Searching for moving objects in HSC-SSP: Pipeline and preliminary results

Abstract

The Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP) is currently the deepest wide-field survey in progress. The 8.2 m aperture of the Subaru telescope is very powerful in detecting faint/small moving objects, including near-Earth objects, asteroids, centaurs and Tran-Neptunian objects (TNOs). However, the cadence and dithering pattern of the HSC-SSP are not designed for detecting moving objects, making it difficult to do so systematically. In this paper, we introduce a new pipeline for detecting moving objects (specifically TNOs) in a non-dedicated survey. The HSC-SSP catalogs are sliced into HEALPix partitions. Then, the stationary detections and false positives are removed with a machine-learning algorithm to produce a list of moving object candidates. An orbit linking algorithm and visual inspections are executed to generate the final list of detected TNOs. The preliminary results of a search for TNOs using this new pipeline on data from the first HSC-SSP data release (2014 March to 2015 November) present 231 TNO/Centaurs candidates. The bright candidates with H_r < 7.7 and i > 5 show that the best-fitting slope of a single power law to absolute magnitude distribution is 0.77. The g − r color distribution of hot HSC-SSP TNOs indicates a bluer peak at g − r = 0.9, which is consistent with the bluer peak of the bimodal color distribution in literature.

1 Introduction

Minor planets are the proxy to understand the history and evolution of the solar system. In the past two decades, surveys have used different facilities to discover near-Earth asteroids (NEAs), main belt asteroids (MBAs), Centaurs, and trans-Neptunian Objects (TNOs). For the nearby objects (NEAs, MBAs), small telescopes with quick response times are very efficient at detection and are thus useful to help understand the population of Earth’s neighborhood. For more distant objects (Centaurs, TNOs), large telescopes are used to collect more photons from objects with less reflecting light (Elliot et al. 2005; Kaiser et al. 2010; Petit et al. 2011; Alexandersen et al. 2016; Bannister et al. 2016). The physical properties of only the brightest or largest objects have been well studied, because it is difficult to obtain accurate measurements for small objects at such large distances. However, the fainter or smaller objects can provide important clues towards understanding the collisional and accretion processes in the evolution of the solar system (Kenyon & Bromley 2004; Pan & Sari 2005; Benavidez & Campo Bagatin 2009). Recent spacecraft missions, including the Rosetta mission to the comet 67P/Churyumov-Gerasimenko (Fornasier et al. 2015) and the Hayabusa mission to 25143 Itokawa (Fujiwara et al. 2006) reveal that our understanding of small solar system objects is quite limited.

The Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP) is a large program on the 8.2 m Subaru telescope, using the large 1.7 deg² field-of-view (FoV) camera, the Hyper Suprime-Cam (HSC), to survey around 1400 deg² of the sky. The uniqueness of this facility makes HSC-SSP the deepest wide-field survey currently in operation. Having started in 2014, HSC-SSP will use 300 Subaru telescope nights over six years (2014–2019).

The cadence of a wide-field survey is crucial to efficiently detect moving objects. The general methodology to detect TNOs in the following projects is to search near (or nearest) neighbor detections and produce a pair or a triplet corresponding to the moving rates of real moving objects, then verify the candidates with Initial Orbit Determination (IOD) software. For a dedicated survey of TNOs, the survey cadence usually requires a pair or a triplet of exposures with one to a few hours’ separation and the same pointing to discover the objects. The Deep Ecliptic Survey (DES) was one of the first wide-field surveys focused on the outer solar system objects (Elliot et al. 2005). After that, the Canada–France Ecliptic Plane Survey (CFEPS) was the first dedicated survey with a full characterization including orbital parameter determination and detection efficiencies (Petit et al. 2004; Kavelaars et al. 2009; Petit et al. 2011). The CFEPS used a set of three exposures (∼1 hr cadence) to resolve the motions of TNOs. Following the CFEPS, the Panoramic Survey Telescope and Rapid Response System 1 (Pan-STARRS 1 or PS1) project searched for solar system objects in a 3π solid angle of the sky. The major goals of PS1 were to detect NEAs (Wainscoat et al. 2014) and TNOs (Chen et al. 2016; Lin et al. 2016) with a sub-hour cadence. In the above projects, a specific pipeline was designed to operate with the preferred cadence. The PS1 moving objects pipeline, the Moving Object Processing System (MOPS: Denneau et al. 2013), was applied to detect asteroids and NEAs using catalogs of transient detections generated from subtracted images. The PS1 Outer solar system (OSS) team developed a different pipeline to detect TNOs using catalogs of individual exposures to increase the detectability of slow-moving objects (Holman et al. 2015).

