HD 219134: Take Three

Figure 1. Analyses of longitudinal radial velocity data by Johnson & colleagues have confirmed three planets orbiting HD 219134, a small Sun-like star of spectral class K3 located at a distance of only 6.53 parsecs (21 light years). Additional low-mass planets were reported in this system by Motalebi & colleagues (2015) and Vogt & colleagues (2015), but Johnson’s group had insufficient data to confirm or reject those candidates. In the figure, the planets colored aquamarine (b, d) are supported by Johnson et al. 2016, Motalebi et al. 2015, and Vogt et al. 2015; the large blue planet (e (h)) is supported by Johnson et al. 2016 and Vogt et al. 2015; and the orange planet (c) is supported by Motalebi et al. 2015 and Vogt et al. 2015

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I love science! Replication of results, falsification of invalid hypotheses! Teams of scientists working on singular questions, converging on robust answers, shining the light of understanding on the farthest reaches of the universe!

Or at least that’s the ideal.

Since last summer, we’ve seen science in action around HD 219134, an appealing amber star of 0.78 Solar masses (0.78 Msol) located very nearby in the northern constellation of Cassiopeia. That star and its planetary system have been featured in three previous blog posts (here, here, and here), which record unfolding developments both in the number of the reported planets and in the most appropriate characterization of the system architecture.

Two major studies last year presented conflicting analyses based on two different datasets. Motalebi & colleagues (2015; hereafter M15) proposed a four-planet architecture comprising three low-mass planets inside 0.25 AU and a gas giant of 0.19 Mjup (62 Mea) just outside 2 AU. In order of distance from the star, the planets were designated b through e. Almost simultaneously, Vogt & colleagues (2015; hereafter V15) proposed a six-planet architecture with five low-mass planets inside 0.4 AU and a gas giant of 0.34 Mjup (108 Mea) just outside 3 AU. In the manuscript circulated before publication, these six were designated b through g in order of distance from the star, but on publication they were renamed b through h without reference to their distance, omitting e altogether (perhaps reserving that letter for the planet reported by M15?). M15 also proposed a rotation period of 42.3 days for the host star, while V15 proposed a period of approximately 20 days.

Now a third team, one of whose members (Meschiari) also participated in V15, has weighed in on this system (Johnson et al. 2016; hereafter J16). Most of the authors are based at the University of Texas at Austin and involved in the McDonald Observatory Planet Search. A key strength of this work is its radial velocity coverage, which spans 27 years. Another is its data on stellar activity, which span 17 years and were obtained by the Keck/HIRES spectrograph. A third strength is the analytical acumen of the investigative team, which includes Artie Hatzes and Paul Robertson. A notable limitation, as the authors concede, is the low precision of the radial velocity data, which did not permit definitive results regarding any of the proposed low-mass planets apart from the innermost, planet b (see Figure 1).

The most direct contribution of J16 is their finding that HD 219134 has a stellar activity cycle with a period of 11.6 years. This is very similar to the 11-year cycle of our Sun, which manifests in the ebb and flow of sunspots on the Sun and auroras on Earth. Identifying this cycle in HD 219134 assisted the analysis of the radial velocity data, enabling J16 to rule out systematic effects originating in stellar activity. However, they were unable to determine the star’s rotation period, which is essential for a robust data analysis.

As the authors note, a star’s rotation has a critical relationship with its age. For HD 219134, a period of about 20 days would imply an age of about 1.3 billion years. Notably, V15 reported a period of 22.8 days for their planet f – very close to their estimate of the stellar rotation period. A period of 42.3 days, as reported by M15, would imply an age of 4.1 billion years, making the star a bit younger than our Sun. J16 favor a period similar to M15’s estimate, which they say is most consistent with the stellar activity data.

Table 1. Summary of findings on the HD 21934 planetary system

Tags: P = approximate periodicity in days; PL = planet designation; d = reported period in days; Mea = reported mass in Earth units; a = semimajor axis in astronomical units (AU; Earth’s semimajor axis = 1 AU); e = orbital eccentricity.

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In broad terms, J16 support M15’s analysis of the low-mass planets in the inner system and V15’s analysis of the gas giant in the outer system (Table 1).

