Interstellar Interloper 1I/2017 U1: Observations from the NOT and WIYN Telescopes

We present observations of the interstellar interloper 1I/2017 U1 ('Oumuamua) taken during its 2017 October flyby of Earth. The optical colors B-V = 0.70$\pm$0.06, V-R = 0.45$\pm$0.05, overlap those of the D-type Jovian Trojan asteroids and are incompatible with the ultrared objects which are abundant in the Kuiper belt. With a mean absolute magnitude $H_V$ = 22.95 and assuming a geometric albedo $p_V$ = 0.1, we find an average radius of 55 m. No coma is apparent; we deduce a limit to the dust mass production rate of only $\sim$ 2$\times$10$^{-4}$ kg s$^{-1}$, ruling out the existence of exposed ice covering more than a few m$^2$ of the surface. Volatiles in this body, if they exist, must lie beneath an involatile surface mantle $\gtrsim$0.5 m thick, perhaps a product of prolonged cosmic ray processing in the interstellar medium. The lightcurve range is unusually large at $\sim$2.0$\pm$0.2 magnitudes. Interpreted as a rotational lightcurve the body has semi-axes $\sim$230 m $\times$ 35 m. A $\sim$6:1 axis ratio is extreme relative to most small solar system asteroids and suggests that albedo variations may additionally contribute to the variability. The lightcurve is consistent with a two-peaked period $\sim$8.26 hr but the period is non-unique as a result of aliasing in the data. Except for its unusually elongated shape, 1I/2017 U1 is a physically unremarkable, sub-kilometer, slightly red, rotating object from another planetary system. The steady-state population of similar, $\sim$100 m scale interstellar objects inside the orbit of Neptune is $\sim$10$^4$, each with a residence time $\sim$10 yr.

The orbit has perihelion distance q = 0.254 AU, eccentricity e = 1.197 and inclination i = 122.6 • . Perihelion occurred on UT 2017 September 09, five weeks before discovery. While 337 long-period comets are known with e > 1, in each case these are Oort cloud comets which have been accelerated above solar system escape velocity by planetary perturbations and/or reaction forces due to asymmetric outgassing (e.g. Królikowska & Dybczyński 2017).
U1 is special because the velocity at infinity is ∼25 km s −1 , far too large to be explained by local perturbations. It is the first interstellar interloper observed in the solar system (de la Fuente Marcos and de la Fuente Marcos 2017) and, as such, presents an opportunity to characterize an object formed elsewhere in our galaxy.

Observations
Observations were obtained on UT 2017 October 25/26 and 29/30 using the 2.5 meter diameter Nordic Optical Telescope (NOT), located on La Palma, the Canary Islands. We used the Andalucia Faint Object Spectrograph and Camera (ALFOSC) optical camera, which is equipped with a 2048×2064 pixel "e2v Technologies" charge-coupled device (CCD), an image scale of 0.214 pixel −1 and a vignet-limited field of view approximately 6.5 ×6.5 .
Broadband Bessel B (central wavelength λ c = 4400Å, full width at half-maximum FWHM = 1000Å), V (λ c = 5300Å, FWHM = 800Å) and R (λ c = 6500Å, FWHM = 1300Å) filters were used. The NOT was tracked at non-sidereal rates to follow U1, while autoguiding using field stars. We obtained a series of images each of 120 s integration during which time field objects trailed by ∼7.5 . The images were first bias subtracted and then normalized by a flat field image constructed from images of the sky. The target was readily identified in the flattened images from its position near the center of the image and its stellar appearance while all other field objects were trailed. Photometric calibration of the data was obtained by reference to standard stars L92 355, L92 430 and PG +0231 051. Measurements of the stars show that both nights were photometric to ∼ ± 0.01 magnitudes. Seeing was approximately 1.1 FWHM. Image composites formed by shifting the R-band images to a common center are shown in Figure (1).
Observations were also taken on UT 2017 October 28 using the 3.5 meter diameter WIYN telescope, located at Kitt Peak National Observatory in Arizona. We used the One Degree Imager (ODI) camera, a large CCD array which is mounted at the Nasmyth focus and has an image scale of 0.11 pixel −1 (Harbeck et al, 2014). Observations were taken through the Sloan g' (λ c = 4750Å, FWHM = 1500Å), r' (λ c = 6250Å, FWHM = 1400Å) and i' filters (λ c = 7500Å, FWHM = 1250Å). Seeing was variable in the range 0.8 to 1.2 . Non-sidereal guiding with ODI is implemented through a guide window in the focal plane and is limited by the window size. We obtained 40 red filter integrations each of 180 s, each resulting in stellar images trailed by ∼ 9.5 . Data reduction was performed using the Quickreduce pipeline (Kotulla 2014), and photometric calibration of the data was made with reference to the Pan STARRS system (Magnier et al. 2016). Subsequent transformation from the Sloan filters to BVR filters employed at the NOT was made according to Jordi et al. (2006).

