The Pan-Pacific Planet Search. VII. The Most Eccentric Planet Orbiting a Giant Star

The AAT/UCLES data for HD 76920 are relatively constant, save for two observations nearly 300 m s⁻¹ higher on 2010 January 29/30. These spectra were of similar S/N to the others for this target, and the observing conditions were typical, ruling out the possibility of observer error or systematic errors (e.g., scattered moonlight) for the aberrant velocities. Reprocessing the spectra through an independent reduction and Doppler pipeline gave similar results, ruling out errors in data reduction or barycentric correction. We attempted a single highly eccentric planet fit using the genetic algorithm employed by our team for other Pan-Pacific Planet Search (PPPS) data sets with sparse sampling (e.g., Wittenmyer et al. 2011a, 2015, 2017b). We searched a period range of 100–1000 days and allowed eccentricities up to e = 0.9, running for 50,000 iterations (about 10⁷ possible configurations). The best-fit solution had a high eccentricity and a period of ∼420 days.

Our team obtained access to CHIRON in 2015 for follow-up of interesting candidates from the PPPS, and HD 76920 was put in the queue to catch the next predicted large velocity excursion of 2015 October. We were fortunate to catch the peak and the drop-off, confirming the period at 415 days. FEROS observations were also added and corroborated the orbit fit obtained from AAT and CHIRON. For the final fitting process, we used the Keplerian model in the Systemic Console version 2.2000 (Meschiari et al. 2009). For all orbit fitting, 7 m s⁻¹ of jitter (excess white noise) has been added in quadrature to the internal instrumental uncertainties of each data set. This estimate is derived from the velocity scatter of 37 stable stars in the PPPS as first described in Wittenmyer et al. (2016b). While correlated noise is known to affect radial velocity data (Baluev 2013; Feng et al. 2017), we find that a white noise model is favored for all three data sets. The Bayes factors for a first-order moving average noise model ("MA(1)") are as follows: AAT—2.3; FEROS—1.5; CHIRON— −1.7. The data and best-fit model are shown in Figure 1. Uncertainties in the system parameters were obtained with the Markov Chain Monte Carlo tool within Systemic. The normalized probability density functions for key parameters, resulting from a chain of 10⁷ steps, are shown in Figure 2. The best fit to the data results in a planet with P = 415.4 ± 0.2 days, m sin i = 3.93±0.15 M_Jup, and e = 0.856 ± 0.009 (Table 3). There is no evidence for additional Keplerian signals or velocity trends that might indicate a distant massive companion, as shown in Figure 5.

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Table 3.  Keplerian Orbital Solution for HD 76920b

Parameter	Value
Period (days)	415.4 ± 0.2
Eccentricity	0.856 ± 0.009
ω (degrees)	${352.9}_{-1.1}^{+1.9}$
Mean anomalya (degrees)	46.5 ± 0.4
K (m s−1)	186.8 ± 7.0
m sin i (MJup)	${3.93}_{-0.15}^{+0.14}$
a (au)	1.149 ± 0.017
rms about fit (m s−1)	9.74
Zero point—AAT m s−1	7.0 ± 3.6
Zero point—CHIRON m s−1	−23.7 ± 4.9
Zero point—FEROS m s−1	−13.5 ± 4.7

Note.

^aAt epoch BJD 2454867.07428.

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As a further test of the validity of the detected signal in the time series, we also ran the Exoplanet Mcmc Parallel t Empering Radial velOcity fitteR (EMPEROR; J. Jenkins & P. A. Pena 2017, in preparation¹¹ ) code to determine if the parameter estimations were robust. EMPEROR employs thermodynamic integration methods (Gregory 2005) following an affine invariant MCMC engine, performed using the emcee package (Foreman-Mackey et al. 2013) in Python. Correlated noise in the measurements are taken care of within EMPEROR by using a first-order moving average model, an approach that has been shown to robustly detect small amplitude signals with various morphologies and across numerous radial velocity data sets (e.g., Jenkins et al. 2013, 2017; Tuomi et al. 2013; Jenkins & Tuomi 2014). Model selection is performed automatically by EMPEROR, whereby a Bayes Factor of five is required, a threshold probability of 150 that the more complex model is favored over the less complex one. The code also automatically determines which of the signal parameters, such as period and amplitude, are statistically significantly different from zero, and some basic priors are applied to those parameters whereby all are assumed to be flat except for the eccentricity and jitter priors that are folded Gaussian and Jeffries priors, respectively.

