`Oumuamua as a messenger from the Local Association

With a hyperbolic trajectory around the Sun, `Oumuamua is the first confirmed interstellar object. However, its origin is poorly known. By simulating the orbits of 0.23 million local stars, we find 109 encounters with periastron less than 5 pc. `Oumuamua's low peculiar velocity is suggestive of its origin from a young stellar association with similar velocity. In particular, we find that `Oumuamua would have had slow encounters with at least five young stars belonging to the Local Association thus suggesting these as plausible sites for formation and ejection. In addition to an extremely elongated shape, the available observational data for `Oumuamua indicates a red colour suggestive of a potentially organic-rich and activity-free surface. These characteristics seem consistent with formation through energetic collisions between planets and debris objects in the middle part of a young stellar system. We estimate an abundance of at least 6.0$\times10^{-3}$ au$^{-3}$ for such interstellar objects with mean diameter larger than 100 m and find that it is likely that most of them will be ejected into the Galactic halo. Our Bayesian analysis of the available light curves indicates a rotation period of $6.96_{-0.39}^{+1.45}$ h which is consistent with the estimation by Meech et al. 2017 and shorter than other literature. The codes and results are available on https://github.com/phillippro/Oumuamua.


INTRODUCTION
A/2017 U1 was discovered in the Pan-STARRS survey in Hawaii by Robert Weryk and was later found to be on a hyperbolic orbit with an eccentricity of e = 1.1994 ± 0.0002, semi-major axis of a = −1.2805 ± 0.0009, perihelion of q = 0.25529 ± 7.8 × 10 −5 , and an inclination of i = 122.682 ± 0.007 based on the NASA/JPL Horizons On-Line Ephemeris System (Giorgini et al. 2001). This leads to a pre-encounter velocity of 26.33±0.01 km/s and (U, V, W ) = (−11.427 ± 0.006, −22.425 ± 0.004, −7.728 ± 0.007) km/s. Its high pre-encounter velocity strongly favor an interstellar origin leading to its Hawaiain name of Oumuamua is intended to reflect that this object is like a scout or messenger sent from the past to reach out to us. As the first interstellar object discovered in the Solar System its original discovery name of A/2017 U1 has been revised by the International Astronomical Union with the new designation of "I" for interstellar objects, with Oumuamua being designated 1I and maybe known as 1I, 1I/2017 U1, 1I/'Oumuamua and 1I/2017 U1 ('Oumuamua) 1 .
No coma of 'Oumuamua is detected (Jewitt et al. 2017) and spectroscopic observations do not show any signs of activity on 'Oumuamua (Fitzsimmons et al. 2017;Masiero 2017;Ye et al. 2017;Meech et al. 2017). Thus it is probably an asteroid ejected from the warm part of an extra-solar system (Ye et al. 2017). Photometric monitoring of this target support a double peaked rotation period of about 8 h (Knight et al. 2017;Bolin et al. 2017;Jewitt et al. 2017) while (Meech et al. 2017) reported a shorter period of 7.34 h based on more than 100 data points. The rotation-induced magnitude variation suggest a semi-axes of about 230 m×35 m, corresponding to a 6:1 axis ratio and thus indicating albedo variation on the surface (Jewitt et al. 2017). A higher axis ratio is estimated by Meech et al. (2017), indicating a rare cigar-shaped body.
Various scenarios have been proposed to explain 'Oumuamua's origin (Mamajek 2017;Gaidos et al. 2017;Portegies Zwart et al. 2017). Gaidos et al. (2017) argue that it was probably from the young Carina and Columba Associations due to similar UVW velocities. Its small peculiar velocity also suggests a lack of close encounters with stars and thus a short period of drifting in the Galaxy. On the other hand, Mamajek (2017) and Portegies  propose the Galactic interstellar-object debris as its origin due to a lack of appropriate candidates for its original home and an apparent thermalization of 'Oumuamua's velocity.
In this work, we argue that 'Oumuamua was plausibly ejected from a stellar system in the Local Association (or Pleiades moving group; Montes et al. 2001) based on numerical and statistical arguments. The paper is structured as follows. We identify stellar encounters of 'Oumuamua based on numerical integration of stellar orbits in section 2. Then we argue that 'Oumuamua is young by investigating its kinematics and light curves in section 3. We discuss and conclude in section 4.

