© The Authors 2025

1. Introduction

Although the majority of exoplanets are detected around stars on the main sequence (MS), the study of planets orbiting red giants (RGs) provides insights on the impact of stellar evolution on the orbital and physical properties of planetary systems, which is one of the key scientific goals of the future PLATO mission (Rauer et al. 2025). Studying planets around RGs is also crucial to understand the fate of planets around white dwarfs, which represent the ultimate evolutionary stage of ∼97% stars. Indeed, the dramatic changes in the stellar structure during the red giant branch (RGB) phase are thought to impact the planets orbits in two opposing ways: orbital decay caused by the expansion of the stellar radius and orbital expansion caused by the stellar mass loss (e.g., Nordhaus & Spiegel 2013). Characterizing these physical processes calls for observational studies of the evolution of planets along the RGB. So far, ∼440 evolved stars have been found to host planets (∼230 subgiants and ∼210 RGs, e.g., Chen et al. 2023).

In the event of a planet being engulfed, the angular momentum conservation of the star-planet system implies an acceleration of the host star’s rotation, generating a more efficient dynamo and, thus, a stronger magnetic field (Aurière et al. 2015). Thus, the detection of rapid surface rotation and/or high magnetic activity could be a detectable signature of planet engulfment (Privitera et al. 2016a,b; Tayar et al. 2022; Ong et al. 2024). Additionally, the existence of a misalignment between the core and the envelope rotation axes has also been shown to potentially result from planet engulfment in the case of the rapidly-rotating RGB star Kepler-56 (Ong 2025; Tokuno 2025). The lack of observed hot Jupiters and the prevalence of multiple planetary systems around subgiants and RGs are potential indicators of planet engulfment as the stellar radius increases (Lillo-Box et al. 2016). Moreover, it has been estimated that ∼10% of stars with M ∼ 1 − 2 M_⊙ will engulf a planet of mass 1−10 Jupiter masses during their evolution as red giants (e.g., O’Connor et al. 2023).

Gaulme et al. (2020) observed that the fraction of active RGs (i.e., those exhibiting photometric rotational modulation due to the existence of spots in co-rotation with their photosphere) is larger on the horizontal branch (HB), where stars undergo core-helium burning, than on the RGB, where stars undergo shell-hydrogen burning around the inert helium core, for low-mass (LM) stars with M ≲ 1.5 M_⊙. These authors interpreted such an observation as a potential signature of planet engulfment, resulting in LM stars gaining angular momentum during their ascent of the RGB; hence, they would appear more active once they settle on the HB. This scenario is reinforced by the fact that Gaulme et al. (2020) did not observe any such trend for intermediate-mass (IM) stars with M ≳ 1.5 M_⊙. For IM stars, they found that the fraction of active stars decreases from the RGB to the HB phase, as expected. This difference in the activity of LM versus IM stars could result from the much smaller maximum radius reached at the RGB tip for IM stars compared to LM stars, allowing LM stars to potentially engulf more planets that can further increase their angular momentum and, as a result, boost their activity (Gaulme et al. 2020). However, the possibility that the activity increase observed by Gaulme et al. (2020) for LM stars actually results from an observational bias has not been excluded. Indeed, large and/or long-living spots result in a larger photometric variability than smaller and/or short-living spots, which could lead to a higher detection rate of the associated surface rotation period (Rackham et al. 2018; Basri & Shah 2020). Since the stellar structure changes dramatically between the RGB and the HB, with a significant expansion of the radius followed by shrinking (Kippenhahn et al. 2013) as well as mass loss (Harper 2018), we could expect the surface magnetic field properties to also be impacted (including the spots distribution and/or properties). It might be the case that spots are also present for a similar fraction of LM RGB stars than for LM HB stars, but might not be detected if they are smaller and/or with shorter lifetimes than on the HB phase.

To get a more complete view of the activity of RGs with different evolutionary stages and masses, we need independent indicators tracing the activity level regardless of whether or not spots are detected on the photosphere. To that end, I use several spectral lines whose depths trace the level of chromospheric activity; namely, the Ca II H&K lines (3969 & 3934 Å), one of the MgI lines (5184 Å), the Hα line (6563 Å), and one of the Ca II infrared (IR) lines (8542 Å). The depths of these lines have been measured by Gehan et al. (2022, 2024) using optical spectra from Data Release 7 of the Large Sky Area Multi-Object Fiber Spectroscopic Telescope survey (LAMOST) for ∼3000 RGs whose photometric variability was previously measured by Gaulme et al. (2020) using Kepler data.

Here, I aim to investigate how the magnetic activity of RGs evolves for LM versus IM stars along the RGB and towards the HB, setting the results in the context of planet engulfment. In Sect. 2, I explain the method I used to study the measured magnetic activity indicators as a function of stellar evolution and describe the data set. I present my results in Sect. 3. In Sect. 4, I discuss the results and emphasizes the observational indications of potential planet engulfment by combining existing envelope rotation measurements, models of internal stellar structure, and properties of the planets known up-to-date. Section 5 is devoted to the conclusions.

