Radial Velocity Discovery of an Eccentric Jovian World Orbiting at 18 au

Radial velocity (RV) and transit surveys have characterized very few planets beyond 5 au (Howard et al. 2010; Mayor et al. 2011; Fressin et al. 2013; Petigura et al. 2013), leaving the population characteristics of long-period planets largely unknown. Direct imaging is sensitive to such planets, but the current generation of instruments is limited to planets several times the mass of Jupiter orbiting young, massive stars (Bowler 2016; Nielsen et al. 2019). Microlensing is also sensitive to planets at large separations from their stars, and microlensing results already allow for occurrence calculations of planet mass as a function of separation (Suzuki et al. 2016). However, mircolensing results will not enable detailed orbital or system architecture characterization. On the other hand, RV surveys are limited by their baselines. Several authors have used RV trends or other incomplete orbital arcs to constrain the properties of long-period planets and substellar objects (Wright et al. 2007, 2009; Knutson et al. 2014; Bouchy et al. 2016; Bryan et al. 2016; Rickman et al. 2019), but it is challenging to pin down the physical parameters of planets with orbital periods much longer than the survey baseline. Some authors assume circular orbits in order to cut down the wide parameter space of possible orbits (e.g., Knutson et al. 2014), but even so posteriors over semimajor axis and minimum mass span wide ranges.

Long-baseline RV surveys dating back to the mid-1980s (Campbell 1983; Marcy 1983; Mayor & Maurice 1985; Campbell et al. 1988; Marcy & Benitz 1989; Marmier et al. 2013; Zechmeister et al. 2013; Fischer et al. 2014; Wittenmyer et al. 2014; Moutou et al. 2015; Endl et al. 2016) are beginning to fill this characterization gap as their time baselines increase. The long-period (>1 yr) planets discovered by these surveys share characteristics with the directly imaged planets and the shorter-period RV-discovered planets. As these surveys mature, they will allow us to characterize the transition from older, less massive, shorter-period RV-detected planets to younger, more massive, longer-period imaged planets. These new discoveries will also enable us to calculate the fundamental properties of planets in wider mass and age ranges than those currently accessible to direct imaging alone, examine the rarity of the Earth–Jupiter–Saturn architecture, and test giant planet formation theories (Cumming et al. 2008; Wittenmyer et al. 2006, 2011, 2016).

Here, we present the discovery of HR 5183 b, a highly eccentric planet with a semimajor axis of ${18}_{-4}^{+6}$ au orbiting a V = 6.3 G0 star. HR 5183 has been monitored for more than 20 yr as part of the California Planet Search at Keck/High Resolution Echelle Spectrometer (HIRES) and the long-duration RV planet survey at McDonald Observatory. After over 10 yr of relatively constant RV measurements, HR 5183 began rapidly accelerating. In 2018, the RV measurements flattened out and turned over, an event associated with the planet's periastron passage. As we discuss later in the paper, this periastron passage event was information-rich, and allowed precise constraints on the planet's orbital parameters even without RV coverage over the entire orbital period. With an orbital period of ${74}_{-22}^{+43}$ yr, HR 5183 b is the longest-period planet with a well-constrained orbital period and minimum mass detected with the RV technique.

This paper is organized as follows. In Section 2, we present our RV measurements of HR 5183. In Section 3, we provide precise estimates of the stellar parameters of HR 5183, and in Section 4, we characterize the planet HR 5183 b. In Section 5, we describe an extremely widely separated (>15,000 au) stellar companion to HD 5183, and present the results of searches for additional stellar and planetary companions. In Section 6, we discuss prospects for multi-method detection of HR 5183 b. In Section 7, we relate HR 5183 b to other exoplanet systems, comment on formation scenarios, and conclude.

We began Doppler monitoring of HR 5183 in 1997 at Keck/HIRES and in 1999 at McDonald/Tull. We have also monitored HR 5183 on the Automated Planet Finder (APF) with high cadence since its commissioning in 2013. The RVs from all three spectrographs are shown in Figure 1 and tabulated in Table 1.

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2.1. HIRES Spectra

2.2. Tull Spectra

2.3. APF Spectra

HR 5183 is a nearby slightly evolved G0 star. We derived precise stellar parameters for HR 5183 using the method described in Fulton et al. (2018). Briefly, this method uses Gaia DR2 parallaxes (Gaia Collaboration et al. 2018), spectroscopic effective temperatures computed from our Keck template spectrum with the SpecMatch code (Petigura 2015), and Two Micron All Sky Survey (2MASS) photometry (Skrutskie et al. 2006) to compute precise stellar radii. log g, [Fe/H], and v sin i are also calculated from the Keck spectrum using SpecMatch. Stellar mass, age, and distance are derived using the isoclassify²¹ package (Huber et al. 2017). The stellar properties derived from this analysis are presented in Table 2, along with other useful stellar parameters.

Table 2.  Stellar Properties

Parameter	Value	Unit
R.A.	13 46 57	hh:mm:ss
Decl.	+06 20 59	dd:mm:ss
HD Name	HD 120066	⋯
2MASS ID	J13465711+0621013	⋯
Gaia Source ID	3721126409323324416	⋯
Parallax	31.757 ± 0.039	mas
K	4.85 ± 0.02	mag
V	6.30	mag
Teff	5794 ± 100	K
log g	4.02 ± 0.1	dex
[Fe/H]	0.10 ± 0.06	dex
v sin i	3 ± 1	km s−1
R*	${1.53}_{-0.05}^{+0.06}$	R⊙
M*	1.07 ± 0.04	M⊙
Age	${7.7}_{-1.2}^{+1.4}$	Gyr
Distance	31.49 ± 0.04	pc

Note. T_eff, log g, [Fe/H], and v sin i were calculated from the stellar spectrum using the SpecMatch code. R_* was calculated as described in Section 3. M_*, age, and distance were calculated using the isoclassify code.

