The Role of Planets in Shaping Planetary Nebulae

Soker (1997) established an observationally based framework whereby planetary nebulae (PN) with different morphologies were mapped to the shaping mechanism that could produce them. These mechanisms ranged from single stars to a multitude of binary interactions with stellar and substellar (brown dwarf and planetary) companions.

Many discoveries, both observational and theoretical, have been made in the last 10 years that have thickened the debate of what shapes PN. Key to the debate have been the theoretical works of Soker (2006b) and Nordhaus et al. (2007) (but see previous work by Soker & Zoabi 2002), who described the difficulty with which single asymptotic giant branch (AGB) stars can sustain rotation and global magnetic fields for long enough to affect the geometry of the mass loss and the shape of the subsequent PN. In the case of single stars, rotation and global magnetic fields have been the leading mechanisms suggested for the shaping of nonspherical PN (e.g., García-Segura et al. 2005). Lacking a full understanding of how single AGB stars can produce winds that greatly diverge from a spherical distribution, several authors started looking more favorably to binary origin explanations (for a review, see De Marco 2009), where the companion is either an AGB wind shaping agent (i.e., via gravity) or it induces primary envelope rotation and magnetic fields.

Irrespective of what camp of the debate each researcher favors, the scheme of Soker (1997) has been used as a basis against which to test various hypotheses (e.g., García-Segura et al. 1999; Parker et al. 2006a; Lü et al. 2009). Therefore, in light of the last decade of observational and theoretical results, there is scope for a revision of that framework. In particular, the role of planets in shaping PN was already discussed in the late 1990s, but could not be observationally quantified at that time. Today, we know more on the statistics of planetary systems, and, although many questions still remain, this is enough to update our estimate of the role of planets in shaping PN.

Finally, new planetary discoveries are changing our understanding of stars. New questions are being asked as to the influence planets have on stellar evolution and, conversely, how stars affect planet evolution and survival (see, for instance, Schuh et al. 2011). The role of planets in PN shaping is topical in this context.

In § 2 we explain the PN shaping framework laid out by Soker (1997). In § 3 we discuss new results in the field of PN (§ 3.1) and planets (§ 3.2), which allow us to reassess the work of Soker (1997) in § 4. In § 5 we present some arguments regarding the detection of naked central stars, and in § 6 we conclude.

Soker (1997) presented a classification of 458 PN, based on the morphological systems of Schwarz et al. (1993) and Corradi & Schwarz (1995), with the aim of distinguishing between the role of stellar and substellar companions. Soker (1997) further classified elliptical PN into those with large and small departures from sphericity. He divided PN morphologies into four categories and flanked each category with the physical process most likely to give rise to that shape using a series of observational arguments.

• 1.  
  Spherical PN are formed by progenitors that did not have a companion or did not interact with their companion. Some departure from sphericity (though no axisymmetry) may be expected if the companion separation is large, but still interacting in some way with the primary and the PN is formed over a span of time comparable with the orbital period.
• 2.  
  Bipolar PN are formed by a close stellar companion that avoided a common-envelope phase or that entered the common envelope only late in the evolution. The stellar companion accretes a substantial fraction of the AGB wind and blows two opposite jets that shape the nebula into a bipolar structure. Point-symmetric structures are also possible due to precession of the accretion disk around the companion.
• 3.  
  Elliptical PN with large departure from sphericity are formed by stellar companions in a common envelope. The companion in the envelope does not blow strong jets (or blows no jets at all), but the interaction with the envelope ensures high equatorial mass loss that leads to an expanding ring structure.
• 4.  
  Elliptical PN with small departure from sphericity are formed by a substellar companion (a brown dwarf or a planet) that spins-up the envelope of the AGB progenitor. Weak jets may be present.

The preceding framework was based primarily on a series of key observational results and in part on a handful of theoretical studies, which we summarize next:

• 1.  
  The theoretical argument was then, and is still now, that the axisymmetric structure (including point-symmetric) requires the presence of a stellar or substellar companion (Soker 2001b, 2004, 2006b). The rarer point-symmetric PN cannot be explained by a model based on shaping by the fast wind during the PN phase and seem to require precessing accretion disks. Theoretical models showed that binary interactions have the ability to produce the observed PN morphologies (e.g., Morris 1987).
• 2.  
  From population synthesis studies, the fraction of PN that were derived from binary interaction was far lower than the needed 90% (that is, the entire PN population minus 10% spherical PN). For instance, Han et al. (1995) derived that only 38 ± 4% of all PN derive from binary interactions (common envelopes, mergers, and wider binary interactions).
• 3.  
  We knew observationally that ∼10% of all PN are round. We also knew that ∼15% of PN are bipolar, while the remaining ∼75% are elliptical (mildly, extremely, and with or without additional structures). The detailed classification does change from author to author (e.g., Corradi & Schwarz 1995), so we refrain here from describing additional subdivisions.
• 4.  
  At the time, it appeared that the PN observed around post–common-envelope central stars were not bipolar, but rather elliptical (Soker 1997).
• 5.  
  Bipolar PN have relatively higher expansion velocities, more in line with the escape velocities of main-sequence, rather than AGB, stars (Corradi & Schwarz 1995). Elliptical PN, on the other hand, have expansion velocities that can be explained by winds from AGB stars.
• 6.  
  The spherical halos of many PN are much fainter than the elliptical inner region. In the binary model this is accounted for by a binary interaction that occurs at a late stage in the superwind phase, the period of enhanced mass loss that is observed to take place toward the end of the AGB (Delfosse et al. 1997). The interaction both increases the mass-loss rate and causes the departure from axisymmetry; even a planet can play a role in this process (Soker 2000).
• 7.  
  Planet statistics were poor in that year.

Later, Soker (2001a), realizing the possible importance of wider stellar companions, added a fifth class of wide (but not very wide) companions that accrete mass and blow jets. The shaping is only by the jets. A moderately elliptical PN is formed, with pronounced signature of jets (although not as strong as in the preceding scenario 2). Finally, De Marco & Moe (2005) and Soker & Subag (2005) introduced the concept that not all 1–8 M_⊙ stars actually make a PN. Single stars can make a spherical PN of a subluminous nature that is harder to detect; Soker & Subag (2005) termed this class "hidden PN."

In Table 1 we summarize the conclusions of Soker (1997; col. [3]), Soker (2001a, 2001b; col. [4]) and Soker & Subag (2005; col. [5]), based on the preceding results, as well as the conclusions of the present work, which will be justified in the following sections. Once the spherical PN are accounted for by mechanisms involving no interaction and bipolar PN are accounted for by close companions outside the common envelope (∼10% and ∼15%, respectively), the remaining ∼75% of all PN needs to be accounted for by other interactions. Soker (1997) expected that the only other PN shaping interaction would be a common-envelope interaction, and these interactions are not frequent enough to account for 75% of all PN. This led Soker (1997) to conclude that there are not enough stellar companions to produce the large fraction of nonspherical PN. Even including much wider binaries in the class of interacting binaries (Soker 2001a), there was still a need for a relatively large number of planetary companions to help shape PN.

Since the mid-2000s, several results of both a theoretical and observational nature allowed us to refine the conclusions of Soker (1997, 2001a, 2001b) and Soker & Subag (2005). Here, we divide the new results into two classes. Those pertaining PN and those that regard the presence and frequency of planets around main-sequence and evolved stars.

3.1. Highlights of Relevant PN Research in the Last Decade

3.2. Highlights of Relevant Exoplanet Research in the Last Decade

In light of the new discoveries (§ 3), we now reframe the results of Soker (1997) and subsequent updates by Soker (2001a, 2001b) and Soker & Subag (2005). The work discussed in § 3.1 releases the tight constraint that brought Soker (1997) to conclude that a large number of PN should be shaped by planets. The increasing numbers of brown dwarf and planet discoveries around evolved stars also give support to the idea that planets play a role in shaping PN, provided that they are at a suitable distance from the star to interact during the AGB. Finally, the larger fraction of planets detected recently around main-sequence stars, compared with what was believed a decade ago, provides us with more flexibility when discussing the role of planets in shaping PN.

In what follows we quote percentage figures with an accuracy of 1%. This accuracy is unrealistically high. However, we do so for ease of following some of the arguments. At the end, we will discuss what should be considered reasonable errors on these percentage estimates.

We start by returning to the discussion of § 3.1: instead of considering the PN population as the inevitable child of the 1–8 M_⊙ star population, needing to reflect its binary fraction, we can think of the PN population as deriving from only a subset of the 1–8 M_⊙ stars. We adopt the subdivisions of PN morphological types envisaged by Soker (1997), with the changes brought in by the MASH morphological discoveries (§ 2; Table 2).

First of all, we determine the fraction of all 1–8 M_⊙ stars that result in a PN of any shape. Moe & De Marco (2011, in preparation) concluded that only 21 ± 8% of all 1–8 M_⊙ stars (13,000/61,000) make PN and 82 ± 8% make no PN, or do not go through the AGB at all (see § 3.1). This estimate rests on single stellar evolution, the initial mass function, the galactic star formation history, and observations. It is almost independent of the binary fraction and period distribution.

