THE OUTER SOLAR SYSTEM ORIGINS SURVEY. I. DESIGN AND FIRST-QUARTER DISCOVERIES

The OSSOS discovery and tracking program uses the CFHT MegaPrime/MegaCam (Boulade et al. 2003). In 2013 and 2014, the MegaPrime/MegaCam focal plane was populated by thirty-six 4612 × 2048 pixel CCDs in a 4 by 9 arrangement, with a 096 × 094 unvignetted field of view (FOV) (0.90 deg²) and 005 full width at half maximum (FWHM) image quality (IQ) variation between center and edge. The plate scale is 0184 per pixel, which is well suited for sampling the 07 median seeing at Maunakea.

We observed our 2013 discovery fields in MegaCam's r.MP9601 filter (564–685 nm at 50% transmission; 81.4% mean transmission), henceforth referred to as r, which is similar to the Sloan Digital Sky Survey (SDSS) r' filter (see Section 3.5). Using this filter optimizes the tradeoff between reflected solar brightness (TNOs have colors B − R ∼ 1–2; Hainaut et al. 2012), the telescope's and CCDs' combined quantum efficiency curve, and sky brightness. The r band delivers the best IQ distribution at CFHT and minimizes IQ distortion from atmospheric dispersion, especially useful as tracking observations often occur months from opposition when the airmass is >1.3. Obtaining all discovery observations using the same filter simplifies the design of the survey's simulator (Section 5) and avoids object-color based biases in tracking.

Our integration length was set at 287 s. This exposure length achieves a target depth of m_r = 24.5 in a single frame in 07 median CFHT seeing. It reduces loss of signal-to-noise ratio (S/N) due to trailing, with motion during the exposure of less than half a FWHM for objects at d ≥ 33 au, also aiding the detection of TNO binarity. The number of fields in a block is set by the requirement of being able to observe one-half of a block three times (three observations provide the minimal initial orbital constraints for discovery) in three hours, the maximum time over which both airmass and IQ stability can typically be maintained. Given the 40 s MegaCam readout overhead on top of the integration time, this requirement allows a grid of approximately 20 fields per block, with the exact number set to give a symmetric grid. The survey target depth allows detection of Plutinos with radii larger than 20 km at their perihelion (per Luu & Jewitt 1988; assuming a 10% albedo per Mommert et al. 2012; Peixinho et al. 2015), potentially examining the size distribution where models (Kenyon & Bromley 2008; Fraser 2009) and observations (Bernstein et al. 2004; Fraser & Kavelaars 2009; Fuentes et al. 2009; Shankman et al. 2013; Alexandersen et al. 2014; Fraser et al. 2014) suggest a transition in the size distribution.

MegaPrime/MegaCam operates exclusively as a dark-time queue-mode instrument for CFHT. The OSSOS project thus has between 10 and 14 potentially observable nights each month, weather considerations aside. Through CFHT's flexible queue-schedule system we requested our observations be made in possibly non-photometric conditions (discussed in Section 3.5) with 06–08 seeing and <0.1 mag extinction for discovery, and requested image quality of 08–10 seeing for follow-up observations. Images were taken entirely with sidereal guiding and above airmass 1.5. This aided the quality of the astrometric solution and the point-spread function, and retained image depth: median extinction on Maunakea is 0.10 mag per airmass in this passband (Buton et al. 2012).

The OSSOS project has used a dense (for outer solar system surveys) observing cadence to provide tracking observations that enable orbital solutions within the discovery year. In the discovery year we observed in each lunation that a given block is visible. These observations evenly bracket the date of the block's opposition: precovery in the months before, discovery observations at opposition, recovery in the months after (Figure 2). Precovery and recovery observations on each field of each block were either a single image or a pair of images spaced by at least an hour. Each field of a block was imaged at least 19 times in the discovery opposition.

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During the discovery year the blocks were shifted over the sky at mean Kuiper Belt orbital rates (Figure 2). The shift rate was set at the mean motion of objects in the CFEPS L7 model (Petit et al. 2011); some 3'' hr⁻¹ at opposition, declining to a near-zero shift away from opposition toward the stationary point. Almost all of the sample that is present within the block at discovery is retained through the entire year by this strategy, reducing the effects of orbit shear. The shifting is done independent of any knowledge of the sky positions of the TNOs actually present in the field.

The MegaCam mosaic has 13'' (70 pixels) gaps between each CCD and between the middle two CCD rows, and two larger gaps of 79'' (425 pixels) separating the first and last CCD rows from the middle two rows. To enable tracking of TNOs whose sky motions place them in the region overlapping these chip gaps, a dither was applied to some observations. We applied a north dither of 90'' to the observations at least once per dark run.

A typical sequence of observations in each lunation n leading up to the opposition lunation at time t was thus:

• 1.  
  $t-3n$: a single observation, another north-dithered single several days later;
• 2.  
  $t-2n$: a single observation, another north-dithered single several days later;
• 3.  
  t − n: a pair of observations, followed by either a single or paired north-dithered observation several days later; and
• 4.  
  t: a triplet of observations, a single image a day later, followed by a north-dithered single image a day after that.

