Plausible Home Stars of the Interstellar Object 'Oumuamua Found in Gaia DR2

Gaia DR2 provides 6D phase space information—positions, parallaxes, proper motions, radial velocities—for 7.2 million stars (Gaia Collaboration 2018). We first select the subset of these that have positive parallaxes, i.e., have $\varpi -{\varpi }_{\mathrm{zp}}\gt 0$, where ${\varpi }_{\mathrm{zp}}=-0.029$ mas is the parallax zero point (Lindegren et al. 2018).¹⁰ To remove possibly erroneous astrometric solutions, we cut according to the criteria discussed and adopted by Bailer-Jones et al. (2018a): we remove stars that have visibility_periods_used $\geqslant 8$ or unit weight error $u\geqslant 35$. This leaves us with 7,039,430 stars, which we will refer to as the full sample. The 5th and 95th percentiles on their $G$-band magnitude distribution are 10.1 and 13.9 mag, respectively.¹¹

We then use linear motion approximation (LMA) to identify which stars in the full sample came within 10 pc of 'Oumuamua at some time in the past. The LMA, described in Bailer-Jones (2015; but modified here to involve the position and velocity of a star relative to 'Oumuamua), assumes all objects move on unaccelerated orbits. This produces a simple analytic approximation for the three encounter parameters: the time of the encounter relative to 2015.5, ${t}_{\mathrm{enc}}$; the separation of the star and 'Oumuamua at encounter, ${d}_{\mathrm{enc}}$; and their relative velocity at encounter, ${v}_{\mathrm{enc}}$. We apply the superscript "lma" to indicate when these quantities come from the LMA.

For each of the six asymptote solutions for 'Oumuamua in Table 1, we find about 1500 stars that satisfy the conditions ${t}_{\mathrm{enc}}^{\mathrm{lma}}\lt 0$ and ${d}_{\mathrm{enc}}^{\mathrm{lma}}\lt 10$ pc. We call these the encounter candidates. As the LMA is not precise, we use this large limit on ${d}_{\mathrm{enc}}^{\mathrm{lma}}$ to avoid omitting stars that may encounter within 2 pc when using the orbit integration (the next step). As we summarize later, extending this initial search out to ${d}_{\mathrm{enc}}^{\mathrm{lma}}\lt 20$ pc did not uncover additional close encounters.

To improve the accuracy of the encounter parameters, we integrate the paths of the encounter candidates and 'Oumuamua through a smooth Galactic potential. We characterize the uncertainties at the same time by resampling the initial 6D coordinates of each star (and of 'Oumuamua) according to their Gaussian covariances, then integrating the orbits of each of the resulting "surrogate" objects. Specifically, for each encounter candidate in each asymptote solution, we draw from the star's 6D Gaussian distribution to give one surrogate star and then integrate its orbit. We do the same for 'Oumuamua and find the parameters of its encounter with the surrogate star.¹² Repeating this 2000 times produces a 3D distribution over ${t}_{\mathrm{enc}}$, ${d}_{\mathrm{enc}}$, and ${v}_{\mathrm{enc}}$ for that star and 'Oumuamua. We characterize the marginal distributions using the medians—${t}_{\mathrm{enc}}^{\mathrm{med}}$, ${d}_{\mathrm{enc}}^{\mathrm{med}}$, ${v}_{\mathrm{enc}}^{\mathrm{med}}$—as well as their 5th and 95th percentiles (which together form a 90% confidence interval, CI). This is repeated for each encounter candidate for each of the six asymptote solutions.

The Galactic potential (a three-component axisymmetric model) and parameters of the Sun's orbit are the same as those described in Bailer-Jones (2015) and also used in Bailer-Jones et al. (2018a). Encounter parameters depend only weakly on these choices because it is only the differences in the potential experienced by the stars and 'Oumuamua that influence their mutual encounters. Note that the velocity of 'Oumuamua relative to the LSR mentioned in Section 1 is a consequence of this model, not an input. We ignore the mutual gravity between individual stars, and between individual stars and 'Oumuamua (the latter at least is probably irrelevant; see Section 6).

