# The New Horizons Extended Mission Target: Arrokoth Search and Discovery

Marc W. Buie Southwest Research Institute, 1050 Walnut St., Suite 300,
Boulder, CO 80302  John R. Spencer Southwest Research Institute, 1050 Walnut
St., Suite 300, Boulder, CO 80302  Simon B. Porter Southwest Research
Institute, 1050 Walnut St., Suite 300, Boulder, CO 80302  Susan D. Benecchi
Planetary Science Institute, 1700 East Fort Lowell, Suite 106, Tucson, AZ
85719  Alex H. Parker Southwest Research Institute, 1050 Walnut St., Suite
300, Boulder, CO 80302  S. Alan Stern Southwest Research Institute, 1050
Walnut St., Suite 300, Boulder, CO 80302  Michael Belton Belton Space
Exploration Initiatives, 430 S. Randolph Way, Tucson, AZ 85716; Emeritus
Astronomer, Kitt Peak National Observatory, Tucson, AZ 85719  Richard P.
Binzel Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts
Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139  David
Borncamp Space Telescope Science Institute, INS, Baltimore, MD, 21218
Francesca DeMeo Department of Earth, Atmospheric, and Planetary Sciences,
Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA
02139  S. Fabbro National Research Council of Canada, Herzberg Astronomy &
Astrophysics Program, 5071 West Saanich Road, Victoria, BC, V9E 2E7, Canada
Cesar Fuentes Northern Arizona University, Flagstaff, AZ  Hisanori Furusawa
Astronomy Data Center, National Astronomical Observatory of Japan, Osawa
2–21–1, Mitaka, Tokyo 181–8588, Japan  Tetsuharu Fuse Public Relations Center,
National Astronomical Observatory of Japan, Osawa 2–21–1, Mitaka, Tokyo
181–8588, Japan  Pamela L. Gay  Southern Illinois University  Stephen Gwyn
National Research Council of Canada, Herzberg Astronomy & Astrophysics
Research Centre, 5071 West Saanich Road, Victoria, BC V9E 2E7, Canada  Matthew
J. Holman Center for Astrophysics, Harvard & Smithsonian, 60 Garden Street,
Cambridge, MA 02138  H. Karoji  National Astronomical Observatory of Japan,
Osawa 2–21–1, Mitaka, Tokyo 181–8588, Japan  J. J. Kavelaars National Research
Council of Canada, Herzberg Astronomy & Astrophysics Research Centre, 5071
West Saanich Road, Victoria, BC V9E 2E7, Canada  Daisuke Kinoshita  Institute
of Astronomy, National Central University, Jhongli, Taiwan  Satoshi Miyazaki
Subaru Telescope, National Astronomical Observatory of Japan, 650 N Aohoku
Place Hilo Hawaii 96720 USA  Matt Mountain  Space Telescope Science Institute,
INS, Baltimore, MD, 21218  Keith S. Noll NASA Goddard Spaceflight Center, 8800
Greenbelt Rd., Code 693.0, 20771, Greenbelt, MD  David J. Osip Carnegie
Observatories, Las Campanas Observatory (Chile)  Jean-Marc Petit Institut
UTINAM UMR6213, CNRS, OSU Theta F-25000 Besancon, France  Neill I. Reid  Space
Telescope Science Institute, INS, Baltimore, MD, 21218  Scott S. Sheppard
Earth and Planets Laboratory, Carnegie Institution for Science, 5241 Broad
Branch Rd. NW, Washington, DC 20015  Mark Showalter SETI Institute, 189
Bernardo Ave., Mountain View, CA 94043  Andrew J. Steffl Southwest Research
Institute, 1050 Walnut St., Suite 300, Boulder, CO 80302  Ray E. Sterner
Johns Hopkins University Applied Physics Laboratory, 11100 Johns Hopkins Road,
Laurel, MD 20723  Akito Tajitsu Subaru Telescope Okayama Branch, National
Astronomical Observatory of Japan, 3037-5, Honjou, Kamogata, Asakuchi, Okayama
719-0232, Japan  David J. Tholen Institute for Astronomy, 2680 Woodlawn Drive,
Honolulu, HI 96822  David E. Trilling Department of Astronomy and Planetary
Science, Northern Arizona University, P.O. Box 6010 Flagstaff, AZ, 86011;
School of Informatics, Computing, and Cyber Systems, Northern Arizona
University, P.O. Box 5693, Flagstaff, AZ, 86011  Harold A. Weaver Johns
Hopkins University Applied Physics Laboratory, 11100 Johns Hopkins Road,
Laurel, MD 20723  Anne J. Verbiscer University of Virginia, Charlottesville,
VA  Lawrence H. Wasserman  Lowell Observatory, 1400 W Mars Hill Road,
Flagstaff, AZ 86001  Takuji Yamashita  Thirty Meter Telescope (TMT) Project,
National Astronomical Observatory of Japan, Osawa 2–21–1, Mitaka, Tokyo
181–8588, Japan  Toshifumi Yanagisawa  Chofu headquarters, Japan Aerospace
Exploration Agency, Jindaiji Higashimachi 7–44–1, Chofu, Tokyo 182–0012, Japan
Fumi Yoshida School of Medicine, Department of Basic Sciences, University of
Occupational and Environmental Health, 1-1 Iseigaoka, Yahata, Kitakyusyu,
Fukuoka 807-8555, Japan; Planetary Exploration Research Center, Chiba
Institute of Technology, 2-17-1 Tsudanuma, Narashino, Chiba 275-0016, Japan
Amanda M. Zangari  Southwest Research Institute, 1050 Walnut St., Suite 300,
Boulder, CO 80302

###### Abstract

Following the Pluto fly-by of the New Horizons spacecraft, the mission
provided a unique opportunity to explore the Kuiper Belt in-situ. The
possibility existed to fly-by a Kuiper Belt object (KBO) as well as to observe
additional objects at distances closer than are feasible from earth-orbit
facilities. However, at the time of launch no KBOs were known about that were
accessible by the spacecraft. In this paper we present the results of 10 years
of observations and three uniquely dedicated efforts – two ground-based using
the Subaru Suprime Camera, the Magellan MegaCam and IMACS Cameras, and one
with the Hubble Space Telescope – to find such KBOs for study. In this paper
we overview the search criteria and strategies employed in our work and detail
the analysis efforts to locate and track faint objects in the galactic plane.
We also present a summary of all of the KBOs that were discovered as part of
our efforts and how spacecraft targetability was assessed, including a
detailed description of our astrometric analysis which included development of
an extensive secondary calibration network. Overall, these efforts resulted in
the discovery of 89 KBOs including 11 which became objects for distant
observation by New Horizons and (486958) Arrokoth which became the first post-
Pluto fly-by destination.

††journal: PSJ

=4

##  1 Introduction

NASA’s New Horizons mission (Stern, 2008) flew by Pluto in July 2015 and then
deeper into the Kuiper Belt, providing the opportunity of close encounters
with other objects. This is the only opportunity for close-up observations of
Kuiper Belt objects (KBOs) for the foreseeable future. Prior to the launch of
New Horizons, no KBOs were known that were accessible within the propulsion
limits of the spacecraft. Finding suitable targets became a critical need for
the extended mission. We estimated that objects numerous enough to be
targetable with available $\Delta$V were likely to be in the 50 km size range,
with apparent R magnitudes near 26 (Spencer et al., 2003). The search area lay
in the Milky Way, in Sagittarius, because of the location of Pluto and the
trajectory of the spacecraft, requiring KBOs to be found against a very high
density of background stars.

Map showing the search areas on the sky during the timespan of this project.
The sky is shown with an overlay of the equatorial sky-plane coordinates.
Superimposed are ellipses for the area that includes 67% of the encounterable
cold-classical KBO population at opposition for the indicated year. Also shown
are curves for the ecliptic and the galactic plane.

A key element affecting our search efforts was the size and orbit distribution
of the KBO population. Based on the orbit distribution known even in the early
2000’s, it was clear that the spacecraft trajectory would be passing through
the cold-classical KBOs (CCKBOs) that are characterized by low inclination and
low eccentricity orbits and represent a dynamically cold and presumably
undisturbed primordial population. The nature of this component of the KBO
population was thus very important to the outcome of the search. The hot
classical component provided an additional small chance for an encounterable
option. No other dynamical types of object were considered when designing our
search program.

The size distribution also strongly affected the outcome of our search
efforts. Our search needed to reach to fainter brightness and thus smaller
size than was fully characterized at the time. There were already hints of a
break in the slope of the size-frequency distribution when we started the
project, but a firm consensus had not yet been reached (eg., Bernstein et al.,
2004; Fraser et al., 2008). Ongoing work has provided much better
characterization of this important attribute of the CCKBOs (Fraser et al.,
2014; Kavelaars et al., 2021). Our earliest estimate of the sky-density of
flyby targets used a single-slope power law based on objects in the 20-23 mag
brightness range. Now we know that this provided a very optimistic prediction
for the outcome of the search.

We will not review all the work and improvements to the characteristics of the
general KBO population that was happening during this project. But, we were
well aware of such work going on and folded such new results into our search
efforts as they came available. Equally important to our work and the orbit
estimation needed to support New Horizons mission operations was the
astrometric catalog produced by the Gaia mission (Gaia Collaboration et al.,
2016a, b; Lindegren et al., 2016). By the end of this project, the astrometric
support catalog was a solved problem but along the way this was a major
challenge to overcome prior to the Gaia DR2 catalog release (Brown et al.,
2018; Lindegren et al., 2018).

In this paper we describe the full extent of our efforts to locate objects for
both a fly-by visit by the spacecraft as well as observations of objects at
distances that provide higher resolution than the Hubble Space Telescope
(HST). Fig. 1 shows the search area by year as well as the background field.
We first describe our initial wide and shallow search for objects which began
in 2004 and set the stage for determining what actually needed to be done to
ensure finding a fly-by target. We then describe our dedicated ground-based
searches from 2011-2014 and our HST large program which ran during the summer
of 2014 and resulted in the discovery of (486958) Arrokoth which became the
New Horizons fly-by target. We describe our various reduction techniques for
each of the different observing configurations, ground- and space-based, and
our efforts to assess and determine the targetability of potential objects
both in our search area and then of the discovered objects themselves.
Discussion details include the astrometric catalogs used in our work and the
development of this process over time. An appendix provides extensive
documentation of the mathematics, library routines, and other support tools
developed for this project as well.

##  2 Wide and Shallow Search – 2004-2005

Our initial search, intended as a pilot study to assess the effort required
for a future deeper search, was carried out in 2004 and 2005 with the then
newly commissioned SuprimeCam prime focus imager at the Subaru telescope on
Mauna Kea. The search area to cover was then about 7 deg2. The field-of-view
(FOV) of SuprimeCam was 0.3 deg2, then the largest FOV on any of the
sufficiently large telescopes. The readout time was about 20 seconds, crucial
for part of our observing strategy. Additional details about this camera
system can be found in Miyazaki et al. (2002). As expected, the biggest
problem for this search was the large number of stars in the background. Our
intent from the beginning was to use optimal image subtraction as described by
Alard & Lupton (1998) to remove the stellar background, leaving the solar
system objects to be identified and measured. Our observing strategy for this
project was to collect a series of relatively short exposures (either 90 or
120 seconds depending on sky conditions) at multiple distinct epochs, or
visits. Using short exposures minimized saturated stars and by stacking many
images we built up longer integration times to reach a fainter limit. At this
stage in our efforts we did not attempt to shift the images to track target
motions. As a result, the length of time for any set of frames to be stacked
was kept below the threshold where trailing losses could begin to affect our
sensitivity. The limiting magnitude targeted for this search was $R=25$ and
was largely dictated by the relatively large search area and the amount of
telescope time we could obtain. In total, we were allocated 16 nights of time
in 2004 and 6 in 2005 to this project and realized 67 hours of integration
time on 58 distinct search fields. Table 1 gives an overview of the these runs
and Table 2 provides the pointing details and the estimated relative
probability of finding a targetable KBO on that field. In a given run a field
was imaged on at least 2 nights with two visits on one night and one visit on
an adjacent night.

Map showing the field pointings for the 2004 search plotted on the plane of
the sky in equatorial coordinates. The solid blue line is the galactic equator
and the center of the displayed segment is just 10∘ from the galactic center.
The solid green line at the bottom is the ecliptic. The green boxes are the
size of the SuprimeCam FOV and show the positions from Table 2. The solid
ellipse shows the 1-$\sigma$ search area in 2004 and the dash ellipse shows
the search area in 2005.

The search pattern for this phase of the project is shown in Fig. 2. Each tile
in this pattern represents a single FOV on the sky for a single pointing of
the telescope (Table 2). The gridded area covers 87% of the distribution of
targetable objects on the sky. The highest probability tile contained 4.2% of
the distribution. The goal for each surveyed field was to get five visits over
a small number of days to serve as the discovery dataset. This choice was
dictated by the software requirements of the Japanese search team members who
already had software for the search based on this required number of visits.
Additional observations in 2004 and 2005, consisting of pairs or triplets of
visits were used for followup observations. The coverage of fields in the
search area was such that covering the search area also served for followup
without needing to specifically target the newly discovered objects. This part
of our strategy was driven by the realized expectation that data analysis
would take a very long time to complete compared to the observational phase of
the project.