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Allen & Monroy-Rodríguez (2014) found evidence that HR 5183 is in the halo of the Milky Way using reduced proper motion diagrams following Salim & Gould (2003). However, HR 5183 is younger and more metal-rich than typical galactic halo objects (Carollo et al. 2016), which led us to scrutinize this claim. To investigate the galactic population membership of HD 5183, we performed a kinematic analysis of its galactic orbit, following Johnson et al. (2018). We used the galpy²² package (Bovy 2015) to compute 50 random realizations of galactic positions and U, V, Wspace velocities for HR 5183 consistent with its Gaia DR2 parameters (Gaia Collaboration et al. 2018). For each realization, we then calculated the galactic orbit of HR 5138 in galpy's "MWPotential2014" galactic potential. The resulting orbits never achieve a height above the galactic midplane of more than 200 pc. This result supports the claim that HR 5183 is a thin-disk member, and not a halo object.

The curvature we saw in the RVs (see Figure 1) alerted us to the existence of HR 5138 b, and motivated us to characterize its orbital properties. We modeled the RV time series using the open-source toolkit radvel²³ (Fulton et al. 2018). The code and data used to perform the analysis in this paper are available on GitHub.²⁴ We chose to perform this fit using the following parameterization of the Keplerian RV function: log P, T_C, $\sqrt{e}\cos \omega$, $\sqrt{e}\sin \omega$, and log K. We imposed uninformative uniform priors on each of these parameters except log P, for which we defined as an informative baseline prior. Because we detected a long-period planet by observing a single, short-duration event (the planet's periastron passage), we made an analogy to detection by transit and defined the following prior on period, often used in the exoplanet transit community (e.g., Vanderburg et al. 2016; Kipping 2018):

$$\begin{eqnarray}p(P,{t}_{d},B)=\left\{\begin{array}{ll}1 & \mathrm{if}\ P-{t}_{d}\lt B\\ (B+{t}_{d})/P & \mathrm{else}\end{array}\right.,\end{eqnarray} \tag{ 1 }$$

where t_d is the duration of the event (in this case, the periastron passage), P is the orbital period, and B is the observing baseline. See Section 4.1 for a justification of this choice of prior and a detailed comparison to other possible models and prior parameterizations. Unlike in the case of a transit detection, the duration of the periastron passage event of HR 5183 is not easily defined. We performed fits with t_d = 0 and t_d = 3.5 yr, ultimately finding that the results were indistinguishable and sidestepping this issue. We adopted t_d = 0 for convenience.

We also included jitter (σ) and RV offset (γ) terms for each of our four RV data sets (we treated HIRES pre-2004 and post-2004 measurements as separate data sets in our fit; see Section 2.1). We assumed uninformative uniform priors on each of these instrumental terms as well. The logarithm of the complete likelihood for this model is

$$\begin{eqnarray}&&\mathrm{ln}\,{ \mathcal L }=-\displaystyle \frac{1}{2}\displaystyle \sum _{i=0}^{n}\left[\displaystyle \frac{{\left({v}_{i}-{M}_{i}\right)}^{2}}{{\left({\sigma }_{i}+{\sigma }_{\mathrm{jit},i}\right)}^{2}}+2\mathrm{ln}\sqrt{2\pi {\left({\sigma }_{i}^{2}+{\sigma }_{\mathrm{jit},i}^{2}\right)}^{\tfrac{1}{2}}}\right],\end{eqnarray} \tag{ 2 }$$

where n is the total number of RV measurements, v_i is the ith RV measurement, σ_i is its uncertainty, M_i is the Keplerian model prediction for observation i, and σ_jit,i is the jitter parameter for the instrument that took observation i (Fulton et al. 2016).

We computed the MAP fit with radvel, obtaining an orbital period of 72.85 yr, a minimum mass of 3.24 M_J, and an eccentricity of 0.84. This orbital solution is shown in Figure 1, and a bird's-eye view comparing this orbit to the orbits of the solar system planets is shown in Figure 2. We next performed an Affine-invariant Markov chain Monte Carlo (MCMC) exploration of the parameter space with the ensemble sampler emcee²⁵ (Foreman-Mackey et al. 2013). Our MCMC analysis used 8 ensembles of 50 walkers and ran for 1552 steps per walker, achieving a maximum Gelman–Rubin (Gelman et al. 2003) statistic of 1.001. A corner plot showing posterior distributions and covariances between T_P, P, M sin i, a, a(1 − e), e, and ω is shown in Figure 3. These values are also recorded in Table 3.

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Table 3.  Fit Parameters and Derived Planet Properties