In the inner system, J16 had no difficulty recovering a signal corresponding to planet b, which was characterized by M15 and V15 as a planet less massive than 5 Mea with a period just over 3 days. J16 also recovered periodicities at 22.8 days and 79.1 days, but they concluded that both signals were caused by stellar rotation (as an alias or harmonic of the period) rather than by planets. They were much more confident of another signal at about 47 days, which corresponds to planet d in the models of M15 and V15. However, the two earlier studies provided conflicting estimates of this object’s minimum mass, with M15 proposing 8.67 Mea and V15 proposing 21.3 Mea. J16 did not comment on this candidate’s mass.

J16 also failed to recover any periodicity corresponding to planet c. Nevertheless, both M15 and V15 characterized this object in very similar terms, while J16 noted that their own radial velocity precision was significantly lower than that of the two earlier studies. Thus it seems safe to regard planet c as validated.

In the outer system, J16 confirmed the small gas giant detected by M15 and V15, noting that the duration of M15’s dataset was too brief to inform a robust estimate of the planet’s orbital period. Benefiting from their extended radial velocity coverage, J16 calculated a period similar to that reported by V15 (2121 days versus 2247 days from V15), but they favored a mass closer to M15 (76 Mea, versus 62 Mea from M15 and 108 Mea from V15). Sadly, they retained the confusing designation of planet h for this object.

I say “sadly” because h implies a system with seven exoplanets, whereas only one extrasolar system with that many companions has been confirmed to date: Kepler-90. The planeticity of this remarkable system is rivaled only by HD 10180, which has six exoplanets (c through h) confirmed by radial velocity measurements and a seventh (b) whose existence has remained tentative ever since the system’s initial publication in 2011. Notably, no study has yet proposed more than six planets for HD 219134, and J16 were dubious (though not dismissive) of two of the six reported by V15. So I contend that planet e is a more appropriate designation for the cool gas giant in this system, on the grounds of logical consistency.

Figure 2. Selected mixed-mass planetary systems

Tags: ME = Earth masses; RE = Earth radii; AU = astronomical units (Earth-Sun separation = 1 AU). Selection criteria: At least two low-mass planets and at least one gas giant on an exterior orbit. In each system with transiting planets, all transiting orbits are co-planar. Note that gas giants Kepler-89d and WASP-47b are also observed in transit, while a single transit is reported for the innermost planet of HD 219134.

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As we learn more and more about its architecture, HD 219134 becomes a more and more interesting example of what I might call “a rich mixed-mass system.” Figure 2 illustrates the construct I have in mind. It updates Figure 3 from a recent posting (Almost Jupiter) by revising the orbit of the outer planet of HD 219134 and adding our Solar System.

These 11 systems look like variations on a single theme. All center on a Sun-like star (o.70-1.25 Msol) and include at least two low-mass planets with at least one gas giant on a wider orbit. In 9 out of 11 systems, at least one low-mass planet orbits inside 0.1 AU, and in 8 out of 11, the gas giant orbits outside 1 AU. In three systems (including our own), at least one additional low-mass planet orbits outside the (outer) gas giant. One system (WASP-47) hosts two gas giants inside the system ice line, such that one dominates the inner cluster of planets and the other orbits in the system habitable zone. Another (Kepler-90) might host two warm giants, since planets g and h both have radii larger than 8 Rea.

Although the Solar System is typically the oddball in any line-up of planetary systems orbiting Sun-like stars, it bears a distinct family resemblance to most systems in Figure 2. Specifically, it is one of nine systems in this sample with a pronounced gap between the inner aggregation of low-mass planets and the cool giant. In our system the gap appears in the void between Mars and Jupiter. Such a gap is absent only from the two most compact systems (Kepler-89, 289), where all known planets orbit inside 0.6 AU.

Even one of our system’s oddest features – the absence of planets inside 0.3 AU – has an extrasolar counterpart, since Kepler-289 reveals a similar dearth of planets inside 0.2 AU. Evidently gaps can appear almost anywhere within 5 AU of a host star.

Nevertheless, the Solar System’s two cold gas giants make it unique among the systems considered here. Ours is also the only one with confirmed or even proposed objects of habitable mass (i.e., 0.3-3.0 Mea) orbiting in the liquid water zone. Three other systems in this line-up harbor planets in that favored region (WASP-47, Kepler-68, HD 10810). Unfortunately, none are habitable: two are gas giants and the third, HD 10810 h, is more massive than Neptune.