Table 1: Summary of 2004 Search Runs

UT Start Date | N nights | N fields | N images | Total time [h]
---|---|---|---|---
2004-06-09 | 3 | 24 | 486 | 13.9
2004-06-16 | 2 | 11 | 96 | 3.2
2004-06-22 | 3 | 22 | 290 | 9.7
2004-07-14 | 4 | 36 | 459 | 15.3
2004-08-09 | 4 | 35 | 307 | 10.2
2005-04-02 | 4 | 23 | 265 | 7.8
2005-08-02 | 2 | 30 | 208 | 6.9

Note. — Total time is the aggregate on-target exposure time in hours.

Table 2: Summary of 2004 Search Fields

Name | R.A.1 | Dec.1 | Prob2 |  | Name | R.A.1 | Dec.1 | Prob2 |
---|---|---|---|---|---|---|---|---|---
NH001 | 17:40:04.4 | -23:03:45 | 0.001 |  | NH037 | 17:40:12.3 | -21:42:45 | 0.005 |
NH002 | 17:42:32.3 | -23:03:45 | 0.002 |  | NH038 | 17:42:38.8 | -21:42:45 | 0.009 |
NH003 | 17:45:00.2 | -23:03:45 | 0.005 |  | NH039 | 17:45:05.2 | -21:42:45 | 0.012 |
NH004 | 17:47:28.1 | -23:03:45 | 0.007 |  | NH040 | 17:47:31.7 | -21:42:45 | 0.028 |
NH005 | 17:49:56.0 | -23:03:45 | 0.009 |  | NH041 | 17:49:58.1 | -21:42:45 | 0.029 |
NH006 | 17:52:23.8 | -23:03:45 | 0.011 |  | NH042 | 17:52:24.5 | -21:42:45 | 0.033 |
NH007 | 17:54:51.7 | -23:03:45 | 0.007 |  | NH043 | 17:54:51.0 | -21:42:45 | 0.042 |
NH008 | 17:57:19.6 | -23:03:45 | 0.006 |  | NH044 | 17:57:17.4 | -21:42:45 | 0.026 |
NH009 | 17:59:47.5 | -23:03:45 | 0.006 |  | NH045 | 17:59:43.9 | -21:42:45 | 0.021 |
NH010 | 18:02:15.4 | -23:03:45 | 0.004 |  | NH046 | 18:02:10.3 | -21:42:45 | 0.014 |
NH011 | 18:04:43.2 | -23:03:45 | 0.001 |  | NH047 | 18:04:36.8 | -21:42:45 | 0.012 |
NH012 | 18:07:11.1 | -23:03:45 | 0.002 |  | NH048 | 18:07:03.2 | -21:42:45 | 0.006 |
NH013 | 17:40:07.1 | -22:36:45 | 0.001 |  | NH049 | 17:40:14.8 | -21:15:45 | 0.001 |
NH014 | 17:42:34.5 | -22:36:45 | 0.003 |  | NH050 | 17:42:40.8 | -21:15:45 | 0.004 |
NH015 | 17:45:01.9 | -22:36:45 | 0.009 |  | NH051 | 17:45:06.8 | -21:15:45 | 0.005 |
NH016 | 17:47:29.3 | -22:36:45 | 0.017 |  | NH052 | 17:47:32.8 | -21:15:45 | 0.017 |
NH017 | 17:49:56.7 | -22:36:45 | 0.021 |  | NH053 | 17:49:58.8 | -21:15:45 | 0.023 |
NH018 | 17:52:24.1 | -22:36:45 | 0.021 |  | NH054 | 17:52:24.8 | -21:15:45 | 0.022 |
NH019 | 17:54:51.5 | -22:36:45 | 0.025 |  | NH055 | 17:54:50.8 | -21:15:45 | 0.022 |
NH020 | 17:57:18.9 | -22:36:45 | 0.020 |  | NH056 | 17:57:16.8 | -21:15:45 | 0.012 |
NH021 | 17:59:46.3 | -22:36:45 | 0.011 |  | NH057 | 17:59:42.8 | -21:15:45 | 0.014 |
NH022 | 18:02:13.6 | -22:36:45 | 0.006 |  | NH058 | 18:02:08.8 | -21:15:45 | 0.007 |
NH023 | 18:04:41.0 | -22:36:45 | 0.005 |  | NH059 | 18:04:34.8 | -21:15:45 | 0.005 |
NH024 | 18:07:08.4 | -22:36:45 | 0.004 |  | NH060 | 18:07:00.8 | -21:15:45 | 0.004 |
NH025 | 17:40:09.7 | -22:09:45 | 0.002 |  | NH061 | 17:40:17.2 | -20:48:45 | 0.001 |
NH026 | 17:42:36.7 | -22:09:45 | 0.010 |  | NH062 | 17:42:42.8 | -20:48:45 | 0.002 |
NH027 | 17:45:03.6 | -22:09:45 | 0.014 |  | NH063 | 17:45:08.3 | -20:48:45 | 0.004 |
NH028 | 17:47:30.5 | -22:09:45 | 0.024 |  | NH064 | 17:47:33.9 | -20:48:45 | 0.007 |
NH029 | 17:49:57.4 | -22:09:45 | 0.036 |  | NH065 | 17:49:59.4 | -20:48:45 | 0.009 |
NH030 | 17:52:24.3 | -22:09:45 | 0.035 |  | NH066 | 17:52:25.0 | -20:48:45 | 0.008 |
NH031 | 17:54:51.2 | -22:09:45 | 0.035 |  | NH067 | 17:54:50.6 | -20:48:45 | 0.010 |
NH032 | 17:57:18.1 | -22:09:45 | 0.023 |  | NH068 | 17:57:16.1 | -20:48:45 | 0.006 |
NH033 | 17:59:45.1 | -22:09:45 | 0.020 |  | NH069 | 17:59:41.7 | -20:48:45 | 0.006 |
NH034 | 18:02:12.0 | -22:09:45 | 0.014 |  | NH070 | 18:02:07.2 | -20:48:45 | 0.003 |
NH035 | 18:04:38.9 | -22:09:45 | 0.011 |  | NH071 | 18:04:32.8 | -20:48:45 | 0.002 |
NH036 | 18:07:05.8 | -22:09:45 | 0.009 |  | NH072 | 18:06:58.3 | -20:48:45 | 0.001 |

Note. — (1) The coordinates are all equinox J2000. (2) “Prob” is the estimated
relative probability of finding a targetable KBO.

###  2.1 Image calibration and characterization

The raw images were processed using standard techniques prior to analysis.
These steps include overscan corrections, bias-frame corrections, and flat-
fielding corrections. Our flat fields were generated from the imaging data
directly with a robust stack of all data. Building flats and other image
stacking operations required a good characterization of the sky signal in each
image. We developed a new routine (skyfit.pro111All references to software
with a name ending in “.pro” are routines from the Buie IDL Library,
http://www.boulder.swri.edu/~buie/idl and further details about these programs
are covered in Appendix B.), that includes robust estimation and simultaneous
fitting of a low-order 2-D polynomial to the sky background that uses
incomplete information on the distribution of sky signal due to the crowded
fields to reconstruct the full noise distribution. See Appendix B for more
details about this process. The spatially variable sky signal was subtracted
from the images, and the mean value near the center of the array was added
back to roughly preserve the original detected signal level.

The required data processing was facilitated by collecting key derived
quantities for each image and saving all of this in a relational database to
prevent having to recompute these values in each step of the processing.
Information collected in this way was the image quality, photometric depth,
sky signal properties, detector gain. Some derived information was too
voluminous to be practical for storage in the database, such as lists of
detected sources and the full astrometric solution for each image at every
step in that process. This derived information was very valuable for examining
data from a given night as a whole to help detect those images where the
processing failed for some reason.

###  2.2 Astrometric support catalogs

Accurate astrometric solutions for the images is essential to the stacking and
subtraction process. SuprimeCam exhibits a large amount of spatial distortion
in the focal plane between the center and corners of the mosaic. The positions
near the corner are offset compared to what a linear focal plane would
provide. It was not practical to control the pointing for the search images to
the sub-pixel accuracy needed for stacking so the distortion had to be
directly addressed.

We were well aware of the need to avoid saturation, hence the plan to take
multiple short exposures and stack. Under good sky conditions, the limiting
magnitude was 23.9 mag. More importantly, stars brighter than 18.2 were
saturated and of no use for astrometric calibration. This brightness limit
meant that the best data had an insufficient number of astrometric reference
stars to permit determining an astrometric solution of the distorted field.

We used the USNO-B1.0 catalog (Monet et al. (2003)) for this phase of the
project. This catalog includes proper motions, but we used the form of the
catalog extracted for use with the Deep Ecliptic Survey (Elliot et al., 2005)
where the format of the earlier USNO-A1.0 catalog files was used with all
stars saved at an epoch of 2005. Our first attempt was to use this catalog on
a chip-by-chip reduction, but the combination of strong distortion and minimal
overlap in brightness between the catalog and images made this simple approach
insufficient. Obtaining good astrometric solutions required two adjustments in
procedure. First, we had to create a secondary astrometric catalog that went
to a fainter limiting magnitude. Second, we developed tools to treat the
entire mosaic as a single astrometric device.

To create the secondary catalog we identified the data taken with the worst
transparency from each field. Every field had at least a few images taken with
several magnitudes of extinction. These low-throughput images could then be
processed using the USNO-B catalog since most of the catalog stars were now
not saturated. More importantly, even though these images were photometrically
shallower, they still pushed significantly deeper than the USNO-B catalog and
we could extract the fainter stars for a deeper secondary catalog. Note that
the secondary catalog was constructed from the average of all data. No attempt
was made to correct or otherwise adjust these positions for proper motion.

Obtaining an astrometric solution was also complicated. The large number of
frames pushed us to automatic pipeline processing rather than a supervised
manual operation. The automatic tools available then were effective on only
about half of the data. To overcome this problem, we used the focal plane
distortion map provided by NAOJ (Miyazaki et al., 2002) for an initial mapping
of pixel coordinates onto the sky plane. This map was provided in the form of
software rather than as formulas and coefficients.

For each image, we used the NAOJ tool to convert the pixel positions of all
measured sources in the image to RA and Dec given the knowledge of the
telescope pointing. The result of this step served to linearize the positions.
From here, the RA and Dec estimates were converted to tangent plane
coordinates using the header position. The overlapping secondary star catalog
positions were also converted to tangent plane coordinates using the same
tangent point. These two lists were close to each other in position, but
always had offsets to be determined as well as occasionally needing to be
rotated up to a couple of degrees.

Once the lists were correlated, a new astrometric solution was relatively easy
to derive. To support a full-mosaic coordinate system, we developed our own
method for describing the focal plane distortion. This mathematical
description and its mapping onto a set of FITS keywords is described more
fully in appendix A. Deriving a full solution required an iterative approach
for our fourth order fit. Given a solution, we calculated the new location of
the center of the mosaic, thus changing the tangent point. This required a new
solution, leading to a new tangent point. This process converged within 3
iterations to provide a self-consistent tangent point and astrometric fit.

Another component of the astrometric fit is the relative offset and
orientation of all the detectors. One chip (#2) was selected as the reference
device and its coordinate system is extended to cover the full focal plane. In
principle, the choice of reference chip is arbitrary, but we found it
convenient to use a device in the center of the mosaic where the distortion is
lower. The original distortion map for SuprimeCam was used to initially
determine these chip offsets and orientations. For all images, the fit is held
constant and the offset and orientation is adjusted to find the best fitting
solution.

In principle, this method assumes that the astrometric solution can be
different on each image. The constant and linear terms are always seen to vary
with time. The quadratic and higher-order terms were never seen to exhibit
statistically significant variations within a run. We found the results to be
more internally consistent and stable when the mean values of the high-order
terms were imposed on the fit, leaving only the constant and linear terms to
be fitted for each image.

Additionally, the relative locations of the chips was not expected to vary.
This expectation seems like a reasonable assumption, but we chose a more
conservative assumption that the devices don’t perceptibly move during an
observing run. Finding the offsets is not entirely straightforward. In
general, there is a coupling between the astrometric solution for the entire
mosaic and the values of the offsets and rotations used for each chip. We did
not have the computing resources and tools at that time to attempt a
simultaneous determination of the solution and the chip positions. Instead, we
iteratively determined one while fixing the other and repeating until the
answer converged. This proved to be a very effective method if somewhat
tedious. Doing this required a starting guess for the offsets and rotations
which we had from the NAOJ documentation. Then, we fixed these chip locations
and solved for the chip-by-chip astrometric solution. These solutions where
then averaged to get mean high-order coefficients and the linear and constant
terms were refit. From this point, the solutions were fixed and the chip
offset and rotation relative to the reference was scanned to find the values
most consistent with the fixed solution. This is done for all images in a run.
Given these values, a mean offset and rotation is computed using a robust mean
estimator (robomean.pro). These mean values were then adopted, and the
solutions were iterated again. This process was repeated two or three times
for each run.

The measure of success in all of this intense astrometric calibration was in
looking at multiple views of the same patch of sky. A high-speed animation
loop looking at the same region registered by their astrometric solutions
should only reveal the usual variations in transparency and image quality
induced by the atmosphere, but there should be no apparent motion in the
positions of the sources. In the early stages when chip-by-chip independent
solutions were used, there was a lot of residual motion – sometimes many
pixels in the corner chips. After this more involved calibration process, the
images were seen to be internally consistent. Given that this process is
referenced to an astrometric catalog, the final absolute astrometric positions
should be as good as the underlying catalog.