Parameter	Median Value and 68% CI	MAP Value	Unit
ln P	${10.21}_{-0.35}^{+0.46}$	10.2	ln(days)
Tc	${18965}_{-40}^{+44}$	18964	JD - 2440000
$\sqrt{e}\,\cos \,\omega$	0.86 ± 0.02	0.86
$\sqrt{e}\,\sin \,\omega$	−0.32 ± 0.03	−0.32
ln K	3.64 ± 0.01	3.64	ln(${\rm{m}}\,{{\rm{s}}}^{-1}$)
σ (HIRES pre-upgrade)	${3.4}_{-0.6}^{+0.8}$	3.09	${\rm{m}}\,{{\rm{s}}}^{-1}$
σ (HIRES post-upgrade)	3.3 ± 0.4	3.16	${\rm{m}}\,{{\rm{s}}}^{-1}$
σ (Tull)	${5.8}_{-0.5}^{+0.6}$	5.67	${\rm{m}}\,{{\rm{s}}}^{-1}$
σ (APF)	${3.7}_{-0.4}^{+0.5}$	3.58	${\rm{m}}\,{{\rm{s}}}^{-1}$
γ (HIRES pre-upgrade)	$-{52.6}_{-1.5}^{+1.3}$	−52.5	${\rm{m}}\,{{\rm{s}}}^{-1}$
γ (HIRES post-upgrade)	$-{52.4}_{-2.1}^{+2.0}$	−52.4	${\rm{m}}\,{{\rm{s}}}^{-1}$
γ (Tull)	$-{19.2}_{-2.1}^{+1.9}$	−19	${\rm{m}}\,{{\rm{s}}}^{-1}$
γ (APF)	$-{47.2}_{-2.2}^{+2.0}$	−47.2	${\rm{m}}\,{{\rm{s}}}^{-1}$
P	${74}_{-22}^{+43}$	72.85	yr
K	${38.25}_{-0.55}^{+0.58}$	38.21	m s−1
e	0.84 ± 0.04	0.84
ω	−0.35 ± 0.03	−0.35	rad
TP	58121 ± 12	58120.0	JD - 2440000
M sin i	${3.23}_{-0.14}^{+0.15}$	3.24	MJ
a	${18}_{-4}^{+6}$	18.0	au
a(1 − e)	${2.88}_{-0.08}^{+0.09}$	2.89	au
Teq (peri)	${171.0}_{-5.1}^{+5.2}$	170.94	K
Teq (apo)	${50.2}_{-7.6}^{+7.0}$	50.58	K

Note. T_eq values were calculated assuming a visible albedo of 0.5. ω refers to the orbit of the star HR 5183 induced by the planet HR 5183 b.

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4.1. Model Choice

We performed three additional orbit fits to evaluate our choice of model. First, we performed two fits without informative baseline priors on log P: one fitting in P and K (as opposed to log P and log K), and another in log P (fitting in log P versus P imposes an implicit Jeffrey's prior on P). Period posteriors obtained from these two models and the informative prior are compiled in Table 4. All three orbital period posteriors are consistent within 1σ, but the informative baseline prior pushes the median orbital period to shorter values. Neither of these priors significantly change the posteriors on the other orbital parameters; for example, fitting in log P gives M sin i = ${3.28}_{-0.15}^{+0.16}$ ${M}_{{\rm{J}}}$ and e = 0.87 ± 0.05. The slight dependence of the solution on our prior choice ultimately points to the need for more data, but in the meantime we adopt the informative prior.

Table 4.  Period Prior Comparison

Prior	Median Period and 68% CI
uniform in P and K	${125}_{-54}^{+113}$ yr
uniform in $\mathrm{log}\,P$ and $\mathrm{log}\,K$	${103}_{-41}^{+103}$ yr
inf. baseline prior (adopted)	${74}_{-22}^{+43}$ yr

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Next, we performed a fit including a $\dot{\gamma }$ parameter to account for potential additional wider-separation companions influencing the RV signal of the star. Adding this free parameter has the effect of pushing the eccentricity posterior to higher values (e = 0.92 ± 0.03) and the period posterior to lower values (P = ${71.87}_{-27.07}^{+52.26}$ yr), but the posterior distribution of $\dot{\gamma }$ is consistent with 0 ($\dot{\gamma }$ = ${0.12}_{-0.19}^{+0.22}$ m s⁻¹ yr⁻¹). The adopted model has lower bayesian information criterion (BIC) (ΔBIC = 5.4) and Akaike information criterion (AIC) values (ΔAIC = 1.7), indicating that the added free parameter does not substantially improve the fit. We cannot unequivocally rule out a trend, but since including one is not statistically warranted and does not affect the conclusions of the paper, we adopt the fit with no trend.

The lack of an unambiguous trend in the RVs is consistent with our failure to detect companion objects in the Hubble Space Telescope (HST) and Nasmyth Adaptive Optics System (NAOS) Near-Infrared Imager and Spectrograph (CONICA), hereafter NaCo, images (see Section 3 and Appendix B). The possible bound companion at 15,000 au (Section 5.2.1) would not produce a measurable $\dot{\gamma }$.

4.2. Orbit Information Density

Our measurements of the properties of this planet may seem surprisingly precise (see Table 3) given observations spanning only about one-third of the orbit. These constraints are possible because we tracked the system through periastron passage, when the information density of the Keplerian signal is highest.

High-eccentricity orbits have unique shapes that sensitively depend on e and ω (see Figure 2 of Howard & Fulton 2016 for a helpful visualization). The shape of the HR 5183 RV curve is fit only by a narrow range of these parameters, as Figure 3 shows.

The relatively flat RV curve from ∼1998 to 2015 followed by a sharp uptick and subsequent turnover are consistent only with e ≃ 0.8 and ω ≃ −0.4. All other Keplerian curves have shapes that are inconsistent with our measurements. More complicated models involving additional planets or a $\dot{\gamma }$ term are also excluded by the peculiar RV pattern.