Fig. 1. Activity indicators as a function of νmax (inverted axis). LM and IM stars on the RGB are represented by grey and blue dots, respectively. LM and IM stars on the HB are represented by red and orange triangles, respectively. KIC 9267654 and KIC 9780154, which might have engulfed one or more planets since their surface rotates faster than their envelope, are shown with the magenta cross and star symbols, respectively. Vertical dotted lines indicate νmax = 100 μHz. Continuous and dashed lines represent a fit by a power law to the RGB stars and the corresponding 2σ prediction interval around the fit, respectively.

2. Method and data

I used the chromospheric activity indicators measured by Gehan et al. (2024) for ∼3000 RGs, using the Ca II H&K lines, the Mg I line at 5184 Å, the Hα line, and the Ca II IR line at 8542 Åfrom the optical spectra of Data Release 7 of LAMOST to investigate stellar activity along the RGB and on the HB. The resulting chromospheric indicators are S​_{Ca II H&K}, S_Mg I, S​_Hα, and S_Ca II,IR, respectively.

On the RGB, I considered two sets of stars, one on the early RGB with ν_max ≥ 100 μHz and the other slightly more evolved with ν_max < 100 μHz. I used ν_max = 100 μHz to separate the two sets of stars to keep a significant number of stars in each set. In addition, I considered LM and IM stars separately on the RGB and on the HB. I assumed that LM stars have M ≤ 1.5 M_⊙ and IM stars have M > 1.5 M_⊙ in accordance with the findings of Gaulme et al. (2020), namely, that the active star fraction evolves differently between the RGB and the HB for stars below and above 1.5 M_⊙; therefore, they are increasing for M ≤ 1.5 M_⊙, while decreasing for M > 1.5 M_⊙. The numbers of LM and IM stars for each evolutionary stage and activity indicator are presented in Table 1. The values for ν_max and stellar mass were obtained by Gaulme et al. (2020) and, in this table, I also indicate the corresponding numbers of RGs from Gaulme et al. (2020). To take into account the evolution of each activity indicator along the RGB, I fit a power law as a function of ν_max to the stars on the RGB (Fig. 1) to get a reference activity level along the RGB, which I also used to compare activity on the HB with respect to the RGB.

For each activity indicator (except the Hα indicator), I then computed the active star fraction as the fraction of stars with an activity index above the corresponding 2σ prediction interval around the fit. As regards the Hα indicator, Gehan et al. (2024) strikingly noticed that it is correlated with the oscillations amplitude, which is at odds with the expectation that higher activity levels lead to the suppression of oscillations, which was what Gehan et al. (2024) observed with the other activity indicators. The authors interpreted this observation as resulting from the more important contribution of dark filaments to the Hα line compared to the other spectral lines (Meunier & Delfosse 2009). The number and size of dark filaments are expected to increase with the level of activity in the case of the Sun (Mazumder et al. 2021), which could result in a smaller Hα indicator at higher stellar activity levels. Furthermore, the absorption in the Hα line has been observed to first increase with the activity level in Ca II H&K, before switching to emission for a high enough level of activity in Ca II H&K (Cram & Mullan 1979; Cram & Giampapa 1987; Scandariato et al. 2017; Meunier et al. 2022). This is also consistent with the observation of high Hα indices for the RGs in close binaries that also exhibit high activity levels in the other spectral lines (Gehan et al. 2024). Since most of the RGs studied here are not very active, I expect the Hα index to be anticorrelated with the activity level on average. Hence, I consider that stars are active in Hα if S​_Hα lies below the 2σ prediction interval around the fit, by contrast with the other activity indicators analyzed in this study.

I checked to ensure that taking the 3σ prediction interval instead of the 2σ prediction interval around the fit in Fig. 1 would not significantly change the trends derived in this study; although, it did significantly decrease the number of stars considered active (see Appendix A). Indeed, the active star fractions derived using the 3σ prediction interval are much lower and are not in agreement overall with the active star fractions derived by Gaulme et al. (2020) based on the photometric detection of rotation periods. Hence, I chose to keep the 2σ prediction interval in the present study as a threshold for determining the active star fractions from different chromospheric activity indicators.

3. Results

The numbers and fractions of active LM and IM stars on the early RGB, medium RGB, and the HB are presented in Table 2 and displayed in Fig. 2. In addition, I recomputed the fraction of photometrically active RGs from Gaulme et al. (2020) by selecting the RGs that have a detected rotation period and discriminating between LM and IM RGs on the low RGB, the medium RGB, and on the HB in the same way as I did for the other activity indicators.

Fig. 2. Evolution of the active star fractions using different activity indicators from the lower RGB (νmax ≥ 100 μHz) to the medium RGB (νmax < 100 μHz) and the HB (on the right-hand side of the vertical dashed lines). Blue bars and arrows correspond to low-mass stars. Orange bars and arrows correspond to IM stars. Bottom panel indicates in addition the fractions of active LM (green bars and arrows) and IM (red bars and arrows) stars computed over the whole RGB without discriminating between the lower (νmax ≥ 100 μHz) and medium (νmax < 100 μHz) RGB.