The major goal of HSC-SSP is to address outstanding astrophysical questions such as the nature of dark matter and dark energy, the cosmic re-ionization, and galaxy evolution over cosmic timescales. In this survey, a wide-dithering pattern (∼1/3 field of view, ∼ 0.°6) with sub-hour cadence (10–30 min) under similar weather conditions is applied to fill up the gaps between CCDs of HSC in order to obtain complete coverage of a targeted field (see figures 5 and 7 and subsection 3.3 in Aihara et al. 2018a). The average visit numbers of gr and izy for a specific sky position are 4 and 6, respectively (see Aihara et al. 2018a for the detail of survey design). The observations of one dithering pattern for a given filter are implemented in a single night, i.e., no further observation of a given filter will be obtained in following HSC-SSP observations. Such a survey strategy makes it extremely difficult to detect moving objects using the conventional techniques used by the TNO surveys described above. Another issue regarding HSC-SSP data is that there are too many false transient detections after removing stationary sources. The KD-Tree (Bentley 1975; Kubica et al. 2005) algorithm was extensively adopted in searching moving objects to provide fast and scalable performance (Denneau et al. 2013; Holman et al. 2015; Vereš & Chesley 2017). As mentioned in Denneau et al. (2013), the abundant false tracklets linked from a database with high false transient detection rates can clog and contaminate subsequent data processing. Then PS1 MOPS used the flags and the relation of magnitude and signal-to-noise to reduce the false transient rate, because most of the false detections are residual patterns produced by image subtraction. However, most of the false transient detections in HSC-SSP catalogs are real astronomical sources, i.e., faint stars or galaxies, which were detected in better weather conditions and could not be removed using stationary catalog (see subsection 3.4). In addition, the clumped false transient detections around bright stars also produce a significant number of false tracklets and require an unreasonable amount of CPU time in following steps. Nevertheless, we would still like to utilize the HSC-SSP data set to search for small TNOs. A larger database of small TNOs is essential for determining the intrinsic size distribution of TNOs and understanding collisional history. The survey parameters of HSC-SSP in FoV and depth have a unique potential in finding a large number of such objects.

In order to search for TNOs in this data set, we thus needed to develop a new moving object pipeline, HSC-MOP, to detect solar system objects in the HSC-SSP data. The pipeline is capable of detecting the moving objects in a wide-field survey with a non-uniform dithering cadence like that of the HSC-SSP. This pipeline has the ability to detect moving objects in images with different time separations and different limiting magnitudes.

The rest of this paper is organized as follows. In section 2, we introduce the first data release of the HSC-SSP, which includes observations taken from 2014 to 2015 (Aihara et al. 2018b). In section 3, we describe our moving object pipeline. In section 4, we present the preliminary results of a search for TNOs using our pipeline on the first HSC-SSP data release. Finally, in section 5, we conclude the paper with a summary of our results.

2 Data status

The HSC-SSP survey is executed by the HSC, which consists of 116 2048 × 4176 pixel CCDs (104 of the CCDs are for science), with a pixel scale of 0|${^{\prime\prime}_{.}}$|168 (Miyazaki et al. 2012). With a 1.76 deg² FoV, HSC-SSP will survey ∼1400 deg² using Sloan-like g, r, i, z, and y broad-band filters. The first data set was released on 2017 February 27 (Aihara et al. 2018b).¹

