomical Observatories of China, New Mexico State University, New York University, University of Notre Dame, Observatário Nacional/MCTI, The Ohio State University, Pennsylvania State University, Shanghai Astronomical Observatory, United Kingdom Participation Group, Universidad Nacional Autónoma de México, University of Arizona, University of Colorado Boulder, University of Oxford, University of Portsmouth, University of Utah, University of Virginia, University of Washington, University of Wisconsin, Vanderbilt University, and Yale University.

Facilities: Du Pont (APOGEE) - , Sloan (APOGEE) - , 2MASS - , Gaia - , Kepler - , HERMES. -

Software: apollinaire (Breton et al. 2022), Astropy (Astropy Collaboration et al. 2013, 2018), corner (Foreman-Mackey 2016), george (Ambikasaran et al. 2015), h5py (Collette 2013), Matplotlib (Hunter 2007), NumPy (van der Walt et al. 2011), pandas (pandas development team 2020), SciPy (Virtanen et al. 2020).