Planetary Engulfment Prognosis within the ρ CrB System

Exoplanets have been detected around stars at various stages of their lives, ranging from young stars emerging from formation to the latter stages of evolution, including white dwarfs and neutron stars. Post-main-sequence stellar evolution can result in dramatic, and occasionally traumatic, alterations to the planetary system architecture, such as tidal disruption of planets and engulfment by the host star. The ρ CrB system is a particularly interesting case of advanced main-sequence evolution, due to the relative late age and brightness of the host star, its similarity to solar properties, and the harboring of four known planets. Here, we use stellar evolution models to estimate the expected trajectory of the stellar properties of ρ CrB, especially over the coming 1.0–1.5 billion yr as it evolves off the main sequence. We show that the inner three planets (e, b, and c) are engulfed during the red giant phase and asymptotic giant branch, likely destroying those planets via either evaporation or tidal disruption at the fluid-body Roche limit. The outer planet, planet d, is briefly engulfed by the star several times toward the end of the asymptotic giant branch, but the stellar mass loss and subsequent changing planetary orbit may allow the survival of the planet into the white dwarf phase of the stellar evolution. We discuss the implications of this outcome for similar systems and describe the consequences for planets that may lie within the habitable zone of the system.


INTRODUCTION
From the plethora of exoplanet discoveries, a vast array of system architectures have been revealed, many of which differ significantly from the solar system (Ford 2014;Winn & Fabrycky 2015;Horner et al. 2020;Kane et al. 2021;Mishra et al. 2023a,b).The majority of these exoplanet discoveries have occurred through the use of the transit or radial velocity (RV) methods.Although the stellar target sample is dominated by main sequence (MS) stars, there are numerous surveys that have focused their efforts on evolved stars, such as subgiant and giant stars (e.g., Hekker & Meléndez 2007;Wittenmyer et al. 2015;Jeong et al. 2018).There are several prominent examples of exoplanets around giant stars, such as the highly eccentric planet orbiting iota Draconis (Frink et al. 2002;Kane et al. 2010;Hill et al. 2021;Campante et al. 2023) and the planetary companion to Pollux (Hatzes et al. 2006;Reffert et al. 2006).
skane@ucr.eduSuch giant star system architectures are of particular interest with respect to the effects of post-MS evolution (Villaver & Livio 2009;Veras 2016;MacLeod et al. 2018;Rapoport et al. 2021).Predicting the fate of the planets in these systems is of interest from a stellar evolution, orbital evolution, and planetary habitability perspective.The predicted effect of giant star engulfment of a substellar companion can vary depending on the mass of the host star and companion (Hon et al. 2023).For example, engulfed giant planets may experience substantial drag, resulting in orbital decay and eventual tidal disruption at the Roche limit well interior to the stellar radius (O'Connor et al. 2023).On the other hand, brown dwarf companions may survive the red giant phase and continue to orbit the subsequent white dwarf host relatively unscathed (Maxted et al. 2006).
Moreover, the Habitable Zone (HZ) of the host star (Kasting et al. 1993;Kane & Gelino 2012;Kopparapu et al. 2013Kopparapu et al. , 2014;;Kane et al. 2016;Hill et al. 2018Hill et al. , 2023) ) is profoundly affected by the change in luminosity and effective temperature that occurs with post-MS evolution (Ramirez & Kaltenegger 2016) with corresponding dramatic effects for HZ terrestrial planets (Lopez et al. 2005;von Bloh et al. 2009;Kozakis & Kaltenegger 2019).Thus, old MS stars are useful templates from which to consider the consequences of stellar evolution on the harbored planets.
One of the earliest exoplanet discoveries was that of the Rho Coronae Borealis (HD 143761, HIP 78459, hereafter ρ CrB) system.ρ CrB is a bright (V = 5.39) and nearby (d = 17.51 pc) MS star, with a spectral type of G0.Although the star has properties similar to solar, it is ∼5% less massive, ∼30% larger, and has sub-solar metallicity (Santos et al. 2003;Takeda et al. 2007;von Braun et al. 2014;Rosenthal et al. 2021;Brewer et al. 2023).Age estimates for the star have yielded consistently high values, making ρ CrB one of the nearest solar-type stars with close proximity to evolving off the MS (Metcalfe et al. 2021).The planetary system associated with the star was first discovered by Noyes et al. (1997) via the RV detection of a giant planet orbiting with a period of ∼40 days.Subsequent RV monitoring by Fulton et al. (2016) revealed a second planet in the system with an orbital period of ∼100 days.More recent RV efforts have focused on extreme precision RV (EPRV) methods, pushing RV detection efficiency to significantly smaller planetary masses and longer orbital periods than previous instruments were capable of achieving (Fischer et al. 2016).One such instrument, the EXtreme-PREcision Spectrograph (EX-PRES) (Blackman et al. 2020;Petersburg et al. 2020), monitored ρ CrB and discovered two more planets with orbital periods of ∼13 days and ∼281 days, raising the total planet inventory for the system to four (Brewer et al. 2023).The relative proximity of the ρ CrB system, the even spacing of the known planetary orbits, the sub-solar metallicity of the host star and its large age, make the system an interesting case study regarding the aftermath of MS evolution for the planets in the system.
Here, we present a stellar evolution model for ρ CrB in the context of the planetary orbits and the effect of post MS evolution on their survivability.Section 2 describes the stellar and planetary parameters, and the system architecture.Section 3 provides details of the stellar evolution model, and the modifications to the fundamental stellar parameters as the star evolves off the MS.Section 4 overlays the stellar evolution model on the system architecture, quantifying the limits whereby specific planets are engulfed by the host star.We discuss the implications of our results in Section 5, including outcomes for known planets and potential HZ planets, and provide concluding remarks in Section 6.