###  2.3 Photometric calibration

The usual process of flat-fielding an image preserves surface brightness. This
is useful for removing pixel-to-pixel variations, over small and large spatial
scales. In the presence of optical distortions, flat fielding can introduce
systematic shifts to point-source photometry. The reason for this is that the
area of a pixel, on the plane of the sky, varies with such distortion. To
correct for the effect of this distortion on fixed-aperture photometry, we
compute the area of each pixel in arcsec2. The map is normalized by the
largest area. Then, the flux of any source is divided by the value from the
normalized map at the location it was measured before converting to an
instrumental magnitude. For SuprimeCam, this correction is as large as 30%
towards the more heavily distorted corners of the mosaic. The computation of
this map is time-consuming but straightfoward given a good astrometric
description of an image. We did not apply this correction to the images
themselves, but used it to correct the extracted photometry.

###  2.4 Image registration

Given an accurate astrometric solution, image registration is straightforward.
In the early phase of the project we tried to determine a polynomial expansion
approximation for the mapping from one image to another image. The goal in
this case was to pick the best image of a set and then resample the other
images to match. Operationally, this method should work but the high-order
differences between two distorted images required too many terms and that fit
was numerically unstable for a significant number of images. A better
methodology turned out to be to resample all images to a linear grid defined
by the mean position and orientation of all images of the same field within a
run. Image scale for the output images was set to the scale of the image at
the center of the mosaic. The astrometric fit already determined was
sufficient to map the observed images onto the idealized grid. The output grid
was sized to bound all of the input images, meaning that there could be pixels
that map onto only a subset of the input images.

The images were all re-sampled with a flux conserving interpolation that is
functionally equivalent to sinc interpolation. This process used the Buie
library routine dewarp.pro that itself uses the built-in IDL image
interpolation tool, congrid.

###  2.5 Image subtraction

The power of image subtraction for picking out changes in images cannot be
denied. What sets this project apart is its time-dependent nature. We
routinely needed to work on data with a much larger range of image quality
than is typically tolerated by other investigations of a largely static sky.
The quality of subtraction was seen to degrade as the difference in seeing
between two images increased.

The first step in the subtraction process is to take all of the images for a
given field that are consecutive in time and average them together. This
averaging process rejects outliers such as cosmic ray strikes and fast moving
objects in the field but preserves stars and KBOs. Prior to the stacking
process, each image had its spatially variable sky level subtracted and then
flux scaled to match the flux of the best image in the set. The constant term
of the sky fit from the best image was then added to the average to return the
image to pixel values closely approximating the original to facilitate
tracking the noise properties of the images. All images in a set were used to
build the stack.

Any pair of stacked images can be used for image subtraction at this point,
but not all pairs were equally effective. For each image, we computed the
difference against the best quality stack. The final difference pairs were
computed and saved for the next step of searching.

###  2.6 Searching for objects

After the visit difference images were completed, we visually examined the
data to look for slow-moving objects. This process was essentially the same as
used by the Deep Ecliptic Survey in using color composites for comparing two
epochs of data at a time. Traditional image blinking could be used if desired.
When an object was noted, its position was measured in the difference image.
Since the astrometric grid is known, it then becomes a simple matter to
convert from pixel coordinates to sky coordinates. This tool used a low-order
polynomial short-arc predictor to project the position of a measured object
onto each image not yet measured. This system allowed finding an object across
the chip gaps.

Much later in the project, we implemented a parallel system for finding
objects as a citizen-science project. A broad discussion of what citizen
science entails can be found at https://www.citizenscience.gov/. In our case,
we engaged our participants by providing image data to search for transient
sources that included variable stars and moving objects with distinctions
between main-belt asteroids and KBOs. This system was called “Ice Hunters” and
hosted as part of the “Zoo” collection of citizen science arenas
https://www.zooniverse.org/. After analyzing data from a number of observing
runs we found no difference in the detection list between our scanning and Ice
Hunters. In the end we found that technology constraints at the time served to
make the citizen-science approach much slower and more effort to manage than
just using a local tool with a couple of people working to scan the data. More
details about this experiment can be found in Appendix C.

###  2.7 Wide and shallow search results

Our search effort was able to find 24 objects. Table 3 summarizes our results.
The faintest object seen was at R=24.9, exactly as expected from our initial
estimates prior to the search. Of those objects detected, 14 (58%) were likely
cold-classical and the lowest $\Delta$V for New Horizons was 1.1 km/s, or
about 10 times bigger than the available amount. The closest candidate is one
of two objects that are currently designated (though clearly there are others
with good enough orbits for designations). NI09 (or 2004 LW31) now has a much
better orbit than was available from just our search data. It now has a
15-year arc with 39 unique observations (including ours). The $\Delta$V
estimate shown in Table 3 for this object is good to 10% showing that even
short-arc data is sufficient to strongly constrain the list of potential
targets.

Table 3: Summary of 2004 Search Discoveries

Object | $a$ | $e$ | $i$ | $H_{V}$ | $R_{d}$ | arc | discovery | Nobs | Desig | CA Date | CA |  $\Delta$V
---|---|---|---|---|---|---|---|---|---|---|---|---
| (AU) |  | (deg) |  |  | (days) | UT |  |  |  | (AU) | (km/sec)
NI01 | 42$\pm$22 | 0.03$\pm$0.57 | 4.1$\pm$1.7 | 8.1 | 24.3 | 1.0 | 2004/06/16 | 3 |  $\cdots$ | 2017-07-17 | 3.5 | 7.9
NI02 | 40$\pm$ 7 | 0.18$\pm$0.30 | 9.1$\pm$0.7 | 7.9 | 23.4 | 61.8 | 2004/06/09 | 7 |  $\cdots$ | 2015-01-07 | 5.2 |  $\cdots$
NI03 | 49$\pm$ 6 | 0.30$\pm$0.17 | 3.16$\pm$0.00 | 6.8 | 24.8 | 419.9 | 2004/06/09 | 12 |  $\cdots$ | 2019-11-24 | 2.0 | 2.3
NI04 | 59$\pm$26 | 0.33$\pm$0.31 | 13.0$\pm$2.4 | 7.0 | 24.4 | 35.9 | 2004/06/09 | 7 |  $\cdots$ | 2018-02-02 | 4.0 | 8.2
NI05 | 48$\pm$25 | 0.03$\pm$0.57 | 34$\pm$15 | 8.0 | 24.9 | 2.1 | 2004/06/09 | 5 |  $\cdots$ | 2019-06-03 | 8.7 | 11.3
NI06 | 40$\pm$21 | 0.02$\pm$0.57 | 3.9$\pm$1.3 | 8.6 | 24.2 | 2.1 | 2004/06/09 | 5 |  $\cdots$ | 2017-08-17 | 1.2 | 3.2
NI07 | 59$\pm$33 | 0.47$\pm$0.40 | 2.97$\pm$0.27 | 8.1 | 24.0 | 37.0 | 2004/06/09 | 8 |  $\cdots$ | 2017-01-19 | 0.9 | 3.3
NI09 | 46.2$\pm$0.1 | 0.003$\pm$0.004 | 3.062$\pm$0.002 | 6.9 | 24.8 | 420.0 | 2004/06/09 | 12 | 2004 LW31 | 2019-11-26 | 1.0 | 1.1
NI10 | 41$\pm$19 | 0.35$\pm$0.72 | 7.1$\pm$0.6 | 8.3 | 24.6 | 50.9 | 2004/07/14 | 6 |  $\cdots$ | 2019-01-18 | 2.5 | 3.6
NI11 | 41$\pm$19 | 0.42$\pm$0.90 | 4.1$\pm$1.6 | 8.3 | 24.9 | 36.9 | 2004/07/16 | 7 |  $\cdots$ | 2020-07-14 | 2.6 | 2.6
NI12 | 42$\pm$221 | 0.02$\pm$0.57 | 3.7$\pm$1.3 | 8.3 | 24.4 | 1.0 | 2004/06/22 | 3 |  $\cdots$ | 2018-02-23 | 2.4 | 4.9
NI13 | 52$\pm$9 | 0.29$\pm$0.33 | 8.5$\pm$0.5 | 8.2 | 24.3 | 51.0 | 2004/07/15 | 8 |  $\cdots$ | 2017-12-26 | 2.4 | 5.2
NI14 | 39$\pm$21 | 0.03$\pm$0.57 | 5.0$\pm$1.8 | 8.8 | 24.0 | 2.1 | 2004/06/16 | 4 |  $\cdots$ | 2017-02-08 | 1.6 | 5.9
NI16 | 39$\pm$19 | 0.23$\pm$0.76 | 0.96$\pm$0.06 | 7.2 | 23.3 | 21.7 | 2004/06/23 | 7 |  $\cdots$ | 2015-01-25 | 3.2 |  $\cdots$
NI17 | 46$\pm$5 | 0.17$\pm$0.30 | 2.27$\pm$0.00 | 8.6 | 24.9 | 419.9 | 2004/06/09 | 7 |  $\cdots$ | 2020-01-10 | 2.2 | 2.4
NI18 | 42$\pm$6 | 0.15$\pm$0.77 | 6.2$\pm$0.7 | 8.0 | 24.1 | 54.9 | 2004/06/16 | 6 |  $\cdots$ | 2017-03-08 | 4.8 | 16.2
NI19 | 40$\pm$13 | 0.11$\pm$0.70 | 18.7$\pm$3.1 | 8.9 | 23.9 | 37.0 | 2004/06/09 | 8 |  $\cdots$ | 2016-08-24 | 4.4 | 24.3
NI20 | 51$\pm$7 | 0.39$\pm$0.15 | 6.63$\pm$0.01 | 8.7 | 24.2 | 420.0 | 2004/06/09 | 10 | 2004 LV31 | 2017-09-18 | 2.1 | 5.1
NI21 | 46$\pm$24 | 0.03$\pm$0.56 | 3.0$\pm$1.6 | 8.7 | 24.7 | 1.0 | 2004/06/10 | 3 |  $\cdots$ | 2019-04-27 | 1.8 | 2.4
NI22 | 47$\pm$24 | 0.02$\pm$0.56 | 13.1$\pm$4.9 | 8.6 | 24.8 | 2.1 | 2004/06/09 | 4 |  $\cdots$ | 2019-10-31 | 3.0 | 3.5
NI25 | 36$\pm$19 | 0.03$\pm$0.58 | 0.77$\pm$0.23 | 7.7 | 23.6 | 1.0 | 2004/07/16 | 3 |  $\cdots$ | 2015-11-08 | 2.9 | $>$
NI30 | 38$\pm$19 | 0.03$\pm$0.56 | 6.5$\pm$2.3 | 8.6 | 23.9 | 37.9 | 2004/06/09 | 5 |  $\cdots$ | 2016-08-07 | 4.0 | 23.1
NI34 | 48$\pm$25 | 0.44$\pm$0.46 | 2.54$\pm$0.30 | 7.8 | 24.4 | 46.9 | 2004/06/24 | 5 |  $\cdots$ | 2018-03-06 | 1.8 | 3.6
NI35 | 45$\pm$23 | 0.02$\pm$0.56 | 2.7$\pm$1.2 | 8.3 | 24.7 | 1.1 | 2004/06/09 | 4 |  $\cdots$ | 2019-03-06 | 2.4 | 3.3

Note. — The astrometry for these objects from this search is provided in the
supplemental data file for this table. All values given here are from the
discovery data only. Blank $\Delta$V values indicate that close approach
conflicted with the Pluto encounter (on or before). $\Delta$V values listed as
‘$>$’ indicate a non-physical value.

Even though this early search work did not result in the detection of a
mission target, important lessons were learned that were carried forward to
the later search efforts. Here we summarize the more important of these
lessons. Also, one of these objects (2004 LW31) made it to the list of bodies
to be observed with long-range encounters by New Horizons before and after its
encounter with Arrokoth (Porter et al., 2022).

The search area was variegated enough to include some areas of “dark lanes”
where foreground dust in our galaxy obscures the stars that would normally
have been seen. We did not specifically target these areas, but recognized
that they would enhance our probability of finding objects due to a reduced
amount of confusion. unfortunately, nothing useful was found in those limited
areas.

###  2.8 Lessons learned

The results of this effort showed us that we clearly needed a much deeper
search to have a reasonable chance to find an extended mission target. This
effort also clearly showed the critical need for a secondary reference star
catalog that could be directly tied to the search data. It likewise
demonstrated the influence of high quality seeing ($<0.7$ arcsec) on our
object discovery rate; quality seeing with lower transparency was better than
poor seeing with clear skies. All of these lessons provided essential
information that guided the implementation of the next search effort.

Finally, nearly all the software tools and the lessons learned therein were
then available as a starting point for follow-on searches that were
characterized by ever shortening timescales for data processing. This initial
search effort did not result in finding a targetable object, but was an
absolutely essential step along the way.

##  3 Deep Ground-based Search – 2011-2014

A deeper search was undertaken starting in 2011. By this time, the search area
for 80% of the candidate pool had dropped down to $\sim$2 deg2 and we needed
only 7 discrete SuprimeCam fields to cover the search region. The reduction in
the area made it feasible to consider much longer integrations and thus deeper
image stacks to reach a fainter limiting magnitude while still covering most,
if not all, of the search area. Once again we used the Subaru SuprimeCam
imager, but there was a second option available with Megacam (McLeod et al.
(2015))and IMACS (Dressler et al. (2006)) on the Magellan telescopes. A list
of observing runs for this search effort which includes a run identification,
the instrument used, the UT start and end time for each run, the number of
distinct fields imaged and the number of individual frames collected can be
found in Table 4.