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Under the aforementioned constraints, EMPEROR found two statistically significant signals in the radial velocity time series. The primary signal was found to be the planet signal at ${415.59}_{-0.22}^{+0.19}$ days, with an amplitude and eccentricity of ${177.5}_{-3.8}^{+6.4}\,{\rm{m}}\,{{\rm{s}}}^{-1}$ and ${0.859}_{-0.005}^{+0.005}$, respectively. This result highlights the robustness of the planet detection result, showing that a long chain (×10⁷) MCMC analysis to probe the posterior parameter space, along with Bayesian selection criteria, can place hard constraints on the planet signal detection and the orbital characteristics of the planet. For completeness, we show a corner plot of the posterior distribution in Figure 6.

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The EMPEROR analysis found a secondary signal, which we discuss briefly here. A comparison of evidence is given in Table 4. This second signal was found with a period of ${28.4}_{-0.57}^{+0.04}\,\mathrm{days}$ and an amplitude of ${11.1}_{-1.5}^{+1.5}\,{\rm{m}}\,{{\rm{s}}}^{-1}$. The amplitude is at the level expected for the jitter of HD 76920: allowing the excess white noise ("jitter") to vary in the single-planet model, we obtained the following for each instrument: AAT—10.4 ± 1.5 m s⁻¹, CHIRON—8.3 ± 1.6 m s⁻¹, FEROS—2.9 ± 1.9 m s⁻¹. Hence, this secondary signal is likely to originate from an intrinsic stellar process; attributing the periodicity of the secondary signal to a planet implies an orbit that crosses that of HD 76920b. Crossing orbits are almost certainly a recipe for dynamical disaster, with catastrophic instabilities occurring on timescales of a few years (e.g., Horner et al. 2011, 2013; Wittenmyer et al. 2013a; Hinse et al. 2014).

As a matter of course for new planet discoveries, we searched for activity-related signals in the spectra and publicly available photometry. Examination of 8.8 years (1403 epochs) of All-Sky Automated Survey (ASAS) photometry (Pojmanski 1997) shows no periodicities of significance near the planet's orbital period (Figure 7). The ASAS V-band photometry has a mean value of 7.827 ± 0.013 mag. We also investigated the variability in the Hα line for our 17 AAT spectra. Variable levels of chromospheric activity can produce changes in the level of line profile reversal in some line cores, resulting in changes to the line centroid and hence the measured radial velocity (Martínez-Arnáiz et al. 2010). These effects will also produce changes in the line's equivalent width (EW), and so measurement of the EW can provide an indicator of the presence of activity-induced radial velocity variations (Robertson et al. 2014). Figure 8 shows the stacked spectra of HD 76920 and the radial velocity as a function of the Hα EW. No correlation is evident: the two velocity extrema, obtained on consecutive days, have quite different EW, one of which is consistent with the EW of the remaining spectra. Lest this discrepancy raises concerns about the candidate planetary signal, we perform one final test: Figure 9 shows the periodogram of our data with all three "high" velocities removed. The highest peak remains at 413 days with a false-alarm probability of 0.6%.

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If a highly eccentric gas giant happens to transit, it becomes all the more valuable, as it will offer a unique window into the physics and composition of "cold Jupiters." At present, only one such planet is known, HD 80606b, with e = 0.93 and an orbital period of 111 days. It was discovered to transit in 2009 (Fossey et al. 2009; Garcia-Melendo & McCullough 2009; Moutou et al. 2009), and the transit was further characterized in a multi-site ground-based observing campaign by Winn et al. (2009). A Spitzer campaign centered on the periastron passage (Laughlin et al. 2009) allowed for the direct measurement of the atmospheric heating due to the ∼30 hr close approach. For comparison, HD 80606b passes to within 5.5 stellar radii of the star's surface at its closest approach (compared to 4 host-star radii for HD 76920b).