3.1. Fractions of active stars along the red giant branch

On the low RGB, I observe that the fraction of active IM stars is higher than for LM stars for all the activity indicators considered here (Fig. 2). This is expected because during the main sequence, IM stars have a shallow convective envelope, or even no convective envelope at all for M ≥ 1.3 M_⊙, contrary to LM stars that have a deep convective envelope. As a consequence, LM stars spin-down due to magnetic braking (Kraft 1967; Skumanich 1972), which consists of a coupling between the surface magnetic field and the stellar wind (Schatzman 1962; Weber & Davis 1967; Mestel 1968). By contrast, IM stars do not undergo magnetic braking during the main sequence and are therefore expected to enter the RGB with a faster surface rotation and higher level of activity than LM stars see Sect. 4.1.1.

I observed clear differences in the evolution of the fraction of active LM versus IM stars along the RGB for all the activity indicators used. The fraction of active IM stars decreases for all the activity indicators considered in the present study, while the fraction of active LM stars decreases only for the Hα indicator and for RGs with a photometric rotation period as a signature of the existence of magnetic activity, for which the decrease is systematically sharper for IM stars compared to LM stars. I note that the fraction of active LM stars becomes larger than that of IM stars for the Ca II H&K, Mg I, and Ca II IR indicators, while it remains below that of active IM stars for the Hα indicator and for RGs with a photometric rotation period.

In addition, the left panel of Fig. 3, along with the data in Table 3, show that the decrease in the fraction of active stars on the medium RGB compared to the low RGB is larger for IM stars than for LM stars for almost each given activity indicator. The exception lies for RGs with a photometric rotation period as a signature of the existence of magnetic activity; in this case, I observed instead that the fraction of active stars on the medium RGB decreases to a greater extent compared to the low RGB for LM stars. Overall, the fractions of active stars between the low and the medium RGB decrease by a median factor of 2.8 for IM stars and increase by a median factor of 1.1 for LM stars when considering only chromospheric activity indicators (see Table 3). This stands in contrast with the results I obtain by by discriminating RGs that have a photometric rotation period on the early and the medium RGB, for which I find an increase of the active stars fraction by a factor of about 10−11 for both LM and IM stars. This may reflect the bias that photometric spot detections can be susceptible to (Rackham et al. 2018; Basri & Shah 2020).

Fig. 3. Ratios between the fractions of active stars for different evolutionary stages for the different activity indicators used in this study (written on the x-axis). LM and IM stars are represented in blue and in orange, respectively. Horizontal dashed lines in bold indicate a ratio of 1, while the other horizontal dashed lines indicate ratios of 2 and 3. Left: Ratios between the low RGB (νmax ≥ 100 μHz) and the medium RGB (νmax < 100 μHz). Right: Ratios between the HB and the medium RGB. For RGs with detected Prot, we indicate in addition the ratios obtained for active LM (green cross) and IM (magenta cross) stars when considering stars across over the whole RGB without discriminating between the lower and medium RGB.

3.2. Fractions of active stars on the horizontal branch

I also observe that the fraction of active stars increases for both LM and IM stars on the HB compared to the medium RGB, for all the activity indicators except the Ca II indicators: the fraction of active LM stars remains roughly the same for the Ca II H&K indicator, while the fraction of both LM and IM stars decreases for the Ca II IR indicator. This stands in partial contrast with the findings of Gaulme et al. (2020), who observed that the fraction of photometrically active stars does indeed increase on the HB in the case of LM stars and, on the contrary, it decreases for IM stars. However, Gaulme et al. (2020) did not discriminate between stars on the early RGB and the medium RGB as I have for the purposes of the present study. When I consider LM and IM stars on the RGB altogether, for which Gaulme et al. (2020) detected the rotation period through photometry (green and red bars and arrows in the bottom panel of Fig. 2), I also observed the same trend as Gaulme et al. (2020): the fraction of active LM stars increases on the HB compared to the RGB, while the fraction of active IM stars decreases. I also note that the fraction of active stars on the HB is larger for IM stars compared to LM stars, except for the Ca II IR indicator for which the opposite trend was observed.

In addition, the right panel of Fig. 3 and Table 4 show that the increase in the fraction of active stars on the HB compared to the medium RGB is larger for IM stars compared to LM stars for almost all activity indicators, except for the Ca II IR indicator and when considering RGs that have a photometric rotation period. Overall, the fractions of active stars between the HB and the medium RGB increase by a median factor of 2.8 for IM stars and of 2.5 for LM stars when considering only chromospheric activity indicators (see Table 4). These results differ significantly from those of Gaulme et al. (2020) obtained by considering RGs that have a photometric rotation period (green and magenta cross in Fig. 3), who found that the fraction of active stars is indeed two to three times larger on the HB than on the RGB for LM stars, but it is 1.5−2 times smaller for IM stars on the contrary. This also stands in contrast to the results I obtained when considering stars with a photometric rotation period and exclusively located on the medium RGB. For these, I found an increase in the fraction of active stars on the HB by a factor of almost 5 for IM stars and almost 15 for LM stars. This may reflect the detection bias that might affect spots in the light curves, as noted in Sect. 3.1.

