The Size Distribution of Trans-Neptunian Bodies

By G. Bernstein, D. Trilling, R. Allen, M. Brown, M. Holman, R. Malhotra. 2003

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We search 0.02 deg2 of the invariable plane for trans-Neptunian objects (TNOs) 25 AU or more distant using the Advanced Camera for Surveys (ACS) aboard the Hubble Space Telescope. With 22 ks per pointing, the search is more than 50% complete for m606W ≤ 29.2. Three new objects are discovered, the faintest with mean magnitude m = 28.3 (diameter ≈25 km), which is 3 mag fainter than any previously well-measured solar system body. Each new discovery is verified with a follow-up 18 ks observation with the ACS, and the detection efficiency is verified with implanted objects. The three detections are a factor of ∼25 less than would be expected under extrapolation of the power-law differential sky density for brighter objects, Σ(m) ≡ dN/dm dΩ ∝ 10αm with α ≈ 0.63. Analysis of the ACS data and recent TNO surveys from the literature reveals departures from this power law at both the bright and faint ends. Division of the TNO sample by distance and inclination into "classical Kuiper belt" (CKB) and "Excited" samples reveals that Σ(m) differs for the two populations at 96% confidence, and both samples show departures from power-law behavior. A double power-law Σ(m) adequately fits all data. Implications of these departures include the following: (1) The total mass of the "classical" Kuiper belt is ≈0.010 M⊕, only a few times Pluto's mass, and is predominantly in the form of ∼100 km bodies (barring a secondary peak in the mass distribution at sub–10 km sizes). The mass of Excited objects is perhaps a few times larger. (2) The Excited class has a shallower bright-end magnitude (and, presumably, size) distribution; the largest objects, including Pluto, make up tens of percent of the total mass whereas the largest CKB objects are only ∼2% of its mass. (3) The derived size distributions predict that the largest Excited body should be roughly the mass of Pluto, and the largest CKB body should have mR ≈ 20—hence, Pluto is feasibly considered to have originated from the same physical process as the Excited TNOs. (4) The observed deficit of small TNOs occurs in the size regime where present-day collisions are expected to be disruptive, suggesting extensive depletion by collisions. The Excited and CKB size distributions are qualitatively similar to some numerical models of growth and erosion, with both accretion and erosion appearing to have proceeded to more advanced stages in the Excited class than in the CKB. (5) The lack of detections of distant TNOs implies that if a mass of TNOs comparable to the CKB is present near the invariable plane beyond 50 AU, that distant population must be composed primarily of bodies smaller than ≈40 km. (6) There are too few small CKB objects for this population to be the reservoir of Jupiter-family comet precursors without a significant upturn in the population at diameters under 20 km. With optimistic model parameters and extrapolations, the Excited population could be the source reservoir. Implications of these discoveries for the formation and evolution of the outer solar system are discussed.

Subfields: Aerospace Engineering, Astronomy and Astrophysics, Instrumentation

View Paper: https://www.semanticscholar.org/paper/59be5fff42da6a1a55b19419c21126d00915c696