SYSTEM ARCHITECTURE
The ρ CrB system consists of a central star and four known orbiting planets.Given the brightness of the star (V = 5.39), there are numerous stellar parameters available in the literature.We adopt both the stellar and planetary parameters provided by Brewer et al. (2023).The star has the following properties: mass and an age of 10.2 Gyr.The orbits for the four known planets of the system are relatively evenly spaced, and the planets have masses ranging from super-Earth to Jovian.The properties of the planets are summarized in Table 1, and their orbits are depicted in a top-down view of the system in Figure 1, where the letter designation of the planets are shown.The parameters shown in Table 1 are the orbital period, P , semi-major axis, a, eccentricity, e, argument of periastron, ω, and the minimum planetary mass, M p sin i.
Based on the stellar properties described above, we calculated the HZ of the star using the methodology of Kopparapu et al. (2013Kopparapu et al. ( , 2014)).The traditional HZ, also referred to as the conservative HZ (CHZ), is bounded by limits of runaway and maximum greenhouse for an Earth analog.The HZ can be empirically extended beyond the CHZ via the assumption that Venus and Mars previously harbored surface liquid water, resulting in an optimistic HZ (OHZ).The calculations of the CHZ and OHZ are described in detail by Kane et al. (2016).Since ρ CrB is near the end of its MS lifetime, the large radius and luminosity compared to solar moves the HZ beyond the orbit of the outermost planet, and the inner edge of the OHZ lies at ∼1.01 AU.The inner OHZ is shown as the green regions in Figure 1, the evolution of which will be discussed further in Section 5. To investigate the stellar evolution of ρ CrB, we utilize the MESA Isochrones & Stellar Tracks (MIST; version 1.2) to calculate an interpolated evolutionary track (Paxton et al. 2011(Paxton et al. , 2013(Paxton et al. , 2015;;Choi et al. 2016;Dotter 2016;Paxton et al. 2018Paxton et al. , 2019)).As described by Choi et al. (2016), MIST treats mass loss associated with advanced stages of stellar evolution via the prescriptions provided by Reimers (1975) and Bloecker (1995a).Initial bulk metallicities are computed by MIST assuming the protosolar abundances provided by Asplund et al. (2009).Using the Brewer et al. (2023) stellar parameters of mass M ⋆ = 0.95 M ⊙ and metallicity [Fe/H] = −0.20 dex (see Section 2), the MIST algorithm estimated an initial helium fraction of Y init = 0.2627.We set the initial stellar surface velocity to 40% of the critical (break-up) velocity, v/v crit = 0.4.It is worth noting that, due to atomic diffusion processes, the resulting evolutionary track is largely unaffected by small (< 0.1 dex) changes in initial metallicity.It is further of note that MIST tracks apply specifically to single-star evolutionary models, and do not account for interactions with other stars, such as the case of Hon et al. (2023).Since ρ CrB is known to be a single star, the MIST tracks are well-suited to the analysis reported here.
The resulting stellar evolution model is shown in Figure 2 for the final few billion years leading to the pro-gression of the star into the red-giant branch (RGB).Specifically, Figure 2 shows the changes in stellar mass, radius, and luminosity in solar units.The vertical dotted line indicates the age estimate from (Brewer et al. 2023), and the gray shaded region represents the 1σ uncertainty on the age.The sub-solar metallicity of ρ CrB results in an accelerated evolution of the star into the RGB (Gehrig et al. 2023).The first peak in the stellar radius/luminosity at ∼11.6 Gyr corresponds to the helium flash and the transition into the horizontal branch (Bloecker 1995a,b).The stellar radius decreases at this transition, along with a ∼5% mass loss.The horizontal branch phase lasts for ∼10 8 years, beyond which the core helium depletion again increases the radius as the star enters the asymptotic giant branch (AGB).The MIST model predicts that the AGB phase will peak at a stellar age of ∼11.7 Gyr, followed by a shedding of the stellar envelope and dramatic mass loss.The consequences of these stellar evolutionary processes for the known planets will depend on their masses and semi-major axis relative to the changing stellar radius.

