THE ORIGIN OF ASTEROID 162173 (1999 JU₃)

The orbital elements of JU₃ are given in Table 1; based on this orbit, it is possible to constrain the region of the main belt where it originated. A method for estimating the origin of Near Earth Objects (NEOs) is described in Bottke et al. (2002). More specifically, they numerically integrated the orbits of thousands of test particles, starting from the five most efficient source regions of NEOs. These source regions are (1) the ν₆ secular resonance at ∼2.15 AU, which marks the inner border of the main belt; (2) the Mars-crossing asteroid population, adjacent to the main belt; (3) the 3:1 mean-motion resonance with Jupiter at 2.5 AU; (4) the outer main-belt population between 2.8 and 3.5 AU; and (5) the Jupiter-family comets. According to this model for NEO sources, the orbit of JU₃ has a ∼80% probability to have been reached by objects that escaped through the ν₆ resonance, a ∼20% probability through the Mars-crossing asteroid population, and a negligible chance to have originated from the 3:1 mean-motion resonance with Jupiter or further away from the Sun, including Jupiter-family comets.⁷ Furthermore, all ν₆ source orbits have initial inclinations lower than 12° and 90% of them lower than 8°. The ν₆ secular resonance does not have a strong effect on the inclination of the asteroids that enter it. However, these asteroids have their orbital eccentricities increased to values that can render them Earth-crossers (Bottke et al. 2002).

In principle, the Mars-crossing asteroid population can originate from anywhere inward of 2.8 AU (Bottke et al. 2002). However, the simulations in Bottke et al. (2002) show that none of the Mars-crossing objects that originate beyond 2.5 AU reach the JU₃ orbit, so we consider the 20% probability of a Mars-crossing source to also be originally from the inner belt. These dynamical arguments constrain strongly the most likely source region to orbits between 2.15 and 2.5 AU and with inclinations lower than 8°.

In order for the Yarkovsky effect to move objects from the inner-belt region into the ν₆ resonance by decreasing the semi-major axis, their rotation has to be retrograde, as is the case of JU₃ (Müller et al. 2011). However, the spin axis of this asteroid could have changed either due to small impacts while the object was in the main belt or due to the YORP effect. So, although the current spin state of JU₃ does not necessarily constrain what it was when it formed, its current spin axis orientation is consistent with an inward orbital evolution into the ν₆ resonance.

The geometric albedo for JU₃ is p_v = 0.07 ± 0.01 (Müller et al. 2011; Campins et al. 2009; Hasegawa et al. 2008). The low-inclination inner belt contains four low-albedo asteroid families (defined here as geometric albedo <8%). These are the Clarissa, Erigone, Polana,⁸ and Sulamitis families (Figure 1(a)). The average geometric albedo of these three families is 0.059 ± 0.025 for Clarissa asteroids, 0.054 ± 0.013 for Erigone asteroids, 0.057 ± 0.015 for Polana asteroids, and 0.056 ± 0.013 for Sulamitis asteroids, based on NASA's Wide-Field Infrared Survey Explorer (WISE) observations (Masiero et al. 2011). In addition, this region contains a recently identified group of primitive asteroids (Gayon-Markt et al. 2012; Walsh et al. 2013), not contained within these four families. Although this group was identified by its Sloan Digital Sky Survey (SDSS; Parker et al. 2008) colors, asteroids with primitive colors or spectra (B, C, and P asteroids in the Tholen classification system) also have low albedos measured by NASA's WISE (Mainzer et. al 2011). Hence, we refer to this background group as the low-albedo and low-inclination background, and in Figure 1(b) we use the WISE observations to show its structure.

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Small asteroids like JU₃ (diameter ∼1 km) are unlikely to be primordial objects because their collisional lifetime is much shorter than the age of the solar system (Bottke et al. 2005). Thus, JU₃ must be a fragment of a larger object. Asteroid families and any collisionally evolved population of asteroids will yield small fragments in the size of JU₃, either during the family-forming event (a catastrophic disruption of a large asteroid tens to hundreds of kilometers in size) or during the collisional evolution that normally occurs in the asteroid belt.

