© ESO 2018

1 Introduction

The problem of the lack of evident interstellar visitors in our solar system has been discussed for decades. Recently, Engelhardt et al. (2017) considered the implications of not observing such interstellar visitors. Now, the situation has changed.

The first interstellar small body penetrating our solar system was discovered on Pan-STARRS1 images taken on 2017 Oct. 18.5 UT at mag 19.8 (MPC CBET 4450). Initially, it was designated as a comet (C/2017 U1) due to its near-parabolic orbit. Later on, due to the lack of any cometary activity it was renamed as A/2017 U1 (M.P.E.C. 2017-U183, issued on 2017 Oct. 25, 22:22 UT). Ten days later, in M.P.E.C. 2017-V17, issued on Nov. 6, 21:00 UT, a new concept for naming such unusual objects was announced and accordingly, A/2017 U1 was renamed as 1I/2017 U1 (’Oumuamua).

The unique dynamical nature of this object was first noted by Bill Gray in his Oct. 25 posting to the Minor Planet Mailing list (MPML)¹. He obtained a preliminary orbit based on a six-day arc and noticed an atypically high eccentricity of approximately 1.2. ’Oumuamua travels at a relatively high velocity with respect to the Sun (on the order of 25 km s⁻¹). Several preprints on the kinematics of this extraordinary object have recently appeared. Mamajek (2017) analysed the stars nearest the Sun for similar spatial velocity while Gaidos et al. (2017) suggested the origin of ’Oumuamua in a nearby young stellar cluster.

’Oumuamua seems to be unique for its physical characteristics as well. Meech et al. (2017) estimated its shapeto be extremely elongated while Fraser et al. (2017) and Drahus et al. (2017) determined it to be a tumbling body. An interesting paper on the determination of physical parameters for ’Oumuamua has also been presented recently by Jewitt et al. (2017).

Since the nature of this object is still unknown, it might be desirable to study its dynamical history before entering the solar system interior.

This paper is organized as follows: the following section describes the model of solar vicinity dynamics which we use to track ’Oumuamua’s past motion. The main task was to collect data on potential stellar perturbers. Section 3 presents the results of our numerical experiments. In the last section, we interpret these results and discuss their importance. In appendices we present complete numerical results, all stellar parameters used in this work with their references, and several examples of the geometry of the Qumuamua – star encounters.

2 Approach to the problem

To analyze the interstellar path of ’Oumuamua in the solar neighbourhood it is necessary to numerically integrate its equations ofmotion, taking into account both the overall Galactic potential and all important individual stellar perturbations from the known nearby stars.

To work with contemporary stellar data, we searched the whole SIMBAD astronomical objects database² for all stars with known positions, proper motions, parallaxes and radial velocities. To make sure we were working only with reliable data, we ensured that parallaxes were positive and radial velocities were ≦500 km s⁻¹ in modulus. The result of this search, performed on 2017 Nov. 5, consists of 201 763 individual objects. Such a great number is the result oflarge observational projects, mainly Gaia (Gaia Collaboration 2016b) and RAVE (Kunder et al. 2017). As it concerns a homogeneity of the data taken from the SIMBAD database weobserve that 84% of astrometric measurements of these 201 763 stars were copied from the TGAS catalogue (Gaia Collaboration 2016a) and another 11% from the HIP2 catalogue (van Leeuwen 2007). The situation is slightly more complicated with radial velocity sources but still the majority of measurements (70%) were taken from RAVE data releases (Kunder et al. 2017; Kordopatis & RAVE Collaboration 2014) and another 11% from the Pulkovo compilation (Gontcharov 2006). The remaining radial velocity measurements taken by us from the SIMBAD database were copied from a large number of individual papers.

This stellar data set allowed us to perform accurate calculations, namely the numerical integration of ’Oumuamua’s motion. To account for mutual stellar gravitational interactions, we had to integrate the N-body problem, consisting of ’Oumuamua, the Sun, and all individual stellar perturbers, all of which are under the influence of the overall Galactic potential. However, integrating the simultaneous motion’s of over 200 000 bodies would be a waste of time – a great majority of these bodies never came close enough to ’Oumuamua to disturb its motion. Instead we first prepared a short list of perturbers; see below.