PLANETARY ENGULFMENT PROGNOSIS
The expansion of a host star into the red giant phase can have a variety of repercussions for the planets in the system.The engulfment of planets can itself have several outcomes, depending on the specific architecture of the system.Hydrodynamic simulations suggest that engulfed planets may in-spiral over years or decades, and are eventually destroyed either through evaporation or tidal disruption at the Roche limit, puffing up the star in the process (Staff et al. 2016b).Some models indicate that sub-Jupiter mass planets will not survive if initially located interior to 3-5 AU (Villaver & Livio 2007).Dynamical interactions between planets in the system can rescue even smaller planets, as the stellar mass loss and tidal effects can drive planetary orbits toward mean motion resonances and increased separation from the host star (Ronco et al. 2020).Such surviving planets can remain long-term stable well beyond the RGB and AGB phases of the star's evolution (Duncan & Lissauer 1998).On the other hand, planetary dynamics and tidal interactions may actually precipitate planetary engulfment of close-in planets during the giant star phase (Villaver & Livio 2009).These scenarios have been investigated for several known exoplanet systems that are either approaching (Rapoport et al. 2021), presently in (Bear et al. 2011), or post (Charpinet et al. 2011) the RGB/AGB phases of the host star.
To determine the effect of the stellar evolution model described in Section 3 on the ρ CrB system planets, we overlaid the evolving stellar properties against the or-  bits of the planets.A 7 × 10 8 year segment of the stellar radius evolution is shown in the top panel of Figure 3 as a blue line and in units of AU.The semi-major axes of the planets are indicated by the horizontal dashed lines, and have been recalculated at each epoch to incorporate stellar mass loss and conservation of angular momentum for each orbit.The dotted line represents the location of the fluid body Roche limit for the star which, despite the dramatic change in stellar radius, remains relatively constant since it is dominated by the stellar mass.The bottom panel of Figure 3 further zooms in on the final 10 7 years at the end of the AGB phase before the transition to the white dwarf phase.The stellar radius fluctuations visible in the range 11.708-11.709Gyrs are the signatures of thermal pulses caused by shell hydrogen and helium fusion within the giant star.
As the star swells in size during the RGB phase, the inner planets of e, b, and c are engulfed by the star at stellar ages of 11.5630, 11.5785, and 11.5846 Gyrs, respectively.The star achieves a maximum RGB size of ∼158 R ⊙ (0.736 AU) at an age of 11.5874 Gyrs, at which point the star encompasses all planets except for the outer planet, d.After the helium flash, the star decreases in size as it enters the horizontal branch, and plateaus at a minimum size of ∼10.4 R ⊙ (0.048 AU).As the helium fuel is depleted, the stellar radius increases again into the AGB, exceeding its RGB maximum size, and reaching ∼216 R ⊙ (1.005 AU) at 11.7088 Gyrs.This period during the AGB is also characterized by the aforementioned radius fluctuations due to shell fusion burning along with significant mass loss.Conservation of angular momentum causes the semi-major axis of planet d to increase to 0.965 AU, but this is insufficient to save the planet from engulfment.Planet d is swallowed by the star during the AGB phase at 11.7085 Gyrs.It remains 0.05 AU interior to the star for about a thousand years, after which the star contracts again.At 11.7088 Gyrs, the star engulfs planet d again, where it is once again 0.05 AU interior to the star for several thousand years.If planet d can survive this phase, it will settle into a 1.459 AU orbit as the star rapidly transitions into a white dwarf.Thus, all four of the known planets will likely be engulfed by their star within the next 1.0-1.5 billion years.