The post-opposition sequence then unfolded in reverse. The original cadence simulation only tested t ± 2, but it became possible and desirable to add t ± 3 during the execution of the observations (partly due to the ongoing nature of the survey operations, which could continue across CFHT semester boundaries).

The triplet of observations are the only data used for object discovery of a given block: they were acquired in the lunation that the block came to opposition. The triplet observations spanned at least two hours in the same night, with at least half an hour between each image of a field. This permits detection of sky motion by objects at distances out to ∼300 au. Due to the length of observing time required, the triplet would generally be taken on half the fields of the block one night, and on the other contiguous half on a subsequent, often adjacent, night. The block location was shifted between these two nights, as part of our continuous shift strategy, reducing the chance that a TNO might be present in both half-blocks.

This paper covers OSSOS blocks that had their discovery observations in 2013A. Forthcoming papers will cover the subsequent discovery observations (Table 1). The 2013A blocks were 13AE, centered at R.A. ${14}^{{\rm{h}}}{20}^{{\rm{m}}}$, decl. −12°52' at discovery, spanning ecliptic latitude range b = 0°–3°, and 13AO, centered at R.A. ${15}^{{\rm{h}}}{57}^{{\rm{m}}}$, decl. −12°30' at discovery, spanning ecliptic latitude range b = 6°–9° (Figure 1). Being very close to the trailing ortho-Neptune point (90° behind the planet), 13AO is well placed to detect low libration amplitude 3:2 and 5:2 resonators where they are most likely to come to perihelion. The sky locations of the 13A blocks are at 44° and 30° galactic latitude, comparatively close to the galactic plane for a TNO survey: the higher density of background stars increases the likelihood of occultations in the coming years as the OSSOS objects' astrometric positions descend into the galactic plane.

While the quality of detection is limited by the worst image in the triplet, variability in imaging conditions within blocks, and between blocks, is taken into account by the OSSOS characterization process (Section 5). There is a single detection efficiency dependent on magnitude and moving-object motion rate for each block of observations. The 13AE discovery triplets were taken under some minor (<0.04 mag) extinction and with IQ that ranged from 065 to 084. The 13AO discovery triplets exhibited no extinction and IQ that ranged from 049 to 074. 13AO exhibited a uniformly elevated sky background from low-level nebulosity, due to its proximity to the galactic plane. Although Saturn was close to the top corner of the 13AE block (Figure 1, blue block), the excellent rejection of off-field scattered light by MegaCam prevented much effect on the sky background of the overall mosaic, with the background of only the chip closest to Saturn affected. All the increased sky noise is characterized by our detection efficiency (Section 5).

Subsequent imaging to track the discoveries was acquired through 2013 August. Not all discoveries were observed in every lunation due to objects falling in chip gaps or on background sources on some dates, faint magnitudes, or variable seeing in the recovery observations. In much of 2013, poor weather conditions prevented observations in sufficient IQ for us to recover the faintest objects. To compensate, from 2013 November onward we used alternative 387 s exposures in 08 ± 01 seeing for single-image passes on the block. This significantly improved the ease of later arc linkage on the discoveries (Section 6.1). Even with the occasional loss of an expected measurement, the orbital quality from the available set remains very high.

For the seven February–August lunations that the blocks were visible in 2014, the 13AE and 13AO discoveries brighter than the characterization limit (Section 5) were observed with pointed recoveries; this was possible because the high-frequency cadence in the discovery year shrank the ephemeris uncertainty to a tiny fraction of the MegaPrime FOV. A handful of fainter objects not immediately recovered in the first pointed recovery images were targeted with spaced triplets of observations in subsequent lunations until recovery was successful on all of them (Section 6.1). Generally, two observations per object per lunation were made. The large camera FOV allowed 2–10 TNOs to be observed per pointing through careful pointing choice, ensuring that the small error ellipses of all objects avoided the mosaic's gaps between CCDs. Each targeted pointing center was shifted throughout the lunation at the mean motion of the discovered TNOs within the FOV, ensuring the targeted TNOs would be imaged. Combined with the nonlinear improvement in object orbit quality (Section 6.1), which meant not all TNOs required imaging every lunation, we were able to make the necessary observations each lunation with fewer than the discovery opposition's 21 pointings.

The internally generated catalog provides a high-precision reference for our measurements; these highly precise measurements must then be accurately tied to an external reference system. The 13AE and 13AO blocks were not completely within the area imaged by the SDSS (Ahn et al. 2014), which if available would have been preferentially used due to its superior accuracy and depth. Instead, 2MASS (Skrutskie et al. 2006) was used, with corrections based on UCAC4 (Zacharias et al. 2013). 2MASS is deeper than UCAC4 and therefore has a higher source density. However, there are small but significant zonal errors in 2MASS. When UCAC4 and 2MASS are compared, small zones of ∼01 shifts between the two catalogs are apparent. The shifts occur with a periodicity of 6° in declination, corresponding to the observing pattern of 2MASS, which indicates that the errors lie in 2MASS (see Figure 2 of Gwyn 2014). Therefore we use the 2MASS catalog which provides the source density needed to precisely link our internal catalog to the external reference, corrected to the UCAC4 catalog, which provides a more accurate translation to the International Celestial Reference System.²⁹

3.1.1. Proper Motions

We assessed the stellar proper motions to create our corrected astrometric catalog. The mean proper motion of the stars is due to the motion of the Sun relative to the mean galaxy. Figure 3 shows the cataloged mean proper motion represented as vectors plotted in equatorial coordinates, computed by taking the median per square degree of the proper motions of all stars in the region in the UCAC4 catalog. Neighboring vectors from each square degree are close to identical. TNOs move only a few degrees over the course of the four-year survey, and thus differential proper motions do not measurably affect the internal astrometry.