Of the five possible source populations mentioned in Section 2.3, the low-albedo and low-inclination background is closest to the ν₆ resonance; in fact, the inner edge of this population is this resonance (Figure 1(b)). Hence, this background population has been and is currently delivering asteroids to the ν₆ resonance, with many of these asteroids large enough (∼1 km diameter) to produce JU₃. In fact, the background population contains more kilometer-sized objects than each of the four families. More specifically, the observed size distribution of the background population allows us to obtain an estimate of the abundance of kilometer-sized objects in it using Gayon-Markt et al. (2012, their Figure 5). Although the absolute magnitudes in Gayon-Markt et al. are complete only to about H_v = 15 (diameter of about 5 km assuming a 5% albedo), all plausible extrapolations yield a number of kilometer-sized background asteroids roughly twice those of the Polana family. A similar analysis for the other three families yields even greater ratios of kilometer-sized background to Erigone, Sulamitis, and Clarissa objects, respectively. Hence, the abundance of kilometer-sized objects favors background asteroids over each of these four families.

Since the cores of the four families are further from the ν₆ resonance than the background group of asteroids, it is important to estimate the ability of these families to deliver objects the size of JU₃ to the ν₆ resonance. Dynamical arguments show that the Polana family has already delivered objects with diameters of 1 km (and smaller) to the ν₆ resonance; this evidence has been described in Campins et al. (2010), so we will not go into details here. However, other factors make this family an unlikely source for JU₃; as we discuss in the next section, the colors and spectra of Polana family members are different from those for JU₃. In the other three families, the dynamics do not favor the delivery of objects the size of JU₃ to the ν₆ resonance. More specifically, the absolute magnitude (H_v) versus proper semi-major axis plot is used to estimate the size of the family members that reach the ν₆ resonance. Starting with the Erigone family (Figure 2(upper panel)), we see the characteristic "V"-shape, a feature known to be associated both with the size-dependent ejection velocity field, as well as with the drift in the proper semi-major axis "a_p" induced by the Yarkovsky effect⁹ (e.g., Vokrouhlický et al. 2006). The dashed curves in the figure show the H-dependent semi-major axis distribution induced by the Yarkovsky effect that best fit the boundaries of the observed distribution. Bodies below these curves are expected to be interlopers, i.e., not genetically linked to this family, or ejected with a sufficiently large initial velocity to have reached a significantly larger distance from the original semi-major axis. As expected, objects in these plots extend to both sides of the family's main fragment.

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In the direction of shorter semi-major axes¹⁰, the extrapolated Yarkovsky-induced distribution for the Erigone family predicts that objects with magnitude H_v ∼20.2 should reach the outer edge of the ν₆ resonance (at ∼2.15 AU for the inclination of 5° characteristic of this family; Morbidelli & Gladman 1998). For an Erigone-like albedo of p_v = 5.4%, this absolute magnitude translates into a diameter D = 0.5 ± 0.05 km, i.e., about half that of JU₃ (the uncertainties in fitting the Yarkovsky curves are approximately 20% in magnitude, which translate into diameter estimate uncertainties of 10%). Thus, no JU₃-sized Erigone family fragments have reached near-Earth orbits through the ν₆ resonance yet. There are other resonances between the core of the Erigone family and the ν₆ resonance that could deliver objects to near-Earth space, albeit with much lower efficiencies than the ν₆ resonance. For example, the 7:2 with Jupiter at 2.25 AU and the 5:4:1 three-body resonance Jupiter–Saturn–asteroid at 2.32 AU could deliver objects (Morbidelli & Nesvorny 1999); thus, JU₃-sized Erigone family fragments may have reached near-Earth orbits through these resonances. However, the background population is also contributing to these resonances, and in larger numbers, so the background asteroids seem to always dominate the Erigone family as a likely source of JU₃.

