OSSOS. VI. Striking Biases in the Detection of Large Semimajor Axis Trans-Neptunian Objects

To be consistent with Trujillo & Sheppard (2014) and Batygin & Brown (2016a), we use the following criteria to define our sample of TNOs: a > 150 au and q > 30 au. OSSOS detected eight TNOs satisfying the above criteria, four of which have a > 250 au. The discovery circumstances for two of these TNOs are described elsewhere: o3e39 (Bannister et al. 2016, 2013 GP₁₃₆) and uo3l91 (Bannister et al. 2017, 2013 SY₉₉). The six new TNOs we present here were found during the rest of the survey: all are characterized discoveries with well-quantified detection efficiencies. The discoveries have a ranging from 150 to 735 au, and all but one have q > 37 au (Table 1).

One might be tempted to impose a q cut higher than 30 au on the sample to select only TNOs that do not have strong gravitational interactions with Neptune (found to be those with q ≲ 37 au by Lykawka & Mukai 2007), the argument being that TNOs with q sufficiently close to Neptune will undergo evolution in a and orbital orientation angles on short timescales and thus should be removed from the sample. Embedded in this argument is the assumption that the observed clustering for the sample described above does not result from observation bias. This work seeks to test that assumption, so we employ a q lower limit of 30 au to be consistent with prior studies and the region where the MPC TNOs show clustering in orbital angles.

It has also been suggested that only TNOs presently dynamically stable with respect to Neptune should be used to define the sample that is examined for clustering (Batygin & Brown 2016a), the idea being that the TNOs under consideration should be stable to perturbations from Neptune if one is to invoke an additional planet to explain their apparent clustering. If there is a massive planet in the distant solar system, the region between this planet and Neptune would be, in general, unstable. Such a planet would cause pericenter cycling and give dynamical kicks to these large-a TNOs, creating a population analogous to the centaurs, which is seen in multiple simulations with a variety of additional planet candidates (Batygin & Brown 2016b; Lawler et al. 2016; Shankman et al. 2017). TNOs beyond Neptune that are "presently" stable would not necessarily be stable in the case of an additional massive planet beyond Neptune.

In any case, if the q threshold is set to a higher limit, one must still be able to explain why TNOs with q further in, which should be less stable, appear clustered in the MPC sample. To reiterate, this analysis examines observational biases and looks for evidence of clustering in the OSSOS sample. Thus we select our sample using the same orbital element ranges for which arguments of clustering have been made.

OSSOS is a characterized survey with measured and reported biases. The pointing directions of the survey itself (Table 1, Bannister et al. 2016) are of key importance for the observing biases in orbital angles, as we will demonstrate. For the purposes of this analysis, we provide the relevant OSSOS TNOs (Table 1), and a full implementation of the survey simulator including an example model distribution is available by request.

We perform simulated surveys on a set of distributions of orbits with a > 150 au, q > 30 au to probe the effects of the OSSOS observing biases on the detectability of TNOs in the phase space of interest. A detailed description of this established survey simulation suite can be found in Jones et al. (2006) and Petit et al. (2011), and recent examples of the use of the survey simulator in TNO studies can be found in Nesvorný (2015), Alexandersen et al. (2016), Shankman et al. (2016), and Pike et al. (2017).

We construct test distributions that fully cover ranges of orbital phase space that include the detected large-a TNOs. The models tested are not intended to reproduce the observed distributions. They were designed to probe a variety of forms of distributions to test the sensitivity of the analysis to the specific choice of distribution. The models tested are combinations of distributions covering the following parameter spaces and forms.

• 1.  
  a: distributions spanning 150–1000 au. Distributions were either uniform in a or $\propto {a}^{x}$, with exponents x spanning 0.5–1. Distributions with an upper limit of 800 au were also tried to test for sensitivity to the a cutoff.
• 2.  
  Eccentricity, e: uniform from 0.7 to 0.95. A q lower limit was imposed at 30 au.
• 3.  
  Inclination, i: two forms were tested: (1) A uniform distribution from 0° that extends up to 55° (the range of the observed OSSOS sample) and (2) a distribution that scales as sin(i) × Gaussian (as in Brown 2001). A variety of Gaussian centers (between 0°, and 20°) and Gaussian widths (between 5° and 15°) including different combinations of centers and widths were used.
• 4.  
  Absolute magnitude, H: single slope from H_r of 6 to 9.5 with a slope of 0.9. Divot and knee distributions as in Fraser et al. (2014) and Shankman et al. (2016) were also tested.
• 5.  
  ω, and Ω uniform from 0° to 360°, making ϖ uniform as well.