As Gaia DR2 does not list radial velocities for most of its 1.33 billion sources that have astrometry, we searched Simbad for non-Gaia radial velocities for these sources. We found 222,275 stars that also satisfy the criteria on parallax and parallax metrics in Section 3.1. Of these, 476 have ${t}_{\mathrm{enc}}^{\mathrm{lma}}\lt 0$ and ${d}_{\mathrm{enc}}^{\mathrm{lma}}\lt 10$ pc for solution 2 k = 2 (and similar for the other solutions). After performing the orbital integration, 13 have ${d}_{\mathrm{enc}}^{\mathrm{med}}\lt 2$ pc.

The closest encounter with 'Oumuamua is at 0.7 pc, but with a relative velocity of 266 $\mathrm{km}\,{{\rm{s}}}^{-1}$, and so is uninteresting. The only good home candidate is the second closest encounter in the sample, Gaia DR2 3666992950762141312, which we name "home-4". Its closest approach to 'Oumuamua of 0.9 pc was 1.1 Myr ago with a relative velocity of 18 $\mathrm{km}\,{{\rm{s}}}^{-1}$. Full details are given in the last line of Table 2, and it is plotted in Figures 4 and 5 in red. The relatively large uncertainty in its encounter velocity is mostly due to the low signal-to-noise ratio of its radial velocity (which is from Terrien et al. 2015). Alonso-Floriano et al. (2015) give its spectral type as M5V, which agrees with its position in the CMD (Figure 5) and the ${T}_{\mathrm{eff}}$ of 3530 K (68% CI 3290–4100K) listed in Gaia DR2. It has several names and references in Simbad, and appears in various catalogs of nearby M dwarfs.

The other 11 encounters are more distant and faster, and are less interesting than the other candidates already mentioned.

A few other stars in Table 2 have close approaches to 'Oumuamua, but in all cases their velocities are rather too high for plausible ejection scenarios, and/or their encounter parameters have large uncertainties. We therefore consider HIP 3757, HD 292249, home-3, and home-4 as our main home candidates. All four stars have good astrometric and radial velocity measurements and quality metrics in Gaia DR2. HIP 3757's astrometry is consistent with that in both Hipparcos (Perryman et al. 1997) and Hipparcos-2 (van Leeuwen 2007; it is not in TGAS). HD 292249's astrometry agrees with that in TGAS (Gaia Collaboration 2016; it is not in Hipparcos). None of these stars are known to harbor exoplanets or to be binary systems.

To ensure that our LMA-based selection with ${d}_{\mathrm{enc}}^{\mathrm{lma}}\lt 10$ pc was not too restrictive, we extended it to ${d}_{\mathrm{enc}}^{\mathrm{lma}}\lt 20$ pc. This produced a further 4500 encounter candidates (for the complete Gaia data), for which we ran the orbital integration with surrogates. Only two of these candidates had ${d}_{\mathrm{enc}}^{\mathrm{med}}\lt 2$ pc, both at around 1.7 pc, but with large 90% CIs (0.4–4.9 pc) and velocities of 25 $\mathrm{km}\,{{\rm{s}}}^{-1}$ and 47 $\mathrm{km}\,{{\rm{s}}}^{-1}$.

We can use the same procedure described so far to determine 'Oumuamua's outbound trajectory from the Sun and identify future close encounters. For model 2 k = 2 in Micheli et al. (2018), the asymptote is $(\alpha ,\delta ,{v}_{\infty })=(357\buildrel{\circ}\over{.} 8512,24\buildrel{\circ}\over{.} 7164,26.40776\,\mathrm{km}\,{{\rm{s}}}^{-1})$ (Galactic coordinates $l=106^\circ ,b=-36^\circ$). We searched both the Gaia sample and the Simbad supplement. There are not as many close/slow encounters as for the inbound trajectory.