3.3. Candidate red giants for planet engulfment

I note that my sample includes KIC 9267654, a LM star on the RGB that was identified by Tayar et al. (2022) as having a surface rotation period from spectroscopy more than four times shorter than its envelope rotation period from asteroseismology (see Table 5), which the authors interpreted as a possible signature of planet engulfment. I also checked for stars in my sample that have an asteroseismic envelope rotation rate measured by Li et al. (2024), along with a photometric surface rotation period measured by Gaulme et al. (2020). I found only one star in common, KIC 9780154, an IM star on the RGB. I found that KIC 9780154 exhibits a surface rotation twice faster than its envelope (see Table 5), which might also indicate that it has engulfed one or more planet(s). I highlight the positions of KIC 9267654 and KIC 9780154 in Fig. 1.

4. Discussion

Here, I interpret and discuss the results obtained in Sect. 3.

4.1. Expected evolution of magnetic activity

The efficiency of the generation of stellar magnetic fields is expected to depend on the interaction between differential rotation and sub-photospheric convection (Skumanich 1972) and characterized by the Rossby number, Ro = P_rot/τ_c, where P_rot is the stellar rotation period and τ_c is the convective turnover time (e.g., Noyes et al. 1984; Charbonneau 2014). Thus, I needed to estimate how the Rossby number evolves to infer how magnetic activity is expected to evolve in a single-star evolution scenario.

4.1.1. Envelope rotation

I relied on existing asteroseismic measurements for stars on the RGB (Li et al. 2024). I considered the set of 1973 stars with significant non-negative envelope rotation rate measured by Li et al. (2024), instead of solely the 243 stars with significant positive measurements because the latter are biased toward fast rotation rates and not fully representative of most red giants. Overall, the 1730 measurements consistent with zero are nevertheless representative of the global evolution of the envelope rotation rate for both LM and IM stars, which are expected to suffer from the same biases on their envelope rotation measurements. I inferred the evolution of the envelope rotation along the RGB by fitting a power law to the envelope rotation rate as a function of the radius for LM and IM stars separately (Fig. 4), expressed as

$$\begin{array}{c}\hfill {⟨\mathrm{\Omega }⟩}_{\mathrm{env}}=\alpha {\left(\frac{R}{R_{\odot }}\right)}^{\beta }.\end{array}$$(1)

I obtained α = 2.92 and β = −2.16 for LM stars, compared to α = 11.54 and β = −2.53 for IM stars. Therefore, it is clear that the envelope rotation slows down at a slightly faster rate for IM stars than for LM stars and is steeper than an evolution proportional to R⁻² that would be expected in the frame of angular momentum conservation due to the expansion of the radius. This probably reflects magnetic braking along the RGB, which is expected to be more efficient for faster rotating stars (Kawaler 1988; Krishnamurthi et al. 1997; Sills et al. 2000; van Saders & Pinsonneault 2013). I also observed that the envelope rotation tends to be faster for IM stars than for LM stars on the early RGB, which is expected as magnetic braking during the main sequence is less efficient for IM stars (see Sect. 3.1). The envelope rotation period can then be derived via

$$\begin{array}{c}\hfill P_{\mathrm{env}}=\frac{2\pi }{{⟨\mathrm{\Omega }⟩}_{\mathrm{env}}}·\end{array}$$(2)

On the HB, envelope rotation measurements are available for only seven IM stars (Deheuvels et al. 2015) and there are none at all for LM stars; this is a too small a dataset to infer typical values of the mean envelope rotation for stars on the HB. However, magnetic braking and mass loss act along the RGB, removing angular momentum and, thus, leading to the expectation that typical envelope rotation rates would tend to be slower on the HB than on the RGB. My models indicate that mass loss remains below 2% up to R = 15 R_⊙; this is the case for the RGB stars in my sample, although it tends to be most important on the evolved RGB and strongly mass-dependent. My models estimate that the fraction of mass that is lost at the RGB tip with the Reimers prescription represents only ∼0.4% for a 2.5 M_⊙ star, but up to ∼40% for a 1 M_⊙ star (Fig. 5). This could contribute to removing more angular momentum out of LM stars, thereby slowing them down more than IM stars once they reach the HB. However, the Reimers prescription appears to be inadequate as mass loss may also be metallicity-dependent (Li 2025). Therefore, as of today, we cannot accurately predict the typical envelope rotation rates for stars on the HB, especially when considering that magnetic braking also comes into play.

Fig. 4. Asteroseismic envelope rotation measurements from Li et al. (2024) for 1973 stars on the RGB, discriminating between LM stars (in blue) and IM stars (in orange), as a function of the stellar radius. The black and orange lines correspond to the fit of a power law to LM and IM stars, respectively.

Fig. 5. Fraction of the initial mass that is lost at the RGB tip based on the Reimers law for models of different masses computed with MESA.