The eccentricity of planetary orbits can have a major impact on the expected transit properties of the planet (Barnes 2007; Kane & von Braun 2008). The eccentric nature of the HD 76920 b planetary orbit, combined with the relatively large size of the host star (see Table 2), make this planet an intriguing prospect for transit observations. A similar case was studied by Kane et al. (2010) for the planet orbiting iota Draconis. In that case, the eccentricity is smaller, but the star is larger and the periastron passage of the planet occurs very close to inferior conjunction (where the true anomaly f ∼ 0°). By contrast, the orbital fit from Table 3 and the orbit visualization shown in Figure 3 demonstrate that inferior conjunction for HD 76920 b occurs at a true anomaly of f ∼ 90°. At this ___location in its orbit, the star–planet separation will be 0.342 au, where the calculated orbital velocity of the planet will be a factor of 1.85 larger than the Earth's orbital velocity. The net effect of these factors is to produce a transit probability of 10.3% and a transit duration of 2.3 days, assuming a Jovian planetary radius. By comparison, if the planet were in a circular orbit with the same semimajor axis of a = 1.1491 au, then the transit probability would be 3.1% and the transit duration would be ∼4 days. The relatively large transit duration makes this a difficult observation from the ground, but the most difficult aspect is the small predicted transit depth of 0.02% resulting from the large stellar radius. The combination of transit probability and depth means that transiting giant planets around giant stars are likely plentiful but few have been detected. Currently, the largest stars (R_⋆ = 6.3 R_⊙) for which a planet has been detected are Kepler-91 (Lillo-Box et al. 2014) and TYC 3667-1280-1 (Niedzielski et al. 2016). Precision space-based photometry of giant stars will provide valuable information for the mass–radius relationship of giant planets around evolved stars. These opportunities will by provided by TESS (Ricker et al. 2014) and CHEOPS (Broeg et al. 2013).

In Wittenmyer et al. (2017b), we investigated the possibility of debris disks orbiting the giant stars HD 86950 and HD 29399, both of which were identified by McDonald et al. (2012) as having a possible infrared excess based on the presence of excess emission at 9 μm in the AKARI/IRC All-Sky Survey (Ishihara et al. 2010). Because McDonald et al. (2012) also noted an infrared excess for HD 76920 with a fractional luminosity (L_dust/L_star) of ∼1.2 × 10⁻³ peaking at 12 μm, we undertook a similar analysis in this work. We compiled a spectral energy distribution from photometry spanning optical to mid-infrared wavelengths, including optical BV, near-infrared 2MASS JHK_s (Skrutskie et al. 2006), WISE (Wright et al. 2010), AKARI 9 μm (Ishihara et al. 2010), and the IRAS faint source catalog (Moshir et al. 1990). We illustrate the stellar photospheric emission with a model from the BT-SETTL/Nextgen (Allard et al. 2012) stellar atmospheres grid appropriate for the spectral type (K0 III; T_eff = 4700 K, log g = 3.0, [Fe/H] = 0.0), and scaled to the stellar radius and TGAS distance (Gaia Collaboration et al. 2016; Wittenmyer et al. 2016c). We color-corrected the AKARI and WISE flux densities assuming blackbody emission from the star. The resulting spectral energy distribution is shown in Figure 10. No significant evidence of infrared excess is present. The infrared excess noted in McDonald et al. (2012) is based on AKARI 9μ, IRAS 12μ, and IRAS 25μ data points. We have added WISE  3 and WISE 4 photometry to that mix. No evidence of significant excess from the target is present after color correction of data points (IRAS12, IRAS25 have K = 1.4 for a 5000 K blackbody) and the calibration uncertainties of WISE  3 and 4 (∼5% and 6%, respectively) are taken into account.

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Planet–star tidal interactions become very strong when stars leave the main sequence. The increase in stellar radius means that the planet's gravity can more easily deform the star, and the star's deep convective envelope is highly efficient at dissipating the energy required for this deformation. The result is a damping of the planet's orbital semimajor axis and eccentricity. The dominance of the tide raised on the star and the large stellar moment of inertia, mean that the planetary semimajor axis and eccentricity can continue to decay until the star engulfs the planet. This contrasts with the case of an eccentric planet orbiting a main-sequence star, for which the tide raised on the planet usually dominates, and the eccentricity decays to zero at a non-zero semimajor axis (see Figure 8 of Villaver et al. 2014). Engulfment of the planet by the star is also aided by the rapidly expanding stellar radius. Working against this, as the star ascends the red giant branch (RGB), stellar mass loss begins to accelerate, causing the planet's orbit to expand. The fate of the planet thus depends on the stellar radius expansion, tidal forces dragging the planet inwards, and mass loss moving the planet out. The high eccentricity and modest semimajor axis of HD 76920b mean that it is likely to be ingested by its host star as the latter ascends the RGB.