Numerical integration of motion was performed in a right-handed, non-rotating, rectangular Galactocentric frame with the OX axis directed in the opposite direction to the Sun’s position at the starting time. We use the Model I variant of the Galactic gravitational potential described by Irrgang et al. (2013). As the starting position and velocity of the Sun we use vectors: R_⊙ = (x_⊙, y_⊙, z_⊙) = (−8400, 0, 17) in pc and Ṙ _⊙ = (u, v, w) = (+11.352, +260.011, +7.41) in pc Myr⁻¹. In the former, we adopted the vertical position of the Sun given by Joshi (2007). A detailed description of the Galactic reference frame orientation and the Galactic potential form and parameters can be found in Dybczyński & Berski (2015). Here we use exactly the same dynamical model and equations of motion.

The starting position and velocities of ’Oumuamua for dynamical calculations outside a planetary zone were obtained from its original orbit. We determined this orbit elements from all positional observations available in the MPC database³ on 2017 Nov. 12. Through careful data processing, we obtained an osculating orbit given in Table 1. Next, in order to observe the uncertainties in the motion of ’Oumuamua at every stage of our research, we cloned its orbit and built a swarm of 10 000 orbits resembling the observations, using a method described by Sitarski (1998) which fully utilises the covariance matrix obtained during the orbit determination. Then, we numerically propagated all of these orbits forward and backward up to a heliocentric distance of 250 AU (the distance at which planetary perturbations are negligible). The resulting barycentric elements of the original and future orbits of ’Oumuamua, along with their uncertainties, are presented in Table 2. We used the barycentric positions and velocities of each individual clone of ’Oumuamua at 250 au as starting data for a dynamical study of this body under the gravitational influence of stars and the full Galactic potential.

We suppose that due to the lack of cometary activity, non-gravitational forces (we found them non-detectable from positional data) could not have changed the orbit of ’Oumuamua significantly during its close perihelion passage and that the original orbit is rather reliable, with the uncertainties presented in Table 2. To observe how these uncertainties influence the minimal distance between ’Oumuamua and all stars included in our model, we repeated our numerical integration for all 10 000 clones of ’Oumuamua. Each encounter parameters obtained from this complex calculation as well as their variation intervals are presented in Table A.3.

However, the most important source of the close passage distance uncertainty, not estimated in this paper, is the stellar data errors. This cannot simply be modelled by the simultaneous drawing of N clones for all 57 stars and ’Oumuamua because that would require N⁵⁸ numerical integrations. In this paper, we restrict the error budget calculations to the influence of the ’Oumuamua orbit uncertainty.

To refine (and considerably shrink) our set of stellar perturbers, we first numerically followed the past motion of ’Oumuamua with each of the 201 763 stars individually along with the Sun, forming a three-body problem under the influence of the full Galactic potential. During this preliminary calculation, we assumed all stellar masses to be 1.0 M_⊙. Using these results, we selected 109 stellar objects that passed ’Oumuamua at a distance of closer than 3.5 pc. The parameters of all these encounters, derived from a nominal ’Oumuamua orbit and nominal stellar data, can be found in Table A.1.

After a detailed inspection involving the removal of obsolete objects and replacing components of multiple stellar systems with their respective centre of mass parameters, we finally collected a list of 57 stars or stellar systems which should be taken into account when studying ’Oumuamua’s past motion in the solar neighbourhood. To use these stars as perturbers it was necessary to find estimations of their masses. It appeared that a lot of them are red (or even brown) dwarfs with a very small mass. Additionally, we recognised several pairs of stars forming double systems as well as one triple system (Alpha Centauri A,B + Proxima) and calculated their centre of mass coordinates, total mass, and a systemic velocity. The most massive perturbers in our list are the Alpha Centauri and Sirius systems. A list of these perturbers with their estimated masses, starting positions and velocities is presented in Table A.2. In the last column of this table we present references for all values used by us. Some adopted mass values are rather crude estimations, but due to ’Oumuamua’s large velocity it turned out that the change in a perturbers mass does not significantly influence the path of ’Oumuamua. This of course might be false for mutual interactions of perturbers.

Finally, we integrated the N-body problem, consisting of ’Oumuamua, the Sun, and all 57 individual stellar perturbers, a 59-body system under the influence of the overall Galactic potential (hereafter 59B model).