###  3.1 Astrometric support catalog

Driven by the lessons learned in the initial 2004-2005 pilot search, we
developed a special astrometric support catalog for the calibration of the new
search data. Targeted observations with the Canada-France-Hawaii Telescope
(CFHT) were obtained in queue mode. The goal each year was to cover the sky
for the following year so that the catalog was ready for each new apparition
of search data. All observations were taken with MegaCam (Boulade et al.,
2003) and an $r^{\prime}$ filter with 30 second exposures. Good image quality
was essential for these crowded fields and the queue observing system ensured
we got the necessary quality data. Most data were taken under photometric
conditions even though this wasn’t absolutely required. The data were
processed at CADC using their standard tools for the MegaCam mosaic (Gwyn,
2014). With its 1 deg2 FOV camera it was able to easily cover the search
region. Toward the end of the search phase this catalog was extended to cover
the entire field through the expected target position at the time of the New
Horizons encounter. The catalog reaches a useful depth of r=23-24 which
provided ample overlap with the brightness range of the ground-based data and
the available astrometric star catalogs. Initially, the UCAC4 catalog
(Zacharias et al. (2012)) was used as the underlying reference upon which the
support catalog was based. As the project progressed we moved to hybrid
catalogs, URAT1 from Zacharias et al. (2015), and the Gaia DR1 catalog (Gaia
Collaboration et al., 2016a, b; Lindegren et al., 2016), and then ultimately
to the Gaia DR2 catalog (Brown et al., 2018; Lindegren et al., 2018). Mean
proper motion corrections were applied so that the support catalog had a mean
epoch contemporaneous with the search. This catalog ensured that there were at
least a couple of hundred reference stars for each detector in the search
cameras.

Sample SuprimeCam image data from 2011. Two epochs are shown of the discovery
images for 2011 HL103. The red arrow (or image) shows the location at the
first epoch and the cyan arrow (or image) shows the location at the second
epoch. The stacked images are in the left column. Template subtracted images
are in the middle column. The right column shows the color stack of the two
epochs. See text for more details.

###  3.2 Data Processing

The data analysis for this phase of the search was very similar to that used
for the prior search, but there were some improvements and other changes
needed. First, we had multiple independent pipelines for searching the data.
Algorithmically, these pipelines performed similar operations and are not
separately described. The Subaru data was again processed as a single multi-
chip astrometric device. The Magellan data were processed with each image in
the detector mosaics as independent systems.

Table 4: Summary of 2011-2014 Search Runs

RunID | Observatory | Instr | UT start. | UT end | Nf | Ni
---|---|---|---|---|---|---
m1104 | Magellan | MegaCam | 2011-04-25 09:28:55 | 2011-05-06 09:00:11 | 9 | 589
m1105 | Magellan | MegaCam | 2011-05-27 06:00:37 | 2011-06-04 10:31:09 | 5 | 399
1105 | Subaru | SuprimeCam | 2011-05-29 09:41:57 | 2011-06-01 14:39:17 | 12 | 6090
m1107a | Magellan | IMACS | 2011-07-01 01:02:04 | 2011-07-02 08:42:21 | 9 | 2752
1107 | Subaru | SuprimeCam | 2011-07-02 06:35:18 | 2011-07-02 13:32:49 | 12 | 1730
m1107b | Magellan | IMACS | 2011-07-22 23:34:14 | 2011-07-24 03:31:46 | 4 | 1256
m1108 | Magellan | IMACS | 2011-08-27 23:37:14 | 2011-08-30 04:36:53 | 7 | 2400
m1204 | Magellan | MegaCam | 2012-04-17 06:48:17 | 2012-04-22 07:33:43 | 3 | 485
m1205 | Magellan | IMACS | 2012-05-24 03:51:35 | 2012-05-24 07:24:44 | 4 | 232
m1206 | Magellan | IMACS | 2012-06-13 23:43:04 | 2012-06-15 07:51:39 | 1 | 400
m1207 | Magellan | IMACS | 2012-07-11 05:01:52 | 2012-07-23 04:29:45 | 9 | 3512
1207 | Subaru | SuprimeCam | 2012-07-16 10:07:35 | 2012-07-18 12:09:21 | 2 | 2320
1208 | Subaru | SuprimeCam | 2012-08-13 05:52:22 | 2012-08-16 11:00:24 | 2 | 4780
m1306 | Magellan | MegaCam | 2013-06-03 04:37:07 | 2013-06-13 09:05:56 | 3 | 753
m1307 | Magellan | MegaCam | 2013-07-02 03:42:05 | 2013-07-04 06:56:15 | 2 | 192
1307 | Subaru | SuprimeCam | 2013-07-04 07:15:26 | 2013-07-14 12:42:26 | 4 | 10079
m1308 | Magellan | MegaCam | 2013-08-28 00:35:57 | 2013-09-06 03:12:50 | 1 | 431
m1404 | Magellan | MegaCam | 2014-04-25 05:58:51 | 2014-05-06 10:04:02 | 3 | 608

Note. — Nf is the number of distinct fields imaged and Ni is the number of
individual images collected. The UT times are the start times of the first and
last images collected in that run.

Table 5: Logs Notes from 2011-2014 Observing Runs (Sample1)

Field | UT Date | UT Start Time | FWHM (′′) | Quality | Comments |
---|---|---|---|---|---|---
MA05 | 110428 | 04:56 | 0.7 | 1 | 0.85′′ at start, some elongation, transparency good |
MA04 | 110428 | 05:40 | 0.6 | 1 | Good image quality |
MA07 | 110428 | 06:12 | 0.6 | 1 | Up to 0.7′′ for some exp. |
MA01 | 110428 | 06:48 | 0.55 | 1 | Moonrise 06:57 UT |
MA05 | 110428 | 07:26 | 0.5 | 1 |  |
MA04 | 110428 | 07:59 | 0.45 | 1 |  |
MA07 | 110428 | 08:36 | 0.55 | 1 | Cross meridian so more rotation |
MA01 | 110428 | 09:19 | 0.55 | 1 |  |
MA04 | 110428 | 09:51 | 0.55 | 3 | Elevated bkg due to twilight |
MA06 | 110429 | 04:52 | 1.0 | 1 | 0.9-1.1“ Photometric all night |
MA03 | 110429 | 05:29 | 0.8 | 1 |  $<$1.0“ down to 0.7“ |
MA02 | 110429 | 06:04 | 0.7 | 1 |  $<$0.7“ |

Note. — (1) This table is available in its entirety in machine-readable and
Virtual Observatory (VO) forms in the online journal. A portion is shown here
for guidance regarding its form and content.

This search used much longer dwell times per visit to extend the search to
fainter objects, but still took short exposures to be stacked. An important
change was in the creation of template images for each pointing. This time, we
used all available images to build a master template image optimized for each
pointing for each telescope. Given the range of image quality in the data, we
could not use all images for the template but needed to ensure a sufficient
range of time so that any KBOs were filtered out of the template images.

To make a template image, all of the candidate images were sorted by
photometric depth. We tried using a list sorted by image quality, but that
does not de-weight images that might be taken through some clouds. The
photometric depth is dependent on both transparency and image quality and
worked best as the sorting metric. A reference image was defined based on the
mean pointing of all images, the mean orientation on the sky, and a linear
image scale that matched the nominal scale of the images in the center of the
mosaics. All images were resampled to this reference.

As the list of images is traversed from good to bad, each new image is
assessed for its ability to improve the stack. We used a simple noise model
based on the sky signal, sky noise, and photometric depth of the image to
estimate the change in SNR from adding each new image. If the new image would
improve the SNR, it was added to the stack list and the SNR was updated. Any
image not improving the SNR was dropped from inclusion in the template. In all
cases, every search field had enough data and enough distinct epochs to ensure
a good template where moving objects and cosmic ray strikes were filtered out.
Once the templates were complete, all individual short-exposure images were
differenced against the appropriate template image.

The consequence of moving to longer dwell times was that trailing losses were
no longer negligible, even for KBOs. A simple stack as done for the previous
search would leave a smeared image of a KBO that would adversely affect our
limiting magnitude. To generate the shift needed we used a population of
synthetic KBOs that matched the orbital element distribution of cold-classical
KBOs. The mean velocity of this population was computed for each visit, field,
and device within the detector mosaic. This single shift value was applied to
the subtracted images requiring another resampling of the images. Once these
images were shifted, they could then be stacked. At this stage, cosmic ray
strikes and some of the residuals of the stellar background were removed. The
resulting image products could be searched using our standard color-composite
and blinking tools.

A very small sample image that is typical of our dataset is shown in Fig. 3.1.
This sample image shows two of the twenty-two epochs of data on object 2011
HL103. Each of these images is a stack of seven 90-second images for a total
of 630 seconds of integration. The first epoch had a FWHM of 3.4 pixels and
the second epoch was 3.5 pixels. All displayed images are stretched
identically from $-3\sigma$ to $+8\sigma$ about the sky mean where $\sigma$ is
the measured noise in the sky at the first epoch. In the figure, the left
column shows the stacked images from the same region in the two images with
the first epoch on the top and the second epoch on the bottom. The arrows
point to the position of the object and the red arrow is for the first epoch
and the cyan arrow is for the second epoch. The middle column shows the same
data but after the template image is subtracted. The object is clearly visible
at both epochs in the each type of presentation, but is clearly easier to see
once the background stars are subtracted.

The images in the right column show what we examined to discover the objects.
On the top is a color composite of both epochs where the red channel contains
the first epoch and the green and blue channels contain the second epoch. The
static sky shows as shades of grey to white. The transient component shows as
either red or cyan depending on its location or properties in the two epochs.
Once again the object can be seen in both epochs, but is much easier to spot
in the lower right where the background template has been subtracted. It was
this background subtracted color image composite that was used for all object
detections. Note that additional transient features are apparent in this image
product. Most notable are three apparent variable stars, two of which were
brighter in the first epoch and thus show as red, and one that was brighter in
the second epoch and shows as cyan. These transients are discarded during the
search when there is no pairing at a sensible KBOs sky-plane velocity.

In addition to the manual search process described above, the 2011 data were
also searched by automatic computer searching methods as well as by the “Ice
Hunters.” As with the earlier results, Ice Hunters did no better than our
internal team search efforts and was not pursued for later epochs of search
data. The computer search tools did provide some complementary coverage to the
visual searching that increased the aggregate completeness of the search
effort. From 2012 onward, the search continued with just in-house processing
and search efforts by manual and computer searches.

