key: cord-0554716-xi4k1j8r
authors: Hegazi, Ahlam; Bear, Ealeal; Soker, Noam
title: On the role of reduced wind mass-loss rate in enabling exoplanets to shape planetary nebulae
date: 2020-04-20
journal: nan
DOI: nan
sha: de8b09a9563b61bb2b207d0961a862736a6f40b5
doc_id: 554716
cord_uid: xi4k1j8r

We use the stellar evolution code MESA-binary and follow the evolution of six exoplanets to determine their potential role in the future evolution of their parent star on the red giant branch (RGB) and on the asymptotic giant branch (AGB). We limit this study to planets with orbits that have semi-major axis of 1AU0.25, and having a parent star of mass M>1Mo. We find that the star HIP 75458 will engulf its planet HIP75458 b during its RGB phase. The planet will remove the envelope and terminate the RGB evolution, leaving a bare helium core of mass 0.4Mo that will evolve to form a helium white dwarf. Only in one system out of six, the planet beta Pic c will enter the envelope of its parent star during the AGB phase. For that to occur, we have to reduce the wind mass-loss rate by a factor of about four from its commonly used value. This strengthens an early conclusion, which was based on exoplanets with circular orbits, that states that to have a non-negligible fraction of AGB stars that engulf planets we should consider lower wind mass-loss rates of isolated AGB stars (before they are spun-up by a companion). Such an engulfed planet might lead to the shaping of the AGB mass-loss geometry to form an elliptical planetary nebula.

Hundreds of observational and theoretical studies in recent years have converged on the understanding that binary interaction shapes the majority, and possibly all, planetary nebulae (PNe) (e.g., limiting to a sample from the last five years, Jones et al. 2016; Chiotellis et al. 2016; Akras et al. 2016; García-Rojas et al. 2016; Jones 2016; Hillwig et al. 2016a; Bond et al. 2016; Chen et al. 2016; Madappatt et al. 2016; Ali et al. 2016; Hillwig et al. 2016b; Jones & Boffin 2017b; Barker et al. 2018; Bond, & Ciardullo 2018; Bujarrabal et al. 2018; Danehkar et al. 2018; Frank et al. 2018; García-Segura et al. 2018; Hillwig 2018; MacLeod et al. 2018; Miszalski et al. 2018; Sahai 2018; Wesson et al. 2018; Aller et al. 2019; Desmurs et al. 2019; Jones 2019; Kim et al. 2019; Kővári et al. 2019; Miszalski et al. 2019; Orosz et al. 2019; Akras et al. 2020; Bermúdez-Bustamante et al. 2020; Jones 2020) . Substantially smaller number of studies deal with the possibility that planets and brown dwarfs might also shape PNe (e.g, De Marco & Soker ahlam.hegazi@campus.technion.ac.il; ealealbh@gmail.com; soker@physics.technion.ac.il A stellar companion can strongly deform the envelope of the asymptotic giant branch (AGB) progenitor of the PN, by spinning-up the envelope and by the direct effects of its gravity, mainly during a common envelope evolution (CEE) phase and during the termination of the CEE. One of the extreme outcomes at the termination of the CEE might be two opposite 'funnels' along the symmetry axis of the bloated AGB envelope, which can collimate bipolar outflows (e.g., Soker 1992a; Reichardt et al. 2019; García-Segura et al. 2020; Zou et al. 2020) . A stellar companion can also deform the envelope by accreting mass and launching jets during the CEE (e.g., Chamandy et al. 2018; López-Cámara et al. 2019; Schreier et al. 2019; Shiber et al. 2019; Lopez-Camara et al. 2020) . All these processes shape the descendent nebula to possess large-scale highly non-spherical morphologies. Planet companions, on the other hand, are not expected to have these large effects. It is not clear yet whether planets can launch jets. Even if they do (e.g., Soker 2020), the outcome might be two opposite small clumps along the symmetry axis (ansae; FLIERS).

It seems that the main effect of a planet in shaping the mass-loss toward a non-spherical PN is by spinningup the envelope, to the degree that the mass-loss becomes axisymmetrical. Soker (1998b) discussed the way by which a planet can enhance mass-loss and can lead to a non-spherical outflow from giant stars, like AGB stars, or red giant branch (RGB) stars. It goes as follows. A planet-spun-up AGB envelope might sustain a dynamo (e.g., Nordhaus & Blackman 2006) , that in turn leads to non-spherical mass-loss by the effect of magnetic fields (e.g., Leal-Ferreira et al. 2013; Vlemmings 2018) , including possibly the influence on dust formation and distribution (e.g., Soker 2000 Soker , 2001a Khouri et al. 2020) . Another effect of massive planets that are deep inside the envelope of giant stars, after the dynamical in-spiral phase, is the excitation of waves that become large on the surface and might influence the rate and morphology of dust formation and therefore of the outflow (e.g., Soker 1993 ). On a more general ground, dust formation seems to be an important process in the last phases of the CEE, both for sub-stellar and stellar companions (e.g., Soker 1992b Soker , 1998b Glanz, & Perets 2018; Iaconi et al. 2019 Iaconi et al. , 2020 .