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Removal of individual stellar proper motions would improve the accuracy of the resulting astrometric calibration. For the fainter sources that form the majority of the UCAC4, however, the individual proper motion measurements are too noisy. Figure 4 shows the proper motion of stars over a quarter of a square degree. The typical uncertainties on the proper motions are about 10 mas, which, multiplied by the 10 year difference in epoch between UCAC4 and OSSOS, results in a 100 mas uncertainty in position. Furthermore, the individual proper motions are only known for the UCAC4 sources. The median annual proper motion on the other hand (in red in Figure 4) is relatively well defined, and could be used to apply a systematic correction between the catalogs.

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The corrections were therefore applied to each image by taking a subset of the UCAC4 and 2MASS catalogs from Vizier (Ochsenbein et al. 2000), determining the mean proper motion in that area, applying that to UCAC4, and matching the UCAC4 and 2MASS catalogs to each other. Working in 0.2 deg² patches, the median shift between UCAC4 and 2MASS was then applied to 2MASS. A diagnostic plot, similar to Figure 5, was produced for each image. 0.2 deg² provided a good compromise: at smaller scales, the number of sources common to both catalogs drops to the point where the precision of the shift is less than the accuracy of the reference, leading to larger random error in the shift measurements; at larger scales, the zonal errors would average out, leading to larger systematic errors in the shift measurements. The corrected result was a catalog as deep as 2MASS, but essentially as accurate as UCAC4. As better astrometric catalogs become available, such as UCAC5 (N. Zacharias 2016, private communication), followed by Pan-STARRS and Gaia, it may be possible to recalibrate the data.

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We detrended each image as it was taken each night of the dark runs, subtracting the bias and correcting the flat-field response. These preprocessed images contain a basic world coordinate system (WCS) and initial zero point. An observed source catalog was generated for each image with SExtractor (Bertin & Arnouts 1996) and cleaned of faint and extended sources. The cleaned source catalog was then matched to the external astrometric reference catalog. Once the observed source catalog and the external astrometric reference catalog were matched, the field distortion could be measured. This process is described in detail in Gwyn (2008). All OSSOS images have at minimum this level of calibration before any analysis is made. After Level 1 calibration, the astrometric residuals of the WCS are about 100 mas.

The initial matching and fitting procedure was applied to the input images. The computed WCS was then applied to the observed source catalogs to convert the x, y pixel coordinates to R.A. and decl. The R.A./decl. catalogs were then combined to produce a merged astrometric catalog covering the whole block. A given OSSOS field can be observed repeatedly on a single night (Section 2.2); including all the images would weight some parts of each field preferentially. Therefore, in such cases only the image with the best seeing was used to make the merged catalog. To merge the catalogs, sources in two different catalogs were deemed to be the same object if their positions lie within 1'' of each other, irrespective of magnitude. To avoid confusion, no source is used if it has a neighbor within 4''. Sources often lie in more than two catalogs, due to the drift of pointing centers from night to night (Section 2.2); all matches were grouped together. The result was a catalog on the original reference frame (e.g., SDSS or 2MASS, corrected to UCAC4) but with smaller random position errors and a higher source density. This merged astrometric reference catalog was then used to re-calibrate the astrometric solution of each individual image. This procedure was repeated two to three times, until the internal astrometric residuals stopped improving. The Level 2 calibration brought the astrometric residuals down to 60 mas.

To further enhance the internally generated astrometric reference frame, we generated a reference catalog from stacked images. In this step, the images with the updated Level 2 WCS in their headers were combined using SWarp (Bertin et al. 2002),³⁰ producing a large stacked image covering an entire survey block. SExtractor was run on this stacked image to generate the final astrometric catalog, and this catalog was used to calibrate the original images. This image stacking step effectively combines all the available astrometric information from each star in each image at the pixel level. In contrast, the merge by catalog method described in the previous section (and many other astrometric packages) only combines information about the centroids of the astrometric sources. The process is used to produce the final plate solution used in all OSSOS astrometry. The internal astrometric residuals were typically 40 mas after the Level 3 calibration, as shown in Figure 6.

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However, a few nearby or high-inclination TNOs (Centaurs and some scattering TNOs) moved rapidly off the main block. These were re-observed in small, single-pointing patches off the main block. These pointings are stacked separately from the main block, resulting in a plate solution not tied directly to the solution for the main block. These measurements are thus less precisely connected to others. This only occurs, however, for objects that have large intrinsic motions and thus have easier-to-compute orbits, decreasing the impact of the less precise astrometry.