The closest encounter is with the high proper motion star Gaia DR2 2279795617408467712 (= TYC 4600-1769-1) at a distance of 0.332 pc (90% CI 0.313-0.351 pc), which takes places in 0.716 Myr with a large relative velocity of 112 $\mathrm{km}\,{{\rm{s}}}^{-1}$. One of the slowest encounters will be with Gaia DR2 335659463780716288 in 2.7 Myr with a median velocity of 30 $\mathrm{km}\,{{\rm{s}}}^{-1}$ and a distance of 1.4 pc. In just 0.029 Myr, 'Oumuamua will pass the M5 dwarf Ross 248 (= Gaia DR2 1926461164913660160) at 0.459 pc (90% CI 0.458–0.460 pc) with a relative velocity of 104 $\mathrm{km}\,{{\rm{s}}}^{-1}$. Ross 248 is currently one of the closest stars to the Sun, at 3.15 pc.

We consider a system comprising a central star with mass M_*, a giant planet with mass ${m}_{{\rm{p}}}$ on a (nearly) circular orbit of semimajor axis ${a}_{{\rm{p}}}$, and planetesimals such as 'Oumuamua. Numerical simulations of Oort cloud formation indicate that planetesimals usually undergo a random walk through diffusion up to escape energies. This diffusion occurs through distant encounters with the planet(s) in which the periastron distance is $q\sim \tfrac{9}{8}{a}_{{\rm{p}}}$ (Duncan et al. 1987; Brasser & Morbidelli 2013). This evolution eventually leads to highly eccentric orbits, because the energy changes occur at periastron and the semimajor axis undergoes a random walk while the periastron distance remains approximately constant (Duncan et al. 1987). If we describe the total specific energy of a planetesimal such as 'Oumuamua by $-1/(2a)$, then the typical energy change during each periastron passage due to distant interactions with the planet is (Duncan et al. 1987; Tremaine 1993)

$$\begin{eqnarray}&&| {\rm{\Delta }}E| =\displaystyle \frac{10}{{a}_{{\rm{p}}}}\displaystyle \frac{{m}_{{\rm{p}}}}{{M}_{* }}\ {\mathrm{au}}^{-1},\end{eqnarray} \tag{ 2 }$$

which is applicable for low-inclination orbits; at higher inclination, the energy kicks are gentler. Before its last periastron passage, 'Oumuamua is expected to have a total specific energy of $-\tfrac{1}{2}{\rm{\Delta }}E$. After its last periastron passage, it will typically have a total energy of $\tfrac{1}{2}{\rm{\Delta }}E$, and the typical escape velocity from the solar system is then

$$\begin{eqnarray}&&{v}_{\mathrm{esc}}=\sqrt{\displaystyle \frac{{{GM}}_{* }{\rm{\Delta }}E}{2}}.\end{eqnarray} \tag{ 3 }$$

For encounters with Jupiter, ${\rm{\Delta }}E=2\times {10}^{-3}$ au⁻¹ and ${v}_{\mathrm{esc}}\sim 1\,\mathrm{km}\,{{\rm{s}}}^{-1};$ these values are consistent with various numerical studies (Duncan et al. 1987; Brasser & Morbidelli 2013). In this simple approximation, ${v}_{\mathrm{esc}}\propto {({m}_{{\rm{p}}}/{a}_{{\rm{p}}})}^{1/2}$, so that a Jupiter-mass planet at 1 au will eject planetesimals with a typical velocity close to 2 $\mathrm{km}\,{{\rm{s}}}^{-1}$. Ejection with a velocity close to the inferred encounter velocity of 10 $\mathrm{km}\,{{\rm{s}}}^{-1}$ or more from Section 4 would require either an extremely massive object close to the central star (such as a binary system), or a rare, deep encounter with a giant planet, for which v_esc ∼ v_p, the orbital velocity of the planet (∼13 $\mathrm{km}\,{{\rm{s}}}^{-1}$ for Jupiter).