What about the seven systems where the gap occupies the habitable zone? In one of them (Kepler-90), an adjacent planet might prevent habitable planets from forming or surviving. But in six other systems (HD 219134 and Kepler-48, 87, 89, 167, 289) the habitable zone looks empty. For each of these, I’d love to see dynamical simulations of the long-term stability of hypothetical Earth-mass planets on habitable orbits.

migration through a radially structured disk

We have lots of theories about the evolution of our Solar System. These days, the most popular hinge on the unique relationship between Jupiter and Saturn. As noted above, however, none of the other systems in Figure 2 contain such a power couple. Could some other aspect of system evolution, some factor independent of primordial resonance between two gas giants, be responsible for the structural commonalities visible in these systems?

Gavin Coleman and Richard Nelson recently produced two studies in quick succession on their developing model of system evolution (2016a, 2016b; hereafter CN16A and CN16B). Each study reports a set of N-body simulations of planet formation around a star of 1 Msol in a realistic protoplanetary disk that includes gas, pebbles, boulders, planetesimals, and a cavity inside a radius of 0.05 AU. The simulations modeled key physical processes known to affect planet formation and disk evolution, such as magnetohydrodynamic turbulence at the inner edge, aerodynamic drag on planetesimals, gas accretion on planetary cores, Type I migration, Type II migration, and photoevaporation. Both sets of simulations produced planetary systems similar to examples in Figure 2.

CN16A reported an ensemble of 72 simulations. Each one began with a disk of radius 40 AU containing 52 protoplanets (also called planetary embryos) of 10% Earth mass each (0.1 Mea), traveling on orbits between 1 and 20 AU. The full ensemble used initial gas disks that were either 1, 1.5, or 2 times the mass of the minimum mass Solar nebula, with disk metallicities of either 0.5, 1, or 2 times Solar.

This set of simulations readily formed Hot Jupiters, sometimes with low-mass companions on adjacent orbits; the latter systems recall WASP-47. The same setup also produced compact systems of low-mass planets similar to Kepler-11. However, it failed to produce any gas giants with periods longer than 10 days.

The second study, CN16B, reported an unspecified number of simulations with disks initially containing 44 planetary embryos of 0.2 Mea each on orbits between 1 and 20 AU. The full ensemble used initial disk masses that were either 1 or 2 times the minimum mass Solar nebula, with metallicities of either 0.5, 1, or 2 times Solar. Disk lifetimes ranged from 3.5 to 8.5 million years.

The most significant change in the new setup was the inclusion of radial structures in the protoplanetary disk arising from discontinuities in viscous stress and the local surface density of solid particles. Such structures can also be described as planet traps or dead zones: well-defined regions with finite lifetimes where migrating solids become stranded and mutual interactions result in the accretion of planetesimals and protoplanets. Each simulation in CN16B included four radial structures whose location and duration varied from run to run. As one structure subsided, another formed at a different radius. All were located outside the system ice line at semimajor axes wider than 5 AU (see Figure 5 in CN16B).

Figure 3. The protoplanetary disk around TW Hydrae

This young star has a huge protoplanetary disk whose fortuitous alignment enables a face-on view from the Solar System. The disk is about 5% as massive as our Sun (0.05 Msol), and its radius is about 90 AU. Radial structures can be observed throughout (Nomura et al. 2016, Debes et al. 2016).

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For disks of sufficient mass and metallicity, the improved setup produced both Hot Jupiters and long-period gas giants. Overall results replicated the widely reported “period valley” between 0.1 and 0.5 AU (the range of semimajor axes where gas giant planets are rare). Final architectures included systems with a Hot Jupiter plus an outer giant companion; compact inner systems of low mass planets bounded by a gap with a cool giant orbiting outside it (siblings of HD 219134 and Kepler-167); and systems with two cool gas giants analogous to Jupiter and Saturn. This setup also produced compact low-mass systems, some with inner gaps resembling those around Kepler-289 and our Sun.

As Coleman & Nelson readily concede, they’re working with a “toy model” that isn’t intended to exactly recapitulate planet formation or predict the relative frequency of system architectures. Nevertheless, their model incorporates the latest theoretical perspectives and observational insights (e.g., high-resolution imaging of the protoplanetary disks around HL Tauri and TW Hydrae), and its most recent iteration compares very well with other available approaches. As far as I’m aware, it’s the only evolutionary model proposed to date that can produce system architectures whose diversity rivals reality. I’m eager to see the next study this team produces.

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REFERENCES
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