There are three layers of the HSC-SSP survey which cover WIDE, DEEP, and UDEEP fields, each with different coverage areas and limiting magnitudes. The WIDE layer covers ∼1400 deg² with 10–20 min total exposure time. The DEEP and UDEEP layers are the smaller (<7 deg²) and deeper layers, aimed at chosen fields with >1 hr total exposure time. We only process the WIDE layer of data in this study to maximize the FoV for the search of TNOs. Note that the first data release of HSC-SSP only includes the sky regions covered in all five filters, which is different from what we analyzed in this study—we did not require the fields to be imaged in z or y bands because the low flux of TNOs in z and y bands result in very poor detectability. We reduced the HSC-SSP data internally and did not use the released data set. The HSC-SSP observations are acquired in patches, each patch covering a sky area formed by a dithered layout of the 1.7 deg² HSC FoV. As mentioned in section 1, the average visit numbers of gr and izy for a specific sky position are 4 and 6, which have the total time span of approximately 0.6–2 hr. Using this dithering pattern, the gaps between CCD chips could be filled and the survey area would have the required exposure depth for the primary science goals.

Because the weather conditions and schedule arrangements vary in each run, the HSC-SSP has a flexible schedule for its sequence of observations. As a result, the patches observed with each filter in a single dark run have different sizes. In this study, we analyzed the images with deepest limiting magnitudes i.e., ∼3 min exposures taken in HSC-g, HSC-r, and HSC-i filters. The calibration images using a shorter exposure time (∼30 s) are not included in this study. The limiting magnitude of each HSC-r exposure is typically 25.0 to 25.5 mag. Note that the original r- and i-band filters of HSC (“HSC-r” and “HSC-i”) were replaced with new ones (“HSC-r2” and “HSC-i2”) in 2016 June and 2015 November, respectively. The transmission curve for the old filters and the new ones are similar, but the new HSC-r2 and HSC-i2 filters have more uniform transparency than HSC-r and HSC-i across the effective area. There is no data using new filters in this study.

Because the HSC-SSP is not a dedicated survey for solar system science, many observations are not suitable for searching for moving objects. Two conditions have to be considered in our analysis. First, the solar elongation is a crucial celestial parameter for observing solar system objects. Due to the phase effects, objects become fainter the further their locations from opposition. Furthermore, for objects observed at opposition (∼180° solar elongation angle), the parallax from the motion of the Earth dominates the apparent motion of objects across the sky (except for NEAs), such that the rate of apparent motion is strongly dependent on the distance of the objects. The actual motion of the objects provides substantial contributions to the apparent motion only when the solar elongation is ≲140° or ≳220° (≳40° from opposition). The rates of motion of asteroids and TNOs are thus occasionally identical when the observations are far from opposition, causing confusion (2–3 arcsec hr⁻¹, see figure 1). To avoid possible confusion in our detections, we limit our search to data taken within ±40° from opposition (see figure 2). Secondly, we only consider the dark runs that have enough overlapped area among two bands and/or days observations in this study. With these limits, ∼221 deg² out of the 333.5 deg² survey area taken from 2014 March to 2015 November was used for this study (see figure 3 and table 1). For example, the observations around RA ∼130° have solar elongations of ≳220° or ≲140° (opposition angle ≳40°), so these data are excluded in our analysis.

3 Pipeline

This section contains details about each step of our moving object detection pipeline, HSC-MOP. We begin with a brief overview, followed by detailed explanations of each step.

3.1 Overview

Our process starts from the reduction of raw images with hscPipe, the official HSC-SSP pipeline. hscPipe generates the catalog of detected sources for each exposure. Each field is then divided into different sky regions using HEALPix (Górski et al. 2005). The catalogs for each exposure which overlap each HEALPix partition are combined into a master catalog. Objects which appear at the same place in multiple exposures are entered into a stationary catalog. A combination of machine-learning algorithm and hscPipe flags are then used to find candidate non-stationary (that is, moving) sources. After we build catalogs of non-stationary sources, a linear search algorithm is applied to identify possible moving objects. Such candidates would appear as non-stationary objects in different exposures with offset positions consistent with a moving object. These candidates are then verified with initial orbit determination (IOD) to generate the list of possible candidates. Finally, all candidates are checked by visual inspection, using the Zooniverse platform. Figure 4 shows the flowchart of this pipeline.