The basis of the OSSOS photometric calibration is the SDSS. The SDSS photometry is converted into the MegaCam system using the following color term³¹ :

$$\begin{eqnarray}&&{r}_{\mathrm{Mega}}={r}_{\mathrm{SDSS}}-0.024({g}_{\mathrm{SDSS}}-{r}_{\mathrm{SDSS}}).\end{eqnarray} \tag{ 1 }$$

For typical TNO colors g − r ∼  0.5–1.0, MegaCam r and Sloan r are thus separated by only 0.01–0.02 mag. The MegaCam zero-point varies from chip to chip across the mosaic. These variations are stable to better than 0.01 mag within a single dark run and are relatively stable between dark runs. The chip to chip variations are measured for each dark run by using any available images which overlap the SDSS footprint; because we are measuring the differential zero-point, it does not matter for this purpose if the night was photometric.

On photometric nights, all available images overlapping the SDSS were used to determine the overall zero-point of the camera for that night. OSSOS data taken on nights that did not overlie the SDSS were calibrated using a combination of the mosaic zero-point computed nightly, and the differential chip-to-chip zero-point corrections computed for each dark run. The nominal MegaCam r-band extinction coefficient of 0.10 mag/airmass was used throughout.

The data acquired in non-photometric conditions were calibrated using overlapping images. The catalogs for each of the images were cross matched and the zero-point difference for each overlapping image pair was measured. The image overlaps are substantial; typically 2000 stars could be used to transfer the zero-point to a neighboring non-photometric image. The images overlapping with photometric images were in turn used to calibrate further images iteratively until an entire block was calibrated. At each iteration, the photometric consistency was checked. If a pair of ostensibly photometric images were found to have a large (>0.02 mag) zero-point difference, both were flagged as non-photometric and re-calibrated in the next iteration.

At Level 1 (Section 3.2), the photometric accuracy is 0.01 mag for images on the SDSS. For images not overlying the SDSS, the accuracy falls to 0.02–0.03 mag if the images were taken under photometric conditions. By Level 3 (Section 3.4), the internal photometric zero-point calibration between images within a block using this method is accurate to 0.002 mag rms (Figure 7). The photometric residuals with respect to the SDSS are better than 1% (Figure 7). Note that data are not directly calibrated with the SDSS, but rather that the ensemble of the SDSS is used as photometric standards.

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The detection efficiency of distant moving objects is a function of their apparent magnitude and their rate and direction of motion on the night of the discovery triplet observations. We characterize this detection efficiency by implanting tens of thousands of artificial PSF-matched moving objects in a temporally scrambled copy of the data set and running object detection in a double-blind manner. Additionally, we use the method of Alexandersen et al. (2014) to obtain an absolute measure of the false positive rate.

First, we create a copy of the detection triple and then re-arrange the time of acquisition in the three discovery image headers, shuffling the three images to the order 1, 3, 2. These images are passed through the software detection pipeline. Any source that is found in a time-scrambled set that was not implanted must be false; no real outer solar system object reverses apparent sky motion in two hours. Any such detections thus provides an absolute calibration of the false-positive rate (Alexandersen et al. 2014). Second, we then plant artificial objects into this time-scrambled copy and pass that through the pipeline. In the 13A data, 43,800 sources were implanted per block (57 per CCD) (Table 2). In the implanted copy, any detections must thus be either artificially injected or false positives; none can be real. Characterizing the detection efficiency in the scrambled data also avoids planted sources obscuring detection of real ones.

Each CCD thus has three sets of moving candidates, each from running a distinct set of three images through the detection pipeline:

• 1.  
  from the discovery images: potential TNOs;
• 2.  
  from the temporally scrambled discovery images (which have no planted sources): if accepted through the next stages of evaluation these become false positives; and
• 3.  
  from the temporally scrambled and planted images: planted discoveries, which if subsequently rejected are false negatives.

The detection pipeline produces 2268 sets of moving candidates per block (3 sets for each of 36 CCDs in each of the 21 fields of 13A's block grid), which are stored in a central repository. The numbers of candidates detected for the planted, scrambled and potential TNO sets are listed in Table 2. In the 13A data, only 13–19000 of the 43800 planted candidates were recovered by the pipeline. At the bright end, m_r ∼ 21, the fraction of planted sources recovered by the entire process does not reach 100%, as about 10% of the sky is covered by stars at OSSOS magnitudes. If a moving object transits any fixed source in one of the three images, it tends not to be found by the automated search algorithms unless it is much brighter than the confusing source. A gradual drop in efficiency occurs with increasing magnitude due to the increased frequency of stellar/galactic crowding. More candidates are planted with magnitudes faintward of m_r > 23.5, so that the eventual drop in detection efficiency is well quantified, and in the 13A data most were planted fainter than could be detected.

The moving candidates are assessed by visual inspection, in two phases. In the first round of visual inspection, 25,287 candidates from 13AE and 18,909 candidates from 13AO were assessed (Table 2, "Detected" columns). Our interface is configured as a model–view–controller stack, using ds9 as the windowing GUI. The images are stored on a cloud server and image stamps retrieved as needed (Kavelaars 2013). Each person is presented with the candidates from a randomly selected set; they do not know the nature of the set being inspected. During evaluation, the set is locked to that person. A set is released back to the pool if the person exits the interface before evaluating all sources in the set. Once fully evaluated, the set's metadata are updated (identifying that it was completely examined, and who inspected it) and the results of the inspection are uploaded to the central repository. This robustly supports multiple people simultaneously working to examine a block's discovery characterization. There is remarkably little variation in detection efficiency between the five people who assessed subsets of the 13A data (Figure 8); most importantly, there is strong agreement on the characterization threshold (specified below).