4.1.2. Convective turnover timescale

I used the stellar evolutionary code MESA (Paxton et al. 2011, 2013, 2015, 2018, 2019; Jermyn et al. 2023) to produce a set of models with M = {1.0,  1.3,  1.6,  1.9,  2.2,  2.5} M_⊙. The abundances mixture follows Grevesse & Noels (1993) and I chose a metallicity close to the solar one (Z = 0.02, Y = 0.28). Convection is described with the mixing length theory (Böhm-Vitense 1958) as presented by Cox & Giuli (1968), using a mixing length parameter α_MLT = 2. I use the OPAL 2005 equation of state (Rogers & Nayfonov 2002) and the OPAL opacities (Iglesias & Rogers 1996), complemented by the Ferguson et al. (2005) opacities at low temperatures. The nuclear reaction rates come from the NACRE compilation (Angulo et al. 1999). The surface boundary conditions are based on the classical Eddington gray T–τ relationship. Since this study is only aimed at sketching out general features, the effect of elements’ diffusion and convective core overshooting are ignored. I also included Reimers law for mass loss along the RGB resulting from the decrease of the gravitational binding energy of the envelope (Reimers 1975). The models were evolved from the pre-main sequence to the end of the HB phase, when the center helium mass fraction drops to 10⁻⁴. The end of the main sequence is identified as the model corresponding to a center hydrogen mass fraction of 10⁻³. I identified the transition between the subgiant branch and the RGB as the moment when the helium core mass reaches the Schönberg–Chandrasekhar limit; namely, 10% of the stellar mass (Schönberg & Chandrasekhar 1942). I estimated the convective turnover time based on the analytical approach of Corsaro et al. (2021). They showed that the convective flux can be approximated by

$$\begin{array}{c}\hfill F_c\simeq \frac{15}{8\pi \sqrt{2}}{\alpha }_{\mathrm{MLT}}^2\frac{M}{R^3}{\left(\frac{\mathit{GM}}{R}\right)}^{3/2}{(\mathrm{\nabla }-{\mathrm{\nabla }}_{\mathrm{ad}})}^{3/2},\end{array}$$(3)

where ∇ is the temperature gradient and ∇_ad is the adiabatic temperature gradient. Since F_c ≃ L/R², we obtain

$$\begin{array}{c}\hfill (\mathrm{\nabla }-{\mathrm{\nabla }}_{\mathrm{ad}})\simeq {\left(\frac{8\pi \sqrt{2}}{15}\right)}^{2/3}{\alpha }_{\mathrm{MLT}}^{-4/3}{\left(\frac{\mathit{LR}}{M}\right)}^{2/3}\frac{R}{\mathit{GM}}·\end{array}$$(4)

The convective velocity can then be estimated via

$$\begin{array}{c}\hfill v_c\simeq c_s\sqrt{\mathrm{\nabla }-{\mathrm{\nabla }}_{\mathrm{ad}}}\simeq {\left(\frac{8\pi \sqrt{2}}{15}\right)}^{1/3}{\alpha }_{\mathrm{MLT}}^{-2/3}{\left(\frac{\mathit{LR}}{M}\right)}^{1/3},\end{array}$$(5)

where $c_s\simeq \sqrt{GM/R}$ is the sound speed. Finally, the convective turnover time, τ_c, corresponds to the ratio between the extent of the convective envelope and the convective velocity; hence,

$$\begin{array}{c}\hfill {\tau }_c\simeq (R-r_{\mathrm{BCZ}}){\left(\frac{15}{8\pi \sqrt{2}}\right)}^{1/3}{\alpha }_{\mathrm{MLT}}^{2/3}{\left(\frac{M}{\mathit{LR}}\right)}^{1/3},\end{array}$$(6)

where r_BCZ is the radius coordinate associated with the base of the convective envelope and α_MLT = 2. The resulting τ_c values are represented in the left panel of Fig. 6. In the following, I focused on models with 1.3 M_⊙ and 1.6 M_⊙ (highlighted in bold) because these masses are very close to the median masses of LM and IM stars in my sample; namely, 1.28 M_⊙ and 1.65 M_⊙, respectively. The convective turnover time is systematically shorter for LM stars than for IM stars along the RGB, implying that LM stars would require a faster envelope rotation to reach a similar Rossby number and, hence, a similar level of magnetic activity to that of IM stars. Additionally, τ_c is systematically shorter on the HB compared to the RGB, implying that a faster envelope rotation is required on the HB to reach a similar Rossby number and, hence, a similar level of magnetic activity as that seen for the RGB.

Fig. 6. Evolution of stellar properties for models of masses 1 M⊙ (dark blue), 1.3 M⊙ (light blue), 1.6 M⊙ (green), 1.9 M⊙ (magenta), 2.2 M⊙ (orange), and 2.5 M⊙ (red) computed with MESA, as a function of νmax (in log scale, inverted axis), from νmax = 300 μHz up to νmax = 20 μHz. Plain lines represent the evolution along the RGB while dots indicate median values on the HB. Models with masses of 1.3 M⊙ and 1.6 M⊙, representative of the median masses for LM and IM stars on the RGB, respectively, are highlighted in bold. The vertical dashed lines indicate νmax = 100 μHz. Left: Convective turnover timescale. Right: Rossby number.

4.1.3. Rossby number

Next, I estimated the Rossby number based on the measured envelope rotation periods from Sect. 4.1.1 and the modelled convective turnover time from Sect. 4.1.2, which is represented in the right panel of Fig. 6 for stars of different masses. As noted in Sect. 4.1.1, we have envelope rotation measurements for an overly small number of stars on the HB to infer typical values of the mean envelope for such stars; hence, to infer how the Rossby number behaves on the HB.