With each distribution, we conducted an OSSOS survey simulation that "detected" 10,000 simulated TNOs. These survey simulations revealed the observing biases present in the survey and show any gaps or preferences in the sensitivity to certain orbits. We found that the choice of model does not affect the conclusions about the intrinsic orbit angle distribution (see Figure 6).

Figure 1 plots the results of the survey simulation. Our simulations find that OSSOS has a range of sensitivities to and biases in different orbital parameters of TNOs. We discuss in turn our sensitivity to each angle of TNO orbit orientation. All discussions of panels in this section refer to panels in Figure 1. Panels (A)–(C) plot the orbital angles versus a with histograms of the simulated detections for these angles. All statements of the sensitivity in OSSOS are made exclusively with respect to the TNO model constraints as outlined above.

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ω sensitivity: OSSOS has some sensitivity to all argument of pericenter ω values, which can be seen in panels (A). Panel (A) shows that the TNOs on orbits with ω values near 0° or 180° are more likely to be detected. This effect arises in near-ecliptic surveys when TNOs are detected near their pericenter. The OSSOS pointings were not centered exactly around the ecliptic, with almost all the off-ecliptic coverage being north of the ecliptic. Blocks that are off the ecliptic no longer have symmetric sensitivity with 0° and 180° favored, but instead have only one area of reduced sensitivity, as also discussed in Sheppard & Trujillo (2016). This lack of sensitivity is caused by the fact that some pericenter locations are not possible to detect for a survey off the ecliptic. For example, a survey that points above the ecliptic is unable to see any sky points below the ecliptic and thus has a lower sensitivity to detecting orbits that come to pericenter below the ecliptic. This effect results in less OSSOS sensitivity to TNOs with ω near −90° than near 90°. OSSOS still has some sensitivity to TNOs away from their pericenter due to its deep limiting magnitudes, resulting in some sensitivity to TNOs with ω near −90°, as seen in panel (A).

Ω sensitivity: there exists clear and initially non-intuitive structure in the OSSOS observing bias in longitude of the ascending node Ω. Panel (B) shows that there is a large and substantial gap in Ω sensitivity in the −120° to −20° range. OSSOS, due to its avoidance of the galactic plane and northern hemisphere winter, has virtually no capability for detecting large-a TNOs with Ω between −120° and −20°. Figure 2 shows that this structure arises from a coupling of sensitivity in Ω and i. This striking effect is a simple result of geometry. The Ω and i angles define the plane of the TNO's orbit. In order for the TNO to be detectable by a survey, its plane must intersect the area of sky being observed. For inclined orbits to have a high chance of being detectable in an ecliptic survey, the ascending or descending node must be in the same direction as the survey's pointing. Each of the horizontal spikes in Figure 2 indicates the location of an ascending or descending node that is aligned with one of the OSSOS pointings. The bias structure curves horizontally as inclinations go toward 0°, when orbits become ecliptic grazing, and can thus be seen at more points across their orbit in ecliptic surveys. We plot the OSSOS detections in Table 1 in panel Figure 2 to show that they follow this bias-induced distribution of Ω and i.

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ϖ sensitivity: the sensitivity to detecting longitude of pericenter ϖ is a combination of the sensitivities to detecting Ω and ω. The sensitivity is a double peaked distribution, with less sensitivity to ϖ in the range of 110°–160° (see Panel (C)). OSSOS has some sensitivity to all ϖ values and there is no striking structure in the ϖ sensitivity other than the two broad peaks roughly separated by 180° of longitude.

We examined the three above biases for both the a > 150 au and a > 250 au regions to explore if the sensitivity changes with a. We found that the observing biases are the same for the two regions, which can be seen by comparison of the blue and gray histograms in Figure 1. Once a TNO has a sufficiently large orbit, it is only detectable near pericenter. This bias strongly affects the expected detection of orbital angles as we have shown. The bias structure does not change as a function of increasing a because the bias is a result of the fact that the TNOs are only detectable near pericenter.

Although the biases we demonstrate are specific to OSSOS, all TNO surveys will have complicated detection biases like those shown in this work. Without publishing characterizations of the survey pointings, these complex and often non-intuitive biases cannot be accounted for, and may lead to incorrect assumptions about the intrinsic population.

Having examined the biases of OSSOS, we now examine the detected OSSOS sample (Table 1) for evidence of a clustering in the orbital angles for the large-a TNOs, as first noted in the MPC data set by Trujillo & Sheppard (2014) and Brown & Batygin (2016). We consider the OSSOS sample independently, examining the distributions of the OSSOS TNOs with no a priori expectations about clustering.