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Any moving-object search approaching the noise limit will generate spurious candidates; the detection pipeline has proven its ability to massively reduce the number of such candidates (Petit et al. 2004). The most common type of spurious candidate shown to people as part of the first vetting phase was due was due to a candidate being formed from background noise popping above the noise threshold in three places, approximately linearly spaced with time. These false detections are easily recognized and rejected by visual inspection. The second frequent spurious-candidate class were bright spots along diffraction effects that happened to align, within the allowed angles of movement (Section 4), across the image. Table 2 shows how the potential TNO candidates decrease from some two thousand (Table 2: "Detected: potential TNOs") to under two hundred (Table 2: "Potential TNOs after human review: #1") due to this first inspection.

The second visual inspection evaluated the remaining moving object candidates. For resilience, this second examination was preferentially done by a different person (ensured via the metadata for each moving object candidate). All accepted candidates had aperture photometry measured with daophot (Stetson 1987). We manually assigned standard flags from the MPC³² to the photometry and astrometry of the candidates from the discovery images. These measurements defined the discovery triplet for each object (Appendix A). The potential TNOs are cut by a half to a third from their previous number by this inspection (Table 2: "Potential TNOs after human review: #2"). False positives and negatives from the whole process are given in the final two columns of Table 2. False positives are any candidates from a scrambled set that survived the second examination. False negatives are any planted candidates that were successfully identified by the automated pipeline, but then (incorrectly) rejected during either of the visual inspections. No false positives that were brighter than the characterization limit survived the two-stage visual assessment process. This implies that our efficiency function (discussed below) is of high accuracy and unpolluted. The false negative rate produced during the twofold visual inspection was 0.75%, all due to superposition of a candidate on a bright source or an extended background source. The false negatives were independent of the planted candidate magnitude and of candidate motion rate, instead showing a minor dependence on the sky density of extended background sources. This shows that about 1% of real TNOs would have been rejected, and this is accounted for by the efficiency function (detailed below).

At a certain magnitude depth in the images, about m_r ∼ 24 for OSSOS, the S/N and thus the efficiency with which we can detect sources rapidly falls off, setting a natural completeness limit in magnitude. Petit et al. (2004) determined that at fainter than ∼40% efficiency, a person is no longer confident that the pipeline's moving candidates are real; a small error in the characterization at these low efficiencies would result in a large effect in the subsequent modeling. After all the candidate sets for a given block were examined (Figure 8), a function was fitted to the aggregate of the raw efficiencies produced from each person blinking the planted sets of the 756 chips per survey block (Figure 9). The crucial efficiency versus magnitude behavior was fit to the formulation (shown graphically in Figure 9)

$$\begin{eqnarray}&&\eta ({m}_{r})=\displaystyle \frac{{\eta }_{o}-c{({m}_{r}-21)}^{2}}{1+\exp \left(\tfrac{{m}_{r}-{m}_{L}}{w}\right)}\end{eqnarray} \tag{ 2 }$$

where η_o is roughly³³ the efficiency at m_r = 21. Equation (2) quantifies the strength of a quadratic drop, which changes to an exponential falloff over a width w near the magnitude limit m_L, similar to that used by Gladman et al. (2009, Equation (2)). This function fits the OSSOS detection efficiency better than the frequently used hyperbolic tangent function (Gladman et al. 1998; Trujillo et al. 2001). The parameters we obtained for the motion-rate range 05–7''/hr for 13AE were η_o = 0.89, c = 0.027, m_L = 24.17, w = 0.15, and for 13AO were η_o = 0.85, c = 0.020, m_L = 24.62, w = 0.11.

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We used this fit to set our characterization limit: the magnitude above which we have both high confidence in our evaluation of the detection efficiency, and find and track all brighter objects. This is not at a fixed-percentage detection efficiency, unlike some previous surveys (Jones et al. 2006; Kavelaars et al. 2009; Petit et al. 2011; Alexandersen et al. 2014), but rather set more stringently at the apparent magnitude where OSSOS ceased reaching 100% tracking efficiency due to low flux. In practice this was usually close to the magnitude where the detection efficiency falls to 40% (see Figure 9). The characterization limit is dependent on the moving object rate of motion: our limits are listed in Table 3.

Figure 9 illustrates the variation in sensitivity to different angular rates of sky motion. Our survey is optimized for detection of objects at Kuiper Belt distances: this is reflected in the greatest detection efficiency for objects when they are moving with rates of 05–8''/hr. This gives OSSOS sensitivity to distances out to ∼300 au, where, on a circular orbit, an object would move ∼05/hr. Our sensitivity to close, fast-moving objects (>10''/hr) is similar to our sensitivity to more distant objects for m_r < 23.5, and decreases to 40% detectability at slightly brighter magnitudes than for the slow movers in the Kuiper Belt (Figure 9). As an additional proof of the survey's sensitivity to Centaurs, the proximity of Saturn to the 13AE block placed a few known satellites on one field of 13AE. Our analysis recovered the irregular satellite Ijiraq at 9.8 au (Figure 1), the only moon above the 13AE magnitude limit, exhibiting some minor and expected elongation along its direction of motion.