All along the RGB, the Rossby number is systematically smaller for IM stars compared to LM stars; hence we expect IM stars to be more active than LM stars all along the RGB. However, this is not what I observed in this work (as reported in Sect. 3.1); namely, I found that the fraction of active LM stars tends to become larger than that of IM stars along the RGB. Moreover, we would expect magnetic activity to decrease along the RGB since the Rossby number increases; however, I found, on the contrary, that the fraction of active LM stars tends to increase along the RGB. The results described in Sect. 3.1 are therefore not expected from single star evolution for LM stars and could potentially result from the engulfment of planet(s). I explore this hypothesis below.

4.2. Properties of known planets around main sequence stars

I checked the distribution of the 6065 known planets, particularly with respect to their distance to their host star as a function of their mass and of the mass of their host star, using the Extrasolar Planets Encyclopaedia¹. To match the sample of RGs used in this study (Gaulme et al. 2020; Gehan et al. 2022, 2024), I focused on planets around stars with 0.6 ≤ M ≤ 2.5 M_⊙. To obtain an overview of planets around main sequence stars, I also focused on the planets around stars with R ≤ 4 R_⊙. I was left with 3007 planets, including 1391 with known mass data.

Remarkably, I observed that there are significantly fewer planets known around IM stars than LM stars (Fig. 7). This could reflect an observational bias, as a large number of planet studies focus on LM stars, especially as planet detection through both the radial velocity and transit techniques can be more challenging around IM stars that are bigger, hotter, and faster rotators (and therefore more magnetically active) than LM stars. However, theory based on the core-accretion planet formation scenario supports a global dearth of planets around IM stars (Laughlin et al. 2004; Ida et al. 2013). On the one hand, stars with M ∼ 1.3 − 2.1 M_⊙ have been observed to host twice as many massive planets as Sun-like stars (Johnson et al. 2010; Vigan et al. 2012), as reflected in Fig. 7, where low-mass planets are no longer seen around stars with M ≳ 1.3 M_⊙. This comes from the fact that more massive stars are expected to have more massive disks during the pre-main sequence (Kennedy & Kenyon 2008). On the other hand, the timescale available for giant planets to form (and, hence, the number of formed planets) is largely determined by the lifetime of the protoplanetary disc (Ronco et al. 2017; Guilera et al. 2020; Venturini & Helled 2020; Venturini et al. 2020), which decreases with stellar mass (Ribas et al. 2015; Kunitomo et al. 2021; Komaki et al. 2021; Ronco et al. 2024). Moreover, the core-accretion scenario further supports a dearth of close-in planets around IM stars. Indeed, planets are expected to form further out around IM stars than around LM stars because the various snow lines and photoevaporation limits are more distant around more luminous and, thus, more massive stars (e.g., Murillo et al. 2022; Giacalone & Dressing 2025). Hence, the dearth of planets observed around IM stars in Fig. 7 is likely to be real, although the observed population of planets around IM stars could suffer from observational biases and their number may be underestimated since more distant planets are harder to detect in terms of both radial velocity and transit methods. I also observed that a significant fraction of the known planets are orbiting at a distance shorter than 15 R_⊙, which is the upper radius for the red giants in my sample. Hence, LM stars in my RGB sample, which are not very evolved on the RGB, are nevertheless already much more likely to engulf a planet than IM stars as they evolve along the RGB.

Fig. 7. Properties of the exoplanets with known mass around stars with 0.6 ≤ M ≤ 2.5 M⊙ and R ≥ 4 ≤ R R⊙. Mass of the host star as a function of the semi-major axis of the planet. The color code represents the decimal logarithm of the mass of the planet, in Jupiter masses. The horizontal dashed lines indicate a mass of M = 1.5 M⊙. Green and magenta lines and dots indicate the radius at TAMS and TRGB, respectively, for models of M = {1, 1.3, 1.6, 1.9, 2.2, 2.5}M⊙. The vertical continuous line indicates a radius of R = 15 R⊙.

It is worth noticing that the amount of angular momentum that is deposited in the envelope of the host star does not only depend on the number of engulfed planets, but also on the mass of the engulfed planet(s) and of the star as well as on the initial distance between the star and the planet. Faster rotation rates are reached for massive planets, low-mass stars, and smaller orbital distances (Privitera et al. 2016b). The last condition may seem counterintuitive, however, it is derived from the fact that the shorter the orbital distance, the earlier the engulfment event on the RGB that corresponds to a smaller moment of inertia of the stellar envelope, and, hence, the more important the acceleration of the stellar rotation (Privitera et al. 2016b). Figure 7 shows that LM stars not only host low-mass planets, but also massive planets within short orbital distances. All these considerations are compatible with a milder decrease (or even an increase) in the active LM star fraction along the RGB that I find in Sect. 3.1.

On the HB, we might expect to observe a fraction of active stars that is larger for LM stars than for IM stars, assuming LM stars keep engulfing more planets than IM stars on the upper RGB; however, I observed the contrary for almost all the activity indicators used in this study (Fig. 2 and Table 4). As mentioned in Sect. 4.1.1, the situation is however not straightforward because LM stars lose much more mass on the upper RGB than IM stars, which might contribute to making them less active than IM stars once on the HB.