An independent way to determine the fraction of all 1–8 M_⊙ stars that result in a PN of any shape is to consider only the main-sequence binary fraction and period distribution. A summary of how these fractions are determined can be found in Table 3. Approximately 57% of F and G main-sequence stars are in binaries and ∼30% have an orbital separation of ≤ 30 AU (Duquennoy & Mayor 1991) and will interact at some time during the primary star's life. We have taken a maximum separation that is possibly too large for some types of interaction, but is smaller than the distance between Mira and its interacting companion (see § 3.1). We assume, once again, that an interaction is needed to produce nonspherical PN. We also account for the fact that 14% of all stellar systems suffer a strong interaction on the RGB (orbital separation ≲3 AU; Duquennoy & Mayor 1991) that induces so much mass loss that the system is prevented from ever evolving to the AGB. We then deduce that 30–14 = 16% of all stars suffer an AGB interaction with a stellar companion and go on to form a nonspherical PN. This means that ∼16% of all stars go through an AGB interaction, ∼14% go through an RGB interaction and never ascend the AGB, and the remaining ∼70% suffer no interaction with a stellar companion and evolve into naked central stars or central stars with round PN, unless they have an interaction with a substellar companion. As did Soker (1997), we assume that mildly elliptical PN are shaped by interactions with substellar companions. Hence, ∼16% of all stars go through an interaction with a stellar companion and result in nonround and non–mildly elliptical PN. This is equivalent to stating that ∼16% of all stars result in 61% of all PN (the nonround and non–mildly elliptical ones; Table 3), and this means that 26% (16/61 × 100) of all 1–8 M_⊙ stars make a PN of any shape. This estimate, which has a probable error of ± 5%, is based on approximate binary considerations and is consistent with that outlined previously (compare 26% with 21 ± 8%), obtained by Moe & De Marco (2011, in preparation) almost entirely from single stellar evolution arguments and PN counts.

In Table 4 we finally adopt 26% as the fraction of 1–8 M_⊙ stars that are able to make a PN of any shape. Approximately 14% is the fraction of all stars that do not ascend the AGB because of a strong interaction on the RGB. The remaining ∼60% is the fraction of all stars that do not make a PN because they suffer no interaction (for further discussion, see § 5). Finally, we split 16% into fractions reflecting the PN morphological types presumed to derive from binary interactions with stellar companions; i.e., 13% are bipolar (16 × 0.13/0.61 = 3.4), 28% are extremely elliptical (16 × 0.28/0.61 = 7.3), and 20% are mildly elliptical with jets (16 × 0.20/0.61 = 5.2). The remaining 10% of all 1–8 M_⊙ stars (26–16%) goes to form the two remaining PN classes: the 19% round PN (10 × 0.19/0.39 = 4.9) and the 20% mildly elliptical PN with no jets (10 × 0.20/0.39 = 5.1).

Recently, Moe & De Marco (2011, in preparation) carried out a more precise binary population synthesis model, completely independent of morphological subdivisions, and determined that 8% of all 1–8 M_⊙ stars suffer a strong interaction with a stellar companion on the AGB (common envelopes and interactions outside the envelope). This is in line with the approximate estimate based on binary considerations and morphological subtypes, where ∼11% of all 1–8 M_⊙ stars suffer a strong AGB interaction (3.4 + 7.3% : Table 4 and col. [7] of rows 2 and 3 in Table 1).

In Table 1 (col. [7]) we list a revised subdivision of the evolutionary channels followed by intermediate mass stars and their link to PN morphology. During the last decade of simulations and observations we have learned that a one-to-one correspondence between morphologies and shaping channels is as improbable as the likelihood of finding two identical PN. This is why we stress (see also Table 1, note c) that these are only guidelines. The take-home messages are as follows:

• 1.  
  Common-envelope and other interactions, where the companion is close to the AGB surface, likely result in strong collimation leading to bipolarity and extreme ellipticity.
• 2.  
  Low-mass companions such as planets are likely only to promote small departures from a spherical shape.
• 3.  
  Blowing jets may be promoted not only by an accreting stellar companion at some distance from the primary, but also by a disrupted lower-mass companion that forms a disk around the primary core (Nordhaus & Blackman 2006). If so, this would confuse the distinction between channels 4 and 5 in Table 1

If, as in Soker (1997, 2001a) and Soker & Subag (2005), we assume that mildly elliptical PN with no jets were shaped mainly by a substellar companion, we predict that substellar companions have shaped ∼20% of all PN, which corresponds to ∼5% of all 1–8 M_⊙ stars having suffered an interaction with a planetary companion on the AGB. However, if substellar companions can get disrupted, form a disk around the primary core, and blow jets, then these percentages could rise to as much as ∼40% and ∼8%, respectively.