All objects listed in the MPC that fell on the survey coverage of the discovery triplets were recovered, as seen by the overlapping of symbols in Figure 1 and noted in Table 4. While 2003 HD57 was very close to the survey coverage (Figure 1), it was not within the discovery observations: this object fell two pixels south of the first image of the 13AE discovery triplet. These recoveries of known objects aid our confidence in our measured detection efficiency.

To be usefully compared to the observed orbital distribution, a model of the TNO orbit distribution must be biased in the same way as the observed sample. Although free of ephemeris bias, the OSSOS pointing history (Section 7) and flux limits create a biased view of the intrinsic population. These biases are precisely modeled by the OSSOS survey simulator. Our approach is primarily one of model rejection rather than fitting. The simulator selects a set of detected objects out of a given orbit model. This survey-biased sample of the model orbital distribution forms a valid statistical comparison to the OSSOS TNO discoveries. The decision about how to compare the simulated set of detections to the OSSOS set of characterized discoveries, those brighter than their block's characterization limit, is then a statistical problem. Various approaches are described in Kavelaars et al. (2009), Petit et al. (2011), Gladman et al. (2012), Alexandersen et al. (2014), and Nesvorny (2015).

The simulator is similar to that described in Kavelaars et al. (2009) and Petit et al. (2011). An orbit distribution model is exposed to the survey biases via the survey simulator. Each model object is specified by a set of orbital elements and an absolute magnitude in some reference passband. An improvement in the OSSOS survey simulator is that each model object is also assigned a surface reflectance, specifying that model object's color in all filters. Further detail on model object apparent magnitudes is given in Appendix A. The current implementation of our simulator can take into account rotational variability; we currently have insufficient information in the OSSOS discovery and tracking data to take advantage of this improvement. Our discovery observations, covering a two-hour baseline, do at least potentially measure variability over a moderate fraction of typical TNO rotation periods of 4–14 hr (Duffard et al. 2009; Benecchi & Sheppard 2013). A follow-up program to comprehensively measure rotational variability for the OSSOS discoveries would allow us to assign a light curve to model objects and use this capability of the simulator. The survey simulator can also apply the survey biases of other characterized surveys to the input orbit model, if the discovery and tracking circumstances of the additional surveys are available.

Determining the intrinsic size of a TNO sub-population is an important model constraint. Once a model distribution has been chosen, the simulator can be used to create a model-dependent estimate of the size of the intrinsic population. The simulator will provide as many detected model objects as desired. When the same number of model detections as were found by the input survey is achieved, the number of model objects that were checked is an estimate of the intrinsic TNO population.

Objects found by OSSOS must have their many observations converted into an orbit. Following discovery in the opposition triplet, we knit together observations of each TNO from every lunation into longer orbital arcs, starting within the discovery lunation and working outward in time. This iterative procedure started by sending the discovery arc to the archival search tool Solar System Object Image Search (Gwyn et al. 2012)³⁴ , to query for further available OSSOS imaging containing the TNO. This tool identifies all available archived imaging, but as OSSOS is deeper than most previous wide-field imaging work, we have not yet made use of other data sets. Starting the initial search by only querying for observations near in time to the discovery epoch kept on-sky uncertainties below 30'', minimizing the number of images to examine (Figure 1, Jones et al. 2010). We then visually identified the TNO within or near the predicted 1σ on-sky error ellipse by comparison with OSSOS images of the same piece of sky at a different time. The OSSOS observing strategy of slowly moving pointings (Section 2.2) yielded large numbers of these comparison images. The resulting astrometry was then fed back into the search tool to request more OSSOS imaging in dark runs further from the detection triplet. We iterated until an arc over the entire discovery year was assembled. Extending each 13A OSSOS object's arc with all the images taken in the 13A discovery semester, an arc of 150–183 days, yielded preliminary orbits with fractional semimajor axis uncertainty of σ_a ∼ 0.1%–1% (Figure 10). The small orbit uncertainty was produced by the combination of long arcs in the discovery opposition, frequent sampling, and the high-precision astrometric solution (Section 3). This is an order of magnitude better than that obtained by Petit et al. (2011).

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Even though the locations of the objects were unknown when the first-semester observation suite was acquired, the slow drifting of the blocks at Kuiper Belt mean-motion rates retained almost all objects within the observations. Independent of its characterization limit (Section 5.1), each block has a tracking fraction: what fraction of the objects above the characterization limit were recovered outside of their discovery triplet and generated a high-quality orbit. We recovered 100% of our discoveries that were above the characterization limit in both 13A blocks.