We offer two arguments to build intuition. First, imagine decomposing the RV fitting into a process that matches three orbital properties of the Keplerian curve: (1) the shape (from e and ω), (2) the vertical scale (K), and (3) the horizontal scale (P). Once the shape has been determined by matching the appropriate Keplerian curve, the horizontal and vertical scales can be measured using RVs spanning less than a full orbit, provided the information-rich close approach is covered. Second, consider the how the planet's speed varies over its orbit. We can define the fastest half orbit as the portion of an orbit near closest approach, when the true anomaly (f) is between −π/2 and π/2. The time for the planet to pass through the fastest half orbit, t_fho, can be computed using the relationship between f and time (t),

$$\begin{eqnarray}&&{df}=\displaystyle \frac{2\pi }{P}\sqrt{1-{e}^{2}}{\left(\displaystyle \frac{a}{r}\right)}^{2}{dt},\end{eqnarray} \tag{ 3 }$$

where r is the distance between the orbiting planet and the star (Seager 2010, Equation (2.44)). Substituting an expression for r(f) (Seager 2010, Equation (2.20)),

$$\begin{eqnarray}&&{t}_{\mathrm{fho}}=\displaystyle \frac{P{\left(1-{e}^{2}\right)}^{3/2}}{2\pi }{\int }_{-\pi /2}^{\pi /2}\displaystyle \frac{{df}}{1+e\,\cos \,f}.\end{eqnarray} \tag{ 4 }$$

For a circular orbit, t_fho integrates to P/2, as expected. Eccentric orbits have much shorter timescales of close approach though. Numerically integrating Equation (4) with e = 0.84, we find t_fho ≈ P/18.6. That is, the planet completes the fastest half of its orbit nearly an order of magnitude more quickly than in the circular case. While our fitting procedure did not actually measure t_fho and scale it by a factor of 18.6 to determine P, this exercise illustrates how highly eccentric orbits contain information related to orbital period on short timescales, and thus allow us to measure P with higher precision than one might expect.

This is not to say that we have ruled out 100 yr or more periods and higher (≃0.91) eccentricities. Such orbits appear in our posterior, but because there is less posterior volume in this region of parameter space, they are less probable overall.

5.1. Search for Additional Planets in the System

We searched for other significant periodic signals in the RV data using the χ² difference technique described in Howard & Fulton (2016). In brief, we started by calculating the χ² of a flat line fit to the RVs, and injecting additional Keplerian orbits into the model. We calculated the change in χ² (Δχ²) when including each additional Keplerian orbit over a grid of periods and eccentricities. We constructed a periodogram of the Δχ² values as a function of trial period and fit the distribution of periodogram peak heights to infer an empirical false alarm probability (eFAP) for each detected peak. We detected no signals with an eFAP greater than 1%, indicating no additional planetary companions down to our sensitivity limits.

We characterized our sensitivity limits over a grid of semimajor axes and M sin i values by applying the search algorithm described above to each injected planetary signal. The results of this analysis are shown in Figure 4. As expected, we are most sensitive to Jupiter-mass and heavier planets with a < 30 au. Our data are not sensitive to Earth-mass planets. HR 5183 b itself is at our detection limits because of its large semimajor axis, but its high eccentricity makes it detectable.

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We also searched for transit signals in ground-based photometric observations of HR 5183, finding no significant signals above our sensitivity limits. These data and analysis are described in Appendix A.

5.2. Search for Stellar Companions to HR 5138

We used a two-pronged approach to search for additional bound companions to HR 5183: analyzing archival coronagraphic images of the star and searching the Gaia DR2 database for stars with similar 3D locations and kinematic properties. HR 5138 b is likely much below the detection limit of current coronagraphic imagers (see Section 6), and we did not expect to detect it in these images. We found several archival images of HR 5183: one set of images taken with NaCo on the Very Large Telescope (VLT) and one set taken with the HST Imaging Spectrograph (HST/STIS). Details about the observations and data reduction are presented in Appendix B. We used these images to derive contrast curves illustrating our detection limits for HR 5183 (Figure 5), and found no evidence for companions, with sensitivity down to Δmag = 20 at 4''.

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While our scrutiny of coronagraphic images revealed no companions, through our Gaia DR2 search and the analysis described below, we found that HIP 67291 is likely an eccentric, widely separated (>15,000 au) stellar companion to HR 5138. However, even if this star is gravitationally bound to HR 5183, it is too widely separated to affect the planet HR 5183 b. In addition, it would not be in the field of view of any of the images described in Appendix B.

5.2.1. HIP 67291: A Wide Stellar Companion to HR 5183

Several papers in the literature have presented evidence that HIP 67291, a K7V star (Alonso-Floriano et al. 2015) with a projected separation of more than 15,000 au, is bound to HR 5183 (Allen et al. 2000; Allen & Monroy-Rodríguez 2014; Tokovinin 2014). Using kinematic parameters from Gaia DR2 and an isochrone-derived mass for HIP 67291, we investigated the probability that these two stars are gravitationally bound, and present orbital parameters for the system. This analysis is meant to be exploratory and not definitive; additional undetected companions orbiting HIP 67291 would affect these calculations, for example.

We performed an isochrone fit for HIP 67291 using the isochrones²⁶ Python package (Morton 2015) to interface with the MESA Isochrones & Stellar Tracks (MIST) stellar evolution models (Paxton et al. 2011, 2013, 2015; Choi et al. 2016; Dotter 2016). We defined priors on [Fe/H] and log g using the values and precisions used in the template to compute the Gaia RV of HIP 67291 (rv_template_fe_h and rv_template_logg in the Gaia DR2 database, respectively). In addition, we placed Gaussian priors on parallax and T_eff, informed by the Gaia DR2 values and uncertainties reported for HIP 67291. We also placed a Gaussian prior on the age of HIP 67291, informed by the age of HR 5183 derived in Section 3, but found that this constraint did not affect the mass of HIP 67291. We obtained a mass of 0.67 ± 0.05 ${M}_{\odot }$ from this analysis, which is consistent with the K7V spectral type derived in Alonso-Floriano et al. (2015).

