Editing Kuiper belt (section)

== Mass and size distribution ==

Despite its vast extent, the collective [[mass]] of the Kuiper belt is relatively low. The total mass of the dynamically hot population is estimated to be 1% the [[Earth mass|mass of the Earth]]. The dynamically cold population is estimated to be much smaller with only 0.03% the mass of the Earth.<ref name="Fraser_etal_2014"/><ref name="g01">{{cite journal |last=Gladman |first=Brett |display-authors=etal |title=The structure of the Kuiper belt |journal=Astronomical Journal |date=August 2001 |volume=122 |pages=1051–1066 |doi=10.1086/322080 |bibcode=2001AJ....122.1051G |issue=2|s2cid=54756972 |doi-access= }}</ref> While the dynamically hot population is thought to be the remnant of a much larger population that formed closer to the Sun and was scattered outward during the migration of the giant planets, in contrast, the dynamically cold population is thought to have formed at its current location. The most recent estimate (2018) puts the total mass of the Kuiper belt at {{val|1.97e-2|0.30}} Earth masses based on the influence that it exerts on the motion of planets.<ref name=Pitjeva2018>{{cite journal |last1=Pitjeva |first1=E. V. |last2=Pitjev |first2=N. P. |title=Masses of the Main Asteroid Belt and the Kuiper Belt from the Motions of Planets and Spacecraft |journal=Astronomy Letters |date=30 October 2018 |volume=44 |issue=89 |pages=554–566 |doi=10.1134/S1063773718090050|arxiv=1811.05191 |bibcode=2018AstL...44..554P |s2cid=119404378 }}</ref>

The small total mass of the dynamically cold population presents some problems for models of the [[Formation and evolution of the Solar System|Solar System's formation]] because a sizable mass is required for accretion of KBOs larger than {{convert|100|km|0|abbr=on}} in diameter.<ref name=beyond/> If the cold classical Kuiper belt had always had its current low density, these large objects simply could not have formed by the collision and mergers of smaller planetesimals.<ref name=beyond/> Moreover, the eccentricity and inclination of current orbits make the encounters quite "violent" resulting in destruction rather than accretion. The removal of a large fraction of the mass of the dynamically cold population is thought to be unlikely. Neptune's current influence is too weak to explain such a massive "vacuuming", and the extent of mass loss by collisional grinding is limited by the presence of loosely bound binaries in the cold disk, which are likely to be disrupted in collisions.<ref name="Nesvorny_etal_2011a">{{cite journal |last1=Nesvorný |first1=David |last2=Vokrouhlický |first2=David |last3=Bottke |first3=William F. |last4=Noll |first4=Keith |last5=Levison |first5=Harold F. |title=Observed Binary Fraction Sets Limits on the Extent of Collisional Grinding in the Kuiper Belt |journal=The Astronomical Journal |date=2011 |volume=141 |issue=5 |page=159 |doi=10.1088/0004-6256/141/5/159 |arxiv=1102.5706 |bibcode=2011AJ....141..159N|s2cid=54187134 }}</ref> Instead of forming from the collisions of smaller planetesimals, the larger object may have formed directly from the collapse of clouds of pebbles.<ref name="Morbidelli_Nesvorny_2019">{{cite book |last1=Morbidelli |first1=Alessandro |last2=Nesvorny |first2=David |title=The Trans-Neptunian Solar System |chapter=Kuiper belt: formation and evolution |year=2020 |pages=25–59 |doi=10.1016/B978-0-12-816490-7.00002-3 |arxiv=1904.02980|isbn=9780128164907 |s2cid=102351398 }}</ref>

[[File:TheKuiperBelt PowerLaw2.svg|thumb|upright=1.25|Illustration of the power law]]
The size distributions of the Kuiper belt objects follow a number of [[power law]]s. A power law describes the relationship between ''N''(''D'') (the number of objects of diameter greater than ''D'') and ''D'', and is referred to as brightness slope. The number of objects is inversely proportional to some power of the diameter ''D'':
:<math> \frac{d N}{d D} \propto D^{-q},</math> which yields (assuming ''q'' is not 1):<math>N\propto D^{1-q}+\text{a constant}.</math>
(The constant may be non-zero only if the power law doesn't apply at high values of ''D''.)<!--If it were negative, that would imply negative numbers about a certain size.-->