Figure 1 shows the past trajectories of ’Oumuamua (in black), the Sun (in green), and three example stars selected from Tables 3–4. Their motion is projected onto the Galactic disk plane.

	Fig. 1 Past trajectories of ’Oumuamua, the Sun, and three selected stars during the last 3 Myr. Their positions are projected onto the XY plane of the Galactocentric, non-rotating, right-handed rectangular frame. This plane coincides with the Galactic disk plane. The OX axis is directed opposite to the Galactocentric direction to the Sun at the starting epoch t = 0.
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3 Results

After analysing ’Oumuamua’s past motion within the solar vicinity, we found seven encounters closer than 1 pc between ’Oumuamua and nearby stars. These encounters are described in Table 3 and presented in Fig. 2. The first ’Oumuamua star encounter (with HIP 3757) is a very close one, with a miss distance of only 0.04 pcbut with a rather high relative velocity of over 200 km s⁻¹ taking place 118 000 yr ago. The second encounter, with GJ 4274, happened only 23 000 yr ago with an even greater relative velocity of 316 km s⁻¹. The minimum distance of the third event, with HIP 981, is also very close, but due to the large heliocentric distance of this event and practically unknown radial velocity of the star (rv = 4.00 ± 6.5 km s⁻¹, Barbier-Brossat & Figon 2000) we treat this case as a “false positive”. The remaining cases presented in Table 3 yield a relative velocity of over 60 km s⁻¹ , which also makes them not very promising candidates for ’Oumuamua’s source system.

When searching for the parent star of ’Oumuamua, one probably should look for a close passage with a much smaller relative velocity. From among the over 200 000 tested stars, we found only four such cases; see Table 4.

In Fig. 2 we show how the distance of ’Oumuamuafrom stars listed in Table 3 and Table 4 changed in time.

Almost 820 000 yr ago, ’Oumuamua passed near the star HIP 113020 (also known as BD-15 6290, GJ 876, or Ross 780) with a relative velocity of about 5 km s⁻¹ and at a heliocentric distance of 21.3 pc. For the nominal ’Oumuamua orbit, the minimal distance between these two objects was 2.24 pc. However, it should be noted that (going backwards along its track) the motion of ’Oumuamua was perturbed by six stars from Table 3 as well as 51 other stars acting from larger distances of 1–3 pc. Every close passage of ’Oumuamua near a star magnifies starting point uncertainties, additionally increased by the stellar data errors. While most of the stars included in our calculations are M dwarfs with relatively small masses, some have masses greater thanthe Sun. However, while the stellar kinematics data uncertainties are the most important source of the proximity distance uncertainty, these are not estimated in this paper. To observe how the uncertainties of ’Oumuamua’s orbit affect our results, we repeated our calculation of the 59B model for the 10 000 clones of ’Oumuamua. We individually searched for the closest and the farthest clone at the approach epoch and recorded the encounter parameters for each star, obtaining their variation intervals. For this number of clones, these intervals are wider than 3σ and are presented in the last column of Table 3. Similar data for all the studied stars may be found in Table A.3.

Three more low-velocity encounters happened further than 30 pc from the Sun. We recognised the encounters with the high-proper-motion star UCAC4 535-065571 and the eclipsing binary δ Capricorni as the most interesting ones. TYC 5325-1808-1 cannot be reliably included in our list of perturbers since its mass and spectral type are unknown. The correct mass value is indispensable for dynamically tracing such a long trip (almost 270 pc).