POSSIBLE LOCATIONS FOR THE ORIGIN OF 'OUMUAMUA
To find the origin of 'Oumuamua, we derive the pre-encounter velocity by integration of the orbit of 'Oumuamua backward to AD 1600 using the JPL HORIZONS service, following Mamajek (2017). The heliocentric position and velocity of 'Oumuamua in the Galactic coordinate system is (X, Y, Z) = (1011. 69±0.54, 1982.13±0.35, 684.52±0.66) au and (U, V, W ) = (−11.427 ± 0.006, −22.425 ± 0.004, −7.728 ± 0.007) km/s, respectively. We then adopt the Galaxy model and the Sun's initial conditions from Feng & Bailer-Jones (2014) and follow Feng & Jones (2018) to use the Bulirsch-Stoer method (Bulirsch & Stoer 1964) to integrate the orbit of 'Oumuamua with a time step of 1 kyr under perturbations from the Sun and the Galactic tide back to 100 Myr ago. According to our tests, the energy and angular momentum are conserved to a precision of 10 −8 over 1 Gyr (Feng & Jones 2018). We further identify close encounters by comparing 'Oumuamua's orbit with the orbits of the 0.23 million stars in the FS catalog (Feng et al. 2017a). Finally, we identify 109 encounters with periastron less than 5 pc and with reliable astrometry and radial velocity data. By drawing 1000 clones from the uncertain initial conditions for each encounter and integrating their orbits, we calculate the encounter parameters and their uncertainties. We use 5% and 95% quantiles to measure the uncertainty. We use the minimum encounter distance, d enc to represent the 5% quantile since small d enc is typically not well sampled (see Feng et al. 2017a for details). The results for the 109 encounters are available at http://star-www.herts.ac.uk/~ffeng/Oumuamua/.
From this sample, we select encounters either with periastron less than 2 pc or with relative velocity less than 10 km/s and show them in Table 1. These encounters are plausible candidates of origin because the probability of finding a random encounter with relative velocity less than 10 km/s is about 7×10 −3 , assuming an Maxwell-Boltzmann distribution for the encounter velocity with a mean velocity of 53 km/s (Rickman et al. 2008;Feng & Bailer-Jones 2014). For example, the probability of finding HIP 113020 with v enc = 4.91 km/s and d enc = 2.36 pc in the sample of 24 encounters with d enc < 2.5 pc is about 2%. On the other hand, according to the conservation of energy, 'Oumuamua would be significantly decelerated during its ejection, leading to a relative velocity typically less than 5 km/s (Zuluaga et al. 2017). Thus the slow and close encounters in Table 1 are rare but plausible candidates for the origin of 'Oumuamua.   belonging to five other moving groups and associations. According to Montes et al. (2001), the Local Association has an age ranging from 20 to 150 Myr and a mean U V W of (−11.6, −21.0, −11.4) km/s which only differs from the 'Oumuamua's veloctiy by 4 km/s. Although the Carina and Columba Associations do have similar velocities (Gaidos et al. 2017) and many of these group members are included in the FS catalog, we find no encounters belonging to these two groups. Considering that some members of the Local Association have approached 'Oumuamu with small relative velocity and distance, 'Oumuamua was probably ejected from a young stellar system in the Local Association. We further constrain its origin and age in the following section.