Similar arguments indicate that the Clarissa and Sulamitis families do not extend sufficiently toward the ν₆ resonance to deliver an object the size of JU₃. More specifically, the Yarkovsky-induced distribution for the Sulamitis family (Figure 2, middle panel) predicts that it should reach the outer edge of the ν₆ resonance (at ∼2.15 AU for the inclination of 5° characteristic of this family; Morbidelli & Gladman 1998) for objects with H_v = 20.5. For a Sulamitis-like albedo of p_v = 5.6%, this magnitude translates into a diameter D = 0.4 ± 0.04 km, again significantly smaller than that of JU₃. The Sulamitis family appears to be an important source of asteroids to the 3:1 resonance, but not to the ν₆ resonance. Since the Bottke et al. (2002) model rules out transport via the 3:1 resonance for the origin of JU₃'s current orbit, we do not favor the Sulamitis family as a likely source. For the Clarissa family (Figure 2, lower panel), objects with H_v = 23.6 reach the ν₆ resonance, which for a Clarissa-like albedo of p_v = 5.9%, this magnitude translates into a diameter D = 0.02 ± 0.002 km.

In summary, location and size distribution favor the low-albedo and low-inclination background over the four low-albedo inner-belt families, as the most likely source of JU₃.

We now consider the spectral information available on JU₃ and on the candidate sources. The available spectral evidence is nicely complementary to the dynamical and albedo constraints because it rules out one of the two remaining candidate populations, the Polana family, and is consistent with the background. Figure 3 shows three different spectra of JU₃ at visible wavelengths (0.4–1.0 μm; Binzel et al. 2001; Abe et al. 2008; Vilas 2008), and one near-infrared spectrum (0.8–2.4 μm; Abe et al. 2008). A more recent near-infrared spectrum (Pinilla-Alonso et al. 2013) is essentially identical to that in Abe et al. (2008), but the newer spectrum has lower signal-to-noise because the asteroid was fainter. We note that the three visible spectra are not entirely consistent with each other. For several reasons, we use the visible spectrum with highest signal-to-noise, which was obtained in 2007 September (Vilas 2008). This is the visible spectrum with the best 0.8–0.9 μm overlap with the near-infrared spectrum (Figure 3) and is essentially identical to three new spectra of JU₃ obtained during its 2012 apparition (Lazzaro et al. 2013).

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For the five potential source populations, there are 55 asteroids with available visible spectra from different surveys; these include the SMASS (Bus & Binzel 2002b), the S3 OS2 (Lazzaro et al. 2004), the NEMCASS (the Near-Earth and Mars-Crosser Asteroids Spectroscopic Survey; de León et al. 2010b), and SINEO (Lazzarin et al. 2004, 2005). These populations also have SDSS colors for a significant fraction of their members (Parker et al. 2008). The available spectra and the SDSS colors are sufficiently diagnostic to rule out the Polana family as a likely source of JU_3.

As stated in Section 1, JU₃ has been classified as a Cg-type asteroid in the SMASS classification system, and its near-infrared spectrum (Figure 3) is also consistent with those of C-type asteroids (e.g., DeMeo et al. 2009). Dynamically, the two populations most likely to be the source of JU₃ are the low-inclination and low-albedo background asteroids and the Polana family, in that order. At visible wavelengths, the background contains objects with C-type visible spectra or colors. In contrast, the available visible colors and spectra for the Polana family indicate that B-type objects are most abundant (e.g., Campins et al. 2010; Gayon-Markt et al. 2012). In Figure 4, we illustrate the spectral match between JU₃ and a member of the background (we found more than one good match), asteroid 917 Lyka, and the mismatch with a member of the Polana family, asteroid 142 Polana. So the available spectral and color information favors the background over the Polana family. We note that there is one member of the Polana family with a published C-type spectrum that matches that of JU₃, asteroid 3999, however, dynamical arguments suggest that this object is an interloper and not a real member of the family. In the case of the Erigone, Clarissa, and Sulamitis families, there is very little spectral information. However, this does not impact our conclusions since the orbital dynamics do not favor any of these three families as sources of JU₃.

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