Given the mass of HIP 67291, the mass of HR 5183 derived in Section 3, and the respective parallaxes, R.A./decl. values, proper motions, and RVs of both stars from Gaia DR2 (compiled in Table 5), the orbit of the two stars is in principle completely specified. In practice, the uncertainties on these parameters are significant enough to permit large uncertainties in the orbital parameters. To quantify these uncertainties, we drew samples from Gaussian distributions over both stellar masses and each of the six positional and velocity measurements for each star, then calculated the resulting orbital parameters. We found that 44% of these generated orbits had e < 1 (i.e., are bound). Histograms of the orbital parameters derived from this sampling method (the likelihood over possible bound and unbound/hyperbolic orbital parameters) are shown in Figure 6. Highly eccentric, edge-on orbits are preferred.

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Table 5.  Gaia DR2 Parameters for HR 5183 and HIP 67291

Parameter	HR 5183 Value	Unc.	HIP 67291 Value	Unc.	Unit	Unc. Unit
R.A.	206.74	0.034	206.87	0.042	deg	mas
Decl.	6.35	0.029	6.32	0.028	deg	mas
Parallax	31.76	0.04	31.92	0.05	mas	mas
Proper motion (R.A.)	−510.45	0.07	−509.44	0.08	mas yr−1	mas yr−1
Proper motion (decl.)	−110.22	0.06	−111.02	0.06	mas yr−1	mas yr−1
RV	−30.42	0.20	−30.67	0.15	km s−1	km s−1

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While the likelihood that these two stars are bound is only 44%, the two possible physical explanations for the 66% of hyperbolic orbits (that the two stars are currently flying by one another and that they were bound in the past and recently became unbound) likely have low prior probabilities. Therefore, the posterior probability that the two stars are bound is likely much higher than 44%.

While the presence of an extremely wide stellar companion to HR 5183 is certainly interesting, HIP 67291 is simply too far away from the planet HR 5183 b to affect its orbit in the current orbital configuration. The median periastron distance of the HIP 67291-HR 5183 orbit (neglecting hyperbolic solutions) is ∼10,000 au, well beyond the theorized minimum Sun–Oort-cloud separation of 2000 au (Morbidelli 2005). In the Oort cloud, the galactic potential due to the overall galactic mass distribution is an important driver of orbital evolution, which tells us that even when HIP 67291 is closest to HR 5183 b, its gravitational influence is at most comparable to that of the galactic potential.

Transit probability is given by

$$\begin{eqnarray}&&{p}_{\mathrm{tra}}=\left(\displaystyle \frac{{R}_{* }+{R}_{p}}{a}\right)\left(\displaystyle \frac{1+e\,\sin \,\omega }{1-{e}^{2}}\right)\end{eqnarray} \tag{ 5 }$$

(Winn 2010). Assuming a Jupiter radius for HR 5183 b, p_tra = 0.00185 ± 0.00010. Although this probability is lottery-ticket-like, the prospects for detecting HR 5183 b with stellar astrometry and thermal direct imaging are promising. Detection with either of these methods could address the sin i degeneracy, allowing us to obtain a direct mass measurement.

To investigate prospects for imaging HR 5183 b, we used the orbit-solving code from orbitize²⁷ (Blunt et al. 2019), an orbit-fitting toolkit for direct imaging astrometry. First, we determined the angular separation posterior as a function of time. We randomly sampled from the RV orbit posteriors described in the previous section, assigned each sample orbit an inclination (randomly drawn from a uniform distribution in cos i) and an Ω (randomly drawn from a uniform distribution), and used orbitize to solve for the projected angular separation, ρ, at several future epochs. Posterior distributions in ρ calculated using this procedure for three future epochs are shown in Figure 7. Since the planet passed periastron so recently, the median of its projected separation posterior generally increases with time over the next 5 yr.

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Next, we calculated contrast posteriors, in both reflected visible and thermal infrared (10 μm) wavelengths, using the angular separation posterior. To calculate visible reflected-light contrast, we approximated HR 5183 b as a Lambertian disk with an albedo of 0.5, and assumed that the star emits as a blackbody. These results are shown in Figure 8 on 2025 January 1, along with estimated and required predicted contrast capabilities for future reflected-light coronagraphs. For reference, the phase angle (angle between the observer's line of sight, the planet's location, and the star's location) will be ${137}_{-19}^{+10}$° on this date. Robustly calculating the thermal infrared contrast requires knowing the planet's T_eff (which in turn requires knowledge of non-blackbody effects, such as wavelength-dependent emissivity and age), but as a first optimistic approximation we calculated contrast posteriors assuming the planet emits as a blackbody with temperature given by T_eq at its periastron distance. These results are shown in Figure 9, along with contrast capabilities of two current-generation infrared imagers. In visible reflected light, HR 5183 b appears to be likely beyond the capabilities of even HabEx/LUVOIR, but infrared thermal emission may be a different story. Within 5 yr, the planet will most likely be separated from its star by more than 200 mas, and its contrast at 10 μm, in this optimistic approximation, would be comparable to the performance floors of current-generation infrared imagers like the Gemini Planet Imager (GPI) and SPHERE. Instrument concepts like TIKI (Blain et al. 2018), which aim for 1e − 7 contrast at the approximate projected separation of HR 5183 b, are well suited for this endeavor.

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Another imminent dual-detection prospect for HR 5183 b is with stellar astrometry from Gaia. Gaia will release astrometric time-series data for HR 5183 with the final data release for the nominal mission (after DR3). To assess potential detectability with Gaia, we similarly randomly sample from the RV orbit posteriors, randomly assign inclinations and Ω values as described above, and use orbitize to compute relative ΔR.A. and Δdecl. as a function of time for many possible orbits.