UCAC4 535-065571 is a red dwarf of M6V spectral type and its mass is estimated to be 0.205 M_⊙ (Newton et al. 2016) We obtained an encounter relative velocity of 5.35 km s⁻¹ but with a minimum distance of 3.46 pc. With such a large miss-distance, one might reject this star as a parental candidate for ’Oumuamua. However, we noticed that the kinematics of UCAC4 535-065571 is rather poorly known. In the SIMBAD database we found its parallax, plx = 85.40 ± 3.30 mas (Dittmann et al. 2014), proper motions, pma = −107.0 ± 8 mas yr⁻¹ and pmd = −133.0 ± 8 mas yr⁻¹ (Zacharias et al. 2012), and radial velocity rv = −19 ± 5 km s⁻¹ Newton et al. (2014). By manipulating numbers within their uncertainties, we obtained a miss distance of 0.6 pc but with a relative velocity of 10 km s⁻¹ (by adopting: plx = 82.1 mas, pma = −99 mas yr⁻¹, pmd = 141 mas yr⁻¹ and rv = 14.0 km s⁻¹). Alternative kinematic parameters for this star can also be found in West et al. (2015), where plx = 76 mas and rv = −9.5 km s⁻¹ . The discrepancy between radial-velocity measurements might be connected with the rotational velocity of 43 km s⁻¹ (Newton et al. 2016) for this star. Using these kinematic data, we obtained a nominal proximity distance of 0.4 pc but with a relative velocity of 14.7 km s⁻¹.

δ Capricorni (HIP 107556, GJ 837) is also a good candidate, with high-precision kinematic parameters. It is an eclipsing binary so its mass is also accurate and it has a small relative velocity of 6.9 km s⁻¹ . ’Oumuamua passed this star at a rather large distance of 3.21 pc.

	Fig. 2 Changes in the distance between ’Oumuamua and stars listed in Tables 3 and 4. Only HIP 981 and TYC 5325-1808-1 are omitted due to their unreliable kinematic data. Please note a horizontal scale changein the middle of the plot.
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4 Discussion and conclusions

No obvious parent star has been identified. The closest ’Oumuamua– star proximity found by us, an encounter with HIP 3757 almost 120 000 yr ago, does not indicate that ’Oumuamua originated from this star system; it might be true provided some mechanism of ejecting ’Oumuamua from this system with the relative velocity of 185 km s⁻¹ be proposed.

It seems more reasonable to search for the parent star of ’Oumuamua in the cases of a much smaller relative velocity. Utilising such an approach would make HIP 113020 a more promising candidate. This well known star (known also as BD-15 6290, GJ 876, or Ross 780) has a rich planetary system consisting of four planets: one very small and three other massive and strongly interacting planets; see for example Rivera et al. (2010) and the references therein. Our resulting miss distance is highly sensitive to the systemic radial velocity of the HIP 113020 system. There seems to be some discrepancy between the centre of mass velocity of about 0.5 km s⁻¹ obtained in the paper quoted above and the value presented in the SIMBAD database: −1.519 ± 0.157 km s⁻¹ (Terrien et al. 2015). Taking into account that the motion of ’Oumuamua was perturbed by tens of stars after passing HIP 113020 and that kinematic parameters (and masses) of these perturbers are of a significantly different quality and accuracy, we cannot rule out the possibility that ’Oumuamua originated from the HIP 113020 planetary system. Definitively, we have to wait for much more precise stellar data from the Gaia mission (Gaia Collaboration 2016b).

In our results obtained for the vicinity of the Sun there is yet another nearby star worth mentioning. ’Oumuamua nominally passed HIP 21553 at a distance of 1.02287 pc almost 280 000 yr ago with a relative velocity of less than 35 km s⁻¹. HIP 21553 (also known as HD 232979 or GJ 172) is a M0.5V-type red dwarf according to SIMBAD (Keenan & McNeil 1989). Its astrometric data were recently highly improved by the Gaia mission (Gaia Collaboration 2016b).

Additionally, we found another candidate past the 30-pc heliocentric distance, the star UCAC4 535-065571. By varying this star’s position and velocity within their respective uncertainty intervals, we obtained a very close encounter with ’Oumuamua at a reasonably small relative velocity of 5–15 km s⁻¹. It seems necessary to study the kinematics of this star in more detail in order to make any definitive conclusion on the putative relation between this star and ’Oumuamua. There is also a small probability that ’Oumuamua comes from δ Capricorni.

An equally interesting hypothesis is that this interstellar object came to our planetary system from a more distant source.

Over the studied period of the past few million years, the heliocentric trajectory of ’Oumuamua appears to be almost a straight line with an approximately constant velocity. This is mainly because of its great velocity, relatively large distance from perturbing stars, and their small masses (in most cases). This fact is illustrated in several figures included in Appendix B. One can also see in Fig. 1 that the deviation from the straight line motion is also very slight in theGalactocentric frame over a similar time interval.