Kinematic constraint
The population of asteroids and comets is depleted by the accretion and scattering process during the formation of planets. Thus 'Oumuamua is likely to be ejected from a stellar system during its early evolution when the system is dynamically hot. Hence the age of 'Oumuamua is approximately the time scale of its migration in the Galaxy after being ejected. As observed by Gaidos et al. (2017), 'Oumuamua moves relatively slowly with respect to the Local Standard of Rest (LSR). The velocity difference is less than 10 and 3 km/s for the LSR determined by Coşkunoǧlu et al. 2011 andby Schönrich et al. 2010, respectively. Such a low velocity difference is also observed in many young stellar associations (Montes et al. 2001;Torres et al. 2008), and thus seems to support a young age of 'Oumuamua. As an interstellar object migrates in the Galaxy, its dynamics would potentially be altered by stars, molecular clouds, spiral arms, star clusters, etc. and gradually deviate from the LSR. For example, Oumuamua's encounter with the Solar System will significantly alter its orbit and drive it away from the LSR. This so-called "disk heating" mechanism is intensively studied and observed (e.g., Dehnen & Binney 1998;Holmberg et al. 2009). For example, the total velocity dispersion increases from ∼30 km/s to ∼60 km/s if the age τ (in units of Gyr) increases from 1 to 10 Gyr following the relation of σ tot ∼ τ 0.34 according to Holmberg et al. (2009). Assuming a similar heating mechanism for 'Oumuamua-like objects, the probability of observing them with a velocity less than 10 km/s with respect to the LSR would be 0.50, 0.26, and 0.13 for an age of 0.1 Gyr, 1 Gyr and 10 Gyr, respectively. This probability would be halved for a peculiar velocity less than 5 km/s (e.g., with respect to the LSR determined by Schönrich et al. 2010). Moreover, low mass objects are more likely to be scattered by encounters according to the conservation of momentum. Thus encounters will change the orbits of low mass objects more significantly, which is one of the reasons why low mass (or late type) stars tend to have higher velocity dispersion than massive ones (e.g., fig. 5 of Dehnen & Binney (1998)). Therefore, the kinematics of 'Oumuamua favors a recent origin or ejection.

Physical constraint
We also investigate the origin of 'Oumuamua by estimating its rotation period and axis ratio using the light curves measured by the Nordic Optical Telescope (NOT) and the Wisconsin-Indiana-Missouri-NOAO telescope (WIYN) (Jewitt et al. 2017 According to Meech et al. (2017), 'Oumuamua is a red and extremely elongated interstellar asteroid with an axis ratio of 10:1 if modeling the light curve with a triaxial ellipsoid. A combination of the data from Meech et al. (2017) and the other data sets may lead to an axis ratio between 6:1 to 10:1. Such an elongated shape is rarely seen in the Solar System. Its neutral or slightly red color (Bannister et al. 2017;Meech et al. 2017) indicates an organic-rich surface found in comets/asteroids in the outer Solar System although no cometary activity has been detected (Ye et al. 2017). Considering that the cometary population is a few orders of magnitude higher than the asteroid population in well-evolved Sun-like systems (Feng & Bailer-Jones 2015), 'Oumuamua was more likely to be ejected from the middle part of a young stellar system. If it was too close to the star, it is unlikely to be organic rich. But if it was too far away from its host star, it would be icy and show cometary activity during its encounter with the Solar System. Moreover, a young stellar system is dynamically hot, and abundant in debris objects, and thus are more likely to be the source of interstellar objects like 'Oumuamua. On the other hand, its extremely elongated shape and high density (Meech et al. 2017) is probably related to energetic collisions between minor bodies or planets such as the Late Heavy Bombardments caused by planet migration (Gomes et al. 2005). In addition, the color of 'Oumuamua is not as red as some Kuiper Belt Objects (KBOs) which have been reddened by space weathering such as cosmic ray and interstellar medium (Jewitt 2002;Jedicke et al. 2004). Hence it seems less likely to have travelled for Gyrs before encountering the Solar System. It is interesting to consider the density of interstellar star formation debris, based on Portegies  and Hanse et al. (2017)'s numerical investigations, the population of unbound non-cometary asteroidal objects is much larger than that of cometary objects. Thus along with the likelihood of such objects being readily scattered to a higher velocity distribution (Section 3.1) it appears that they are an unaccounted for constituent of the mass of the halo of our galaxy.