I note that my results do not point toward any engulfment of a stellar companion instead of that of a planet. Indeed, the fraction of multiple systems increases with stellar mass (Whitworth & Lomax 2015; Moe & Di Stefano 2017), while my results indicate that LM red giants engulf more companions. Moreover, stellar mergers generally result in a larger increase of the mass of the resulting star than in the case of planet engulfment. Hence, LM stars undergoing mergers would become IM stars, making IM stars more plausible to be the result of stellar mergers than LM stars. In this scenario, an activity increase associated with mergers would a priori result in more active IM stars compared to LM stars. However, I observed the opposite behaviour, which further favours planet engulfment over stellar mergers as an explanation of increased activity in LM stars, compared to IM stars.

5. Conclusions

Gaulme et al. (2020) observed that the fraction of photometrically active RGs (i.e., those exhibiting rotational modulation in their light curve) is larger on the HB than during the previous RGB phase for LM stars, while they observed the opposite behaviour for IM stars. These authors interpreted such observations as a potential signature of planet engulfment, since LM stars appear more likely to engulf planets as they reach a much larger radius at the RGB tip, compared to IM stars. However, spot detection through photometry can suffer from important biases, which could potentially impact the fractions of active stars computed by Gaulme et al. (2020).

To obtain a more complete view of the activity of RGs with different evolutionary stages and masses, I used several spectral lines whose depth trace the level of chromospheric activity indenpently of the detection of photospheric spots; namely, the Ca II H&K lines (3969 & 3934 Å), one of the Mg I lines (5184 Å), the Hα line (6563 Å), and one of the Ca II IR lines (8542 Å) that were studied by Gehan et al. (2022, 2024) for ∼3000 RGs with 4 ≤ R ≤ 15 R_⊙ using Data Release 7 of LAMOST. I computed the fractions of active LM and IM stars at two different evolution stages on the RGB as well as on the HB, using ν_max as a proxy of evolution along the RGB for the activity indicators mentioned above.

I observe that the fraction of active stars shows different trends for LM and IM stars along the RGB, decreasing by a median factor of 2.8 for IM stars, while increasing by a median factor of 1.1 for LM stars. Such an increase is not expected from the evolution of the Rossby number for single stars given by asteroseismic measurements of the envelope rotation and models of the convective turnover time computed with MESA. It is instead compatible with a scenario of planet engulfment. This is reinforced by the observed dearth of planets observed around IM main sequence stars that is likely to be real, as predicted by the theory of planet formation. This makes LM stars much more likely to end up engulfing planets than IM stars as they evolve along the RGB. The properties of the known planets around main sequence stars moreover indicate that the effects of planet engulfment on the evolution of magnetic activity of LM versus IM stars are indeed already expected to be significant for R ≤ 15 R_⊙ on the RGB; and, hence, for stars on the RGB considered in this study.

Between the medium RGB and the HB, the fraction of active stars tends to increase for both LM and IM stars, by a median factor of 2.5 for LM stars and of 2.8 for IM stars. This stands in partial contrast with the findings of Gaulme et al. (2020), who instead observed that the fraction of photometrically active stars decreases on the HB for IM stars. This can be explained by the fact that Gaulme et al. (2020) did not discriminate between stars on the early RGB and the medium RGB as I have in the present study. The evolution of the active star fraction between the medium RGB and the HB is once again not expected from single star evolution because magnetic braking and mass loss are expected to slow down the envelope rotation on the one side; then, the convective turnover timescales are shorter compared to the RGB on the other side, leading to the expectation of a decrease of magnetic activity between the medium RGB and the HB. The active star fraction increase that I observed between the medium RGB and the HB is compatible with planets keeping being engulfed on the evolved RGB. I note that the fraction of active stars on the HB tends to be larger for IM stars compared to LM stars overall, which is intuitively not expected in the frame of planet engulfment mainly by LM stars. However, the situation is more complicated to interpret on the HB where mass loss during the evolved RGB phase is expected to decrease magnetic activity and where it is significantly more important for LM stars compared to IM stars, making this observation not necessarily incompatible with a scenario of planet engulfment.

Finally, I discovered that the IM RGB star KIC 9780154 might have engulfed one or more planet(s) as its surface rotation from photometry (Gaulme et al. 2020) is twice as fast than its envelope rotation from asteroseismology (Li et al. 2024). Characterizing planet engulfment by RGs provides insights on the evolution of planetary systems and on the fate of planets around white dwarfs, which represent the ultimate evolutionary stage of ∼97% stars.

Acknowledgments

I was supported by a postdoctoral fellowship from the CNES. I dedicate this work to the late Patrick Gaulme, an exceptional and much-missed collaborator without whom it would never have seen the light of day. I thank the referee, who graciously revealed his identity, for his helpful and insightful comments, which greatly contributed to improving this manuscript.