Stars on the upper RGB and AGB can acquire a large amount of angular momentum by engulfing planets (e.g., Soker 1996; Siess & Livio 1999a; Carlberg et al. 2009; Villaver & Livio 2009; Mustill & Villaver 2012; Nordhaus et al. 2010; Nordhaus & Spiegel 2013; García-Segura et al. 2014; Staff et al. 2016; Aguilera-Gómez et al. 2016; Sabach, & Soker 2018a; Sabach & Soker 2018b ). The probability for this process to take place on the upper AGB sensitively depends on the mass-loss rate from the star.

In earlier studies our group considered the possibility that AGB stars that did not (yet) interact with any companion that substantially spun-up the envelope, have much lower wind mass-loss rates than what traditional formulae give (Sabach, & Soker 2018a; Sabach & Soker 2018b) . We termed these angular momentum ( J ) isolated stars Jsolated stars. Sabach, & Soker (2018a) study the fate of four observed exoplanetary systems that have low eccentricity. To follow the evolution of the star they use the single mode of the evolutionary code mesa (section 2). To examine whether tidal forces will cause the planet to spiral-in to the envelope of the star during the AGB phase, they use a simple prescription for the tidal force. Sabach, & Soker (2018a) found that when low-mass stars evolve with the traditional wind mass-loss rate they are not likely to swallow their planets in these four systems. With a lower mass-loss rate, down to about 15% of the traditional one, the stars reach much larger radii on their AGB and much larger luminosities. The larger radii substantially increase the likelihood for the AGB star to swallow the planet. This, by the studies we cited above, might lead to the formation of elliptical PNe. The higher luminosity might account for bright PNe in old stellar population (see relevant discussion in Sabach, & Soker 2018a; Sabach & Soker 2018b . Sabach, & Soker (2018a justified the much lower wind mass-loss rate by their assumption that the stellar samples from which the mass-loss rate formulae were derived were contaminated by AGB stars that suffer binary interaction, and binary interaction increases the mass-loss rate. Specifically for low mass companions, down to planets, Sabach & Soker (2018b) suggest that giant stars that acquire no angular momentum from a companion along their late evolution (beyond the main sequence), i.e., Jsolated stars, have much lower massloss rates than what traditional formulae give. AGB stars with lower mass-loss rates reach much higher luminosities in the post-AGB track, when they ionise the PN. Sabach & Soker (2018b) further argue that it might be that the bright PNe in old stellar populations result from the combination of lower mass-loss rates that they explored, and of higher AGB luminosities that some new stellar models give (e.g., Miller Bertolami 2016; Gesicki et al. 2018; Méndez 2017; Reindl et al. 2017) .

We here adopt the approach of Sabach, & Soker (2018a) and Sabach & Soker (2018b) in considering a much lower wind mass-loss rate (section 2). We differ from them by studying the fate of observed exoplanets with high eccentricities, for which we must use the binary mode of mesa to follow the evolution of the planetary systems (section 2). Our study is another in a series of papers that study the fate of confirmed exoplanets as their parent stars turn to RGB or AGB stars (e.g., Nordhaus & Spiegel 2013; Sabach, & Soker 2018a) . We describe the results of our simulations in section 3, and we summarise our main results in section 4.

To follow the fate of the six observed planets that we study here, we conduct stellar evolution simulations using the Modules for Experiments in Stellar Astrophysics (MESA; Paxton et al. 2011 Paxton et al. , 2013 Paxton et al. , 2015 Paxton et al. , 2018 Paxton et al. , 2019 , version 10398 in its binary mode. In each system we follow the evolution of the parent star, either to the time the star engulfs its planet and the systems enters a CEE phase, or to its post-AGB phase if no engulfment takes place.