Ejection velocities much higher than v_p are rare because they require that, after the encounter, the velocity vector of the planetesimal be parallel to that of the planet. Since encounters are isotropic, the volume of outcomes that achieve this is small. Immediately after such an encounter, the orbital velocity of the planetesimal is v_tp + v_p, and ejection is only possible when ${v}_{\mathrm{tp}}+{v}_{{\rm{p}}}\gt \sqrt{2}{v}_{{\rm{p}}}$, where v_tp is the orbital velocity of the planetesimal before the encounter. Ejection in this manner therefore requires ${v}_{\mathrm{tp}}\geqslant (\sqrt{2}-1){v}_{{\rm{p}}}$. Such a high encounter velocity, and thus ejection velocity, are only possible if the planetesimal crosses the planet's orbit. Numerical simulations show, however, that most planetesimals are ejected on orbits with perihelia greater than the planet's orbit (Brasser & Duncan 2008).

Figure 6 shows the cumulative distribution over the ejection velocity for planetesimals that are scattered by the giant planets in the solar system. The duration of the simulation is 200 Myr, wherein over 90% of planetesimals were removed. Since the giant planets are assumed to be static, the distribution of ejection velocity will reach a steady state on a timescale that is comparable to the dynamical evolution timescale of the planetesimals. For encounters with Jupiter and Saturn, this is about 3 Myr, while for encounters with Uranus and Neptune, it approaches 100 Myr (Duncan et al. 1987). The majority (>70%) of the planetesimals are ejected by Jupiter (Brasser & Duncan 2008), so that the distribution is expected to be close to that from ejection solely by Jupiter. The median ejection velocity of 1.3 $\mathrm{km}\,{{\rm{s}}}^{-1}$ corresponds closely to the value derived from Equation (3). The cumulative distribution of the ejection velocity is approximately log-normal, with a mean of 0.13 and a standard deviation of 0.37. An ejection velocity of 10 $\mathrm{km}\,{{\rm{s}}}^{-1}$ or greater occurs only in 0.3% of the cases. For gas giants residing closer to their host star, the distribution is expected to look similar but shifted toward higher velocities, scaling as ${a}_{{\rm{p}}}^{-1/2}$. A Jupiter-mass planet at 1 au, therefore, is expected to have a 5% probability of ejecting planetesimals at 10 $\mathrm{km}\,{{\rm{s}}}^{-1}$, because the curve will be shifted to the right by a factor of roughly 2 and the 95th percentile for the solar system is then at 5.1 $\mathrm{km}\,{{\rm{s}}}^{-1}$. The probability that such a planet ejects 'Oumuamua at 20 $\mathrm{km}\,{{\rm{s}}}^{-1}$ or greater is still only 0.3%.

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Raymond et al. (2018) note that a planetary system with initially unstable gas giants is a more efficient source of interstellar planetesimals than a system with stable giant planets. The reason is that during a phase of instability, multiple gas giant planets will be on highly eccentric orbits and can thus eject planetesimals over a much wider range of orbital radii than a stable system (Raymond et al. 2011, 2012), although it is unclear from the simulations whether such highly eccentric planetary systems eject planetesimals at higher velocities.

Higher ejection velocities can occur for planetesimals scattered in a binary star system. To demonstrate this, we performed a simple dynamical experiment on a system comprising a 0.1 ${M}_{\odot }$ star in a 10 au circular orbit about a 1.0 ${M}_{\odot }$ star. (This is just an illustration; a full parameter study is beyond the scope of this work.) Planetesimals were randomly placed between 3 au and 20 au from the primary, enveloping the orbit of the secondary. The cumulative distribution of the ejection velocities is shown as the red dashed curve in Figure 6. Once again, most (80%) of the ejections occur at velocities lower than 10 $\mathrm{km}\,{{\rm{s}}}^{-1}$, but a small fraction is ejected at higher velocities in the range of those we observe (and even exceeding 100 $\mathrm{km}\,{{\rm{s}}}^{-1}$). We mention here that the second closest encounter in Table 2, Gaia DR2 3174397001191766400, lies above the main sequence in Figure 5, suggesting it might be a binary.