References

Appendix A: Impact of using a 3σ prediction interval instead of 2σ

I checked the extent to which the computed active star fractions and the overall trends obtained in this study are impacted by taking the 3σ prediction interval around the fit in Fig. A.1 instead of the 2σ prediction interval I use in Fig. 1. The recomputed active star fractions are indicated in Table A.1 and shown in Fig. A.2, highlighting that the overall trends remain unchanged. The active star fraction keeps decreasing for IM stars and increasing for LM stars along the RGB, at the exception of the Hα indicator for which the active fraction increases for IM stars and remains constant for LM stars. The active star fraction on the low RGB remains higher for IM stars than for LM stars, once again at the exception of the Hα indicator. Additionally, the fraction of active stars increases for both LM and IM stars on the HB compared to the medium RGB, except for the Mg I indicator for which it decreases for LM stars and for the Ca II IR indicator for which it remains at zero. The main change compared to using the 2σ prediction interval is that the active star fraction on the HB is now larger for LM stars compared to IM stars, at the exception of the Hα indicator.

Using the 3σ prediction interval instead of 2σ significantly decreases the number of stars that are considered active and thus the derived active star fractions, which are now much lower and even fall at zero in several cases. They do not agree overall with the active star fractions derived by Gaulme et al. (2020) from the photometric detection of rotation periods.

Fig. A.1. Same as Fig. 1, except that the dashed lines represent the 3σ prediction interval around the fit.

Fig. A.2. Same as Fig. 2 for chromospheric indicators, except that the active fractions are determined using the 3σ prediction interval around the fit in Fig. A.1.

All Tables

All Figures

Fig. 1. Activity indicators as a function of νmax (inverted axis). LM and IM stars on the RGB are represented by grey and blue dots, respectively. LM and IM stars on the HB are represented by red and orange triangles, respectively. KIC 9267654 and KIC 9780154, which might have engulfed one or more planets since their surface rotates faster than their envelope, are shown with the magenta cross and star symbols, respectively. Vertical dotted lines indicate νmax = 100 μHz. Continuous and dashed lines represent a fit by a power law to the RGB stars and the corresponding 2σ prediction interval around the fit, respectively.

In the text

Fig. 2. Evolution of the active star fractions using different activity indicators from the lower RGB (νmax ≥ 100 μHz) to the medium RGB (νmax < 100 μHz) and the HB (on the right-hand side of the vertical dashed lines). Blue bars and arrows correspond to low-mass stars. Orange bars and arrows correspond to IM stars. Bottom panel indicates in addition the fractions of active LM (green bars and arrows) and IM (red bars and arrows) stars computed over the whole RGB without discriminating between the lower (νmax ≥ 100 μHz) and medium (νmax < 100 μHz) RGB.

In the text

Fig. 3. Ratios between the fractions of active stars for different evolutionary stages for the different activity indicators used in this study (written on the x-axis). LM and IM stars are represented in blue and in orange, respectively. Horizontal dashed lines in bold indicate a ratio of 1, while the other horizontal dashed lines indicate ratios of 2 and 3. Left: Ratios between the low RGB (νmax ≥ 100 μHz) and the medium RGB (νmax < 100 μHz). Right: Ratios between the HB and the medium RGB. For RGs with detected Prot, we indicate in addition the ratios obtained for active LM (green cross) and IM (magenta cross) stars when considering stars across over the whole RGB without discriminating between the lower and medium RGB.

In the text

	Fig. 4. Asteroseismic envelope rotation measurements from Li et al. (2024) for 1973 stars on the RGB, discriminating between LM stars (in blue) and IM stars (in orange), as a function of the stellar radius. The black and orange lines correspond to the fit of a power law to LM and IM stars, respectively.
In the text

	Fig. 5. Fraction of the initial mass that is lost at the RGB tip based on the Reimers law for models of different masses computed with MESA.
In the text

Fig. 6. Evolution of stellar properties for models of masses 1 M⊙ (dark blue), 1.3 M⊙ (light blue), 1.6 M⊙ (green), 1.9 M⊙ (magenta), 2.2 M⊙ (orange), and 2.5 M⊙ (red) computed with MESA, as a function of νmax (in log scale, inverted axis), from νmax = 300 μHz up to νmax = 20 μHz. Plain lines represent the evolution along the RGB while dots indicate median values on the HB. Models with masses of 1.3 M⊙ and 1.6 M⊙, representative of the median masses for LM and IM stars on the RGB, respectively, are highlighted in bold. The vertical dashed lines indicate νmax = 100 μHz. Left: Convective turnover timescale. Right: Rossby number.

In the text

Fig. 7. Properties of the exoplanets with known mass around stars with 0.6 ≤ M ≤ 2.5 M⊙ and R ≥ 4 ≤ R R⊙. Mass of the host star as a function of the semi-major axis of the planet. The color code represents the decimal logarithm of the mass of the planet, in Jupiter masses. The horizontal dashed lines indicate a mass of M = 1.5 M⊙. Green and magenta lines and dots indicate the radius at TAMS and TRGB, respectively, for models of M = {1, 1.3, 1.6, 1.9, 2.2, 2.5}M⊙. The vertical continuous line indicates a radius of R = 15 R⊙.

In the text

	Fig. A.1. Same as Fig. 1, except that the dashed lines represent the 3σ prediction interval around the fit.
In the text

	Fig. A.2. Same as Fig. 2 for chromospheric indicators, except that the active fractions are determined using the 3σ prediction interval around the fit in Fig. A.1.
In the text