For HR 5183 b to be detectable with Gaia, its orbit must look sufficiently different from a constant rate of change in ΔR.A. and Δdecl., which could be interpreted as a proper motion. We therefore fit a line to each generated orbit in our sample (in ΔR.A. and Δdecl.), and subtracted this fit from the sample orbit. If the maximum value of this residual curve exceeded five times the Gaia uncertainty (assumed to be 35 mas, the current astrometric uncertainty for HR 5183 in the Gaia catalog, and typical for stars of similar spectral type; Gaia Collaboration et al. 2018) in either ΔR.A. or Δdecl., we counted the orbit as detectable (a 5σ detection). We repeated this analysis for 10,000 orbits to estimate the probability of detecting HR 5183 b with Gaia. With this algorithm, we calculate a detection probability of 100%, or in other words, 100% of orbits consistent with our RV posteriors will be detectable with Gaia. Representative detectable orbit tracks are plotted in Figure 10 over the expected Gaia mission length. A histogram of residuals, with the current Gaia uncertainty overplotted, is shown in Figure 11.

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Combining the astrometric baselines of Hipparcos and Gaia (using a method similar to Dupuy et al. 2019) may also render HR 5183 b detectable in stellar astrometric data, and/or increase the signal-to-noise ratio of a Gaia-only detection. Such a project is an excellent avenue for future work on HR 5183 b, especially after the final Gaia nominal mission data release.

HR 5183 b is one of the longest-period exoplanets detected with RVs. Its extreme eccentricity, coupled with one of the longest RV monitoring baselines in exoplanet history, set it apart from other long-period RV-detected planets. Our 22 yr observing baseline includes recent observations (2017–2018 season) of the planet's periastron passage, which allowed us to precisely constrain the planet's minimum mass and eccentricity. Without continuous and high-cadence (at least one observation per year) RV monitoring, we would have missed the information-dense periastron passage of HR 5183 b. However, the odds of detecting such an event in a single star with our observing strategy, which has included regular monitoring of >100 bright stars for 20 yr, are relatively high (roughly one-third); survey design, rather than serendipity, is at the heart of this discovery.

With an age of several gigayears, HR 5183 b is distinct from the several megayear-old population of long-period planets detected via direct imaging. In addition, its minimum mass of ${3.23}_{-0.14}^{+0.15}$ ${M}_{{\rm{J}}}$ means it is likely much less massive than the directly imaged planets, which tend to be closer to 10 ${M}_{{\rm{J}}}$ owing to strong selection effects. HR 5183 b also has a much higher eccentricity and longer orbital period than typical RV-detected planets. Table 6 and Figure 12 compare its orbital properties and those of similar known exoplanets. Although HR 5183 b has an orbital period and mass that make it more similar to directly imaged planets than RV-detected planets, its age and high eccentricity differentiate it from its directly imaged cousins.

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Table 6.  Physical Parameters of HR 5183 b and Close Exoplanet Relatives

Name	Semimajor Axis	Mass or m sin i	Eccentricity	Discovery Method	1st Ref.	Ref.	Notes
	(au)	(MJ)
51 Eri b	${14}_{-3}^{+7}$	2 ± 1	${0.21}_{0.40}^{+0.06}$	Imaging	A	B
HD 95086 b	${62}_{-9}^{+20}$	5 ± 2	<0.205	Imaging	C	D
HR 8799 b	${70.8}_{-0.18}^{+-.19}$	5 ± 1	${0.018}_{-0.013}^{+0.018}$	Imaging	E	F
HR 8799c	${43.1}_{-1.4}^{+1.3}$	7 ± 2	${0.022}_{-0.017}^{+0.023}$	Imaging	E	F
HR 8799 d	${26.2}_{-0.7}^{+0.9}$	7 ± 2	${0.129}_{-0.025}^{+0.022}$	Imaging	E	F
HR 8799 e	16.2 ± 0.5	7 ± 2	${0.118}_{-0.013}^{+0.019}$	Imaging	G	F
β Pic b	11.8 ± 0.9	13 ± 3	0.24 ± 0.06	Imaging	H	I
HIP 65426 b	${120}_{40}^{+90}$	8 ± 1	<0.43	Imaging	J	K
PDS 70 b	∼22		10.5 ± 3.5	Imaging	L	L
LkCa 15 b	15.7 ± 2.1	6 ± 1		Imaging	M	M
GJ 676 A c	6.6 ± 0.1	6.8 ± 0.1		RV	N	N
HIP 5158c	7.7 ± 1.9	15.04 ± 10.55	0.14 ± 0.10	RV	O	O
HD 30177c	9.89 ± 1.04	7.6 ± 3.1	0.22 ± 0.14	RV	P	P
47 UMa d	${11.6}_{-2.9}^{+2.1}$	${1.64}_{-0.48}^{+0.29}$	${0.16}_{-0.16}^{+0.09}$	RV	Q	Q
HIP 70849 b	20.25 ± 15.75	9 ± 6	0.715 ± 0.245	RV	R	R
DP Leo b	8.19 ± 0.39	${6.05}_{-0.58}^{+0.47}$	0.39 ± 0.13	Eclipse Timing Variations	S	T	U
HR 5183 b	${18}_{-4}^{+6}$	${3.23}_{-0.14}^{+0.15}$	0.84 ± 0.04	RV	This paper	This paper

Note. U: this is a binary star. The imaged planets shown in this table are lifted from the top section of Table 1 in Bowler (2016), which compiles planets with median semimajor axis <100 au orbiting main-sequence stars. The recent bona fide discoveries PDS 70 b and HIP 65426 b have been added. Masses for these planets were taken from Bowler (2016) except for these two recent discoveries. All other information was taken from the references in this table. Planets detected by other methods are those on the NASA Exoplanet Archive (accessed 2019 April 14) with orbital periods >7000 days. Objects that present as RV trends or incomplete orbital arcs whose orbital posteriors are unconstrained are not included in this table for simplicity. Our intention here is not to tabulate every potentially similar planet to HR 5183 b, but to compile the parameters of a few illustrative cases. We refer interested readers to references in the 1 for additional examples.

