Naoz, Perets & Ragozzine 2 Fig. 1.— Eccentricity distribution of observed binary asteroids and TNOs (panels (a) and (b) respectively). Panel (c) shows the cumulative distribution of both samples (asteroids and TNO bina- ries, solid lines, respectively) as well as comparison to a thermal distribution (lower solid line). The dashed line shows the cumu- lative eccentricity distribution of binary TNOs excluding binaries that are likely affected by tides ( e < 0 . 05 ). Fig. 2.— Inclination distribution of observed binary asteroids and binary TNOs (panels (a) and (b) respectively). Panel (c) shows the cumulative distribution of both samples as well as comparison to a flat distribution (i.e. random in cos i ). Note that many of the binary TNO inclinations have two degenerate solutions; here only one solution is chosen arbitrarily for each binary to illustrate their likely distribution (see text). served population of binaries comes from very heteroge- neous observing conditions. Although we do not correct for these effects in the current analysis, we discuss them below to recognize the possible biases they may produce. Binary TNOs are primarily discovered in two ways. Ground-based observations can detect two co-moving objects, if the projected separation of the objects is roughly larger than the typical seeing, > 0.5 arcseconds (e.g. Kern & Elliot 2006) or if adaptive optics is used on bright targets (e.g. Brown et al. 2006). The widest bi- naries, such as 2001 QW322 (Petit & Mousis 2004) can be found with this mechanism, assuming that discov- ery and follow-up images have been searched for bina- ries (generally true, but not always). Pan-STARRS and other future surveys will probably detect dozens of bina- ries this way (Holman et al. 2007). The second discovery mechanism is using Hubble Space Telescope (HST) ob- servations combined with PSF-fitting techniques, which has discovered the great majority ( ∼ 80 % ) of known bi- 2.2.1. Binary TNOs nary TNOs. HST can resolve binaries as close as tens of milliarcseconds and generally probes much fainter ob- jects than ground-based telescopes (Noll et al. 2008). Each of these two methods suffer from important ob- servational biases. The main bias is a detection bias: the secondary must be bright enough and far enough away from the primary to be detected. In both the ground- and space-based cases, there is no simple prescription that describes this detection bias, especially since these are coupled close to the primary: a bright secondary can be discovered at smaller separations than a faint secondary. Furthermore, since HST observations are always nearly the same duration (one HST orbit), observations are es- sentially magnitude-limited, implying that low bright- ness ratios (and mass ratios) can only be seen around brighter targets. A discussion of these biases and their effects on the observed population is also given by Noll et al. (2008). Despite the observational biases, these authors believe that there is good evidence that binaries composed of moderate-sized TNOs (diameters less than ∼ 1000 km) are actually clustered at nearly equal brightness, with Δ$_{mag}$ < 1 corresponding to a mass ratio of greater than ∼ 0.25 assuming equal albedos and densities. This lat- ter assumption seems reasonable given that the colors of components of binary TNOs are known to be similar (Benecchi et al. 2009a). Considering now biases in the binary mutual orbital el- ements, we again point out that the majority of binaries are discovered in single HST snapshots. Hence, biases are introduced by the fact that the orbital separation must be detectably large at a single epoch. While Noll et al. (2008) point out that the statistical distribution of ob- served separations is similar to the distribution of semi- major axes, it is clear that systems with larger eccentric- ities are more likely to be seen since the observability is increased at apoapse, both due to wider separations and to the longer residence time. This eccentricity bias is most important near the angular resolution limit where most of the binaries are discovered, but it is not im- portant when semi-major axes exceed ∼ 0.2 arcseconds. Of course, separation-limited observations imply that the smallest semi-major axes are undetectable; these systems are best discovered through photometry, either through doubly periodic light curves or where eclipses and oc- cultations may reveal contact binaries like 2001 QG 298 (Sheppard & Jewitt 2004). Finally, we also note a bias against observations of bi- nary TNOs with large size/mass ratios, due to detection limits. For example, a typical TNO with a radius of 100 km located at 40 AU would have collisional satellites with V < 24 . 5 at separations of ∼ 0.04 arcseconds, perhaps barely detectable by HST if the satellite is at elonga- tion. The most likely way to discover these systems is through photocenter-barycenter shifts (in this case, the size would be ∼ 2 milliarcseconds) detected through long- baseline highly-accurate astrometry, potentially available from future Pan-STARRS or LSST surveys. Detecting a double-periodic light curve (or serendipitous mutual events) may be possible for some systems, though the faintness of the components makes this very difficult and the result may be impossible to distinguish from a single object with arbitrary shape and spin orientation. The size ratio of the binary components can be important for 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1 2 3 4 5 e N 1 2 3 4 5 6 N 0 0.25 0.5 0.75 1 0 0.25 0.5 0.75 1 Cumulative e Binary Asteroids Binary TNOs Binary TNOs Binary Asteroids (a) (b) (c) 1 2 3 4 5 N −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 0 1 2 3 4 cos i N −1 −0.5 0 0.5 1 0 0.25 0.5 0.75 1 Cumulative cos i Binary Asteroids Binary TNOs Binary TNOs Binary Asteroids (a) (b) (c)