###  3.3 Results

Table 6: Summary of 2011-2014 Search Discoveries

Object |  |  | $a$ | $e$ | $i$ | $H_{V}$ | $R^{1}$ | arc | discovery | Nobs | Desig | type | CA Date | CA |  $\Delta$V
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
|  |  | (AU) |  | (deg) |  |  | (days) | (UT) |  |  |  | (UT) | (AU) | m/sec
VNH0008 |  |  | 44.00$\pm$0.01 | 0.04 | 2.60 | 7.32 | 23.22 | 358 | 2011-04-28 | 36 | 2011JY31 | C | 2018-10-07 | 0.15 | 245
VNH0010 |  |  | 43.15$\pm$0.03 | 0.03 | 2.39 | 8.03 | 24.03 | 359 | 2011-04-28 | 33 | 2011HZ102 | C | 2018-11-09 | 0.16 | 250
VNH0007 |  |  | 46$\pm$1 | 0.14 | 1.87 | 7.95 | 23.85 | 357 | 2011-04-29 | 20 | 2011JW31 | C | 2018-08-22 | 0.16 | 259
VNH0006 |  |  | 51$\pm$26 | 0.02 | 2.51 | 7.76 | 24.56 | 3 | 2011-04-30 | 6 |  $\cdots$ |  $\cdots$ | 2021-07-01 | 0.38 | 318
VNH0009 |  |  | 45.2$\pm$0.6 | 0.13 | 3.31 | 6.92 | 23.22 | 359 | 2011-04-28 | 54 | 2011JX31 | C | 2020-07-15 | 0.36 | 358
VNH0050 |  |  | 45$\pm$23 | 0.02 | 2.90 | 9.99 | 26.09 | 0.08 | 2013-06-07 | 3 |  $\cdots$ |  $\cdots$ | 2019-05-21 | 0.3 | 375
VNH0036 |  |  | 43$\pm$22 | 0.03 | 1.88 | 10.54 | 26.54 | 3 | 2013-06-04 | 9 |  $\cdots$ |  $\cdots$ | 2018-09-18 | 0.26 | 421
VNH0044 |  |  | 48$\pm$21 | 0.33 | 3.40 | 11.23 | 27.43 | 33 | 2013-06-03 | 14 |  $\cdots$ |  $\cdots$ | 2020-09-25 | 0.45 | 435
VNH0002 |  |  | 53.34$\pm$0.05 | 0.31 | 6.42 | 9.73 | 25.73 | 862 | 2011-04-28 | 55 | 2011HK103 | S | 2019-09-01 | 0.27 | 441
VNH0005 |  |  | 43.0$\pm$0.2 | 0.04 | 3.05 | 9.46 | 25.46 | 446 | 2011-04-29 | 24 | 2011HF103 | C | 2018-12-12 | 0.30 | 445
VNH0034 |  |  | 44$\pm$1 | 0.06 | 2.99 | 10.62 | 26.72 | 94 | 2013-06-05 | 18 | 2013LU35 | C | 2019-04-20 | 0.33 | 450
VNH0029 |  |  | 67$\pm$31 | 0.04 | 2.77 | 8.09 | 26.09 | 5 | 2011-04-28 | 5 |  $\cdots$ |  $\cdots$ | 2027-06-01 | 1.1 | 457
VNH0054 |  |  | 47$\pm$47 | 0.03 | 2.65 | 11.21 | 27.61 | 1 | 2012-04-17 | 6 |  $\cdots$ |  $\cdots$ | 2019-11-16 | 0.42 | 492
VNH0019 |  |  | 46$\pm$10 | 0.02 | 2.68 | 7.00 | 23.40 | 2 | 2012-04-17 | 6 |  $\cdots$ |  $\cdots$ | 2019-12-24 | 0.44 | 505
VNH0052 |  |  | 44$\pm$23 | 0.25 | 2.57 | 11.34 | 27.34 | 5 | 2013-06-06 | 7 |  $\cdots$ |  $\cdots$ | 2019-06-07 | 0.43 | 562
VNH0021 |  |  | 44.42$\pm$0.03 | 0.10 | 3.03 | 11.11 | 26.81 | 506 | 2012-04-18 | 42 |  $\cdots$ | 9:5 | 2017-12-09 | 0.32 | 716
VNH0014 |  |  | 56$\pm$17 | 0.44 | 3.22 | 10.53 | 26.63 | 355 | 2011-05-02 | 19 | 2011JA32 | C | 2018-02-10 | 0.38 | 767
VNH0058 |  |  | 42$\pm$22 | 0.02 | 2.19 | 10.75 | 26.45 | 7 | 2013-07-07 | 6 |  $\cdots$ |  $\cdots$ | 2018-04-20 | 0.41 | 771
VNH0017 |  |  | 47$\pm$24 | 0.26 | 6.72 |  $\cdots$ |  $\cdots$ | 33 | 2011-04-28 | 10 |  $\cdots$ |  $\cdots$ | 2021-02-02 | 0.93 | 833
VNH0040 |  |  | 48$\pm$25 | 0.02 | 3.17 | 10.05 | 26.45 | 1 | 2011-07-23 | 3 |  $\cdots$ |  $\cdots$ | 2020-05-05 | 0.85 | 886
VNH0003 |  |  | 47$\pm$2 | 0.19 | 5.36 | 9.31 | 25.01 | 65 | 2011-04-28 | 22 | 2011HJ103 | C | 2017-10-13 | 0.40 | 949
VNH0012 |  |  | 43.7$\pm$0.2 | 0.08 | 6.83 | 10.84 | 27.34 | 357 | 2011-04-28 | 24 | 2011HE103 |  $\cdots$ | 2020-04-18 | 0.92 | 975
VNH0022 |  |  | 46.2$\pm$0.4 | 0.21 | 5.44 | 11.35 | 27.25 | 505 | 2012-04-17 | 35 | 516977 | S | 2017-12-10 | 0.49 | 1.1k
VNH0033 |  |  | 58$\pm$30 | 0.58 | 5.93 | 8.89 | 26.09 | 10 | 2013-06-03 | 16 |  $\cdots$ |  $\cdots$ | 2022-05-10 | 1.5 | 1.1k
VNH0025 |  |  | 46$\pm$24 | 0.02 | 2.92 | 7.28 | 23.58 | 1 | 2011-05-31 | 5 |  $\cdots$ |  $\cdots$ | 2019-09-25 | 1.0 | 1.2k
VNH0016 |  |  | 53$\pm$27 | 0.49 | 5.76 | 9.55 | 26.45 | 358 | 2011-04-28 | 24 | 2011HD103 |  $\cdots$ | 2020-11-11 | 1.4 | 1.3k
VNH0047 |  |  | 47$\pm$24 | 0.02 | 14.55 | 9.45 | 26.45 | 0.12 | 2013-06-06 | 3 |  $\cdots$ |  $\cdots$ | 2020-01-10 | 1.4 | 1.5k
VNH0046 |  |  | 45$\pm$23 | 0.02 | 7.43 | 10.45 | 26.45 | 0.17 | 2013-07-07 | 3 |  $\cdots$ |  $\cdots$ | 2019-05-22 | 1.2 | 1.6k
VNH0027 |  |  | 54$\pm$29 | 0.76 | 6.95 | 8.86 | 25.46 | 703 | 2011-07-02 | 8 |  $\cdots$ |  $\cdots$ | 2023-05-11 | 2.5 | 1.6k
VNH0037 |  |  | 58$\pm$30 | 0.02 | 13.83 | 8.98 | 26.18 | 0.08 | 2011-07-01 | 2 |  $\cdots$ |  $\cdots$ | 2023-10-23 | 2.7 | 1.6k
VNH0035 |  |  | 42$\pm$22 | 0.02 | 12.75 | 7.79 | 23.49 | 2 | 2013-06-11 | 4 |  $\cdots$ |  $\cdots$ | 2018-03-05 | 0.84 | 1.7k
VNH0055 |  |  | 48$\pm$18 | 0.23 | 6.96 | 11.56 | 27.16 | 33 | 2013-06-03 | 14 |  $\cdots$ |  $\cdots$ | 2018-03-17 | 0.86 | 1.7k
VNH0032 |  |  | 41$\pm$21 | 0.02 | 7.62 | 8.77 | 24.47 | 4 | 2013-06-04 | 6 |  $\cdots$ |  $\cdots$ | 2018-01-28 | 0.90 | 1.9k
VNH0020 |  |  | 58$\pm$28 | 0.24 | 10.20 | 11.05 | 27.25 | 1 | 2012-04-18 | 15 |  $\cdots$ |  $\cdots$ | 2019-03-30 | 1.4 | 2.0k
VNH0026 |  |  | 45$\pm$23 | 0.02 | 9.08 | 7.57 | 23.67 | 0.19 | 2011-07-02 | 3 |  $\cdots$ |  $\cdots$ | 2019-04-19 | 1.7 | 2.3k
VNH0061 |  |  | 45$\pm$23 | 0.02 | 16.06 | 8.28 | 24.38 | 0.12 | 2013-06-05 | 3 |  $\cdots$ |  $\cdots$ | 2019-04-26 | 1.8 | 2.4k
VNH0059 |  |  | 87$\pm$3 | 0.57 | 9.91 | 10.76 | 26.36 | 88 | 2013-06-08 | 19 |  $\cdots$ | S | 2017-09-29 | 1.1 | 2.8k
VNH0051 |  |  | 43$\pm$18 | 0.06 | 12.01 | 10.91 | 26.81 | 6 | 2013-06-05 | 9 |  $\cdots$ |  $\cdots$ | 2018-06-28 | 1.6 | 2.8k
VNH0024 |  |  | 41.7$\pm$0.9 | 0.15 | 4.56 | 10.62 | 25.82 | 3 | 2012-04-17 | 23 |  $\cdots$ |  $\cdots$ | 2016-05-01 | 0.34 | 3.0k
VNH0018 |  |  | 45$\pm$23 | 0.02 | 16.61 |  $\cdots$ |  $\cdots$ | 0.06 | 2011-06-01 | 8 |  $\cdots$ |  $\cdots$ | 2019-04-01 | 2.3 | 3.2k
VNH0060 |  |  | 40$\pm$12 | 0.09 | 7.26 | 11.57 | 27.07 | 8 | 2013-06-05 | 9 |  $\cdots$ |  $\cdots$ | 2017-03-29 | 1.0 | 3.4k
VNH0042 |  |  | 40$\pm$20 | 0.03 | 19.92 | 11.02 | 26.72 | 2 | 2013-07-04 | 4 |  $\cdots$ |  $\cdots$ | 2018-01-29 | 1.9 | 4.0k
VNH0045 |  |  | 39$\pm$20 | 0.02 | 18.89 | 11.67 | 27.07 | 7 | 2013-07-07 | 6 |  $\cdots$ |  $\cdots$ | 2017-03-15 | 1.6 | 5.3k
VNH0023 |  |  | 39$\pm$3 | 0.02 | 19.28 | 11.12 | 26.72 | 2 | 2012-04-17 | 18 |  $\cdots$ |  $\cdots$ | 2017-03-29 | 1.6 | 5.3k
VNH0057 |  |  | 41$\pm$22 | 0.02 | 31.74 | 10.75 | 26.45 | 1 | 2013-07-05 | 5 |  $\cdots$ |  $\cdots$ | 2018-01-03 | 2.5 | 5.4k
VNH0011 |  |  | 42.3$\pm$0.8 | 0.15 | 14.44 | 6.53 | 24.03 | 65 | 2011-04-28 | 25 | 2011HL103 | 5:3 | 2016-08-29 | 1.4 | 7.8k
VNH0041 |  |  | 45$\pm$19 | 0.62 | 12.20 | 10.33 | 25.73 | 23 | 2013-06-13 | 15 |  $\cdots$ |  $\cdots$ | 2016-07-11 | 1.3 | 8.3k
VNH0013 |  |  | 54$\pm$8 | 0.41 | 12.94 | 9.99 | 25.19 | 63 | 2011-04-30 | 39 | 2011JD32 |  $\cdots$ | 2015-12-26 | 1.1 | 25.9k
VNH0001 |  |  | 30.12$\pm$0.01 | 0.08 | 29.38 | 7.49 | 21.69 | 354 | 2011-04-29 | 131 | 2011HM102 | 1:1 | 2013-11-04 | 1.2 |  $\cdots$
VNH0031 |  |  | 23$\pm$23 | 0.32 | 6.94 | 12.40 | 26.90 | 5 | 2011-04-28 | 5 |  $\cdots$ |  $\cdots$ | 2014-06-29 | 0.73 |  $\cdots$
VNH0048 |  |  | 37$\pm$9 | 0.25 | 22.34 | 12.41 | 26.81 | 9 | 2013-06-04 | 12 |  $\cdots$ |  $\cdots$ | 2014-07-02 | 1.3 |  $\cdots$
VNH0004 |  |  | 37$\pm$14 | 0.30 | 3.81 | 9.40 | 24.20 | 34 | 2011-05-29 | 12 | 2011KW48 |  $\cdots$ | 2015-02-12 | 0.43 |  $\cdots$
VNH0053 |  |  | 34$\pm$18 | 0.25 | 25.09 | 12.02 | 26.72 | 4 | 2013-06-09 | 9 |  $\cdots$ |  $\cdots$ | 2015-06-12 | 0.95 |  $\cdots$
VNH0056 |  |  | 42$\pm$21 | 0.61 | 16.00 | 11.36 | 26.36 | 23 | 2013-06-13 | 9 |  $\cdots$ |  $\cdots$ | 2015-10-15 | 0.90 |  $\cdots$
VNH0015 |  |  | 35$\pm$21 | 0.03 | 18.95 | 9.01 | 24.11 | 5 | 2011-04-28 | 6 |  $\cdots$ |  $\cdots$ | 2015-10-21 | 1.8 | $>$
VNH0039 |  |  | 2000$\pm$1200 | 0.84 | 171.95 |  $\cdots$ | 25.28 | 0.11 | 2011-07-02 | 2 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$

Note. — (1) $R$ magnitude is the apparent brightness at the time of discovery

The search depth of the survey was quite variable due to weather and site
conditions. The best dataset from the entire effort was at Magellan where we
reached a 50% efficiency detection limit of R=26.0 in multi-hour stares with
exceptional seeing of $\sim 0.45$ arcsec. While seeing on individual images
ranging from 0.4 greater than 2.0 arcsec, the average was 0.84, 1.06, 0.75 and
0.71 arcsec per year respectively, from 2011-2014 (Table 5). Likewise, each
run was given a unique set of field names, but with significant overlapping
sky area between the runs in different months. This allowed for orbit
extensions on any new objects to determine their observability/accessability
by the spacecraft. In effect, all of the project search area was observed each
year with multi-month overlap of the fields as conditions allowed. 2011 was
our most productive year accumulating 12.5 degrees of sky area (covering the
search area multiple times at different epochs). The following years
accumulated 4.4, 2.17 and 0.48 degrees, respectively (Table 4). All of our
observations were submitted to the MPC using the standard “OBS80” formatting
at that time. Although it is now possible to include detailed error analysis
in ADES-format submissions, it was not standard at the time, and we did not
re-evaluate this information given the level of effort that would have been
required post-facto. Astrometry for objects that we later observed with New
Horizons were, however, re-analyzed with those uncertainties and that process
is reported in detail in Porter et al. (2022).

Table 6 provides a summary of the objects discovered during this three year
search effort, sorted by increasing $\Delta$V. The information provided also
includes the object orbital elements (a,e,i), the estimated H-magnitude,
measured R-magnitude, accumulated object arc, discovery date, number of
observations, MPC designation if one exists, the dynamical classification for
the object, the encounter date and spacecraft encounter distance as well as
the delta velocity required for such an encounter. The dynamical
classification shown is meant to be a rough guide where “C” is for some type
of classical KBO, “S” is a scattered object, and those with pairs of numbers
denote the type of mean-motion resonance with Neptune. A close-approach date
prior to the planned date of the post-Pluto-encounter trajectory correction
maneuver (TCM) has no $\Delta$V listed. One object had a close approach just
days after the TCM planning date and would have required an extremely large
$\Delta$V. In this case only “$>$” is shown to denote a large value that is of
no interest. The final object in the table is believed to be a real detection
of a KBO, but was only seen twice and had insufficient information to
constrain its orbit well enough to compute useful close approach
circumstances.