DISCUSSION
Although all of the planets will enter the stellar atmosphere of ρ CrB, their individual prognoses vary considerably.Planet e is likely terrestrial in nature and, given it is the first to be engulfed deep into the star, an evaporation scenario may be the most probable outcome.However, planet b is more massive than Jupiter, and the immersion into the stellar envelope will result in viscous drag and in-spiral, ending with tidal disruption at the Roche limit (Staff et al. 2016a;O'Connor et al. 2023), shown to remain relatively stable at ∼0.01 AU in Figure 3.The accretion of planetary material at the base of the convective envelope can cause a further increase in stellar size (Siess & Livio 1999a), which is not taken into account in our model.If indeed such an additional stellar radius increase occurs, then the engulfment of planet c may take place earlier than that stated in Section 4, and may also result in the engulfment of planet d whilst the star is still on the RGB.Both planet c and d are similar in mass to Neptune and will therefore suffer substantial evaporation over an orbital in-spiral scenario.Our model further did not include the effects of orbital dynamics, which has the potential to cause planet d to migrate further outward and possibly escape engulfment (Ronco et al. 2020).Such planetary interactions are particularly important in the case of resonance crossing events (Kane 2023), such as is predicted for the solar system post-MS evolution (Zink et al. 2020).Since the inner planets of ρ CrB are engulfed prior to the AGB phase, it is unlikely that orbital dynamics will play a major role in the system during and after the stellar mass loss.
For cases where planets are consumed by the host star, several mechanisms have been invoked that may yield observable signatures of such consumption events (Siess & Livio 1999b,a;Stephan et al. 2020;Behmard et al. 2023b).These signatures can include enhanced lithium abundance (Aguilera-Gómez et al. 2016;Sevilla et al. 2022), stronger magnetic fields (Privitera et al. 2016b), and faster rotation rates (Privitera et al. 2016a).The latter of these signatures may also be connected to enhanced mass loss on the RGB (Soker 1998;Bear & Soker 2011), further improving the survival rates for outer planets in the system through angular momentum conservation.Thus far, observational evidence for planetary engulfment signatures has remained relatively sparse, suggesting that either engulfment scenarios are rarer than expected, or that signature detection is more challenging than anticipated (Behmard et al. 2023a).
Another signature of planet engulfment may be found through a careful examination of white dwarfs (Nelemans & Tauris 1998;Mustill & Villaver 2012).White dwarf planetary systems are often assumed to be quite prevalent (Zuckerman et al. 2010) with orbital architectures that are intrinsically linked to the prior evolution of the progenitor (Debes & Sigurdsson 2002).Stellar evolution and planetary engulfment is a possible interpretation for white dwarf pollution (Frewen & Hansen 2014;Petrovich & Muñoz 2017), which can also be caused by more recent planetary accretion events (Gänsicke et al. 2019).Numerous giant planets have been discovered orbiting white dwarfs (Vanderburg et al. 2020;Blackman et al. 2021), including those whose presence have been interpreted within the context of RGB survival (Lagos et al. 2021;Merlov et al. 2021).
White dwarf planetary systems are also of interest with respect to the prospects for habitable planets that may be present.Given the relatively large transit depth, searches have been proposed using the transit method that specifically target terrestrial planets in the HZ (Agol 2011).White dwarf HZ planets face additional challenges toward maintaining long-term temperate surface conditions, such as the cooling of the star (Barnes & Heller 2013) and tidal effects (Becker et al. 2023).These HZ planets were almost certainly not in the HZ during the MS or RGB/AGB phases of the progenitor, particularly given the mass loss that occurs during the AGB.Section 2 and Figure 1 provide the current HZ boundaries for ρ CrB, where the OHZ extends in the range 1.01-2.38AU.No planets have yet been detected in the HZ, and the predicted RV semi-amplitude for an Earth-mass planet is 9.1 cm/s and 5.9 cm/s at the inner and outer edges of the OHZ, respectively (assuming that the orbit is close to edge-on).As shown in Section 4, the star will achieve a maximum size of 1.005 AU, almost reaching the inner edge of the OHZ.Due to stellar mass loss during the AGB, a planet that presently lies in the middle of the OHZ (1.70 AU) will move outward to a semi-major axis of ∼3.0 AU.During the horizontal branch, the bottom panel of Figure 2 shows that the luminosity will be two orders of magnitude larger than it is currently.The HZ boundaries defined by Kopparapu et al. (2013Kopparapu et al. ( , 2014) ) scale with L 0.5 ⋆ , and so they will be ∼10 times larger during the horizontal branch, which is beyond the estimated new semimajor axis of ∼3.0 AU.On the other hand, the new semi-major axis will place the planet well exterior to the white dwarf HZ.Thus, neither the possibly surviving planet d or a hypothetical planet currently residing in the HZ will be present in the HZ during either the RGB/AGB or white dwarf phases.