4.1. The Implied Fraction of Planets from the AGB Perspective

The fact that only ∼30% of main-sequence stars have stellar companions close enough to interact, combined with the fact that ∼81% of PN have nonspherical shapes that appear to need a companion, led Soker (1996) to state that "substellar objects (brown dwarfs or gas-giant planets) are commonly present within several AU around main-sequence stars. For a substellar object to have a high probability of being present within this orbital radius, on average several substellar objects must be present around most main-sequence stars of masses ≲5 M_⊙."

We have derived here that ∼5% of all 1–8 M_⊙ stars suffer a strong interaction with a substellar companion on the AGB. This estimate depends critically on (1) the assumption that mildly elliptical PN with no jets are mostly shaped by a substellar companions, (2) the frequency (∼20%) of this specific PN morphology, and (3) the two independent arguments that predict that only 21% or 26% of 1–8 M_⊙ stars make a PN at all (0.21 or 0.26 × 0.20 ∼ 0.05).

These substellar companions should occupy orbits between ∼3 and ∼30 AU around the main-sequence progenitors. Closer companions (whether stellar or substellar) suffer a strong interaction (likely a common-envelope interaction) on the RGB and are either destroyed or preclude the primary from ascending the AGB because of excessive mass loss (Soker et al. 1998; Bear & Soker 2010; Nordhaus et al. 2010). Companions farther out⁴ would not interact.

Using a population synthesis technique, one could use this estimate and work backward to determine the parent population of these star-planet systems. Even without such calculation, we can already draw a few conclusions. The median main-sequence progenitor mass of today's PN population is 1.2 M_⊙ and the median metallicity is approximately solar (Moe & De Marco 2006). Taking the maximum radii on the AGB, R_A, and on the RGB, R_R, from Iben & Tutukov (1985), Soker (1998) derived the following approximation for the ratio of the maximum AGB to maximum RGB radius as a function of mass:

for stars which develop degenerate helium cores, and

for more massive stars, where M is the primary's mass on the zero-age main sequence. From these relations we can state that for stars with spectral types earlier than A, the radius ratio is >2, while for stars with spectral types later than F-G, which correspond to the progenitors of central stars of PN, this ratio is < 2. For the progenitors of PN, therefore, the planetary population has to be relatively far out. We have quoted limits of 3 and 30 AU, respectively. The lower limit depends critically on the adopted prescription of tidal capture and mass-loss (Soker 1996; Villaver & Livio 2007, 2009; Nordhaus et al. 2010).

Considering that the fraction of solarlike stars hosting relatively close-by planets may be of the order of 10–20%, and considering that we predict that a low ∼5% of all solarlike stars have substellar companions farther out than ∼3 AU, it is probable that the substellar companions farther out are the outermost companions in a system of multiple planets.

In this subsection, we want to elaborate further on the suggestion that ∼60% of all 1–8 M_⊙ stars that ascend the AGB do not make a visible PN. This is a surprisingly high number and implies a large population of post-AGB stars that, under the commonly assumed scenario, would have PN, but do not in the revised scenario. To be more precise, Moe & De Marco (2006, 2011, in preparation) predict that ∼61,000 stars in the Galaxy are in the evolutionary phase appropriate to be surrounded by a PN of less than 0.9 pc in radius; i.e., these stars are in a post-AGB with T_eff ≳ 30,000 K, have left the AGB less than 25,000 yr ago, and have mass ≳0.55 M_⊙. This population is about six times larger than the Galactic PN population with radii smaller than 0.9 pc (11,000 PN; Frew 2008), from which we predict that 48,000 (61,000–13,000) stars in the Galaxy are "naked" central stars. It would be much harder to detect naked central stars, because of high reddening in the Galactic plane. However, we should consider that recent surveys have now detected ∼3000 PN (Frew & Parker 2010), which is ≲30% of the total (Jacoby 1980; Moe & De Marco 2006; Frew 2008). PN are particularly bright and have emission lines in the red part of the spectrum, which are less subject to reddening. The fraction of detectable naked central stars should be far smaller.