Early estimates that were based on measurements of the apparent magnitude distribution found a value of q = 4 ± 0.5,<ref name="Bernstein et al. 2004">{{cite journal |last1=Bernstein |first1=G. M. |last2=Trilling |first2=D. E. |last3=Allen |first3=R. L. |last4=Brown |first4=K. E. |last5=Holman |first5=M. |last6=Malhotra |first6=R. |title=The size distribution of transneptunian bodies |journal=[[The Astronomical Journal]] |volume=128 |issue=3 |pages=1364–1390 |doi=10.1086/422919 |arxiv=astro-ph/0308467 |bibcode=2004AJ....128.1364B |date=2004|s2cid=13268096 }}</ref> which implied that there are 8 (=2<sup>3</sup>) times more objects in the 100–200&nbsp;km range than in the 200–400&nbsp;km range. 
<!--If ''q'' was 1 or less, the law would imply an infinite number and mass of large objects in the Kuiper belt. If 1<''q''≤4 there will be a finite number of objects greater than a given size, but the [[expected value]] of their combined mass would be infinite. If ''q'' is 4 or more, the law would imply an infinite mass of small objects. More accurate models find that the "slope" parameter ''q'' is in effect greater at large diameters and lesser at small diameters.<ref name="Bernstein et al. 2004"/> It seems that [[Pluto]] is somewhat unexpectedly large, having several percent of the total mass of the Kuiper belt. It is not expected that anything larger than Pluto exists in the Kuiper belt, and in fact, most of the brightest (largest) objects at inclinations less than 5° have probably been found.<ref name="Bernstein et al. 2004"/>

For most TNOs, only the [[absolute magnitude]] is actually known, the size is inferred assuming a given [[albedo]] (not a safe assumption for larger objects).-->

Recent research has revealed that the size distributions of the hot classical and cold classical objects have differing slopes. The slope for the hot objects is q = 5.3 at large diameters and q = 2.0 at small diameters with the change in slope at 110&nbsp;km. The slope for the cold objects is q = 8.2 at large diameters and q = 2.9 at small diameters with a change in slope at 140&nbsp;km.<ref name="Fraser_etal_2014">{{cite journal |last1=Fraser |first1=Wesley C. |last2=Brown |first2=Michael E. |last3=Morbidelli |first3=Alessandro |last4=Parker |first4=Alex |last5=Batygin |first5=Konstantin |title=The Absolute Magnitude Distribution of Kuiper Belt Objects |journal=The Astrophysical Journal |date=2014 |volume=782 |issue=2 |page=100 |doi=10.1088/0004-637X/782/2/100 |bibcode=2014ApJ...782..100F |arxiv=1401.2157|s2cid=2410254 }}</ref> The size distributions of the [[scattering object]]s, the plutinos, and the Neptune trojans have slopes similar to the other dynamically hot populations, but may instead have a divot, a sharp decrease in the number of objects below a specific size. This divot is hypothesized to be due to either the collisional evolution of the population, or to be due to the population having formed with no objects below this size, with the smaller objects being fragments of the original objects.<ref name="Shankman_etal_2016a">{{cite journal |last1=Shankman |first1=C. |last2=Kavelaars |first2=J. J. |last3=Gladman |first3=B. J. |last4=Alexandersen |first4=M. |last5=Kaib |first5=N. |last6=Petit |first6=J.-M. |last7=Bannister |first7=M. T. |last8=Chen |first8=Y.-T. |last9=Gwyn |first9=S.|last10=Jakubik|first10=M. |last11=Volk |first11=K. |title=OSSOS. II. A Sharp Transition in the Absolute Magnitude Distribution of the Kuiper Belt's Scattering Population |journal=The Astronomical Journal |date=2016 |volume=150 |issue=2 |page=31 |doi= 10.3847/0004-6256/151/2/31 |arxiv= 1511.02896 |bibcode= 2016AJ....151...31S |s2cid=55213074 |doi-access=free }}</ref><ref name="Alexandersen_etal_2014a">{{cite journal |last1= Alexandersen |first1= Mike |last2= Gladman |first2=Brett |last3= Kavelaars |first3=J.J. |last4=Petit |first4= Jean-Marc |last5=Gwyn |first5=Stephen |last6= Shankman |first6= Cork |title=A carefully characterised and tracked Trans-Neptunian survey, the size-distribution of the Plutinos and the number of Neptunian Trojans |journal= The Astronomical Journal |volume= 152 |issue= 5 |pages= 111 |date=2014 |arxiv= 1411.7953 |doi= 10.3847/0004-6256/152/5/111 |s2cid= 119108385 |doi-access= free }}</ref>