Photometry
We used two-aperture photometry to measure the NOT images. By experimentation, we selected a photometry aperture 10 pixels (2.14 ) in radius to measure U1, but scaled the measurement to a 30 pixel (6.42 ) radius aperture using measurements of the standard stars to estimate the flux between the two. Sky subtraction was determined from the median signal in a concentric annulus extending from 6.42 to 17.12 , for both U1 and the standard stars. Two-aperture photometry is useful when, as here, the target is faint because it reduces the uncertainty introduced by the sky noise.
The apparent magnitudes are listed in Table (2). U1 showed strong brightness variations on each night of observation, as well as progressive fading between nights due to the changing observational geometry (Table 1). We computed absolute magnitudes using where r H and ∆ are the heliocentric and geocentric distances expressed in AU, and Φ(α) is the phase function at phase angle α. We used Φ(α) = βα, with β = 0.04 magnitudes degree −1 . This linear darkening function neglects brightening due to opposition surge but is suggested by observations of numerous low albedo asteroids at phase angles comparable to those of U1. It should provide a useful correction for phase effects over the limited range of angles swept by U1 in our data.
From the absolute magnitude we estimate the effective scattering cross-section, C e [m 2 ], using in which p V is the V-band geometric albedo and H V is the absolute V-band magnitude.
The albedo of U1 is observationally unconstrained. However the albedos of most solar system bodies are within a factor of three of p V = 0.1, so we adopt this value.
In the WIYN data, the average absolute red magnitude is H R ∼ 22.5 ( Figure 2). With V-R = 0.45 and using Equation (2), the mean magnitude corresponds to C e = 9.9 × 10 3 m 2 and to an equal-area circle of radius (C e /π) 1/2 = 55 m. With this radius and nominal density ρ = 10 3 kg m −3 , the approximate mass of U1 is ∼10 9 kg.

Lightcurve
Variations in H R ( Table (2) and Figure (2)) strongly suggest rotation of an irregular body. The absolute magnitude varies in the range 21.5 H R 23.5, corresponding to cross-sections 4×10 3 C e 25 × 10 3 m 2 by Equation (2). Interpreted as a shape effect due to rotation of an a × a × b ellipsoid about minor axis a, we find b = 230 m and a = 35 m. The implied ∼6:1 axis ratio is a lower limit because of the effects of projection, and is extreme relative to most asteroids (c.f. Masiero et al. 2009, Dermawan et al. 2011, Hergenrother and Whiteley 2011. However, we note that the 5 km diameter asteroid 4116 (Elachi) shows a range of 1.6 magnitudes (b/a = 4.3:1) that is almost as large (Warner and Harris 2011). The lightcuve of U1 might result from shape and albedo variations combined.
We used phase dispersion minimization to estimate the possible rotational periods of U1. We combine the data from Table (2) with measurements from UT October 30 reported by Knight et al. (2017), which we digitized and reduced to absolute magnitudes. No unique solution was found, owing to aliasing in the data caused by incomplete temporal coverage.
One of the possible lightcurve periods, P = 8.256 hr, is shown for illustration in Figure (3).
We expect that the addition of photometry from other telescopes will be used to improve the accuracy of the rotational period. However, finding the exact period is scientifically less important than the observation that the period of U1 falls squarely within the range of values observed for small asteroids in our solar system (Masiero et al. 2009).
Approximating the shape of U1 as a strengthless a × a × b ellipsoid with b > a and in rotation about a minor axis, we can estimate the density needed to retain material against loss to centripetal forces. We find where G is the gravitational constant. With b/a ∼ 6 and P = 8.3 hr, we obtain ρ ∼ 6,000 kg m −3 , an implausibly high density that means only that U1 has non-negligible cohesive strength.