A star passing close to a home candidate star could in principle eject small bodies such as 'Oumuamua. The more massive/closer/slower the transit, the more likely the ejection. If we assume that 'Oumuamua was originally residing on a wide, weakly bound orbit around a solar-type star, then the change in velocity imparted on it by the impulse of a passing star is (Fouchard et al. 2011)

$$\begin{eqnarray}&&{\rm{\Delta }}V=\displaystyle \frac{2{{GM}}_{* }}{{v}_{* }b},\end{eqnarray} \tag{ 4 }$$

where b is the impact parameter (approximately equal to the closest distance if v_* is high). (This approximation does not apply if either star is a binary system.) A passing star with ${M}_{* }=0.5$ ${M}_{\odot }$ and ${v}_{* }=25\,\mathrm{km}\,{{\rm{s}}}^{-1}$ requires an encounter within 35 au to impart ${\rm{\Delta }}V\gt 1\,\mathrm{km}\,{{\rm{s}}}^{-1}$. Thus, it is a priori very unlikely that 'Oumuamua would be ejected by a typical passing star.

We nonetheless ran models to determine whether any of the 7 million stars in the full sample passed close to the home candidates at the right time, e.g., within the 90% CI on ${t}_{\mathrm{enc}}$ given in Table 2. No good encounters were found for the first three home candidates, HIP 3757, HD 292249, and home-3. Two encounters with home-4 from the LMA were promising enough to be further investigated with the orbital integration. One of these, Gaia DR2 2984656203733095936, had a median closest approach of 1.4 pc at −1.25 Myr (the 90% CI is −1.38 to −1.14 Myr, and so overlaps considerably with home-4's encounter with 'Oumuamua) and a median encounter velocity of 42 $\mathrm{km}\,{{\rm{s}}}^{-1}$. More significantly, it has a 20% chance of approaching closer than 0.51 pc to home-4. This star is in fact listed in Table 2 (not that surprising, as all three objects must come close together at the same time). Its absolute magnitude and color, together with its ${T}_{\mathrm{eff}}$ of 3960 K (68% CI 3870–4010 K) from Gaia DR2, imply it is a late K or early M dwarf, so not very massive. Equation (4) suggests it is extremely unlikely to have ejected 'Oumuamua (as $b\sim 1\,\mathrm{au}$ when ${v}_{* }=42\,\mathrm{km}\,{{\rm{s}}}^{-1}$, ${M}_{* }=0.5$ ${M}_{\odot }$, and ${\rm{\Delta }}V=17.9\,\mathrm{km}\,{{\rm{s}}}^{-1}$). The other star, GaiaDR2 4294690189048270464, also has an encounter in roughly the right time range (90% CI −0.96 to −0.90 Myr) but has a large encounter distance spread (90% CI 0.52–4.97 pc), and so is even less favorable.

In conclusion, we find no convincing star that could have ejected 'Oumuamua from a home candidate star. There could, of course, be other candidates for which we do not have 6D data.

Modeled motions. The derivation of the Gaia DR2 astrometry assumes that stars move on unaccelerated paths over the time range of Gaia's observations. In particular, it assumes that any binarity does not affect the astrometry of their observed center of light. We have also assumed that the non-gravitational forces inferred for 'Oumuamua's observed outbound trajectory also apply to its inbound trajectory.

Restricted sample. The most obvious limitation of our work is that it is restricted to just those 7 million stars in Gaia DR2 with 6D phase space information. This is a small fraction of the stars within some distance horizon for which one could in principle look for home candidates, if the data were available. There are, for example, 35 million stars in Gaia DR2 within 500 pc (most probable distances from Bailer-Jones et al. 2018b), fives times as many as the full sample. For comparison, the median distance of the full sample is 1250 pc; 180 million stars in Gaia DR2 are closer than this. Hence, it is a priori unlikely that we would find the home system in our study. Even when we have full data, searching out to larger distances (100s of pc, and thus 'Oumuamua travel times of order 10 Myr or more) will be difficult, as uncertainties in the Galactic potential become more relevant and N-body effects eventually become significant (e.g., Zhang 2018).