The result of the efforts through the end of 2013 made a significant
improvement by finding objects that New Horizons would pass close to but the
closest, 2011JY31, was not close enough, requiring a factor of two more
$\Delta$V than available. Without any course adjustment we expected to get to
within 0.15 au of 2011JY31 on 7 October 2018. If we used all of the available
fuel, this would still leave us with a flyby distance of $\sim$10 million km
and no fuel to support the encounter. As with the earlier search, many of the
objects we found became useful distant encounter targets for New Horizons.

The results to this point were such that most of the search area was covered
to a brightness limit that could be reasonably reached by the best ground-
based facilities available. There was a still a slim chance that we would find
something suitable in 2014, but it became clear that another tool was required
to ensure finding a target. The tool of choice to extend the search was the
Hubble Space Telescope (HST). The use of HST was by no means assured so a
parallel full search effort was also carried out from ground-based facilities
in 2014. As we began to consider the use of HST, the Hyper Suprime-camera
(HSC) was commissioned for use on Subaru (Miyazaki et al. (2018)). This new
camera had a field of view of 1.5 deg2, considerably larger than the search
area for that year. The time allocated for our search on HSC was granted as
shared-risk and the weather conditions and instrument problems prevented any
new and useful search data. In the end, the ground-based data from 2014 and
the following years were used only for recoveries and orbit refinement work
for the distant encounter targets and will not be discussed further in this
work. A subsequent new search for additional fly-by targets begun on Subaru in
2020 and onward will be discussed in other papers, eg. Fraser et al. 2024
(submitted).

##  4 HST search – 2014

The immutable properties of the New Horizons flyby of Pluto gave rise to
strong constraints on the search efforts. Re-targeting the spacecraft to the
extended mission destination would use the least amount of fuel if it was done
as soon as possible after the Pluto encounter. Due to the slow data
transmission time from New Horizons to the ground, the project wanted a
significant amount of time to downlink critical data before re-targeting. The
time for the trajectory correction maneuver (TCM) was set for October 2015.
The analysis and commanding development for the TCM usually takes a couple of
months so when that work began, a good orbit had to be known for the new
target. It was not enough to have just discovered the object prior to the TCM,
we had to find it soon enough to get sufficient data to get an accurate orbit
for the object as well. Our analysis showed that we needed astrometry spanning
at least a year from which an accurate enough orbit estimate could be obtained
to support the TCM. These constraints meant we absolutely had to find an
object in 2014.

The obvious advantages of HST are the stable PSF and the very fine image
scale. The main difficulty with using HST is that the best survey camera for
this project, the Wide Field Camera 3 (WFC3)/UVIS (with a image scale of
0.0395 arcsec/pixel) has a rather small FOV at just 0.0021 deg2 (Dressel
(2019)). Fortunately, 2014 was the year where the search area reached its
minimum size of 0.3 deg2. Covering 80% of this area thus would require 83
separate pointings of the telescope.

In the end, we secured two allocations of time on HST – 40 orbits for a pilot
study which if successful would lead to another 154 orbits for the full
survey. The pilot study was supported by Director’s Discretionary (DD) time
while the full survey came from the Cycle 23 GO allocation (GO-13633, PI
Spencer). The agreed upon success criteria for the pilot study was to find two
cold-classical KBOs as a rudimentary check on the predicted size distribution
down to this small size. The pilot was successful in finding two objects and
we were given clearance to conduct the full survey (83 search fields - 7.29 sq
arcmin each, $\sim$605 sq arcmin total). 28 orbits from the full survey
allocation were available for additional followup observations on newly
discovered objects.

###  4.1 Survey design

The goal of the search was to find an object that New Horizons could reach for
a close flyby investigation. This goal allowed a much narrower scope for the
search than a generic search for KBOs. In this case, we could fine tune the
data collection and processing to maximize our ability to find the object we
sought. It was entirely permissible to be blind to objects that New Horizons
could not reach.

The area to search was defined by two primary constraints, (1) the region of
space that New Horizons could reach after October 2015 and (2) the properties
of the Kuiper Belt. The predicted trajectory of New Horizons defined a time-
dependent path through space and the amount of fuel on board set the size of a
cone centered on that path. Any KBO in that cone of 130 m/sec $\Delta$V at the
right time is encounterable. The requirement of being in the cone at the right
time provided a constraint on the orbit an object would need to have. Our
knowledge of the spatial distribution of the Kuiper Belt and the size
distribution of KBOs was used with that positional constraint to construct a
virtual population of KBOs that were a subset of all objects having the right
orbital properties to be at the right place at the right time.

There were only two dynamical groups that had a useful probability of being in
the accessible cone: cold-classical and hot-classical objects. Of these, the
cold-classicals were strongly favored over hot-classicals with a ratio of 4:1.
We adopted a KBO population model which used the orbital distribution derived
from the Canada-France Ecliptic Plane Survey (CFEPS) model of the Kuiper Belt
Petit et al. (2011). The size distribution was constrained by the absolute and
apparent magnitude distribution of KBOs from recent models (Fuentes et al.
(2010), Fraser et al. (2014)). At the time of the survey proposal we deemed
this “FEPS/Fraser” model to be somewhat conservative; the true number to be
found might actually be higher. We then used this orbit population to derive a
set of semi-major axis, eccentricity, and inclination values that were
consistent with this model of the Kuiper Belt. From there, we selected random
values of the angular elements. If the randomly drawn elements placed the
virtual object in the accessible cone, the elements were saved. At the end of
this process we had a selection of orbital elements representing virtual
objects that were all encounterable.

Given the set of encounterable virtual objects, we could then project their
positions back to some prior time and thus know the region of sky that needed
to be searched to find a real object. Figure 4.1 shows a plot of the sky plane
centered on the cloud of virtual objects in our sample. Each dot represents
one virtual object and the cloud is roughly described by a two-dimensional
Gaussian distribution. Each square represents one field of the WFC3 camera on
HST and the fields are laid out to cover 80% of the distribution. We chose
this coverage as a compromise between completeness and a practical request of
time for the search. Covering a larger region would have taken much more time
with quickly diminishing returns for that time investment. The properties of
this cloud of virtual objects was time-dependent, but we ignored this in
designing the search, provided the data could be obtained quickly enough.
However, the orientation of the imaging camera is governed by the roll angle
of the spacecraft as a function of time. The figure depicts the image
orientation at the time of the pilot survey, shown in green. The remainder of
the search fields, shown in blue, have the orientation expected for that part
of the full search. In reality, the true search grid could not avoid small
gaps between adjacent fields, but the missed search area was small enough to
ignore.

A special virtual orbit was chosen from the entire cloud. This orbit was the
closest to the center of the cloud and was used to set the pointing and
tracking for HST. This strategy works well because in this case, the
differential rate of motion of the cloud of virtual objects was 0.5 pixels (20
mas) during a single exposure for fields on the outer edge of the distribution
thus avoiding any trailing losses for objects of interest. Other KBOs, such as
resonant or scattered disk objects, would have different rates of motion and
were not expected to be detected at all. All search observations were based on
this same guiding orbit throughout the survey.

A plot of the 83 HST search fields. Each box marks the approximate area of a
combined WFC3/UVIS field using both detectors. 5 fields ended up not being
useful due to guide star failures (red) or moonlight (orange). The green boxes
represent the 40 orbit HST pilot fields and the blue show the additional full
program fields excluding the repeated fields to follow up on the detected
objects. The 5 discoveries from the search are marked with a red X and labeled
with the eventual object designation. The black dots are a simulated KBO
population from the CFEPS model with hot and cold Classical KBOs included.

The search observations were designed as a pair of orbits looking at a given
search field from the set shown in Fig. 4.1. There was a small amount of
motion during one visit and sufficient motion between two visits to get an
initial estimate of the target distance and orbital inclination. This two
orbit time span was sufficient to produce an initial orbit constraint that
reduced the list of objects requiring followup and further orbit refinement,
but was not in itself enough to know if an object was encounterable. However,
by the very nature of the survey design, all detected objects were highly
likely to be interesting.

The optimal time spacing was for back-to-back orbits. In some cases, this was
impossible so 4.2% of the fields had a one-orbit gap between the two epochs.
The increased time base was marginally useful for constraining the orbit of a
detected object, but came at the price of a much larger search effort. Even
longer time gaps were categorically excluded from consideration in scheduling
observations. No other constraints were placed on scheduling the search
observations other than to pick a set of fields near the center of the
distribution for the pilot project. In retrospect, we should have increased
the lunar avoidance distance constraint rather than using the default
settings. Two of our search fields (marked in orange) were taken close enough
to a full moon that the extra scattered light made the images useless for the
survey. Table 7 gives a list of each HST field and the results of our searches
and Fig. 4.1 shows a sample image pair.

Table 7: Summary of New Horizons Search Fields

Dataset | Target Name | R.A. | Dec. | Starting Julian Date | Calendar Date | Exp. Duration | Notes |
---|---|---|---|---|---|---|---|---
|  | J2000 | J2000 |  |  | (hrs) |  |
01 | KBO1-R6C3 | 18:44:42.824 | -20:55:52.32 | 2456830.81797 | Jun-22-2014 | 2.18 | Guide Star Failure |
02 | KBO1-R6C3 | 18:44:41.902 | -20:55:53.28 | 2456831.01196 | Jun-22-2014 | 1.05 | Guide Star Failure |
03 | KBO1-R6C4 | 18:44:55.066 | -20:55:53.02 | 2456830.94559 | Jun-22-2014 | 1.05 |  |
04 | KBO1-R6C4 | 18:44:54.435 | -20:55:53.69 | 2456831.07833 | Jun-22-2014 | 1.05 |  |
05 | KBO1-R7C3 | 18:44:38.045 | -20:53:36.62 | 2456832.87027 | Jun-24-2014 | 1.05 |  |
06 | KBO1-R7C3 | 18:44:37.410 | -20:53:37.30 | 2456833.00301 | Jun-24-2014 | 1.05 |  |
07 | KBO1-R7C4 | 18:44:50.572 | -20:53:37.01 | 2456832.93664 | Jun-24-2014 | 1.05 | 2014MT69 |
08 | KBO1-R7C4 | 18:44:49.937 | -20:53:37.68 | 2456833.06939 | Jun-24-2014 | 1.05 | 2014MT69 |
09 | KBO1-R7C5 | 18:44:58.967 | -20:53:41.77 | 2456833.86583 | Jun-25-2014 | 1.05 |  |
10 | KBO1-R7C5 | 18:44:58.330 | -20:53:42.45 | 2456833.99858 | Jun-25-2014 | 1.05 |  |
11 | KBO1-R7C6 | 18:45:07.032 | -20:53:46.86 | 2456834.86137 | Jun-26-2014 | 1.05 | 2014MU69 |
12 | KBO1-R7C6 | 18:45:06.393 | -20:53:47.55 | 2456834.99411 | Jun-26-2014 | 1.05 | 2014MU69 |

Note. — (This table is available in its entirety in machine-readable and
Virtual Observatory (VO) forms in the online journal. A portion is shown here
for guidance regarding its form and content.)

Sample image from field KBO1-R7R6 in each of 2 visits separated by 1.05 hours.
This field was part of the pilot search and 2014 MU69 is in the top chip on
the right side in the area marked by the white box. The visit numbers of HST
program 13633 are shown on the lower right hand corner of each image.

We used the WFC3/UVIS instrument with the F350LP filter for all observations.
The data volume for the full FOV readout led to a particular exposure time
choice. Five 370-second exposures fully fill a single visit without losing
time to data management overhead. Some visits needed a small tweak (no more
than a few seconds) to get the sequence of observations to fit in a single
visibility window. The pair of visits was further constrained to be taken with
the same guide star pair and same roll angle. Due to the guiding orbit used,
all background stars were trailed in the image. This factor in the images
required the development of new techniques to obtain accurate astrometry of
the discovered KBOs.

###  4.2 Data analysis

Each set of five images from a single visit was processed to generate a
stellar template image. Referenced and stacked on the star positions, the
stack is a median of the images. This template had only stars with cosmic-ray
strikes and KBOs naturally filtered out. Each image was then processed to
subtract the template image. This step suppressed the stars, including the
wings of the stellar images. In the cores, there is too much residual noise to
permit searching those areas for KBOs. In the wings, the KBOs can be
completely hidden until the faint outer part of the star image is subtracted.
For most visits, the trailing of the stellar images is not exactly the same in
all the orbits. As a result, the stacked template does not completely remove
the core of the star trails and leaves a characteristic residual image.

The next step was stacking the set of five images. This process was done
twice, once with and once without subtracting the stars. Two things happen at
the same time: the images are re-sampled to eliminate the distortion and
register on the same linear 40 mas/pixel grid while shifting the image based
on a given velocity vector. Since the images are not Nyquist sampled nor
cleaned of cosmic ray strikes and other blemishes, we chose to use bilinear
interpolation for the re-sampling. This choice was cosmetically much better
than using a proper sinc interpolation.

###  4.3 Rate Corrections

In order to sensitize the search to KBOs on targetable orbits which differed
from the nominal guiding orbit, we conducted a “shift-and-stack” digital
tracking approach. Frames were shifted in software to counter the differential
sky-plane motion between the nominal guide orbit and other potential
targetable KBO orbits. As mentioned previously, the source population of
targetable KBO orbits was drawn from the ”CFEPS/Fraser” model and they were
down-selected to a small set of guide orbits using the methods of Parker &
Kavelaars (2010). Unlike previous KBO searches using the digital tracking
approach, frame-by-frame shifts were not parameterized as a grid of linear
rates of motion in the sky plane; instead, the frame-by-frame motion of each
guide orbit was computed and a frame-wise sky-plane offset was computed from
the exact motion of a KBO on that orbit as seen from the HST reference frame.
The down-selected orbit grid was chosen with a density such that no KBO in the
large source sample of synthetic targetable KBOs would have a single frame-
wise correction that differed by more than a single HST WFC3 pixel
($\sim$0.039 arcsec).