We model the future evolution of HD 76920b using the method presented in (Villaver et al. 2014). This uses the tidal model of Zahn (1977) for the tide raised on the star, which is suitable for highly convective RGB stars, and (Matsumura et al. 2010) for the tide raised on the planet. First, we run a reference grid of planets at a range of semimajor axes (0.1–10 au) and eccentricities (0–0.95) orbiting a 1.17 M_⊙ star (from SSE, Hurley et al. 2000). The mass of the planets is 4 M_Jup. Their trajectories (after the first 1 Gyr, during which planets at the top left circularise quickly) in a − e space are shown in Figure 11 as faint lines. Evolution along the main sequence is shown in gray, while evolution along the subgiant branch and RGB is shown in light brown. Many more planets are affected by tides on the RGB than on the MS. Two tracks starting close to the present orbit of HD 76920b are highlighted. These tracks predict a modest decay of semimajor axis and eccentricity before the planet is engulfed in a little under 100 Myr. Figure 4 shows the periastron distance in terms of the stellar radius. The periastron of HD 76920b is at 4.82 times the stellar radius. Note that at r_p/R_* ≈ 2–3, planets are in jeopardy (Villaver et al. 2014) as that is where the tidal force starts to dominate the orbital evolution. The star HD 76920 still has to evolve a bit up the red giant branch in order to tidally catch the planet at periastron.

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While this planet will certainly end up engulfed by its host star, being too close for stellar mass loss to win over tidal orbital decay, making an exact prediction of its future evolution is challenging, partly because of the uncertainties in modeling tidal forces and partly because of uncertainties on the stellar and planetary mass. As an example, dropping the stellar mass to 1.1 M_⊙ results in much stronger eccentricity decay before engulfment, with eccentricities dropping to around 0.7 at the time of engulfment. The high sensitivity of stellar evolutionary timescales on stellar mass means that at lower stellar masses, there is more time for tidal decay to work to shrink the orbit before planetary engulfment.

The tracks shown in Figure 11 use solar metallicity, while HD 76920 has [Fe/H] = −0.11. This introduces another source of uncertainty in the calculation of the decay timescales. The evolution of the star at a slightly lower metallicity than the one computed here is equivalent to the evolution of a more massive stellar mass at solar metallicity. HD 76920 would in that case evolve a bit faster than is assumed in Figure 11 and thus will move more quickly into the stellar envelope. Also note that mass loss is expected to be affected by the metallicity of the star, and although red giant mass-loss rates are not very prominent, they still have an effect in the final outcome of planetary systems (see Villaver et al. 2014).

Fortuitous observations have enabled us to characterize the orbit of HD 76920b as being unambiguously eccentric. That is, the values of e and ω have produced a radial velocity curve that cannot be mimicked by two low-eccentricity planets, a pathology that is distinctly possible when observations are sparse and poorly sampled (e.g., Shen & Turner 2008; Anglada-Escudé et al. 2010; Wittenmyer et al. 2012, 2013b). It would of course be desirable to achieve better phase coverage of the critical velocity excursion at periastron passage, to obtain a more precise measurement of the radial velocity amplitude (and hence the planet's mass). We predict the next such passage to occur on 2018 January 17 (BJD 2458136.3 ± 0.5), with ∼30 days of significant acceleration on either side of the velocity maximum. Interested observers with dedicated (e.g., MINERVA: Swift et al. 2015) or queue-scheduled (e.g., CHIRON) telescope resources are highly encouraged to make plans to characterize the orbit of HD 76920b at that time. Endl et al. (2006) used the Hobby-Eberly Telescope in this manner to make high-cadence measurements of the periastron passage of HD 45350b, an e = 0.76 planet exhibiting a radial velocity curve similar to that of HD 76920b. Likewise, high-cadence observations capturing the periastron passage of HD 37605b enabled Cochran et al. (2004) to confirm the highly eccentric planet (e = 0.737). These examples highlight the importance of flexibly scheduled radial velocity observations for truly understanding the orbital properties of unusual planets such as HD 76920b.