References. (A) Macintosh et al. (2015), (B) De Rosa et al. (2015), (C) Rameau et al. (2013), (D) Rameau et al. (2016), (E) Marois et al. (2008), (F) Wang et al. (2018), (G) Marois et al. (2010), (H) Lagrange et al. (2009), (I) Dupuy et al. (2019), (J) Cheetham et al. (2019), (K) Chauvin et al. (2017), (L) Keppler et al. (2018), (M) Kraus & Ireland (2012), (N) Sahlmann et al. (2016), (O) Feroz et al. (2011), (P) Wittenmyer et al. (2017), (Q) Gregory & Fischer (2010), (R) Ségransan et al. (2011), (S) Qian et al. (2010), (T) Beuermann et al. (2011).

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The extreme eccentricity and decades-long orbital period of HR 5183 b, coupled with the existence of a widely separated, eccentric stellar companion (Section 5.2.1), raise interesting questions about the system's formation. High eccentricity is a signature of past dynamical interactions (Dawson et al. 2014). Moreover, recent dynamical simulations by Wang et al. (2018) revealed that systems hosting multiple young massive planets, presumably near their formation locations, are likely unstable on gigayear or shorter timescales. Therefore, the HR 5183 system might have initially contained multiple massive planets with moderate eccentricities. Planet–planet interactions in such a system could have ejected some planets and transferred angular momentum to the remaining planet(s), pumping their eccentricities. If this is true, the HR 5183 system could be viewed as the fate of systems like HR 8799. Dynamical work aiming to distinguish between this and other possible formation scenarios (for example, potential past interactions with HIP 67291) would be an excellent avenue for future studies. It will be interesting to learn whether HR 5183 b represents the eventual evolution of multiple giant planet systems like HR 8799, or if it is in a class all its own.

HR 5183 b is poised for dual detection with both thermal infrared high-contrast imaging and stellar astrometry, either of which would break the sin i degeneracy and enable a direct mass measurement. Further work is needed to more convincingly estimate the planet's T_eff as a function of time (taking into account its orbital location and non-blackbody effects), but our optimistic calculations indicate that the planet will be at a favorable projected separation and contrast at 10 μm within the next 5 yr. In addition, our calculations indicate that HR 5183 b will almost certainly be detectable in Gaia data.

The National Academy of Sciences consensus report on Exoplanet Science Strategy states that a key goal of exoplanet science in the next decade is to "determine the range of planetary system architectures by surveying planets at a variety of orbital separations and searching for patterns in the structures of multiplanet systems" (Sciences Engineering & Medicine 2018). In Figure 12, we plot semimajor axis versus mass for planets listed in the NASA Exoplanet Archive and HR 5183 b. From this figure, it is clear that the discovery of HR 5183 b furthers the goal of the characterization at all orbital separations. Our success in discovering and characterizing HR 5183 b demonstrates that RV surveys are capable of detecting exoplanets in a yet unexplored parameter space of eccentric, long-period giant planets. With this discovery, we continue to uncover the astonishing diversity of planetary systems in our the galaxy.

The authors thank those at academic and telescope facilities whose labor maintains spaces for scientific inquiry, particularly those whose communities are excluded from the academic system. The authors would also like to sincerely thank the referee for a thorough and helpful report that greatly improved the quality of this work.

The authors note that we refer to this planet colloquially as "planet pi" because its minimum mass is consistent with π${M}_{{\rm{J}}}$.

S.B. would like to thank Vanessa Bailey, Konstantin Batygin, Dave Charbonneau, Robert De Rosa, Dmitry Savransky, Dimitri Mawet, and Dan Fabrycky for helpful conversations. S.B. is supported by the NSF Graduate Research Fellowship, grant No. DGE 1745303. L.M.W. acknowledges support from the Beatrice Watson Parrent Fellowship and the Trottier Family Foundation. M.R.K. is supported by the NSF Graduate Research Fellowhsip, grant No. DGE 1339067. A.W.H. acknowledges NSF award 1517655. The work of A.V. was performed [in part] under contract with the California Institute of Technology (Caltech)/Jet Propulsion Laboratory (JPL) funded by NASA through the Sagan Fellowship Program executed by the NASA Exoplanet Science Institute. G.W.H. acknowledges long-term support from NASA, NSF, Tennessee State University, and the State of Tennessee through its Centers of Excellence program.

The McDonald Observatory planet search is supported by the National Science Foundation through grant AST-1313075. The authors thank Ivan Ramirez, Stuart Barnes, and Diane Paulson for for their help with some of the Tull spectrograph observations.

Based, in part, on observations made with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute (STScI), which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555. These observations are associated with program numbers 12228, 14714, and 15221. Support for these programs was provided by NASA through grants from STScI.

Finally, the authors wish to emphasize the very significant cultural role and reverence that the summit of Maunakea has long had within the indigenous Hawaiian community. We acknowledge that data used in this paper were collected on lands belonging to the Kānaka Maoli.