3.2 hscPipe

hscPipe is the official pipeline for processing data obtained from the HSC, and is maintained by the HSC-SSP team (Bosch et al. 2018). It was built using the prototype pipeline that is being developed by the Large Synoptic Survey Telescope (LSST) team² (Ivezic et al. 2008). The algorithmic and conceptual foundations were inherited from the Sloan Digital Sky Survey (SDSS) Photo Pipeline (Lupton et al. 2001). The HSC-SSP data are processed through this pipeline, including the steps of debiased, flat-fielded, and astronometric calibration. The standard outputs from hscPipe include FITS table catalogs and calibrated images. hscPipe uses the internal Pan-STARRS 1 catalog (⁠|$ps1\_pv2$|⁠) to calibrate astrometry and photometry (Schlafly et al. 2012; Tonry et al. 2012; Magnier et al. 2013). The average astrometric scatter in an individual chip image is smaller than 30 mas. It should be noticed that the current version of hscPipe still has some limitations in processing CCD chips containing very bright stars.

3.3 HEALPix

To handle the dithering observations, we adopted the Hierarchical Equal Area isoLatitude Pixelation of a sphere (HEALPix) to manage the catalogs acquired in a dark run. HEALPix is an algorithm that produces a subdivision of all the sky, with each pixel covering the same surface area as every other pixel. We adopt nside = 32 (12288 pixels for all-sky) in the pipeline to build a set of reasonably sized sky regions so that the pipeline can detect slower-moving objects within the same HEALPix. The mean diameter for each HEALPix is 1.°8323 (equal to 3.36 deg², see figure 5) to match the HSC FoV. Every detection catalog is separated and saved according to the corresponding HEALPix. A total of ∼100 HEALPix partitions are used in this analysis. HEALPix partitions on the boundary of the survey fields of one dark run have a few detections which only occupy a small sky region. This pipeline simply searches the candidates moving within a single HEALPix partition. The current goal of this pipeline is to discover moving objects which are slow enough to stay at the same HEALPix partition within one observational run. The detection of objects that cross from one HEALPix partition to another will be future work for finding asteroids or other nearby objects.

3.4 Stationary catalog

Most of the sources in the sky are stationary sources, i.e., background stars and galaxies. Detections of stationary sources should be made at identical locations in different exposures, no matter when the images were taken. However, depending on the search criteria, moving objects might be cataloged as stationary objects. For example, objects beyond 50 au could be observed as stationary sources if the time-span between the images is not long enough for the object to move noticeably. To avoid classifying the moving objects beyond the Kuiper Belt as stationary objects, we define a stationary object as one that is (1) detected in at least two images within a radius of 0|${^{\prime\prime}_{.}}$|5, and (2) with a separation between the image epochs longer than 20 min. We use 0|${^{\prime\prime}_{.}}$|5 instead of a larger radius after considering the HSC-SSP cadence, the false-positive rate, and the average seeing conditions of the data. The condition of time separation longer than 20 min is estimated based on the dithering cadence of HSC-SSP (see section 2) and the moving rate of distance objects. Under such conditions, only objects located at opposition and further than 100 au might be erroneously labeled as stationary objects. However, the faint stars near the limiting magnitude might be not identified as stationary sources when the weather is changing. In general, more than 95% of the sources could be removed using the stationary catalog. All theb exposures in each dark run are used to generate the stationary catalog, which is then applied in the next step to remove the stationary detections and false positives.

3.5 Machine learning to remove false positives

After removing the stationary sources, there are still ∼0.5 million unclassified source detections in each HEALPix partition. In addition to the real moving objects and transient events, the unclassified detections also include some stars, galaxies with bad centroids, and other possible artifacts. Therefore, processing all such detections without any further reductions will significantly impact the performance and speed of the moving object detection pipeline. To address this problem, we adapted a machine-learning (ML) based real–bogus system and hscPipe flags to pick up real astronomical detections and to reject the false positives. This system separates the real non-stationary sources and the false positives by using 49 parameters generated from hscPipe. These parameters mostly comprise the various photometric measurements (flux and error) and shape moments. Details of the 49 parameters are presented in Lin et al. (2018).