CONCLUSIONS
The evolution of stars through their progression on the MS, expansion into a giant star, and then final contraction into a white dwarf, has profound consequences for the orbiting planets.The case studied here, that of the ρ CrB system, is particularly interesting due to the brightness and late age of the star, and the diverse planetary system that is currently known to extend to distances of ∼0.83 AU from the host.The sub-solar metallicity of the star truncates the MS lifetime, and our model predicts that it will reach the end of the AGB within 1.0-1.5 billion years.Given the masses and semimajor axes of the four known planets, we predict that planet e will evaporate within the stellar atmosphere, planet b will in-spiral and be tidally disrupted, potentially further inflating the star, and planet c will be evaporated within the stellar atmosphere.The fate of the outermost planet, planet d, remains uncertain but will likely be evaporated within the star during the end of the AGB.If it is able to escape engulfment during stellar mass loss, it may remain in orbit around the white dwarf at a separation of ∼1.5 AU.For HZ planets that may be present in the system but below current detection sensitivity, they will survive the stellar evolution but be interior to the HZ inner edge during the RGB/AGB phase and exterior to the HZ outer edge during the white dwarf phase.
Continued exoplanet monitoring of nearby bright stars that are approaching the end of their MS lifetime will provide additional opportunities to study the effects of stellar evolution on planetary systems.Orbital dynamics may play an important role in the survivability of inner system planets, and thus the detection of outer giant planets can provide essential keys in understand the full prognosis for a given system.In that regard, the addition of astromtric measurements from Gaia (Gaia Collaboration et al. 2021) for the existing RV data of nearby systems will greatly improve the detection sensitivity in the outer regions of exoplanetary systems (Wright & Howard 2009).The further merging in of direct imaging data will provide additional constraints on the system architecture (Brandt et al. 2019;Kane et al. 2019), as well reflected and emission spectra for any detected planets (Stark et al. 2020;Li et al. 2021;Saxena et al. 2021).Connecting such compositional information with stellar abundances may yield critical insight regarding signatures of post-MS planet engulfment.

Figure 1 .
Figure 1.HZ and planetary orbits in the ρ CrB system, where the orbits are labeled by planet designation.The inner edge of the OHZ is shown in green, and can be seen in the corners of the figure beyond the orbit of planet d.The scale of the figure is 1.77 AU along each side.

Figure 2 .
Figure 2. The final predicted stages of MS evolution for ρ CrB based on the MIST model described in Section 3, showing the evolution of stellar mass (top panel), radius (middle panel), and luminosity (bottom panel).The model depicts the transition through the RGB, horizontal branch, and AGB.The vertical dotted line indicates the current stellar age, and the gray shaded region represents the 1σ uncertainty on that age.

Figure 3 .
Figure 3. Distance from the host star in AU for the stellar evolution off the MS over 7 × 10 8 years (top panel) and 10 7 years (bottom panel).The radius of the star is shown as a blue line, and the dashed lines show the semi-major axes of the known planets.The location of the fluid body Roche limit of the star is indicated by the dotted line.