The smallest known Kuiper belt objects with radii below 1&nbsp;km have only been detected by [[stellar occultation]]s, as they are far too dim ([[apparent magnitude|magnitude]] 35) to be seen directly by telescopes such as the [[Hubble Space Telescope]].<ref>{{cite news |title=Hubble Finds Smallest Kuiper Belt Object Ever Seen |url=https://hubblesite.org/contents/news-releases/2009/news-2009-33.html |access-date=29 June 2015 |publisher=HubbleSite |date=December 2009 |archive-date=25 January 2021 |archive-url=https://web.archive.org/web/20210125162801/https://hubblesite.org/contents/news-releases/2009/news-2009-33.html |url-status=live }}</ref> The first reports of these occultations were from Schlichting et al. in December 2009, who announced the discovery of a small, sub-kilometre-radius Kuiper belt object in archival ''Hubble'' [[photometry (astronomy)|photometry]] from March 2007. With an estimated radius of {{val|520|60|u=m}} or a diameter of {{val|1040|120|u=m}}, the object was detected by ''Hubble''{{'s}} star tracking system when it briefly occulted a star for 0.3 seconds.<ref name="Schlichting2009">{{cite journal |last1= Schlichting |first1= H. E. |last2= Ofek |first2= E. O.|last3= Wenz |first3= M. |last4= Sari |first4= R. |last5=Gal-Yam |first5=A. |last6= Livio |first6= M. |display-authors=etal |title=A single sub-kilometre Kuiper belt object from a stellar occultation in archival data |journal=Nature |volume= 462 |issue= 7275 |pages= 895–897 |date=December 2009 |arxiv= 0912.2996 |doi= 10.1038/nature08608 |pmid= 20016596 |bibcode=2009Natur.462..895S|s2cid= 205219186 }}</ref> In a subsequent study published in December 2012, Schlichting et al. performed a more thorough analysis of archival ''Hubble'' photometry and reported another occultation event by a sub-kilometre-sized Kuiper belt object, estimated to be {{val|530|70|u=m}} in radius or {{val|1060|140|u=m}} in diameter. From the occultation events detected in 2009 and 2012, Schlichting et al. determined the Kuiper belt object size distribution slope to be q = 3.6 ± 0.2 or q = 3.8 ± 0.2, with the assumptions of a single power law and a uniform [[ecliptic latitude]] distribution. Their result implies a strong deficit of sub-kilometer-sized Kuiper belt objects compared to  extrapolations from the population of larger Kuiper belt objects with diameters above 90&nbsp;km.<ref name="Schlichting2012">{{cite journal |last1= Schlichting |first1= H. E. |last2= Ofek |first2= E. O.|last3= Wenz |first3= M. |last4= Sari |first4= R. |last5=Gal-Yam |first5=A. |last6= Livio |first6= M. |display-authors=etal |title=Measuring the Abundance of Sub-kilometer-sized Kuiper Belt Objects Using Stellar Occultations |journal=The Astrophysical Journal |volume= 761 |issue= 2 |pages= 10 |id= 150 |date=December 2012 |arxiv= 1210.8155  |doi= 10.1088/0004-637X/761/2/150 |bibcode=2012ApJ...761..150S  |s2cid= 31856299 |doi-access= free}}</ref>

Observations made by NASA's ''[[New Horizons]]'' Venetia Burney Student Dust Counter showed "higher than model-predicted dust fluxes" as far as 55 au, not explained by any existing model.<ref>{{cite journal |last1=Doner |first1=Alex |last2=Horányi |first2=Mihály |last3=Bagenal |first3=Fran |last4=Brandt |first4=Pontus |last5=Grundy |first5=Will |last6=Lisse |first6=Carey |last7=Parker |first7=Joel |last8=Poppe |first8=Andrew R. |last9=Singer |first9=Kelsi N. |last10=Stern |first10=S. Alan |last11=Verbiscer |first11=Anne |title=New Horizons Venetia Burney Student Dust Counter Observes Higher than Expected Fluxes Approaching 60 au |journal=The Astrophysical Journal Letters |date=1 February 2024 |volume=961 |issue=2 |pages=L38 |doi=10.3847/2041-8213/ad18b0|doi-access=free |arxiv=2401.01230 |bibcode=2024ApJ...961L..38D }}</ref>