To derive the density of 'Oumuamua-like objects, we use the following equation to model the encounter rate F , where n is the number density of interstellar objects, v enc is encounter velocity, σ is its cross section. The cross section is approximately πd 2 max , where d max is the maximum encounter distance. The mean encounter velocity is at least 50 km/s according to Rickman et al. (2008);Feng & Bailer-Jones (2014);Feng et al. (2017a). Since 'Oumuamua is the first interstellar object humans have so far recognised, we assume that the encounter rate of an 'Oumuamua-like object (with a size 100 m) with impact parameter less than 0.5 au 2 per 20 years 3 is 1. Hence there would be 1.4 × 10 13 interstellar objects with mean diameter larger than 100 m per pc 3 or 6.0 × 10 −3 au −3 , which is higher than the value of 1.4 × 10 −4 au −3 derived by Engelhardt et al. (2017) who consider interstellar objects with > 1 km diameter.
Our value is lower than the density derived by Portegies  since they only consider the non-detection in the Pan-STARRS1 survey. It is also slightly lower than that in Laughlin & Batygin (2017) probably because they have adopted a low mean encounter velocity. Since the sensitivity of asteroid surveys to 'Oumuamua-like objects increases with time, the non-detection period could be shorter than 20 years. Hence our estimation is a lower limit of the abundance of interstellar objects.

DISCUSSION AND CONCLUSION
Based on the kinematics of 'Oumuamua, we find 109 encounters with a nominal encounter distance less than 5 pc. There are 17 stars with an encounter distance less than 2 pc or with relative velocity less than 10 km/s. Five slow encounters in the whole sample belong to the Local Association while most of the others are field stars, indicating an origin of 'Oumuamua in the Local Association. We note that the reader might be wondering about a future observer in some other solar system who might detect 'Oumuamua and integrate its orbit backwards to discover that the object came directly from the Solar System and then conclude a Solar System origin. While this is a possible way to underestimate the age of 'Oumuamua, we argue that velocity is more important than distance in finding candidates since velocity follows an Maxwell distribution while distance follows a power law distribution. We find that slow and close encounters are rare but plausible candidates for the origin of 'Oumuamua.
Moreover, we consider that 'Oumuamua's low velocity with respect to the LSR indicates a short period of interstellar travel. The interpretation of 'Oumuamua having a relatively young age is further supported by its relatively neutral color due to a lack of long-term exposure to bombardments from the interstellar medium and cosmic rays. Its extremely elongated shape is rarely seen in the Solar System and is probably caused by energetic events such as planetary collisions and impacts. It is asteroidal and its surface is organic rich but without observable cometary activities, suggestive of an origin in the middle part of a young stellar system.
We estimate a number density of at least 6.0 × 10 −3 au −3 for interstellar objects with diameter larger than 100 m, in agreement with previous results. Such a number density seems to be much lower than the expected value assuming that extra-solar systems form in a similar way as the Solar System (Engelhardt et al. 2017). This discrepancy is probably not due to a different formation mechanism as Engelhardt et al. (2017) suggest but due to the gravitational scattering of interstellar objects by stars and floating planets. According to the conservation of momentum, low-mass objects are more likely to be scattered than high-mass ones and thus such objects more easily accelerated to escape the Galaxy or to float into the Galactic halo.
Current microlensing surveys are sensitive down to objects with masses of so called super-Earth planets (Mróz et al. 2017). Future missions such as WFIRST are expected to probe masses down to that of Mars (Spergel et al. 2015). Nonetheless more objects such as Oumuamua will enable a local determination of the density of unbound debris from star formation and thus a comparison with expected interstellar planetesimal flux from the star formation process and an estimation of the contribution of such objects to the mass of the Galactic halo.
Interstellar objects may also bombard the Earth and cause catastrophic events such as mass extinctions (Bailer-Jones 2009). Since these objects are anisotropic in velocity due to the solar apex motion (Feng & Bailer-Jones 2014), they would probably form anisotropic impact craters on terrestrial planets and moons such as the lunar craters (Williams et al. 2016). The high velocity of interstellar objects means that for a given size and frequency they have the potential to cause relatively more catastrophic events such as mass extinctions (Alvarez & Muller 1984) than Solar System minor bodies.
Our search of the origin home of 'Oumuamua is limited by the precision of astrometry and radial velocity data. The upcoming Gaia data releases (Brown 2017) will provide accurate astrometry and stellar parameters for more stars and thus enable a more comprehensive study for the origin of 'Oumuamua.