We study planets with high-eccentricity orbits and so we have to pay attention to tidal forces that act to circularise and synchronise the orbit (the later effect results in a decrease in the semi-major axis). We set the tidal effects in MESA-binary (the parameters do tidal circ and do tidal sync), taking the circularization type 'Hut conv' which is the default of MESAbinary for convective envelope (Hurley et al. 2002) . This is relevant to our study as the planets we follow experience strong tidal interaction only during the RGB and AGB phases of their parent stars, when the envelope is fully convective. We turn off the effects of magnetic breaking (the parameter do jdot mb) as we expect weak magnetic activity during the RGB and AGB phases before the planet enters the envelope. We take all other parameters to have their default values in MESA-binary.

As we mentioned above, we adopt our earlier approach (Sabach, & Soker 2018a; Sabach & Soker 2018b , where there are more details and discussions of the low wind mass-loss rate), and give here only the essential information. For the empirical mass-loss formula for winds from red giant stars we take (Reimers 1975 )

where the giant's mass, M , luminosity L, and radius R, are in solar units, and η is the wind mass-loss rate efficiency parameter. The commonly used value is η = 0.5 (e.g., McDonald & Zijlstra 2015) . With the assumption that Jsolated stars (those that acquired no angular momentum from a companion) experience a much lower wind mass-loss rate than non-Jsolated stars, we also take lower values of η. We follow Sabach, & Soker 2018a and take the value of η to influence the mass-loss rate on both the RGB and AGB. Miglio et al. (2012) , for example, find for the old metal-rich cluster NGC 6791, that this parameter might be as low as η = 0.1, i.e., much lower than typically taken. We follow Sabach, & Soker (2018a) and study the range 0.05 ≤ η ≤ 0.5. One observational finding is directly relevant to our study that aims at the shaping of elliptical PNe. This finding is the observations that many elliptical PNe have an outer faint and spherical halos (e.g. Corradi et al. 2003) . Since single AGB (Jsolated) stars spin extremely slowly on the upper AGB (e.g., Soker 2006), we expect these stars to blow a spherically faint halo. Interacting with a low mass companion on the upper AGB causes these stars to have a non-spherical mass-loss and at a higher mass-loss rate, forming the brighter elliptical inner shell (e.g., Soker 2000) . These PNe might suggest a late interaction with a very low mass companion, e.g., a brown dwarf or a planet.

Our aim is to explore which of the six observed exoplanets that we list in table 1 might enter the envelope of their parent star when the later is on its upper AGB, and for what wind mass-loss rate efficiency parameter η. We study these specific systems that we found by searching the Extrasolar Planets Encyclopaedia; (exoplanet.eu; Schneider et al. 2011 ) because they have the relevant range of all parameters, in particular a semimajor axis in the range of 1 AU a 20 AU. There are many more exoplanets with a semi-major axis in this range, but the mass of the planet and/or the eccentricity are not known. The first five columns of the table list the name and input parameters from observations. We add a subscript '0' to indicate the initial values of the stellar mass M * , of the semi-major axis a, and of the eccentricity e, as these quantities change during the postmain sequence evolution. We do not change the planet mass M p during the evolution. The last six columns of table 1 indicate the outcome for six different values of the wind mass-loss rate parameter η (equation 1). We either indicate that the star does not engulf the planet, and so there is no CEE ('No CEE'), or in cases where the planet does enter a CEE, we indicate the core mass, M core , and the envelope mass, M env at the onset of the CEE.

The planet HIP 75458 b enters the envelope of its parent star when the later is on the RGB for all values of η that we use here. In Fig. 1 we present the evolution of the stellar radius, periastron distance, and eccentricity of this system in the relevant post-main sequence phases. We see that tidal forces circularise the orbit before the onset of the CEE. Although the periastron distance increases, the semi-major axis decreases from its initial value of a 0 = 273R to about a 140R , before it rapidly decreases as the planet dives into the RGB envelope. In Fig. 2 we zoom on a time period of about 10 yr when the planet enters the envelope of its parent star. We also present the evolution of stellar mass (purple line).