Naked central stars would look like subdwarf O and B stars, most of which are post-RGB stars, and would be easily confused with them. In some cases they could be told apart from those sdOB stars that are in a post-RGB phase of evolution on the grounds of higher luminosity and larger surface gravity (although there is an overlap between post-RGB and post-AGB stars on the log g - T_eff plane [Napiwotzki 1999 their Fig. 4]).

The fraction of naked central stars in the sdOB sample should be only a few percent of the total, because of their short lifetimes compared with the post-RGB phase. Any post-AGB object, independent of its mass, will fade below 100 L_⊙ in less than 100,000 yr (Vassiliadis & Wood 1994). All post-AGB objects with M > 0.60 M_⊙ will fade to L = 100 L_⊙ in only 10,000 yr. HB lifetimes are instead of the order of several tens of millions of years (Dorman et al. 1993).

We have an indication that the predicted number of post-AGB sdOB stars are there, but this must be corroborated by a more accurate count. O'Toole (2010, private communication—but see also Hirsch et al. 2008), determined that in about 120 sdO stars, there are several objects that could be in the post-AGB phase. This could constitute the few percent predicted. For the sdB stars, a few hundred of which have determined log g and T_eff, several reside in the log g - T_eff locus appropriate for post-AGB stars (Napiwotzki 1999; Hirsch et al. 2008). There should be fewer sdB post-AGB stars than sdO post-AGB stars, because their evolutionary times for the temperature T_eff < 40,000 K is quite a lot shorter than for T_eff > 40,000 K.

Looking at Fig. 2 of Napiwotzki (1999) or Fig. 3 of Hirsch et al. (2008) we see that there are a number of sdB and sdO stars that are not surrounded by a PN. Several objects are indeed found on the horizontal part of the post-AGB tracks, where a PN is expected. Others are seen on the descending part, but at high core mass such that one might expect that a PN would be present, considering the shorter evolutionary timescales. This sample is not homogeneous, and it is therefore difficult to determine whether the number of naked central stars on this plot is what is expected from the prediction by Moe & De Marco (2006, 2011, in preparation).

Deep imaging surveys may reveal a number of faint and spherical PN around naked central stars. The fact that the deep MASH survey approximately doubled the fraction of circular PN may already have borne out this prediction.

The first assumption we adopt in this article, which is increasingly supported by observations and theoretical considerations, is that single stars are mostly unable to produce PN whose shapes diverge from spherical. Second, we bring to bear the population prediction that the fraction of stars in the initial mass range 1–8 M_⊙ that actually form PN is only ∼20% (see § 3.1).

As in the past, we make the simplistic assumption that mildly elliptical PN with no jets are formed exclusively by planetary interactions. This assumption is broadly justified by the following:

• 1.  
  Simulations show that density contrasts drastically reduce for decreasing companion mass in common envelopes (Sandquist et al. 1998; De Marco et al. 2003) and outside the common envelope (Kim & Taam 2010); such interactions are therefore likely to lead to mildly elliptical shapes at best.
• 2.  
  Known PN around close binaries are, by and large, bipolar or strongly elliptical and have often jets and substructures; if the stellar-mass companions are at larger orbital separations than those that interact in a common envelope, theoretical considerations suggest that accretion onto the companion promotes jets, which, once again, lead to more dramatic departures from spherical symmetry than a mild ellipticity.

Despite these justifications, the one-to-one correspondence between interactions with substellar companion and the generation of mildly elliptical PN should be considered only as a guideline to be confronted by observations and against which to continue testing future shaping theories.

With the preceding premise, we predict that the fraction of PN shaped by planets (∼20%) corresponds to only ∼5% of all 1–8 M_⊙ stars having interacted with a planet on the AGB, indicating that a few percent of 1–8 M_⊙ stars should have Jupiter-class companions farther out than a few AU, a thing that seems increasingly plausible given new discoveries of planets around main-sequence stars (e.g., Johnson et al. 2010; Bowler et al. 2010; see § 3.2). Planets farther out may be the outer planets in planetary systems.

Finally, the implication that ∼60% of all stars in the initial mass range 1–8 M_⊙ do not go through a PN phase may be justified observationally. There are several hot subdwarf stars that occupy a location of the log g - T_eff diagram appropriate for central stars of PN, but that do not exhibit a PN. In order to strengthen this claim, one would have to make a prediction of the fraction of all subdwarf O and B stars that are expected to be post-AGB in origin through a population synthesis. Also, one would have to homogeneously locate a sufficient number of these stars on the log g - T_eff diagram to determine if the prediction is verified.

N. S. acknowledges support by the Asher Fund for Space Research at the Technion—-Israel Institute of Technology and the Israel Science Foundation.