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Citations in the corpus

EVIDENCE FOR SLOW MIGRATION OF NEPTUNE FROM THE INCLINATION DISTRIBUTION OF KUIPER BELT OBJECTS (2015, background): “And finally, (4) the size distribution of the CCs is markedly different from those of the hot and scattered populations, in that it shows a very steep slope at large sizes (e.g., Bernstein et al. 2004; Fraser et al. 2014), and lacks very large objects (Levison & Stern 2001).”
Long-Term Collisional Evolution of Debris Disks (2007, background): “The Kuiper belt is the only source for observational constraints to this parameter so far, and recent surveys suggest a value ofpp = 4.0±0.5 (e.g., Trujillo et al. 2001; Bernstein et al. 2004) orqp = 2.00±0.17.”
THE CANADA–FRANCE ECLIPTIC PLANE SURVEY—L3 DATA RELEASE: THE ORBITAL STRUCTURE OF THE KUIPER BELT (2009, background): “While those slopes are consistent with274 Elliot et al. (2005) they are shallower than Bernstein et al. (2004) and our own estimates.”
The primordial nucleus of comet 67P/Churyumov-Gerasimenko (2015, background): “…it is commonly agreed that the SD is the main source of JFCs. Applying PSD = 0.95% we predict N1−10 = 6.3×107 nuclei with D = 1–10 km and N2−20 = 2.6 × 107 nuclei with D = 2–20 km in the current SD. Bernstein et al. (2004) performed a Hubble Space Telescope (HST) deep survey of D >∼ 15 km objects.”
Origin of the structure of the Kuiper belt during a dynamical instability in the orbits of Uranus and Neptune (2007, methodology): “Bernstein et al. (2004) showed that the hot population has a shallower H distribution than the cold population, which is consistent with the absence of the largest objects in the cold belt.”
The Size Distribution of Kuiper Belt Objects (2004, methodology): “Data from the Advanced Camera for Surveys on the Hubble Space Telescope (HST ) suggest a change in the slope of the size distribution at a break radius rb 10 30 km (Bernstein et al. 2004).”
LSST: From Science Drivers to Reference Design and Anticipated Data Products (2008, background): “…function of color and size; the search for dynamical families (Marcus et al. 2011); studies of shapes and structure using light curves (Duncan & Levison 1995; Trujillo, Jewitt & Luu 2001; Gladman et al. 2001; Bernstein et al. 2004; Elliot et al. 2005; Jones et al. 2006; Doressoundiram et al. 2007).”
Towards initial mass functions for asteroids and Kuiper Belt Objects (2010, background): “Indeed this is about four times the mass of the cold classical population (Bernstein et al., 2004).”
Neptune’s Migration into a Stirred-Up Kuiper Belt: A Detailed Comparison of Simulations to Observations (2005, background): “The ecliptic luminosity function of Bernstein et al. (2004) is shown in Fig.”
FORMATION OF KUIPER BELT BINARIES BY GRAVITATIONAL COLLAPSE (2010, background): “…they are now (e ∼ i ∼ 10−4–10−2 compared to present eccentricities e ∼ 0.1 and inclinations i ∼ 10◦), and (ii) the initial disk mass was ∼100–1000 times larger than the current KB mass, MKB ∼ 0.01-0.1 MEarth (Trujillo et al. 2001a,b, Gladman et al. 2001b, Bernstein et al. 2004, Fraser et al. 2008).”
Asteroids Were Born Big (2009, background): “Moreover, if planetesimals formed in the same way in the Kuiper belt, it is likely that the turn-over observed in its SFD at D 100 km (Bernstein et al., 2004) is also a signature of accretion and not one of collisional grinding, unlike what it is usually assumed (e.”
Discovery of a Planetary-sized Object in the Scattered Kuiper Belt (2005, methodology): “Extrapolation of the size distribution of smaller Kuiper belt objects (KBOs) has sometimes been used to attempt to estimate the numbers of such larger objects (i.e. Bernstein et al. 2004), but such estimates have proven inconclusive.”
THE ABSOLUTE MAGNITUDE DISTRIBUTION OF KUIPER BELT OBJECTS (2014, methodology): “These past surveys typically observed power-law slopes of α < 0.6 for the hot population and ∼0.8 for the cold population (Bernstein et al. 2004; Fraser et al. 2010).”
The Scattered Disk as the Source of the Jupiter Family Comets (2008, methodology): “Taking the Bernstein et al. (2004) population estimate for the scattered disk, the rate at which SDOs become JFCs, and the rate at which the JFCs need to be resupplied, the 2% of SDOs that experience tidal disruption would need to break into roughly 100Y1000 fragments to account for the discrepancy.”
The Birth Environment of the Solar System (2010, background): “For completeness we note that recent measurements (Bizzarro et al. 2007) suggest that the oldest planetesimals formed in the absence of 60Fe, with a ∼ 1 Myr time delay between the oldest bodies and those that contain 60Fe; however, although this data work in favor of the late enrichment picture, sub”