axial ratios remains to be determined, but the important point is that the current best upper limit for axial ratios with respect to VSAs is around 3, and it would be unusual to find a VSA with an axial ratio far above that. There are two caveats worth noting however. Firstly, large axis ratios result in large magnitude variations between telescopic exposures, and may cause high-amplitude bodies to be missed entirely, biasing our sample. Secondly, our method of determining axis ratios from the light curve from the formula of Kwiatkowski et al. (2010a) provides a lower limit. As a result, the axis ratios of small NEAs may be systematically larger than reported here.

Nakamura et al. (2011) concluded that small fast-rotating asteroids have a tendency to be more spherical than slowly rotating asteroids, but Kwiatkowski et al. (2010a) reportedj ust the opposite. In Fig. 3 we find little correlation between the asteroid periods and their \( a / b \) ratios. Least squares fits to our samples do have slight upslopes however, 0.0198 \( \mathrm { h r } ^ { - 1 } \) on the upper panel, and 0.0835 \( \mathrm { h r } ^ { - 1 } \) on the lower panel, so our samples do have a nominal weak correlation. But these slopes are heavily leveraged by a few points at the right-most edge of the figures and should be interpreted with caution.

Histograms of the axial ratios of our two samples are given in Fig. 4. The \( a / b \) ratio sample has mean and median \( a / b \) ratios of 1.43 and 1.29. Our \( D \le \) 60 m sample does not have enough information to compute axis ratios for all its members, but the mean and median \( a / b \) ratios of the 46 members of the \( a / b \) sample with diameters below 60 m are 1.46 and 1.36 respectively, consistent with the idea that size and axis ratio are not strongly correlated.

We note that there has been some discussion in the literature surrounding the determination of \( a / b \) ratios in Nakamura et al. (2011). Already in 2009, Warner et al. pointed out that low light curve amplitudes (which result in concomitantly smaller axis ratios) may simply be a result of finding the highest amplitude spectral peak in noisy data. In the LCDB itself, a significant portion of the data are in the quality range of \( U \leq 1 + \), meaning that they are of doubtful quality. A fuller explanation as to why some of this data were given such a low quality rating can be additionally found in Warner et al. (2009).

# 3.3. Taxonomic class and density

In addition to period and effective diameter, the LCDB also records the taxonomic class. Out of the 88 asteroids in our \( D \le \) 60 m survey, 83 asteroids were of S-type (silicaceous “stony” objects), and out of the 92 asteroids in our \( a / b \) ratio sample (which does overlap partially with the previous sample), 89 were of S-type as well, making it the most common type in our specific asteroid population. The few other spectral types that were seen in the population were four asteroids in the C-group (carbonaceous objects, including one type B and one F), and three others being in the X-group (metallic objects). It is believed that 20% (Brophy et al., 2012) of the near-Earth asteroid population is C-type, but that they are harder to discover because of their lower albedos. Thus the C types are underrepresented in our sample, reflecting the reality that our observed sample is sharply limited by target brightness. We are not arguing here that the real NEA population is low in C types, but the set of potential targets for the ARM mission is likely to be.

Taxonomic class is linked to asteroid density, but for S-type asteroids we must take the size into consideration as well since, as Carry (2012) observes, the density of S-type asteroids appears to increase with mass. If we look at Fig. 9 in the paperj ust mentioned, S-type asteroids in the ARM size range would have an average bulk density of around 2.6 g \( \mathrm { c m ^ { - 3 } } \), though the density of S-type can be as low as 1.9 g \( \mathrm { c m } ^ { - 3 } \) such as for Itokawa (Fujiwara et al., 2006). Given the predominance of S types among the small near-Earth asteroid population, it is reasonable to conclude that the density of most potential ARM targets will be in the same range though the density of a specifically

chosen C-type target would be lower, around 1 g \( \mathrm { c m } ^ { - 3 } \)(Britt et al., 2002). The composition, mass and internal properties (rubble pile versus monolith) will all play a role here.

# 4. Conclusions

We have collected the available data on very small asteroids (VSAs) with the highest quality light curves. Unsurprisingly, a VSA will most likely be found to have a period under the “spin barrier” of 2.2 hrs; the average period from the \( D \le \) 60 m sample analyzed here is 0.67 hrs or 40 minutes. The lower limit for the period of the current sample reaches down to 25 seconds (2010 \( \mathrm { J L } _ { 8 8 } \), a 13 m diameter S-type) or even less (2014 RC, a 12-22 m Sq-type, with a period of 16 seconds) though shorter periods are possible.

With respect to structure, our results imply that a VSA will probably be a monolithic structure in which a singular boulder is held together by its own tensile strength, as opposed to a “rubble pile” in which many boulders are gravitationally bound together, although arguments from Holsapple (2003) and new evidence from Mommert et al. (2014) show that this may not necessarily be true.

We used the information on the light curves provided by various surveys to estimate the axial ratio. The VSAs in our samples have an average minimum \( a / b \) ratio of about 1.4, and the VSA with the greatest axial ratio was found to be 2007 \( \mathrm { T S _ { 2 4 } } \) at 2.8. Alternate analyses of some asteroid light curves have given slightly different values, but all VSAs observed to date are consistent with axial ratios less than three. The mission outlined by the KISS report discussed a capture bag capable of accommodating a 10x15 meter asteroid with a 2:1 axis ratio. Most (\( > \) 90%) of our \( D \le \) 60 m restricted sample have an \( a / b \) ratio less than 2, but a few exceed this value. We do note that our method of determining axial ratios from Kwiatkowski et al. (2010a) provides the minimum axial ratio consistent with the light curve amplitude, and so the values reported here are lower limits.

The composition of most potential targets is likely to be rich in silicates (S-type taxonomic class). The KISS study suggested that C-type asteroids would make more interesting targets be-cause of their more diverse composition, which include water, carbon compounds, rock and metal. However, such asteroids are not common within the currently characterized small near-Earth as-teroid population, though four C-group (including sub-types B and F) and three X-types appear in our sample. Though the real NEA population is not necessarily this low in C types, the list of potential ARM targets is likely to be poorer in carbonaceous bodies than might otherwise be expected.

# 5. Acknowledgements

The authors thank Duncan Steel and David Asher for thoughtful comments which much im-proved this paper. This work was supported in part by the Natural Sciences and Engineering Council of Canada and the Canadian Space Agency (CSA) through the ASTRO CSA Cluster.

# References

Britt, D. T., Yeomans, D., Housen, K., and Consolmagno, G. (2002). Asteroid Density, Porosity, and Structure. Asteroids III, pages 485–500.

Brophy, J., Culick, F., Friedman, L., and 31 others (2012). Asteroid retrieval feasibility study. Technical report, Keck Institute for Space Studies, Pasadena, California.