The planet HIP 75458 b removes the envelope of its parent star during the RGB phase and leaves a bare helium core of mass M core = 0.4M , which then cools as a helium white dwarf. The planet might cause the nebula of the RGB star to have an elliptical shape. By definition this is not a PN. However, it is still a relevant system to our study. The influence of planets on the evolution of RGB stars and on their later evolution to the . The relevant properties of the six exoplanetary systems. The first five columns list the input parameters, the planet name, the present primary star mass M * ,0, the planet mass Mp in units of Jupiter mass MJ, the present semi-major axis and the eccentricity of its orbit, a0 and e0, respectively. The right six columns list the outcome as function of six values of the mass-loss parameter, from η = 0.5 (the common value) to η = 0.05. We either indicate that the star does not engulf the planet and the system avoids a CEE, or in cases where the planet does get into a CEE we list the core mass and the envelope mass at the beginning of the CEE (in M ). If for maximum (η = 0.5) and minimum (η = 0.05 or η = 0.07) mass-loss rate parameters no engulfment occurs, there is no need to simulate the the middle values, hence the empty boxes. horizontal branch has been the subject of a number of theoretical and observational papers (e.g., Soker 1998a; Siess & Livio 1999b; Carlberg et al. 2009; Geier et al. 2009; Heber 2009; Charpinet et al. 2011; Bear & Soker 2012; Silvotti et al. 2014; Carlberg et al. 2016; Jimenez et al. 2020) . We find here that the system HIP 75458 belongs to a class of systems where the planet terminates the evolution of the star on the RGB, or at least causes the star to lose most of its envelope and to become a blue horizontal branch star (Soker 1998a ).

Not including HIP 75458 b that suffers RGB engulfment, we find that out of the other five exoplanets, only beta Pic c might enters a CEE during the AGB phase of its parent star (table 1) . (The other planet in that system, beta Pic b, has a too large semi-major axis to influence the evolution of the star.) We have to reduce the mass-loss rate by about a factor of four below the commonly used value (η = 0.5) for beta Pic c to enter a CEE. Sabach, & Soker (2018a) find that in most cases they require 0.05 η 0.15 for planets to enter a CEE with their parent star when the later is on its AGB. Our result for beta Pic c is compatible with their finding.

We present the evolution of beta Pic c for three values of η in Fig. 3 . We notice that already on the RGB tidal interaction reduces somewhat the eccentricity. Then, during the AGB phase of the parent star when mass-loss rate is high, there are the competing effects of mass-loss that acts to increase the semi-major axis, and of tidal interaction that acts to circularise the orbit and to reduce orbital separation (as the spin of the AGB is much slower than the orbital motion of the planet). For η = 0.5 and η = 0.15 mass-loss rate is high, and the effect of massloss in enlarging the orbital separation wins that of the tidal interaction. In the case of η = 0.15 the tidal force is strong enough to circularise the orbit. For η = 0.12 the AGB reaches a larger radius on the AGB and, because tidal interaction is very sensitive to the ratio of the stellar radius to semi-major axis, tidal interaction manages to bring the the planet into the AGB envelope.

In Figure 4 we zoom on the final million years or so of the evolution of the two lower panels of Fig. 3 . We see the helium-shell flashes effect in causing substantial envelope expansion. This increases the tidal interaction strength, that in turn slows down the increase in the semi-major axis, or even decreases it a little. The star finally engulfs the planet (lower panel) during such an envelope expansion of a helium-shell flash. Figure 3 . The evolution of the stellar radius (blue-thick line), semi-major axis (dashed-purple line; a0 = 585R ), the periastron distance (red line), and eccentricity (blackdashed line) for the system beta Pic c and for three values of the wind mass-loss rate efficiency parameter η. The graphs include the RGB, horizontal branch, and AGB phases of the evolution, and in the upper two panel the early post-AGB phase as well. The scale for the eccentricity is the vertical axis in units of 0.001e. The initial eccentricity is e0 = 0.24. Note the different scales of the three panels.

Consider the possible role of the planet in shaping the descendant PN. The planet beta Pic c, of mass M p = 9.3M J , enters the envelope when its mass is M env 0.6 − 1M for the values of η that we use. Namely, the planet mass is M p 0.01M env . Such a planet might excite large-amplitude (tens of per cents) oscillatory modes on the surface of the AGB star when it is deep inside the envelope (equation 5.7 in Soker 1992a), and might substantially spin-up the envelope (equation 10 in Soker 2001b). We consider the planetary system of beta Pic to be a future progenitor of an elliptical PN due to the expected entrance of the planet beta Pic c to a CEE during the AGB phase of its parent star.

To further reveal the dependence of the fate of the planet on the properties of its orbit we examine the role of eccentricity. We take the planet HD 38529 c with an observed eccentricity of e 0 = 0.36 and search for the initial eccentricity, e n,0 , that would allow the star to engulf the planet during the AGB phase. We make the calculations for one value of the wind mass-loss rate parameter η = 0.12, and find that, keeping all other observed parameters unchanged, an initial eccentricity of e n,0 0.6 would have allowed a CEE to take place. We present the results in Table 2 , where the meanings of the different variables are as in Table 1 . In Fig. 5 we present the evolution of stellar radius, semi-major axis, periastron distance, and eccentricity, in the post-main sequence phases. The result of this simple study is expected, namely, a higher eccentricity for a given semi-major axis, which gives a smaller periastron distance, increases the likelihood of engulfment. However, it is not a straightforward evolution, because as we see in Fig Table 2 . Examining for the eccentricity of the orbit of HD 38529 c that would bring it to form a CEE during the AGB phase of its parent star. The first four columns in the second row are the observed values where units are as in Table 1 . The last three columns indicate the outcomes had the eccentricity of the orbit been larger, keeping all other observed properties unchanged. In all simulations the wind mass-loss rate parameter is η = 0.12. For en,0 = 0.6 the planet enters a CEE, and we list the core and envelope masses (in M ) at the onset of the CEE.