Our real–bogus system can reach a true-positive rate (tpr) of ∼96% with a false-positive rate (fpr) of ∼1%, or tpr ∼99.5% with fpr ∼15% (see figure 6). For the complete set of receiver operating characteristic (ROC) curves, please see figure 1 of Lin et al. (2018). We found that with the 1% fpr threshold, the system can reduce the number of unclassified detections by half. If we relax the threshold to 15% fpr, it can still reduce the number of unclassified detections by one third. After several tests, we found that the pipeline can finish the processes detailed in this section for the remaining two thirds of the detections within few days using 10 CPU cores. We therefore set the threshold of fpr at 15% so that 99.5% of the real detections get passed, while ∼85% of the original false detections get removed. For example, there are ∼0.5 million non-stationary detections in HEALPix for one SSP observation run without any false-positive cut. With the real–bogus system, ∼160000 potentially false detections are rejected. For the remaining ∼0.34 million detections, only about 10% of them are the false positive and other 90% are real astronomical sources. These real sources are dominated by the faint stars and galaxies that are not removed using the stationary source catalogs. Since the detectability of very faint objects is highly sensitive to image quality (e.g., seeing and transparency), some of them cannot be removed using the stationary selection criteria. For details of the real–bogus system, we refer the reader to Lin et al. (2018).

3.6 Grid linear search

The next step of the pipeline is to search for matched detections of a candidate moving object in a single night. To maximize the number of candidates, we developed a new algorithm to detect possible moving objects, with the following steps.

First, all non-stationary catalogs are merged into a single FITS table, which includes the time, zero-point, and image file path. The zero-point is used for calculating magnitude, while the image file path is for making postage-stamp images to be used in the following step (see subsection 3.9).

Secondly, we use a simple Monte Carlo simulation to obtain the mean direction of motion of TNOs on the sky region at the time of the dark run. We generate ∼200 observable synthetic moving objects at the distance of 3–40 au, considering a reasonable orbital inclination with ecliptic latitude. The mean direction of motion is the average vector of these synthetic objects on the sky region. This direction could represent the objects with the barycenter distance >5, including Centaurs and interstellar comets, because the moving rate of the objects beyond Jupiter is dominated by Earth’s motion. We adopt a larger width (±30°) of motion dispersion instead of 15° of general TNOs motion dispersion. Then the linear search scans the full area of a HEALPix partition within ±30° of the resulting mean direction of motion. The scans use (1) 1° as the step of scan angle, (2) 2″ as scan step in the HEALPix partition, (3) 1″ to the line as scan radius. Detections located within 1″ of a line along a given direction of motion are grouped as a subset, which will be verified if any reasonable group exists. This is demonstrated in figure 7.

With the grouped detections (sorted by RA), reasonable tracks (that is, groups of source detections spanning multiple images consistent with moving objects) are then identified using the following conditions: (1) correct time order along the line, (2) rates of motion <49 arcsec hr⁻¹ (ranging from asteroids to TNOs), (3) Δmag <2.0 across the different images, and (4) more than three detections. After the selection, the tracks of the candidates of moving objects are saved into a database. In average, 10–30 k tracks could be found in each HEALPix partition.

3.7 Linking

Once we have a track for a candidate object in the images taken over a single night, we link tracks from different nights that might belong to the same object. The criteria are (1) the ratio of moving rates <2 and the same direction of motion, (2) the position of second track should be inside of the prediction region of first track, which is based on the moving rate of first track and propagating the naive 1″ astrometric error to the time of second track. If the combination of two tracks satisfies the above criteria, the joined tracks are then examined by IOD (Bernstein & Khushalani 2000), which provides estimates of the orbital parameters, in particular semi-major axis, a, and inclination, i. If all residuals of the fit are smaller than 0|${^{\prime\prime}_{.}}$|3, we regard the object as a candidate. In each HEALPix, the pipeline could generally detect less than 2000 candidates in this step. Many candidates in this step are duplicates or objects with unreasonable orbits (a < 0).