A visual examination of the orbital distribution (see Figure 3) shows relatively little evidence of clustering of ω, even in the observationally biased a > 150 au OSSOS sample. The eight OSSOS TNOs are found to be distributed across the full range of ω values (Figure 3 panel (A)). We demonstrated in Section 3.1 that OSSOS has some sensitivity to all ω values; this sensitivity is reflected in the broad distribution of detected ω values. For each orbital angle, we test the hypothesis that the OSSOS sample can be detected from a uniform intrinsic distribution. To do this, we compare the observed distributions to the survey simulator biased models described above (Figure 1). We test the null hypothesis using Kuiper's test (e.g., see Fisher 1995; Pewsey et al. 2013), which is closely related to the Kolmogorov–Smirnov test, but is invariant to cyclic transformations of the test variable. The test is thus well-suited to problems with cyclic variables, as is the case for angles like ω, Ω, and ϖ. The eight TNOs are statistically consistent (i.e., 53% of bootstrapped model subsamples have a larger Kuiper's test distance than the observed sample to the parent model: the hypothesis is rejectable at 47%, i.e., not rejectable) with being detected from an intrinsic uniform distribution of ω values. Our results hold for all tested intrinsic models described in Section 2.3.

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We now examine the Ω and ϖ distributions for the OSSOS TNOs with a > 250 au. We find that the Ω values for three of the TNOs are distributed near 25° with the fourth isolated (Figure 3 panel (B)). OSSOS had effectively no sensitivity to TNOs with Ω between −120° and −20°, and had poor sensitivity to TNOs with Ω between 115° and 165° (see Figure 3 panel (B) histogram). Unsurprisingly, OSSOS did not detect TNOs in regions of limited or no sensitivity. Using Kuiper's test, we find that the OSSOS detections are statistically consistent (rejectable at 61%, i.e., not rejectable) with being detected from an intrinsic uniform distribution of Ω values. We find that the ϖ values cover a large range, with only two values near each other. As with ω and Ω, the OSSOS TNO ϖ values are consistent (rejectable at 62%, i.e., not rejectable) with being detected from an intrinsic uniform distribution of ϖ values.

We conclude that the independent OSSOS sample shows no evidence for intrinsic clustering in the ω, Ω, or ϖ distributions of TNOs.

We now compare the OSSOS sample (known biases) to the MPC sample (unknown biases) to examine the broader question of clustering in the known TNOs. Figure 4 plots the eight OSSOS TNOs and the MPC TNOs satisfying a > 150 au and q > 30 au as reported by the MPC in 2017 April.

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Figure 4 panel (A) shows clearly that the apparent clustering in ω that has been noted in the MPC sample is not present in the OSSOS sample, despite the OSSOS survey biases against ω = ±90°. Where the MPC sample is contained within roughly 50° of 0°, the OSSOS sample spans all values and has as many TNOs inside the apparent clustering region (gray shading of Figure 4 panel (A)) as outside. The OSSOS TNOs that are outside the apparent clustering region have a variety of semimajor axes and all have q > 37 au. With the addition of the OSSOS sample and a few recently discovered TNOs in the MPC sample, the argument for a clustering of ω in the detected TNOs has been substantially weakened.

There is no overlap between the OSSOS sample and the Ω clustering region of TNOs with a > 250 au noted in Batygin & Brown (2016a), with all four OSSOS detections outside the clustered band. The four a > 250 au OSSOS detections span a range of a values and all have q > 37 au. If one were to consider the three OSSOS detections with Ω between 0° and 50° to be part of the clustered grouping, the clustering would then span approximately 150°. Sheppard & Trujillo (2016) noted that their recent discoveries began to erode the signal of clustered Ω in the large-a TNOs; the four OSSOS detections outside the previously reported band continue this trend of eroding the signal. This would be expected if the original signal results from a combination of small number statistics and observing bias.

Two of the OSSOS a > 250 au TNOs with ϖ near 70° are within the Batygin & Brown (2016a) proposed "anti-aligned" cluster. The third, o5m52, with a ϖ of −110°, is approximately 180° away, and would fall in the subsequently postulated "aligned" cluster (Brown & Batygin 2016; Sheppard & Trujillo 2016). Discoveries at these values of ϖ are unsurprising in OSSOS, as the observing bias favors detections with ϖ at these longitudes (Figure 1 panel (C)). The final OSSOS detection, o5p060, however, is approximately 90° away from each of these proposed clustering regions.