Colors
Unfortunately, the color data at NOT were interleaved too slowly to follow the lightcurve variations, so that substantial corrections for the rotational variation of the scattered light must be made when computing the B-V and V-R color indices. For this purpose, we plotted the multi-filter color data as a series and applied vertical adjustments to the measurements in order to produce a smooth lightcurve ( Figure 4). This procedure is valid provided the color of U1 is constant with respect to rotation, as is true for most asteroids. The resulting colors are On a color-color diagram of the small-body populations of the solar system ( Figure 5) the optical colors of U1 are seen to be similar to the colors of the D-type Jovian Trojans and several other inner-solar system groups, including the nuclei of both short-period (Kuiper belt) and long-period (Oort cloud) comets (Jewitt 2015). On the other hand, the colors are quite different from the ultrared matter that is abundant in the outer solar system. Specifically, the ultrared matter has, by definition (Jewitt 2002), a spectral slope S > 25%/1000Å corresponding to B-R > 1.60, whereas the color of U1 is B-R = 1.15±0.05. The normalized optical reflectivity gradient of U1 has been measured from -8spectra, albeit with very large uncertainties, as S = 30±15%/1000Å (Masiero 2017) and S = 10±6%/1000Å (Ye et al. 2017).

Image Profile
The left-hand panel of Figure  3. Discussion

Comet or Asteroid?
In order to place a limit to the outgassing of a coma implied by the non-detection of extended surface brightness, we need to know the morphology of the ejected material in the sky plane. If the coma is produced in steady-state then, by the equation of continuity, the surface brightness of ejected dust should fall inversely with the angular distance from the nucleus, θ. In this case, the relation between the total magnitude of the coma, m C , and the surface brightness at angular distance θ, Σ(θ), is (Jewitt and Danielson 1984) From the profile ( Figure 6) we determine that, at θ = 2 , a systematic brightening of the PSF by ∼1% of the peak surface brightness would be detectable, corresponding to Σ(2 ) = 28.8 magnitudes arcsecond −2 . Substituting into Equation (5) gives the integrated magnitude of such a coma as m C = 25.3, which is fainter that the measured median R-band magnitude on this date, m R = 21.4, by δm = m C − m R = 3.9 magnitudes. Therefore, a steady-state coma can carry no more than 10 −0.4δm ∼ 3% of the total cross-section of U1.
With average C e ∼ 10 4 m 2 , the upper limit to the dust cross-section is only C d < 300 m 2 .
Interpretation of this limit to the dust cross-section is highly model dependent, with the major unknowns being the particle size and the particle velocity. In natural power-law size distributions, the cross-section is usually dominated by particles with size comparable to the wavelength of observation. Given the wavelengths of our observations, we assume a particle radius a = 10 −6 m. We determine an upper limit to the rate of mass loss in micron-sized particles as follows. We assume that the particles are well-coupled to the outflowing gas so that they leave at the sound speed appropriate to the local equilibrium temperature, V d ∼ 500 m s −1 . The mass of dust is M d ∼ ρaC d , where ρ = 10 3 kg m −3 is the assumed dust density. Substituting gives M d < 0.3 kg. The linear distance corresponding to 2 at geocentric distance ∆ = 0.458 AU is = 6.7×10 5 m and the time for a dust particle to cross this distance is τ = /V d ∼ 1400 s. The order of magnitude production rate is then dM d /dt = M d /τ < 2×10 −4 kg s −1 . For comparison, we calculated f s , the sublimation flux from an exposed, perfectly absorbing water ice surface oriented normal to the Sun and located at r H = 1.4 AU, finding f s = 2.3×10 −4 kg m −2 s −1 . The limit to the near-nucleus dust in U1 thus sets a limit to exposed ice on the surface of the body of area A = f −1 s dM d /dt ∼ 1 m 2 . Expressed as the fraction of the projected surface area of the (assumed) ellipsoidal nucleus, this is f A = A/(πab) 10 −5 and we emphasize that this is an upper limit because we have assumed the maximum speed (and minimum residence time) for the dust particles in the near-nucleus environment. For comparison, the nuclei of weakly active cometary nuclei have f A ∼ 10 −2 (A' Hearn et al. 1995).
The absence of measurable coma thus shows that the surface of U1 contains little ice.
However, we cannot conclude from this that U1 is an asteroid. The transport of heat by conduction in a solid is controlled by the thermal diffusivity, κ, equal to the ratio of the thermal conductivity to the product of the density and the specific heat capacity. Common solid dielectric materials (rock, ice) have κ ∼10 −6 m 2 s −1 but the porous materials found in the regoliths of asteroids and comets have much smaller values, κ ∼ 10 −8 m 2 s −1 or even smaller. The timescale to conduct heat over a distance, d, is given by t c = d 2 /κ. U1 travelled from the orbit of Jupiter, where water ice sublimation typically begins, to discovery in about 8 months, or 2×10 7 s. Setting t c = 2×10 7 s and κ = 10 −8 m 2 s −1 , we estimate the thermal skin depth (at which the temperature is ∼ 1/e times the surface temperature), to be d = (κt c ) 1/2 ∼ 0.5 m. Ice at substantially larger depths would remain close to the interstellar temperature ∼10 K, impervious to the heat of the Sun even at perihelion (where the blackbody temperature is ∼ 560 K). Therefore, it is not possible to state based on the current observations whether U1 is an asteroid or a comet, except in the purely observational sense dictated by the absence of measurable coma. A meter-thick mantle of involatile, cosmic ray-irradiated material is expected from long-duration exposure in the interstellar medium (Cooper 2003) and could explain the inactivity of U1. It is even possible that slow inward propagation of perihelion heat will activate buried ice some time in the future, as has been observed in some outbound comets (e.g. Prialnik and Bar-Nun 1992). For this reason, we encourage continued observations of U1 as it leaves the solar system.