3.8 Collection of similar candidates

The linking procedure can eliminate most of the false combinations. However, it is possible that one track in a night can link to two different tracks in another night and produce two valid candidates. It is difficult to distinguish the correct link from the false links without any visual inspection. Therefore, we collect the similar candidates (the candidates that share part of their tracks). These candidates are then visually inspected.

3.9 Visual inspection

Visual inspection is frequently used to check whether moving object candidates are real objects or false positives. A real object moves in sequence exposures with a typical point spread function or trailed shape, while a false positive is usually an artificial source produced by instruments or the sparkle of bright star. The pipeline generates postage-stamp images (fits and png) for each candidate, which are centered in the postage-stamp images (see figure 8). We only inspect objects with a > 20 au (from the IOD orbit fit) in order to exclude asteroids. The number of candidates with a > 20 au in a single HEALPix partition is usually less then 50. A set of six truncated images (three images from day one, three images from day two; the typical Δt of the two sets is within a dark run.) is uploaded to the Zooniverse platform for the inspection by team members. Zooniverse is a website platform for various projects of citizen science, which is used by many scientific projects, including astronomy and ecology (Trouille et al. 2017). The Zooniverse project builder provides a very simple interface to launch a visual inspection project with no required understanding of the backbone structure. Because of the HSC-SSP data policy, we built the visual inspection page as a private project. Every candidate which is validated by at least two team members is listed as a real object.

4 Preliminary results and discussion

We applied the pipeline described in previous section to the HSC-SSP data taken from 2014 March to 2015 November. Around 2000 moving object candidates in each dark run were detected, including asteroids, Centaurs, and TNOs. In this paper, we only present the results of our TNO search, so only the objects with semi-major axes larger than 20 au were selected for visual inspection. More than 500 candidates (including false positives) meet this criterion. A total of 231 TNO candidates were approved via visual inspection by at least two members (see table 2). Although the HSC-SSP had nine dark runs in its first data release, we only analyzed the dark runs with solar elongations in our required range, and which also have a sufficient number of exposures for the detection pipeline to function.

4.1 Detection efficiency

4.2 Orbit

As discussed above, the orbital parameters and uncertainties of each candidate are calculated using the Bernstein and Khushalani (2000) routine. The orbital uncertainties of these candidates are not negligible because the observations generally span less than a month. Because of the short arc of these observations, the predicted uncertainties on the sky grow quickly with time, making the objects difficult to follow up after the semester of discovery. We then tested the Bernstein and Khushalani (2000) routine using known TNOs with a cadence similar to HSC-SSP; the results show that the orbital inclination is the only reliable orbital parameter for a TNO with short-arc observations. We are thus able to separate the sample into a cold population (i + σ_i < 5°) and a hot population (i − σ_i > 5°) (Volk & Malhotra 2011). After this process we find a total of 164 hot objects in our list of TNOs. This simple cut means that there will be a minor contamination of hot objects in the cold population, but our hot population is useful for qualitative analysis.

4.3 Absolute magnitude distribution

Although the orbital uncertainties of these candidates do not allow dynamical classification, flux corrections are still achievable. The absolute magnitude H of each candidate can be calculated using the photometry and initial orbital solutions. Even though the short arcs of these candidates produce uncertainties of around 2 au in the barycentric distance (Bernstein & Khushalani 2000), our results are comparable with those of Fraser et al. (2014). Figure 10 shows the histogram of barycentric distance of HSC-SSP TNOs. These preliminary results have not yet been debiased with the detection efficiencies, so we only consider the bright candidates with H_r < 7.7. In figure 11, the best-fitting slope of a single power law to the absolute magnitude distribution of hot objects with H_r < 7.7 is 0.77. This value is consistent with the results from Fraser et al. (2014), which has a slope of |$0.87^{+0.07}_{-0.2}$| before the break magnitude at H_r = 7.7.