Low-probability encounters. Table 2 lists all of the stars that have ${d}_{\mathrm{enc}}^{\mathrm{med}}\lt 2$ pc and therefore have a probability greater than 0.5 of passing within 2 pc of 'Oumuamua. There are, of course, stars with ${d}_{\mathrm{enc}}^{\mathrm{med}}\gt 2$ pc that could have a non-negligible probability of encountering closer than 2 pc and thus are potentially interesting. For solution 2 k = 2, there are 1440 stars with $2\leqslant {d}_{\mathrm{enc}}^{\mathrm{med}}\leqslant 10$ pc. Sixty-six of these have a probability greater than 0.01 of encountering closer than 2 pc. Their median probability is only 0.05, however. In comparison, the 28 candidates in Table 2 have a median probability of 0.987 of an encounter closer than 2 pc, and the individual home candidates have probabilities of 1.000 (HIP 3757), 0.989 (HD 292249), and 0.957 (home-3). None of these 66 stars have encounter distance distributions that peak below 1.5 pc, so none are close encounters even in a maximum likelihood sense.

Close encounters inevitable. With the same full sample as used here, Bailer-Jones et al. (2018a) inferred the rate of stellar encounters (all masses) within 1 pc of the Sun to be 19.7 ± 2.2 per Myr. The completeness of the survey was estimated to be about 0.15, so one would expect to see three encounters within 1 pc per Myr in Gaia DR2. To a first approximation, this rate should also be valid for 'Oumuamua. Thus, when tracing 'Oumuamua's orbit over a few million years, it is not at all surprising that we do find a few close encounters. Of course, the closer the encounter, the more plausible it is as the home star. But given the inevitable imperfection of the model galaxy potential, plus the fact that the inferred encounter separation is more sensitive to this than the inferred encounter velocity, a low encounter velocity is an important criterion for identifying a home candidate.

Smooth potential. Our orbital integration uses a smooth potential, thereby ignoring N-body interactions between 'Oumuamua and individual stars. A simple calculation of the deflection by passing stars (see Section 5.3 of Bailer-Jones 2015) shows, however, that these can be ignored for more recent encounters. For example, 'Oumuamua travels about 26 pc on its (time-reversed) journey from the Sun to encounter HIP 3757 about 1 Myr ago. (Recall that $1\,\mathrm{km}\,{{\rm{s}}}^{-1}\simeq 1$ pc Myr⁻¹.) 'Oumuamua would have to come within 0.008 pc of a 1 ${M}_{\odot }$ star during this journey in order for its closest approach at HIP 3757 to be deflected by 0.05 pc or more (an amount that is well below the spread in ${d}_{\mathrm{enc}}$ arising from the uncertainties in the 6D coordinates). Adopting a conservatively large local stellar number density of 1 pc⁻³, the probability that 'Oumuamua would have one or more such close encounters on this journey is just 0.005. Potentially more significant is gravitational interactions between stars deflecting each other's paths, and thus changing their encounters with 'Oumuamua. As the referee emphasized, this becomes more relevant if 'Oumuamua was ejected at a low velocity from its home star (as favored by the giant planet scattering mechanism discussed in Section 5), as then the home star too has traveled a long distance. For example, if 'Oumuamua were ejected at 1 $\mathrm{km}\,{{\rm{s}}}^{-1}$ 10 Myr ago, this would have occurred 260 pc from the Sun, yet the home star would currently be only 10 pc away from 'Oumuamua and hence from the Sun. Tracing back its orbit in the absence of relevant perturbations over a long path means we could fail to unite it with 'Oumuamua within the separation limit adopted.