The second year of OSSOS observations provided astrometry that would allow classification of the orbit (Section 6.2). The first-year orbits provided such accurate ephemeris predictions (sub-arcminute 1σ on-sky error ellipses: predominantly <10'') that recovery was almost always immediate in the observations from the first lunation of the second opposition. Those few objects which sheared off the block during the discovery year still had observational arcs spanning at least several lunations. In these cases the uncertainty at the start of the observations the following opposition were ∼30', and a manual, visual search resulted in the recovery of the object (Section 2.3). Initial recovery of the 13A discoveries in 2014 extended their arcs to ∼360 days, dropping the fractional uncertainty in semimajor axis by a factor of 2–3 (depending on which lunations the objects were seen in 2013) to σ_a = 0.03%–0.3% (Figure 10). Later extension of the arc through 2014 brought the 13AE objects to a median ${\sigma }_{a}=0.03 \%$ and a median σ_a = 0.07% for 13AO; the difference is due to the existence of more observations per dark run for the 13AE block. Some objects in particular converged quickly to σ_a < 0.1%; by early in 2014A, nearly half the objects in 13AE, particularly cold classicals, reached sufficiently high orbit quality (Figure 10) that only sparse sampling throughout the remainder of the semester was required (Section 2.3). The total number of observations on the objects varied between 14 and 55, though the median was 26; the number of observations is somewhat correlated with orbital quality (Figure 10), but the distribution of those observations in time is also important for the convergence of σ_a. These two year observing arcs are nominally sufficient to create our final orbit estimate.

We note that the figure-of-merit σ_a is only a useful approximation that does not capture all aspects of orbit quality. For example, resonant libration amplitudes (discussed for OSSOS in Volk et al. 2016) have uncertainties that while dominated by σ_a, also depend on e and the accuracy of angles like the ascending node Ω and the pericenter's longitude ϖ. Location within the resonance also matters: an object with orbital elements on the edge of a resonance might need a much smaller σ_a to determine the libration amplitude to 10° precision than if its elements were near the center of the resonance.

Our subarcsecond astrometry on moving targets travelling several degrees across the sky is a major factor in the high quality of the OSSOS orbits. It is substantially due to the use of a single astrometric solution over the entire area that a given block traces out over the two years of the survey (Section 3). The high quality of the OSSOS astrometric catalogs eliminates nearly all of the astrometric catalog scattering that Petit et al. (2011) encountered: the median OSSOS astrometric residuals around the best orbit fit are twofold lower than those of Petit et al. (2011), who found typical orbit-fit residuals of 025 (Figure 11). The catalog approaches what the future Gaia catalog will provide in absolute astrometry. Only for our very brightest objects is the astrometric scatter in the solution slightly worse than the centroid uncertainty—at the characterization limit, the residuals are centroid-limited. Further improving the internal astrometric solution's scatter will therefore not result in improvement to the OSSOS orbit precision.

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The classification scheme for the OSSOS detections is that described by Gladman et al. (2008), which we briefly summarize here. A best-fit orbit for each OSSOS detection is computed using the Bernstein & Khushalani (2000) algorithm. Maximum and minimum semimajor axis orbits consistent with the observations are found by searching the parameter space, starting at the best fit, via a Monte-Carlo method to identify an orbit in the 6D parameter space with the two extremal values in a, which have residuals no worse than 1.5 times the best-fit orbit's residuals.

These three barycentric orbits are converted to heliocentric, ecliptic coordinates and integrated forward in time for 10⁷ years using the rmvs3 subroutine within the SWIFT integrator package (Levison & Duncan 1994); the planets' positions are taken from the JPL Horizon's service (Giorgini et al. 1996) for the epoch of the orbit fit. These integrations are first checked for resonant behavior, defined as libration of a resonance angle of any resonance up to 30th order within 2% of the object's average semimajor axis (see further discussion in Volk et al. 2016). Objects with a < 30 au and not resonant with any planet are classified as Centaurs. An object is classified as scattering if its semimajor axis varies by more than 1.5 au during the integration. Objects with constant semimajor axis over the 10⁷ yr period are classified as detached if they have e > 0.24 or as classical if they have e < 0.24. As in Gladman et al. (2008), this eccentricity division is arbitrary to maintain a distinction between objects with pericenters decoupled from Neptune and non-resonant low-e TNOs. Classifications are considered secure if all three integrations for an object receive the same classification. The fraction of securely classified objects that we achieve within two years is 94%. In contrast, objects in the MPC ensemble that have been observed since discovery with sparser cadences lack classifiability within this timeframe (Gladman et al. 2008).

However, orbital insecurity is still a property of some characterized, fully tracked OSSOS discoveries. This is not due to poor-precision measurements; even with excellent ground-based data in 05 seeing, there is a fundamental degeneracy to a suite of orbits, all of which produce the same short-arc behavior. Most OSSOS objects were not secure in their first year of observation, when orbital arcs were usually four or five months long. The addition of even a single dark run in the second year usually resulted in a classical-belt object identification being secure. Secure resonant identification usually required the full suite of dark runs in both observation years. During the four-year duration of OSSOS, insecure objects will continue to be tracked until their classifications become secure; for example, ten of the 13A discoveries received another measurement in 2015 January and March to improve orbital quality. All of the currently insecure classifications are due to proximity to resonances of at least second order.