The sample of virtual objects used to design the search provided a means to
calculate the bounds for the search in velocity space. The size for the
velocity bins was set such that the worst-case smear within a bin was no more
than one pixel across the five images in a single visit. There are two
important consequences of this design. First, an object is unlikely to be seen
in more than one velocity bin, especially at the detection limit of the
survey. Second, the number of discrete stacks to search varied with the time-
span of the set. For observation pairs of the same field that occurred on
back-to-back HST orbits (1.05 hours), typically of order 20 guide orbits were
required to achieve the required sampling density leading to 20 image stacks
to search. For observation pairs that spanned larger periods of time, a
rapidly-increasing density ($\propto t^{2}$) of guide orbits was required and
we ended up with as many as 80 stacks to search. Due to the increased workload
and need for rapid turn-around, we adjusted our observation constraints as the
program progressed to strongly prefer the shorter time spacing.

Figure 4.3 illustrates one resulting grid of linear sky-plane offsets — for
the entire population of targetable orbits as well as the chosen guide orbits
— from the first image in a single orbit to the last, computed for visit
icii11 (where (486958) Arrokoth was discovered).

Sky-plane offsets from the nominal guide orbit over the course of a single HST
orbit for visit icii11. Black points are the motion of all targetable KBOs
from the synthetic orbit sample. Red points are the sky plane motions of the
chosen guide orbit grid, and blue circles are the buffers of sky motion each
covers to within a single HST WFC3 pixel. The point at (0,0) is the nominal
guide orbit.

We had five nearly independent teams pursuing their own search tools all built
more or less around the same concepts of the shift-stacking. This discussion
largely concentrates on the pipeline written by Buie since that was
responsible for all five of the discoveries within the survey project. We will
touch on aspects of the other systems as needed.

In one of the final stages of development for the software, we implanted fake
objects into our data. This was designed primarily to measure the sensitivity
limits of our data. In the end, it was far more important as a training
dataset to test the software. During the pilot phase, significant portions of
the data were scanned multiple times with no results. The test data convinced
us that we had the expected sensitivity and that the software was only finding
objects when the shift was zero. This was quickly determined to indicate a
sign error in the velocity stacking and Buie’s detections in the pilot survey
quickly followed after correcting the error.

####  4.3.1 Searching for Candidates

The search methodology employed a mix of automated and manual steps. Each of
the shift-stacked images was scanned for sources. The scanning was done with
findsrc with a background window (WINDOW) of 20 pixels and a separation
between the window and the target pixel (GAP) of 6 pixels. The detection
threshold was set at 3$\sigma$. With this setting, the number of false
detections per stacked images was quite large – typically in the range of 3000
to 6000 per velocity stacked image and well beyond the ability to visually
scan all candidates. To reduce the number of false positives, the pairs of
visits were combined. A candidate worth examining was required to be seen on
both visits with the same velocity and at a relative position within the
stacks that was consistent with that velocity. A threshold on this test was
set to 1.7 pixels multiplied by the ratio of the largest velocity to the mean
velocity in the bin. The value of 1.7 was empirically tuned to set the number
of false positives to a manageable level. No threshold on consistent
brightness was imposed at this step. For good data, there were typically
$\sim$30 candidates per image per velocity, but the worst visit pairs had 10
times more.

The visit-combined detection lists fed a tool that built a composite graphic
image summarizing the detection candidate. This graphic contained small
thumbnail images of the detections in each stack as well as the relevant
portion of the original image. In all cases, the thumbnails were centered to
the nearest pixel of the position of the candidate object. Also included was
an aperture based magnitude estimate. Figure 4.3.1 shows the vetting graphic
for (486958) Arrokoth. In this figure, the circle in the top left image is
drawn at the measured location for the first visit stack. The top right image
shows the stack for the second visit and the circle is drawn at the location
that is predicted based on the stacking velocity. The size of the circles are
comparable to the size of the positional coincidence imposed to find the
candidates. The bottom of the figure contains two rows of five thumbnail
images each. The top set of five is from the first visit and the bottom set is
from the second visit. Each set of five is ordered in increasing time from
left to right. The only processing done on the bottom images is the
suppression of background stars. In this example, stars are seen as white
streaks with some black pixels around the edge. Other than the object itself,
the rest of the bright points are cosmic ray strikes that do not correspond to
any object. This example shows the success of our spurious noise suppression
algorithm. In the stacks there are a few low-level artifacts that are easily
dismissed. For example, in the first stack there is a dark smudge to the lower
right of the object. This is due to the residual of a star that was not
perfectly subtracted. In both visits, there are other faint bright smudges but
these are far enough away and at uncorrelated velocities so they are never
considered. This graphic was designed to allow quick examination of all
candidates for a determination of being real or not. In this case, there is
clear evidence in all ten images for a source that leads to the two stacks.
One of these ten (first image in second row) shows the object as being very
close to a cosmic ray strike. The estimated apparent magnitude in both stacks
is superimposed on the graphic below each detection.

Confirmation graphic for discovery of (486958) Arrokoth.

Figure 4.3.1 shows an example of a false positive that was discarded during
the vetting process. The image stacks show an apparent source and is seen to
agree with the velocity. The first clue against it being real is the lack of
agreement in the magnitudes. This is apparent both in the numbers and visual
appearance. The individual images provide the rest of the evidence against. In
this case, the first visit alone is enough to discard the candidate. Image 1
has no source. Image 2 and 3 are on the edge of a subtracted star. Image 4 has
a bright cosmic ray strike. Image 5 looks more like a background noise
fluctuation. Similar logic applies to the second visit, Image 1 and 5 show
nothing. In this case, there was clearly a confluence of spurious detections
in each set of 5 that triggered a false positive detection. This combined
graphic made it very easy to make a decision on the candidate.

Confirmation graphics for a typical false positive detection.

It is perhaps possible to encode all of the logic used to grade candidate
sources to avoid the manual step. No attempt was made to do this. The vetting
process was already very fast and took much less than 10% of the total time to
process an entire visit pair. Also, the time required to develop a fully
tested automated tool was completely impractical on the timescale in which we
needed to complete our search efforts.

####  4.3.2 Cross-Checking Searches

In order to cross-check our discoveries and to make sure no potentially real
object was missed, our team compared the results of two independent search
algorithms. The second algorithm worked with the HST “drizzled” images which
are both flat-fielded and distortion-corrected through the HST calibration
pipeline. The intensity unit for these images is in electrons/s. Figure 4.3.2
records the steps of the second pipeline. Basically the full visit list of
images for a pair of visits was read into a buffer. A star template was
created by co-adding the images weighted by their exposure times, excluding
high sigma pixels, and stacking on the positions of a selection of 6 user
identified stars, ideally spread across the array. This process could be
iterative if necessary. Once the star template for each visit was created it
was subtracted from each individual image and a composite image for each visit
was created for the family of KBO orbits provided by the rate correction
previously discussed (i.e. if the family of orbit rates had 10 entries one
would have 10 composite images for each HST visit to evaluate). The composite
images for each pair of HST visits to the same position and at the same shift
rate was then automatically searched for KBOs with image stamps of the
discovered objects saved as .png files for visual confirmation. A display tool
allowed one to blink-compare the results and the individual shifted and
differenced images could also be brought up for searching or confirmation.

Sample images from our second reduction pipeline for the 2014 MU69 discovery
image. (Top) Images from a single visit are shifted both by eye, then through
an optimization routine to remove the stars. (Bottom) The star subtracted
images are then searchable for KBOs in the field. The inlay on the bottom
right is an extracted .png used for evaluation of reality.

In addition to identifying potential targets via an algorithm, an independent
manual-visual search was conducted in parallel. To systematically search each
HST visit, a custom IDL program (“HSTlooker”) was created to present side by
side views of stacked and original images from corresponding visits, matching
the predicted locations of an object from one visit to the next, and
connecting the pixels of the stacked image to the data that created them. This
tool drew from the prior work on searching the ground-based data. The
HSTlooker program allowed users to cycle through the stacked and original
images for each velocity shift and systematically cover the full frame to
ensure no part of the image was missed. Each portion of the shifted and
stacked images was visually scanned to identify any artifacts that persisted
through median combination. Artifacts found in the stacks were verified via
visual examination of the five original images to identify the source of the
bright median pixel, be it a KBO or incidental alignment of cosmic rays, star
subtraction remnants, scattered light or bad column. All five KBOs were
independently “discovered” via this process, albeit well after the objects
were first located with the computer driven detection processes.

###  4.4 Measuring KBO Positions

The next step in the processing was to obtain accurate positions for the
validated objects. These measurements were always based on the original
images, not the stacks. To start, a manually supervised aperture-based
centroid was used. At this step, if the centroid looked reasonable for the
position of the object, it was kept. If not, a manually derived position based
on judgement of the position of the object was used. This aperture measurement
is called a navigation position and fixes the region of interest for the next
phase.

Given a navigation location, a region of interest with a half-width of 9
pixels was defined. Within the region, an PSF-fit was performed on the object
with the navigation position as its starting point. The PSF used was generated
by TinyTim (Krist et al., 2011). This location is saved separately from the
navigation location. We used bad-pixel masks for the PSF fitting step to avoid
contamination from cosmic ray strikes or residual blemishes from imperfectly
subtract background stars. Most of the time the measurements were derived from
the star-subtracted images but occasionally a better result was possible on
the untouched data.

###  4.5 Astrometric support catalog

The support catalog developed for the ground-based search turned out to be
ideally suited for the HST data as well. There was useful overlap between the
catalog and well-measured stars in the field such that there were generally
$\sim$200 stars for a single detector in WFC3. The much improved image scale
and smaller PSF enabled even more precise astrometry and the CFHT-based
catalog held up amazingly well. Despite the quality of the catalog, the HST
data clearly showed the limitations of the underlying astrometric catalogs.
This led to the development of more and more intricate corrections to minimize
the obvious systematic errors. None of these difficulties affected our ability
to determine initial orbits or predict future positions for followup but it
became clear that final targeting of an object would benefit from a better
catalog. When the Gaia catalog was released in 2016 (Gaia Collaboration et
al., 2016a, b; Lindegren et al., 2016), we switched to using that as the
reference catalog for the CFHT data. We will return to a more in-depth
discussion of our support catalogs in section 4.7.

###  4.6 Measuring Star Positions and Updating the WCS

The world-coordinate system (WCS) header information (Gennaro et al., 2018)
provides the means to transform pixel coordinates from the image to sky-plane
coordinates. The WFC3 camera suffers from significant distortions and must be
accurately known for precision astrometry. Kozhurina-Platais et al. (2016) did
extensive work to map out the image scale and focal plane distortion. This map
provides relative calibration down to the level of 0.01 pix (0.15 $\micron$)
or better between any pair of pixels in the image. The absolute pointing
information comes from the guide stars observed with the fine-guidance sensors
(FGS) that are providing pointing and guiding control. These stars are known
to have typical errors of 0.1-0.2 arcsec but sometimes are significantly worse
than that. As a consequence, the absolute pointing information is of a much
lower quality and must be improved.

To start with we measured the stars that are in the support catalog with PSF
fitting. Again, we used the TinyTim PSF appropriate for the location of each
star on the detector. Still, the star fitting poses one additional challenge
due to tracking of the KBO cloud. All star images show significant trailing
which changes on every exposure. The dominant apparent motion of the stars is
due to parallax as HST moves around the Earth in its orbit. Even though the
images look like linear trails most of the time, the trailing is actually a
time-dependent quantity and the residence time of a star at any given point on
the trail varies throughout the exposure.

To address this time-variable trail, we modified the PSF fitting process by
introducing a convolution kernel into the model image production. The routine
jitterk.pro takes the time-dependent position and computes the necessary
kernel. More details about this tool can be found in Appendix B. The time-
dependent position is derived from the HST-centric position of the guiding
orbit that represents the center of the cloud of candidate objects. Also
required was the definitive post-observation HST orbit provided by
JPL222http://naif.jpl.nasa.gov/pub/naif/HST/kernels/spk/hst.bsp.

One minor limitation of our tools is that the image distortion was not taken
into account for the star smear kernel. The kernel is computed for the center
of the array and then used over the entire image. There are very subtle
shifting features in the residuals from the fit across the field that look
like the model image is trailed at a slightly different angle from the image.
We looked for patterns in the astrometric analysis that could be traced back
to this approximation but no convincing signatures were found. Once the new
Gaia catalog (Brown et al., 2018) is included the pipeline WCS can be
dramatically improved but this will only ever be constrained by the position
of two stars. By using more stars in the field, the solutions can always be
improved.

Our final WCS update consisted of solving for a translation of the reference
position in the WCS stored as CRVAL1 and CRVAL2 (Gonzaga et al., 2012) and a
small angle rotation to the CD matrix. All other components of the WCS remain
untouched. In practice, the rotation corrections are extremely small and
amount to worst-case corrections in the image corners that are much smaller
than a pixel (a few milliarcsecs at most). The apparent offsets in our data
are larger than one would expect from just the errors in the guide star
catalog but this is due to the bookkeeping of the pointing information for
data taken with moving target tracking. Our pointing solution update removes
all of these effects.