Statistics
Lastly, in Figure (7)  U1 is a very small object fortuitously detected in a magnitude-limited survey because it passed close to the Earth (Figure 7). Consider that the apparent brightness of an object in reflected light, all-else considered equal, depends on the product a 2 ∆ −2 , where a is the object radius. An object 10x larger than U1 would be equally bright at 10x the geocentric distance and could be detected in a magnitude-limited survey, of equal sensitivity, within a volume ∆ 3 = 10 3 times larger. We represent the size distribution of interstellar objects, per unit volume, by a power law such that the number of objects with radii between a and a + da follows N 1 (a)da = Γa −q da, with Γ and q constant. Then the number observationally accessible in a magnitude-limited survey should scale as N 1 (a)a 3 da ∝ a 4−q . The small size of the first detected interstellar object is an indication (subject to the limitations of the statistics of one) that the size distribution index is steep (q 4).
It is interesting to consider the implications of U1 for the statistics of interstellar objects in the solar system. The rate of detections of U1-like objects is S = N 1 π(r 1 + ∆) 2 F v ∞ Ψ, where N 1 is the number of objects per unit volume, r 1 = 1 AU is the radius of the Earth's orbit, F is the gravitational focusing factor by which orbits of interstellar bodies are concentrated owing to the Sun's gravity, v ∞ is the velocity at infinity and Ψ is the probability of passing within a distance ∆ of Earth. The gravitational focusing factor is where v e is the escape velocity at r 1 . We take v e = 42 km s −1 , v ∞ = 25 km s −1 to find F = 4. Given a random distribution of entering objects, Ψ ∼ ∆ 2 /(r 1 + ∆) 2 and, with ∆ = 0.4 AU, we find Ψ ∼ 0.1. The detection of U1 by Pan STARRS (which has been operating at full efficiency for moving object detections for only a year or two) implies a rate S ∼ 0.5 to 1 year −1 . Solving for the density of objects, we find N 1 ∼ 0.1 AU −3 , and ∼10 15 pc −3 . The latter number exceeds even the highest pre-detection estimates by an order of magnitude (Moro-Martin et al. 2009). From N 1 we estimate that, at any one time, there are ∼ 10 4 interstellar bodies of U1-size closer to the Sun than Neptune. Each takes ∼10 years to cross the planetary region before returning to interstellar space.

Summary
We present observations of the interstellar object 1I/2017 U1. We find that: 3. The lightcurve is consistent with a two-peaked period of ∼8.256 hr, but the period is not definitively determined as a result of aliasing in the data. This period is unremarkable relative to the periods of similarly-sized solar system small-bodies. 4. No coma is detected, setting a limit to the rate of loss of micron-sized dust particles 2×10 −4 kg s −1 . Water ice covering a few m 2 of the surface would sublimate at this or a larger rate, in thermal equilibrium with sunlight. The ice-covered fraction of the surface is 10 −5 , some 10 2 or 10 3 times smaller than is typical for the nuclei Jupiter family comets.
5. The thermal conduction skin depth for U1's 8-month plunge through the inner solar system is only ∼0.5 m. Ice could survive at near-interstellar temperatures beneath a thin refractory mantle, perhaps consisting of material rendered involatile by prolonged exposure to cosmic rays in the interstellar environment.
6. The number density of U1-like interstellar objects is ∼0.1 AU −3 , meaning that ∼10 4 such objects exist closer to the Sun than Neptune.       The large yellow circle marks the color of the Sun. Letters show asteroid spectral types according to Dandy et al. (2003). Error bars on U1 are ±1σ from the NOT data. All other error bars are the 1σ errors on the means of many measurements per population.