One of the important findings of Petit et al. (2011) was the substructure present in the a/e distribution of the cold component of the main classical belt. With the OSSOS first-quarter sample, we can test for the existence of this structure in an independent data set. Petit et al. (2011) represented this substructure in the L7 model by two superposed components. A small kernel component compact in a and in e was centered near 44 au. Overlaying this was a second population, the stirred component, which is smooth in semimajor axis distribution, low in inclination, and occupies q = 38–44 au non-uniformly, with a = 42.4–47 au. Its inner edge begins at the ν₈ secular resonance and the outer bound is the 2:1 mean-motion resonance. The stirred component could have been slightly dynamically agitated by weak interactions. The split to two components was informed by the clumped, a-dependent nature of the e distribution. Figure 13, particularly the a/i plot at the lower left, shows that indeed the over-density near a = 44 au is also present in the OSSOS discoveries.

However, to investigate if Petit et al. (2011) over-interpreted the previous detections, we tested the detected OSSOS a distribution in turn against a smooth distribution and against the L7 model of the classical belt substructure (Figure 14), using the same Anderson–Darling tests³⁶ for the a distribution as were done by Petit et al. (2011). The data demand a substructure in the cold component: a model using only a smooth a distribution for the cold component, with no kernel, was rejected at more than 95% confidence by the OSSOS detections. We therefore confirm that there is a real "kernel" concentration in the Kuiper Belt in a narrow semimajor axis range around 44 au. While it is plausible that other two-component models might be used to represent the classical belt, the L7 model at present still provides a valid representation of the orbital distribution for the main belt's cold component: it could not be rejected by the OSSOS sample (Figure 14). However, the greater sample density of the kernel will provide further constraints on scenarios where the kernel formed as a fossil population from the former location of the 2:1 resonance, left as an effect of a discontinuous changof Neptune's semimajor axis during its migration (Nesvorny 2015).

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The first-quarter OSSOS sample includes the newly discovered object o3e45 (2013 GQ₁₃₆), which has a = 48.72 au, e = 0.173, and i = 2031. With q = 40.3 au (Figure 13), this object lies along a natural extension of the stirred component. Crucially, its orbit is beyond the current barrier of the 2:1 resonance (Figure 12). If this object is part of the smoothly a-distributed "stirred" component that we modeled in the cold main belt, there would be strong cosmogonic implications. o3e45 joins only a few other published objects with low-i just beyond the 2:1 resonance (Table 6): in particular, (48639) 1995 TL₁₈ (Gladman et al. 2002), 2003 UY₂₉₁ (Gladman et al. 2008), and 2011 US₄₁₂ (Alexandersen et al. 2014). The key structural features in this region are the 40–42 au range where the kernel perihelia center is located, the a ≃ 44.5 au outer edge of the kernel, and the 2:1 resonance, centered at 47.7 au, with a width ±0.4 au. In this context, these three objects imply a scenario where present a > 44.5 au members of the stirred component are objects shifted from a primordial a < 44.5 au. In a past where Neptune's eccentricity was larger than at present, these objects were stirred by gentle close encounters, which minimally modified their eccentricities and nudged them out into a higher-a population tail. Could there now be a continuous distribution of primordial cold objects, scattered from initial a = 40–42 au orbits, that presently orbit with perihelia in at their original position? This could require cosmogonic models to scatter cold objects into a structure that reaches even beyond the 2:1 resonance, while creating or preserving a concentration of the same cold objects at a ∼  44 au. Alternatively, these low-i a > 48 au objects could be in situ remnants of an original disk extending to at least 50 au (Lykawka & Mukai 2008). Their low number implies a relatively small population (Nesvorny 2015).

The L7 model, which we confirmed in Section 8.1, did not have an "outer" cold main classical Kuiper Belt beyond 47 au, as the hot classical component of the L7 model sufficiently explained the CFEPS detections. We therefore test if the stirred component of the L7 model of the cold main classicals can extend into the outer classical belt: if present, a certain number of detections of this population would be made by OSSOS. We used the same population $P(a)\propto {a}^{-2.5}$ distribution as in Petit et al. (2011) (Appendix A) and as in Section 8. The q distribution of the component was allowed to be wider than in the L7 model, going from 38 au to the a value being tested. We excluded component a values that occurred in the 47.4–48.2 region occupied by the 2:1 resonance. Using the OSSOS survey simulator, we confirm that the detection of one low-i, a > 47 au object, as we found in this survey (o3e45), is consistent with a stirred component smoothly extending to at least 49 au. This model could not be rejected by the detections. The further the stirred component extends, the higher the number of low-i, a > 47 au detections that should be made by OSSOS. Extending this component further to 60 au would imply five low-i, a > 47 au detections by OSSOS. (This continues to hold, though at the 92% confidence level, if the test is instead made with the power law of the distribution steepened up to $P(a)\propto {a}^{-4.5}$). As we have only one such OSSOS detection in the sample presented in this work, we reject a stirred component extending beyond 60 au at the 95% confidence level, under the assumption that the smooth extension is a power law.

An alternate hypothesis is that o3e45 and the three previously discovered low-i, a > 47 au objects are simply the low-i tail of the hot population of the main Kuiper Belt. We find that o3e45 has a low probability of being a member of this hot component. The CFEPS L7 model predicts that the 13A OSSOS blocks have just 5% probability of detecting one or more hot component objects in the a > 47.5 au, i < 5°, q > 40 zone, where we have one detection. Detection of three to four more objects in this zone of orbit parameter space is needed before more conclusive statements can be made, to determine the abundance of such objects in future OSSOS blocks relative to the abundance of the hot population.