Data thus far suggests than there is indeed a cutoff to the classical TNO population around 47 AU, although the discoveries of Sedna and VP suggest an unrecognized population of much more distant objects see below.
Of the 2, outer solar system objects counted above, 92 3. Most if not all of the latter objects may actually be comets no longer showing cometary activity. The graph below click here for larger version shows estimated TNO size versus perihelion distance.
A line indicates the nature of the cutoff that would result from detectability limits; in other words, objects lying along this line would have the same apparent brightness from Earth assuming the same albedo.
Note the lack of detected objects with perihelions beyond 47 AU. The graph below click here for larger version and discussion shows eccentricity versus semimajor axis for outer solar system objects.
Green lines indicate the location of orbital resonances with Neptune where objects have been found. The second resonance from the left is the resonance, location of a cluster of objects the Plutinos.
The 30 largest known TNOs plus one satellite are, with estimated diameters: Pluto plutino , km Eris scattered disk object , km Haumea Haumea family , km OR10 resonance object , km Makemake other TNO , km Charon satellite of Pluto , km FY27 scattered disk object , km?
Diameters with question marks are estimated see discussion here. For comparison, the largest asteroid, 1 Ceres, is km in diameter. A total of 75 TNOs appear to be at least km in diameter and at least km. A note: these size-associated figures are very dependent on the assumed albedo value for these objects. This later crucial parameter contains information on both internal structure i.
An analysis of the obtained size and albedo on possible correlation with the bulk density and other physical and orbital parameters is carried out. Since the probability distributions of parameters are unknown, non-parametric statistical methods are applied. The structure of the paper is as follows.
In Sect. The bulk density estimation is done in Sect. The analysis on correlations of physical and orbital parameters, characterising multiple TNOs, is performed in Sect. Section 6 summarises results of statistical analysis. Table 1 Dataset. Although, the Pluto system was also observed by Herschel , here we have not included it in our analysis because this much more complex system e.
We have adopted dynamical class according to Gladman et al. The information about system mass when available is from the literature mentioned in Table 1. Additionally, in this work we have used parameters of mutual orbit semi-major axis and orbital period from the same literatures as for masses.
The mean bulk density calculation is described in Sect. Two populations, multiple and single TNOs, are compared here through their size distributions. The aim is to clarify whether the both populations are similar and come from the same parent-population.
The Herschel and Spitzer measurements have provided the biggest sample of accurate TNOs sizes, derived from observations at thermal wavelengths. However, regarding the entire TNOs population, this sample is still small and may give an incomplete picture of the real albedo and diameter distributions. We initially start with this full MPC list. For those objects for which the radiometric size is unknown, we assign a diameter using available magnitudes H V from MPC, and following an albedo distribution.
For each object we randomly select an albedo value from the corresponding dynamical group sample, while simultaneously varying this value following given uncertainty.
This Monte Carlo approach combines re-sampling and perturbation techniques. The obtained diameters dataset, completed by those objects for which we have the radiometric size, is used for a statistical test, described below, which compares TNBs and TNOs samples.
The aforementioned diameters sampling is repeated many times in order to calculate an average test statistic. The solid lines mean the probability density functions estimation kernel estimation, Parzen , shaded in red and blue for the TNBs and TNOs datasets respectively. It was mentioned above, that we assume the albedo distribution is not different for binaries and non-binaries.
This fact indicates, that there is no occurred statistically significant difference between TNOs and TNBs albedo samples. The empirical albedo distributions are shown in Fig. The resulting p -value for the average AD test statistic for diameter samples is summarised in Table 2. However, this result may be biased. To check for biases in statistical conclusions, we have repeated the AD test for different sub-samples.
In a first step, the comparison is made for dynamically equivalent samples, namely using the classification of Gladman et al. Thus, it appears that the occurred difference in diameter distributions can be caused by cold classicals, resonant objects, and possibly by cenataurs among which no binaries were observed.
On the other hand, this conclusion can be not very robust from statistical point of view, since the small sizes of certain sub-samples for binary objects e. It should be noticed, however, that the compared samples have significantly different size ranges. On the one side, the sample includes a very low binary fraction of small objects among plutinos, SDOs and centaurs.
On the other side, the largest objects in the sample — dwarf planets — almost all have satellites. Consequently, the size distribution of TNBs may be biased towards the largest objects, whereas the sample of single TNOs may be biased by small objects.
Thus, in a second step, we compare the size distribution over a restricted size range, namely, over the range from km the diameter of the smallest TNB RZ with known D observed by Herschel to km the largest TNO OR10 without satellites in the Herschel sample. In this case, the test indeed shows no significance about difference between two samples.
In order to clarify which objects influence more the statistics, the AD test is repeated for sub-samples without the largest objects, and without the smallest ones. For this purpose we consider, firstly, only objects smaller than km in diameter, and, secondly, only objects greater than km. Therefore, the small objects are the ones that bias the test when all size ranges are considered simultaneously.
It is known that the quality of the MPC information H V magnitudes in particular has been constantly improving over the years.
A second aspect is that the MPC database includes objects for which we do not know if they are binaries or not. The fraction of known binaries decreases as the objects get fainter. This approach allows us to reduce possible discovery biases inherent to the MPC database list.
The obtained results with the reduced MPC list, which consists of 78 binaries and single objects, are summarised in Table 3. Still, the results indicate that small objects are the ones that bias the test when all size ranges are considered simultaneously. To sum up, the difference in size distribution is biased by small TNOs, among which no binaries are observed.
The analysis of size and density is of particular interest. Blue symbols — cold classicals, red symbols — hot classicals, black symbols — resonants including plutinos , magenta symbols — scattered disc objects, green symbols — detached objects.
The radiometric diameter for multiple systems is an effective diameter that means for binary system and for triple system, with D i the diameter of the i th component. We have estimated the bulk density for those objects whose mass is available. The densities for other objects coincide with previously published papers Vilenius et al.
It should be noted that among all objects in our dataset WC19 has an exclusively high density. While, with a nominal diameter of km and density of 3. Improved diameter and mass determinations are needed for this object. Thus, firstly, we assumed that secondaries have higher albedos. This assumption gives smaller bulk densities see Table 4. Secondly, we assumed that primaries have higher albedos and obtained the opposite effect greater densities for all objects except QY, Sila and Quaoar.
In any case, the bulk densities do not change dramatically. Thus, uncertainties in density related to possible albedo differences between the primary and secondary are dwarfed by uncertainties due to system equivalent diameter and mass.
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