We have been acquiring nightly photometric observations of HR 5183 each year since 2002 with the Tennessee State University (TSU) T8 0.80 m Automatic Photoelectric Telescope (APT) located at Fairborn Observatory in southern Arizona. The T8 APT is equipped with a two-channel precision photometer that uses a dichroic filter and two EMI9124QB bi-alkali photomultiplier tubes to separate and simultaneously measure the Strömgren b and y passbands. The observations were made differentially with respect to three comparison stars, corrected for atmospheric extinction, and transformed to the Strömgren photometric system. The resulting precision of the individual differential magnitudes ranges between ∼0.0010 and ∼0.0015 mag on good nights, as determined from the nightly scatter in the comparison stars. Seasonal means of the best comparison stars scatter about their grand means with typical standard deviations of ∼0.0002 mag. Further details on the T8 APT, precision photometer, and the observing and data reduction procedures can be found in Henry (1999).

HR 5183 has been observed as part of TSU's long-term photometric monitoring program of Sun-like stars (Radick et al. 2018). These authors report the intrinsic variability in the year-to-year mean brightness of HR 5183 to be only 0.00028 mag (see their Table 2). We looked for night-to-night variability within each of the 17 observing seasons by computing differential magnitudes of HR 5183 versus the mean brightness of the two best comparison stars. The standard deviations of the nightly observations within each season ranged from 0.00079 to 0.00152 mag, with a mean of 0.00106 mag. These values are consistent with the nightly precision of our observations. We also computed power spectra for each observing season and found no evidence for any periodicity between 1 and 200 days. We conclude that HR 5183 is constant to high precision on both nightly and yearly timescales.

Finally, we searched the complete 17 yr data set for possible transits of unknown planets with orbital periods between 1.5 and 200 days, using a simple box-fit, matching-filter technique. No evidence for any transits, to a limit of ∼0.002 mag was detected in our photometry.

We analyzed two sets of images of HR 5183 to search for additional stellar and substellar companions in the system, ultimately finding no evidence for additional companions. In the sections below, we describe the reduction of these images and calculation of contrast curves to describe our sensitivity.

B.1. HST Images

HR 5183 was observed with HST/STIS in GO programs 12228, 14714, and 15221 (PI: G. Schneider). For GO program 12228, HR 5183 was observed in 2011 as a color-matched PSF template star for the reduction and imaging of the circumstellar disk of HD 107146. HR 5183 was observed identically at two different field orientation angles (approximately 2 months apart, contemporaneous with the HD 107146 observations). At each epoch, two STIS occulting apertures, WedgeA-0.6, and WedgeA-1.0, were used sequentially over a single spacecraft orbit. These observations of HR 5183 were not planned for rotational differential imaging (RDI) reduction and analysis and are non-optimal for that purpose. Our interest in detecting and characterizing any companions to HR 5183 nonetheless motivates our analysis of these archival images. The observations are listed in Table 7; for more details see Schneider et al. (2014).

Table 7.  HST Observations of HR 5183

Visit Id	Date (UTC)	Occulter	Exp. Time (s)	Orientat.
OBIW23	2011 May 3	WedgeA-0.6	24 × 11 s	85978
OBIW23	2011 May 3	WedgeA-1.0	7 × 206.5 s	85978
OBIW27	2011 Feb 22	WedgeA-0.6	24 × 11 s	233038
OBIW27	2011 Feb 22	WedgeA-1.0	7 × 206.5 s	233038
OD5403	2017 Mar 26	WedgeA-1.0	10 × 206.5	204093
OD5413	2017 Jul 28	WedgeA-1.0	10 × 206.5	646028
ODH403	2018 Mar 16	WedgeA-1.0	10 × 206.5	217580
ODH413	2011 Feb 22	WedgeA-1.0	10 × 206.5	64709

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Basic image reduction was performed as described in Schneider et al. (2014). In brief, all raw images were calibrated using the Space Telescope Science Data Analysis System calstisa software,²⁸ and the same-orbit/same-occulter images were median combined into four single visit-level images. Same-occulter image pairs from the different visits were astrometrically aligned to minimize PSF-subtraction residuals using the IDP3 image analysis package²⁹ (Stobie & Ferro 2006). WedgeA-0.6 to WedgeA-1.0 image alignments were established using the "X-marks the spot" diffraction spike centroid method (Schneider et al. 2014) for the unsubtracted images.

We define the image contrast at any stellocentric angular distance (r) to be the ratio of the flux density contained within any pixel in the unocculted stellocentric field to that of the flux density in the (occulted) central pixel in the stellar PSF. As the latter is not directly measurable from these data, we used the high-fidelity TinyTim telescope and instrument PSF modeling code (Krist et al. 2011) as codified in the STIS imaging Exposure Time Calculator³⁰ to calculate the image contrast. This analysis informs us that 22% of the V = 6.3, G0V, stellar flux produced by HR 5183 would be contained in the central 50077 square pixel of the (occulted) PSF. We compared this to the 1σ standard deviations in the subtraction-nulled 2RDI signal at incrementally increasing stellocentric annuli of 1 pixel widths to produce a contrast curve (1σ point-source detection limit in contrast versus. stellocentric angle). The results for both wedges used are shown in Figure 5.

In HST cycles 24 and 25, HST GO programs 14714 and 15221 (G. Schneider, PI) episodically monitored the HD 107146 debris disk with STIS PSF-template subtracted coronagraphy. These programs collected four additional epochs of coronagraphic observations of HR 5183 (see Table 7) to serve as contemporaneous PSF-subtraction templates. These images were analyzed as described above. These observations had longer intra-observational cadence (4–8 months) and did not improve the contrast curve from GO 12228.

B.2. NaCo Data