4.4 Color distribution

The bimodal color distribution of outer solar system objects has been known for a decade (Peixinho et al. 2003, 2012; Barucci et al. 2005; Perna et al. 2010; Lacerda et al. 2014). This bimodal color distribution implies that different evolution processes or surface compositions may occur in the early history of the outer solar system. While the selected targets in the literature include the observational biases, resulting in non-uniform samples, recent research using the Subaru HSC resulted in a robust bimodal color distribution of small objects in the hot population (see figure 3 in Wong & Brown 2017). The g − i color distribution of our sample could enable us to re-examine this bimodal color distribution of small hot TNOs. Although the rotational effects and observational biases have not been removed from our results, the photometry from using two filters in different nights could still provide approximate color properties of the TNO surfaces.

As mentioned in above, the HSC-SSP is not optimized for solar system science, so the survey cadence in the choice of filters is decided by the survey team. The g − r colors distribution of 116 hot TNOs indicate a peak at 0.6 (see figure 12). The g − i color distributions of only 24 hot TNOs are available in the first data release (images taken between 2015 March and May). In figure 12, a sharp bluer peak at g − i = 0.9 is consistent with the bluer peak (g − i = 0.91) of the bimodal color distribution in Wong and Brown (2017). Unfortunately, the sample of redder TNOs (g − i > 1.0) found in the HSC-SSP is currently too small to compare with the redder peak at g − i = 1.42 reported by Wong and Brown (2017). With additional discoveries of TNOs beyond the first HSC-SSP data release, a larger database of the hot TNO g − i colors will be available to examine the bimodal color distribution and further explore the surface properties of these objects.

4.5 Existence of vertical Centaur/TNO belt?

The recent discovery of a possible common plane in the giant planet region provides evidence of the existence of a high-inclination (60° < i < 120°) and high-perihelion (q > 10 au) belt (HiHq) (Chen et al. 2016). The clustering of ascending nodes is the significant feature of this common plane. To further confirm the existence of the vertical plane, the total numbers of high-inclination Centaurs/TNOs need to be increased to improve the significance in statistics. The surface density of high-inclination Centaurs/TNOs “on” and “off” this common plane is a probe of intrinsic population. Although the survey fields of the entire HSC-SSP have almost no overlapping region with the proposed sky region of this belt [see figure 3 in this study and figure 4 in Chen et al. (2016)], the HSC-SSP could provide the “off” plane observations as a control sample for the examination of this hypothesis.

In our candidates, the highest inclination of prograde objects is 53°; none of the eight retrograde objects are in this vertical plane (60° < i < 120°). As a sense check, we used another orbital fitting code, OpenOrb (Granvik et al. 2009), to validate the inclinations of the retrograde objects. The results show that two of the eight retrograde objects are possibly main-belt asteroids with low inclinations, and the other six have the orbital solutions with inclinations near ∼30° or ∼130°. Although both orbit-fitting codes show the very low possibility that these eight retrograde objects are orbiting in this vertical plane, additional follow-up observations should provide a robust inclination solution.

If HiHq TNOs are homogeneously distributed in the ecliptic plane, i.e., without the clustering of ascending nodes, HSC-SSP should be able to detect few TNOs with 60° < i < 120°. The result of a non-detection of HiHq TNOs in the survey fields of HSC-SSP corresponds to a low surface density of the “off” vertical plane area [RA range: 100°–225° and 300°–40°, see figure 4 in Chen et al. (2016)]. However, to produce a relevant upper limit, the combination of the HSC-SSP results, follow-up observations, and future on-common plane observations using also the HSC will provide a statistically valid test of the existence of this vertical Centaur/TNO Belt.

4.6 Asteroids

The pipeline described in this section has the ability to find the asteroid tracks in a single night, and thousands of asteroids were detected in this data set. However, the orbital fitting code we used was designed for identifying TNOs, and the orbit-fitting for asteroids is not robust. We will use an alternative code for asteroids in a future analysis.