3 for the planet beta Pic c). The periastron distance a p = (1 − e)a, though, increases. As the initial eccentricity e n,0 increases, the decrease in the semi-major axis and eccentricity on the RGB becomes more significant. The evolution with e n,0 = 0.6 has a smaller semi-major axis than the other two cases when the system leaves the RGB. This smaller semi-major axis makes tidal interaction on the AGB stronger, and the system is more likely to enter a CEE. In Fig. 6 we zoom on the last million years or so. As in the evolution of beta Pic c (Fig 4) , engulfment occurs following a stellar expansion as a result of helium-shell flash, when the orbit is already circular.

The main goal of this study is to better understand the engulfment of planets during the RGB and AGB phases of their parent stars, in particular in relation to the possibility that planets shape the outflow of some AGB progenitors of elliptical PNe (section 1). The approach here followed earlier studies (e.g., Nordhaus & Spiegel 2013; Sabach, & Soker 2018a) in following the evolution of confirmed exoplanets. We specifically focused on planets that have orbits with semi-major axis in the range of 1 a 0 20 AU and high eccentricities. We examined six systems from the Extrasolar Planets Encyclopaedia; (exoplanet.eu; Schneider et al. 2011 ) that fit our requirements. To study their evolution we used the stellar evolutionary code MESA-binary.

We also followed Sabach, & Soker (2018a) and assumed that low mass stars that do not acquire angular momentum from a companion (Jsolated stars) have a much lower wind mass-loss rate during their RGB and AGB phases than the commonly used value (η = 0.5 in equation 1). We summarised the fate of the planets in Table 1 .

We found that out of the six systems, one system, HIP 75458, enters a CEE during the RGB phase of the parent star for all values of η ( Figs. 1 and 2) . The planet removes the envelope and leaves a bare helium core that will evolve to form a helium white dwarf. Only in one system the planet, beta Pic c, enters the envelope of its parent star during the AGB phase. For that to occur, we had to reduce the wind mass-loss rate . Zooming on the final evolution of the two lower panels of Fig. 5 . The upper and lower panels span a time of 1.13 × 10 6 yr and 9.46 × 10 5 yr, respectively. Note the different scales of the two panels.

by a factor of about 4 (η 0.12; table 1). The four other systems do not enter a CEE phase even for the lowest value of η.

Overall, our study of eccentric planetary systems strengthens the early conclusion of Sabach, & Soker (2018a) that was based on circular orbits and used a simple tidal interaction formula. The conclusion is that to have a non-negligible fraction of AGB stars that engulf planets we should consider a lower wind mass-loss rates of Jsolated stars.

We also made a test on the influence of the eccentricity. Keeping all other parameters at their observed value, we examined for what eccentricity of its orbit the planet HD 38529 c would enter a CEE with its parent star during the AGB phase. The observed value of the eccentricity is e 0 = 0.36. We found that we need to increase the eccentricity to a value of e n,0 0.6 for AGB engulfment to take place (table 2) .

In the cases where we do have engulfment on the AGB, the evolution involves some decrease in eccentricity and in the semi-major axis on the upper RGB phase, although the periastron distance (1 − e)a increases (Figs. 3 and 5). The final AGB engulfment takes place after a large envelope expansion as a result of a helium-shell flash (Figs. 4 and 6) . The next step is to conduct a thorough statistical study. However, the number of relevant confirmed exoplanets with semi-major axis of 1 AU a 0 20 AU around potential progenitors of PNe (stars with initial masses of M * ,0 1M ) is too low to conduct a meaningful statistical study. The uncertainty in the wind massloss rate on the RGB, and in particular on the AGB, adds to the uncertainty of such a study. Nonetheless, we encourage future studies to follow the evolution of exoplanets as they are discovered, to better learn about their degree of significance in influencing the post-RGB evolution and/or in potentially shaping elliptical PNe.

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This research was supported by a grant from the Israel Science Foundation. We completed this work while the Technion was closed due to the Coronavirus (COVID-19).