Another important conclusion from our work is that despite the short observational interval of ’Oumuamua, its original orbit uncertainties do not influence our results in any significant way.

There recently appeared a preprint by S. Portegies Zwart and colleagues (Portegies Zwart et al. 2017) in which the authors propose five other stars as potential sources for ’Oumuamua. We carefully checked all these cases and according toour calculations ’Oumuamua did not come closer than 20 pc to any of these stars. A probable reason for this finding is that an approximate dynamical model was used in the quoted paper, where as in all five cases these stars are very distant and therefore their motion is sensitive to the dynamical model details, especially the mutual interactions between all stars involved. Such a disagreement is also noted in Feng & Jones (2018). On the contrary, these authors confirm our results for overlapping stars.

Acknowledgments

We would like to thank Ramon Brasser and the second anonymous referee for helpful comments and suggestions. This research was partially supported by the project 2015/17/B/ST9/01790 funded by the National Science Centre in Poland. This research made use of the SIMBAD database, operated at CDS, Strasbourg, France.

Appendix A Supplementary material

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Appendix B Geometry examples of ’Oumuamua encounters with selected stars

Below we present six plots of the example geometries of the close ’Oumuamua – star passages. We use here a heliocentric,non-rotating, right-handed rectangular frame. The XY plane is parallel to the Galactic disk plane and the OX axis is directed to the Galactic Centre at the beginning of the calculation. Green lines depict the ’Oumuamua motion while the red ones show the star trajectory. Open circles markthe starting positions of ’Oumuamua and the star.

	Fig. B.1 Geometry of the encounter of ’Oumuamua with the star G 108-21 0.2 Myr ago. Depicted is 0.3 Myr of their motion.
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	Fig. B.2 Geometry of the encounter of ’Oumuamua with the star GJ 4274 23 kyr ago. 112 kyr of motion of these bodies is shown here.
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	Fig. B.3 Geometry of the encounter of ’Oumuamua with the star δ Capricorni 1.5 Myr ago. Their past motion over 3.74 Myr is shown.
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	Fig. B.4 Geometry of the encounter of ’Oumuamua with the star HIP 3757 118 kyr ago. 186 kyr of motion of these bodies is shown here.
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	Fig. B.5 Geometry of the encounter of ’Oumuamua with the star HIP 113020 0.8 Myr ago. Past motion during 3.74 Myr is shown.
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	Fig. B.6 Geometry of the encounter of ’Oumuamua with the star UCAC4 535-065571 2.14 Myr ago. Past motion during 3.74 Myr is shown.
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References

All Tables

All Figures

	Fig. 1 Past trajectories of ’Oumuamua, the Sun, and three selected stars during the last 3 Myr. Their positions are projected onto the XY plane of the Galactocentric, non-rotating, right-handed rectangular frame. This plane coincides with the Galactic disk plane. The OX axis is directed opposite to the Galactocentric direction to the Sun at the starting epoch t = 0.
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In the text

	Fig. 2 Changes in the distance between ’Oumuamua and stars listed in Tables 3 and 4. Only HIP 981 and TYC 5325-1808-1 are omitted due to their unreliable kinematic data. Please note a horizontal scale changein the middle of the plot.
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In the text

	Fig. B.1 Geometry of the encounter of ’Oumuamua with the star G 108-21 0.2 Myr ago. Depicted is 0.3 Myr of their motion.
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In the text

	Fig. B.2 Geometry of the encounter of ’Oumuamua with the star GJ 4274 23 kyr ago. 112 kyr of motion of these bodies is shown here.
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In the text

	Fig. B.3 Geometry of the encounter of ’Oumuamua with the star δ Capricorni 1.5 Myr ago. Their past motion over 3.74 Myr is shown.
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In the text

	Fig. B.4 Geometry of the encounter of ’Oumuamua with the star HIP 3757 118 kyr ago. 186 kyr of motion of these bodies is shown here.
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In the text

	Fig. B.5 Geometry of the encounter of ’Oumuamua with the star HIP 113020 0.8 Myr ago. Past motion during 3.74 Myr is shown.
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In the text

	Fig. B.6 Geometry of the encounter of ’Oumuamua with the star UCAC4 535-065571 2.14 Myr ago. Past motion during 3.74 Myr is shown.
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In the text