5 Summary

The HSC-SSP is currently the deepest ongoing survey, and will cover more than 1400 deg². Its data set provides an excellent opportunity to explore various topics in observational astronomy. In this study, we have described in detail the main algorithms of our moving object pipeline, which could be used in a survey with dithering pointings, e.g., HSC-SSP. This search algorithm could provide a better approach to discover solar system objects in future large surveys that have non-optimal cadences or dithered pointings. Compared with other moving object pipelines searching for TNO, this pipeline has fewer limitations on survey cadence and pointing, which are very critical parameters for detecting moving objects. For instance, the number of detected TNOs in this study is compatible with the dedicated search of Wong and Brown (2017). The combination of this pipeline and HSC-SSP-like cadence could also be a potential option for searching TNOs in large sky surveys without disturbing the main program. The false-positive rate in the catalog was significantly reduced to 15% with our ML algorithms. We used this pipeline to examine the first data release of the HSC-SSP (2014–2015).

The preliminary results by using this first data set have yielded 231 TNOs candidates that pass our search criteria. The lack of follow-up observations leads to large uncertainties in orbital parameters except for inclination. The absolute magnitude distribution of bright HSC-SSP TNOs shows a slope of 0.77 which is shallower than a recently study of 1.45 (Wong & Brown 2017), but our value is consistent with the study with proper calibrations (Fraser et al. 2014, |$\alpha = 0.87^{+0.07}_{-0.2}$|⁠). The g − i color distribution of HSC-SSP hot TNOs agrees with the bluer peak of bimodal distribution mentioned in Wong and Brown (2017). More detections in future HSC-SSP surveys will provide a significant number of faint TNOs, which is able to improve our understanding of the formation history of the solar system.

Acknowledgements

We are grateful to Yi-Ching Chiu, Paul Price, and Hisanori Furusawa for their kind suggestions and help in the data process. This work was supported in part by MOST Grant: MOST 104-2119-008-024 (TANGO II) and MOE under the Aim for Top University Program NCU, and Macau Technical Fund: 017/2014/A1 and 039/2013/A2. HWL acknowledges the support of the CAS Fellowship for Taiwan-Youth-Visiting-Scholars under the grant no. 2015TW2JB0001. This publication uses data generated via the Zooniverse.org platform, the development of is which funded by generous support, including a Global Impact Award from Google, and by a grant from the Alfred P. Sloan Foundation. The Hyper Suprime-Cam (HSC) collaboration includes the astronomical communities of Japan and Taiwan, and Princeton University. The HSC instrumentation and software were developed by the National Astronomical Observatory of Japan (NAOJ), the Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU), the University of Tokyo, the High Energy Accelerator Research Organization (KEK), the Academia Sinica Institute for Astronomy and Astrophysics in Taiwan (ASIAA), and Princeton University. Funding was contributed by the FIRST program from Japanese Cabinet Office, the Ministry of Education, Culture, Sports, Science and Technology (MEXT), the Japan Society for the Promotion of Science (JSPS), Japan Science and Technology Agency (JST), the Toray Science Foundation, NAOJ, Kavli IPMU, KEK, ASIAA, and Princeton University.

This paper makes use of software developed for the Large Synoptic Survey Telescope. We thank the LSST Project for making their code available as free software at 〈http://dm.lsst.org〉.

The Pan-STARRS1 Surveys (PS1) have been made possible through contributions of the Institute for Astronomy, the University of Hawaii, the Pan-STARRS Project Office, the Max-Planck Society and its participating institutes, the Max Planck Institute for Astronomy, Heidelberg, and the Max Planck Institute for Extraterrestrial Physics, Garching, The Johns Hopkins University, Durham University, the University of Edinburgh, Queen’s University Belfast, the Harvard-Smithsonian Center for Astrophysics, the Las Cumbres Observatory Global Telescope Network Incorporated, the National Central University of Taiwan, the Space Telescope Science Institute, the National Aeronautics and Space Administration under Grant No. NNX08AR22G issued through the Planetary Science Division of the NASA Science Mission Directorate, the National Science Foundation under Grant No. AST-1238877, the University of Maryland, and Eotvos Lorand University (ELTE) and the Los Alamos National Laboratory.

Based on data collected at the Subaru Telescope and retrieved from the HSC data archive system, which is operated by Subaru Telescope and Astronomy Data Center, National Astronomical Observatory of Japan.

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