N-body effects. Dybczyński & Królikowska (2018) took into account the gravitational interactions of 57 stars in their study of the possible origin of 'Oumuamua (discussed in the next section), although they ignored the (more significant) uncertainties in the stellar astrometry and radial velocities. We explicitly tested the effects of including the gravity of the 100 closest encounters to 'Oumuamua (identified from the orbital integration with solution 2 k = 2) on the orbits of both 'Oumuamua and the stars. To be conservative, we assumed all 100 stars to have a mass of 1 ${M}_{\odot }$. The code we used is described in Chang & Chakrabarti (2011), the results of which have been verified by full SPH simulations (Chakrabarti et al. 2011). We do not include a Galactic potential so that we can compare directly with our LMA solutions. The encounter times are very similar, as are the encounter distances and velocities. This suggests that N-body effects are unlikely to significantly affect the analysis of the origins of 'Oumuamua (although it is possible that stars not in our sample, especially more massive ones, have some impact).

Several searches for a home system have been published using pre-Gaia DR2 data. These searches, which we discuss here, predominantly used TGAS astrometry. This is less precise than Gaia DR2 and limited searches to at most 0.3 million stars (those for which radial velocities were also available). These studies also assumed a purely gravitational trajectory for 'Oumuamua. The difference of about 04 between the purely gravitational solution JPL 13 and 2 k = 2 (Figure 1) corresponds to a difference of 0.35 pc after a journey of 50 pc (for linear motions).

Dybczyński & Królikowska (2018) compiled data from Simbad, which was mostly TGAS and Hipparcos astrometry, and RAVE-DR4 (Kordopatis et al. 2013) and RAVE-DR5 (Kunder et al. 2017) radial velocities. They found HIP 3757 to be the closest encounter, with ${t}_{\mathrm{enc}}=-0.118\,\mathrm{Myr}$, ${d}_{\mathrm{enc}}=0.0044$ pc, and ${v}_{\mathrm{enc}}=185$ $\mathrm{km}\,{{\rm{s}}}^{-1}$, but they sensibly disregarded this as a likely home for 'Oumuamua due to the large encounter velocity. Although the authors do not specify the exact origin of the data for this star, this large velocity is probably a consequence of adopting the large radial velocity of 210.04 ± 34.00 $\mathrm{km}\,{{\rm{s}}}^{-1}$ listed in RAVE-DR4 (and RAVE-DR5).¹³ Yet there is good reason to doubt the validity of this measurement: its uncertainty is large, various quality indicators in RAVE suggest it is unreliable, and the velocity itself is surprisingly high. The smaller radial velocity from Gaia DR2 of 26.88 ± 0.35 $\mathrm{km}\,{{\rm{s}}}^{-1}$ leads to a slower encounter (and a larger separation). Interestingly, RAVE-DR5 lists a second radial velocity for this star, based on a different spectrum, of 26.50 ± 2.20 $\mathrm{km}\,{{\rm{s}}}^{-1}$, with good quality metrics. This is more likely to be closer to the true value. Dybczyński & Królikowska (2018) were lucky that the configuration of the relative motion of 'Oumuamua and HIP 3757 is such that even with an erroneously large radial velocity, one still finds a close encounter.

We note in passing that when using the larger RAVE-DR4 radial velocity and Hipparcos astrometry, Bailer-Jones (2015) found HIP 3757 to approach within 2.0–4.4 pc (90% CI) of the Sun about 0.11 Myr ago. Equipped now with Gaia DR2, this result is no longer valid.

Feng & Jones (2018) used TGAS, Hipparcos, RAVE, and XHIP to search for past encounters with 'Oumuamua. Their closest encounter was HIP 21553 at 1.1 pc, 35 $\mathrm{km}\,{{\rm{s}}}^{-1}$, 0.28 Myr ago. This is Gaia DR2 272855565762295680 and is the 10th closest encounter in our Table 2, with consistent encounter parameters. We do not consider it as a home candidate simply because we have better (closer and/or slower) ones. One redeeming feature of this star, however, is that it is one of the most recent encounters, meaning that the backwards integration of its (and 'Oumuamua's) path to encounter is even less sensitive to misrepresentation of the potential. This is neither a sufficient nor necessary conditions for being a home candidate, however. A potentially more interesting object in the study of Feng & Jones (2018) is HIP 104539, which has a low nominal encounter velocity of 10.2 km s^–1 (90% CI 3.3–17.2 $\mathrm{km}\,{{\rm{s}}}^{-1}$). Unfortunately, it has a huge uncertainty on its encounter distance: the 90% CI is 0.25–55 pc. This object is in Gaia DR2, but without a radial velocity, and so was not considered in our study. These authors also mention that they found HIP 3757 as a fast, close encounter, but give no details, and dismissed it on the grounds of having a noisy spectrum, perhaps a reference to the RAVE-DR4 one.

The closest encounter found in a TGAS-based study from Portegies Zwart et al. (2018) was HIP 17288 (note that the Gaia DR1 source ID they give in their Table 1 is incorrect). The encounter distance of 1.34 pc (with a range of 1.33–1.36 pc) and velocity of 14.9 $\mathrm{km}\,{{\rm{s}}}^{-1}$ make it a reasonable candidate. Using presumably the same data, Feng & Jones (2018) found a similar nominal distance, but surprisingly get a much larger 90% CI of 0.07–7.81 pc. This star is in our full sample, but with ${d}_{\mathrm{enc}}^{\mathrm{lma}}=10.1$ pc, it was not an encounter candidate. The orbital integration with the surrogates on this star gave ${d}_{\mathrm{enc}}^{\mathrm{med}}=4.16$ pc (90% CI 2.92–5.46 pc). Both this large value and spread confirm that this is a poor candidate. The other parameters, ${t}_{\mathrm{enc}}^{\mathrm{med}}=-6.91\,\mathrm{Myr}$ and ${v}_{\mathrm{enc}}^{\mathrm{med}}=15.3$ $\mathrm{km}\,{{\rm{s}}}^{-1}$, are consistent with Portegies Zwart et al. (2018). The very small ${d}_{\mathrm{enc}}$ range they quote (which is not defined) is surely either uncharacteristic or is underestimated. They in any case dismiss this and their more distant encounters as being too distant or too fast to be home candidates.

Zhang (2018) did not find any convincing home candidates among his sample of 68 stars from TGAS within 10 pc of the Sun.

Finally, Zuluaga et al. (2018) describe a method of assigning an origin probability for a particular star based on its encounter distance and velocity. Their most probable candidate, based on Hipparcos data, is HIP 103749, for which they find ${d}_{\mathrm{enc}}=1.75$ pc (with a large uncertainty of up to 5 pc) and ${v}_{\mathrm{enc}}=12.0$ $\mathrm{km}\,{{\rm{s}}}^{-1}$. This is Gaia DR2 1873204223289046272, which we found to have ${d}_{\mathrm{enc}}^{\mathrm{lma}}=16.4$ pc and ${v}_{\mathrm{enc}}^{\mathrm{lma}}=14.8$ $\mathrm{km}\,{{\rm{s}}}^{-1}$. The discrepancy may be a result of the significantly different proper motion in Gaia DR2 compared to both Hipparcos and Hipparcos-2. Their three next best encounters occur at larger separations and velocities. The first of these was excluded from our full sample on account of poor astrometry (u = 38.7). The second is not in Gaia DR2 (the reason is not obvious, as it is isolated and has V = 11.3 mag). The third, HIP 3821 = Gaia DR2 425040000959067008, we find for solution 2 k = 2 to have ${d}_{\mathrm{enc}}$ = 2.62–2.67 pc and ${v}_{\mathrm{enc}}$ = 24.75–25.17 pc (90% CIs).

None of the studies cited in this section mentions HD 292249, home-3, or home-4.