We received a report of errors in the reconstructed trajectory of HST deduced
from astrometric observations of C/2013 A1 (Siding Springs) relevant to its
close passage to Mars (Farnocchia et al., 2016). In that work, the internal
errors from the HST observations did not agree with the post-fit errors when
combined with other sources. In that work the HST data were de-weighted to 0.3
arcsec due to presumed errors in the HST position at the level of 10 km. If
this interpretation is correct, we should presume this same error is present
in our data. However, our targets are nearly 30 times further away and perhaps
that reduces the problem. Taken at face value, this issue indicates HST
positional errors could contribute as much as 10 mas to the total error
budget. However, in light of our successful occultation work on Arrokoth (Buie
et al., 2020), this level of error in our astrometry is just not seen and we
have no evidence in our data and reductions for any problems with the
reconstructed positions of HST that supported our astrometric work.

###  4.7 Final Astrometry on KBOs

The KBO position for each image is derived using the methodology described in
Porter et al. 2018 (sections 2.3-2.4) and further discussed in Porter et al.
2022. In short, a MCMC algorithim is used in combination with Tiny Tim PSFs to
determine the optimum KBO pixel position PDF which then has the WCS applied to
extract the R.A./Dec sky-plane position. All measurements are provided in
J2000 (EME200). Table 8 lists the positions for all objects measured in the
HST survey.

Table 8: HST Astrometry Object | UT Date | RA | Dec | R Mag. |  | Object | UT Date | RA | Dec | R Mag.
---|---|---|---|---|---|---|---|---|---|---
486958 | 2014 06 26.36924 | 18 45 10.671 | -20 53 03.06 | 26.8 |  | 486958 | 2016 07 03.64376 | 18 55 39.182 | -20 43 53.57 | 27.4
486958 | 2014 06 26.37539 | 18 45 10.636 | -20 53 03.10 | 27.0 |  | 486958 | 2016 07 03.64965 | 18 55 39.142 | -20 43 53.65 | 27.4
486958 | 2014 06 26.38153 | 18 45 10.595 | -20 53 03.18 | 27.0 |  | 486958 | 2016 07 03.65595 | 18 55 39.107 | -20 43 53.67 | 27.3
486958 | 2014 06 26.38768 | 18 45 10.557 | -20 53 03.23 | 26.5 |  | 486958 | 2016 07 03.66214 | 18 55 39.070 | -20 43 53.61 | 28.2
486958 | 2014 06 26.39382 | 18 45 10.521 | -20 53 03.31 | 26.7 |  | 486958 | 2016 07 03.66832 | 18 55 39.036 | -20 43 53.48 | 28.4
486958 | 2014 06 26.50197 | 18 45 10.019 | -20 53 03.77 | 26.2 |  | 486958 | 2016 07 03.71002 | 18 55 38.855 | -20 43 54.02 | 27.8
486958 | 2014 06 26.50812 | 18 45 09.983 | -20 53 03.80 | 27.1 |  | 486958 | 2016 07 03.71591 | 18 55 38.819 | -20 43 54.09 | 28.4
486958 | 2014 06 26.51426 | 18 45 09.943 | -20 53 03.88 | 27.2 |  | 486958 | 2016 07 03.72222 | 18 55 38.780 | -20 43 54.12 | 28.7
486958 | 2014 06 26.52041 | 18 45 09.905 | -20 53 03.95 | 27.3 |  | 486958 | 2016 07 03.72840 | 18 55 38.742 | -20 43 54.05 | 27.9
486958 | 2014 06 26.52656 | 18 45 09.870 | -20 53 04.01 | 27.4 |  | 486958 | 2016 07 03.73458 | 18 55 38.708 | -20 43 53.99 | 27.7
486958 | 2014 08 02.54538 | 18 42 15.467 | -20 56 43.22 | 27.5 |  | 486958 | 2016 07 03.77627 | 18 55 38.528 | -20 43 54.50 | 28.0
486958 | 2014 08 02.55152 | 18 42 15.433 | -20 56 43.22 | 27.1 |  | 486958 | 2016 07 03.78216 | 18 55 38.493 | -20 43 54.55 | 27.8
486958 | 2014 08 02.55767 | 18 42 15.402 | -20 56 43.19 | 25.1 |  | 486958 | 2016 07 03.78847 | 18 55 38.454 | -20 43 54.53 | 28.1
486958 | 2014 08 02.56381 | 18 42 15.373 | -20 56 43.16 | 27.0 |  | 486958 | 2016 07 03.79465 | 18 55 38.413 | -20 43 54.53 | 29.2
486958 | 2014 08 03.73983 | 18 42 10.581 | -20 56 50.45 | 26.5 |  | 486958 | 2016 07 03.80083 | 18 55 38.381 | -20 43 54.45 | 28.2
486958 | 2014 08 03.74598 | 18 42 10.547 | -20 56 50.41 | 27.0 |  | 486958 | 2016 07 25.70106 | 18 53 53.037 | -20 46 32.22 | 27.4
486958 | 2014 08 03.75212 | 18 42 10.517 | -20 56 50.40 | 28.1 |  | 486958 | 2016 07 25.70717 | 18 53 53.003 | -20 46 32.26 | 27.1
486958 | 2014 08 03.75827 | 18 42 10.499 | -20 56 50.37 | 27.6 |  | 486958 | 2016 07 25.71328 | 18 53 52.967 | -20 46 32.32 | 26.8
486958 | 2014 08 21.31900 | 18 41 08.704 | -20 58 32.35 | 26.2 |  | 486958 | 2016 07 25.71939 | 18 53 52.930 | -20 46 32.37 | 27.3
486958 | 2014 08 21.32514 | 18 41 08.680 | -20 58 32.41 | 25.8 |  | 486958 | 2016 07 25.72550 | 18 53 52.897 | -20 46 32.43 | 27.5
486958 | 2014 08 21.33129 | 18 41 08.655 | -20 58 32.52 | 26.7 |  | 486958 | 2016 10 21.20737 | 18 51 48.303 | -20 53 07.58 | 28.3
486958 | 2014 08 21.33744 | 18 41 08.627 | -20 58 32.59 | 27.2 |  | 486958 | 2016 10 21.21348 | 18 51 48.318 | -20 53 07.64 | 26.4
486958 | 2014 08 21.34358 | 18 41 08.606 | -20 58 32.63 | 26.6 |  | 486958 | 2016 10 21.22570 | 18 51 48.335 | -20 53 07.52 | 26.8
486958 | 2014 08 21.38535 | 18 41 08.512 | -20 58 32.73 | 27.4 |  | 486958 | 2016 10 21.23181 | 18 51 48.345 | -20 53 07.45 | 27.7
486958 | 2014 08 21.39150 | 18 41 08.486 | -20 58 32.79 | 27.0 |  | 486958 | 2016 10 24.25448 | 18 51 56.623 | -20 53 06.39 | 26.3
486958 | 2014 08 21.39764 | 18 41 08.462 | -20 58 32.88 | 26.8 |  | 486958 | 2016 10 24.26059 | 18 51 56.630 | -20 53 06.39 | 26.5
486958 | 2014 08 21.40379 | 18 41 08.436 | -20 58 32.94 | 26.5 |  | 486958 | 2016 10 24.26670 | 18 51 56.644 | -20 53 06.31 | 26.5
486958 | 2014 08 21.40994 | 18 41 08.412 | -20 58 33.00 | 26.7 |  | 486958 | 2016 10 24.27281 | 18 51 56.654 | -20 53 06.21 | 27.1
486958 | 2014 08 23.17695 | 18 41 03.420 | -20 58 42.47 | 27.5 |  | 486958 | 2016 10 24.27892 | 18 51 56.667 | -20 53 06.16 | 26.2
486958 | 2014 08 23.18310 | 18 41 03.397 | -20 58 42.52 | 27.0 |  | 14OS393 | 2014 06 25.40498 | 18 45 34.850 | -20 37 37.23 |
486958 | 2014 08 23.18924 | 18 41 03.373 | -20 58 42.64 | 27.2 |  | 14OS393 | 2014 06 25.42497 | 18 45 34.740 | -20 37 37.33 |
486958 | 2014 08 23.19539 | 18 41 03.350 | -20 58 42.70 | 27.7 |  | 14OS393 | 2014 06 25.44258 | 18 45 34.668 | -20 37 37.35 |
486958 | 2014 08 23.20153 | 18 41 03.324 | -20 58 42.77 | 26.9 |  | 14OS393 | 2014 06 25.53807 | 18 45 34.190 | -20 37 37.94 |
486958 | 2014 08 23.24332 | 18 41 03.236 | -20 58 42.85 | 26.1 |  | 14OS393 | 2014 06 27.36456 | 18 45 25.216 | -20 37 48.44 |
486958 | 2014 08 23.24946 | 18 41 03.213 | -20 58 42.90 | 26.1 |  | 14OS393 | 2014 06 27.37556 | 18 45 25.161 | -20 37 48.47 |
486958 | 2014 08 23.25561 | 18 41 03.189 | -20 58 42.98 | 26.3 |  | 14OS393 | 2014 07 30.75208 | 18 42 46.475 | -20 41 23.18 | 26.6
486958 | 2014 08 23.26175 | 18 41 03.163 | -20 58 43.05 | 26.9 |  | 14OS393 | 2014 07 30.77051 | 18 42 46.374 | -20 41 23.15 | 26.1
486958 | 2014 08 23.26790 | 18 41 03.140 | -20 58 43.13 | 26.1 |  | 14OS393 | 2014 07 30.96961 | 18 42 45.524 | -20 41 24.49 | 26.1
486958 | 2014 10 15.06699 | 18 40 43.948 | -21 01 45.51 | 26.5 |  | 14OS393 | 2014 07 30.97576 | 18 42 45.495 | -20 41 24.45 | 26.0
486958 | 2014 10 15.07313 | 18 40 43.955 | -21 01 45.55 | 26.2 |  | 14OS393 | 2014 08 21.47018 | 18 41 27.395 | -20 43 44.28 | 26.1
486958 | 2014 10 15.07928 | 18 40 43.962 | -21 01 45.58 | 25.8 |  | 14OS393 | 2014 08 21.54268 | 18 41 27.179 | -20 43 44.74 | 25.7
486958 | 2014 10 15.08542 | 18 40 43.966 | -21 01 45.64 | 25.4 |  | 14OS393 | 2014 08 23.30972 | 18 41 22.194 | -20 43 55.43 | 26.3
486958 | 2014 10 15.09157 | 18 40 43.977 | -21 01 45.65 | 25.5 |  | 14OS393 | 2014 08 23.37606 | 18 41 22.010 | -20 43 55.84 | 26.2
486958 | 2014 10 15.13334 | 18 40 44.093 | -21 01 45.60 | 26.7 |  | 14OS393 | 2014 08 23.38835 | 18 41 21.963 | -20 43 55.99 | 26.2
486958 | 2014 10 15.13949 | 18 40 44.100 | -21 01 45.61 | 26.9 |  | 14OS393 | 2014 08 23.39450 | 18 41 21.938 | -20 43 56.08 | 26.3
486958 | 2014 10 15.14563 | 18 40 44.107 | -21 01 45.65 | 27.1 |  | 14OS393 | 2014 08 23.40064 | 18 41 21.916 | -20 43 56.16 | 25.9
486958 | 2014 10 15.15178 | 18 40 44.113 | -21 01 45.71 | 27.4 |  | 14OS393 | 2014 10 16.06833 | 18 41 05.096 | -20 47 37.17 | 26.4
486958 | 2014 10 15.15792 | 18 40 44.121 | -21 01 45.73 | 26.8 |  | 14OS393 | 2014 10 24.10764 | 18 41 26.554 | -20 47 46.18 | 26.0
486958 | 2014 10 16.19482 | 18 40 46.483 | -21 01 46.56 | 26.9 |  | 14PN70 | 2014 08 06.45430 | 18 41 40.006 | -20 37 42.58 | 26.6
486958 | 2014 10 16.20097 | 18 40 46.508 | -21 01 46.94 | 29.0 |  | 14PN70 | 2014 08 06.46659 | 18 41 39.945 | -20 37 42.56 | 26.3
486958 | 2014 10 16.20711 | 18 40 46.497 | -21 01 46.67 | 27.7 |  | 14PN70 | 2014 08 06.47274 | 18 41 39.915 | -20 37 42.57 | 26.5
486958 | 2014 10 16.21326 | 18 40 46.506 | -21 01 46.71 | 26.9 |  | 14PN70 | 2014 08 06.65952 | 18 41 39.214 | -20 37 43.87 | 26.0
486958 | 2014 10 16.21941 | 18 40 46.513 | -21 01 46.73 | 28.4 |  | 14PN70 | 2014 08 25.25857 | 18 40 39.013 | -20 39 41.71 | 26.6
486958 | 2014 10 22.36438 | 18 41 02.502 | -21 01 49.71 | 26.0 |  | 14PN70 | 2014 09 02.06975 | 18 40 21.481 | -20 40 26.87 | 26.7
486958 | 2014 10 22.37053 | 18 41 02.513 | -21 01 49.82 | 26.9 |  | 14PN70 | 2014 09 02.07590 | 18 40 21.462 | -20 40 26.96 | 27.0
486958 | 2014 10 22.37667 | 18 41 02.524 | -21 01 49.87 | 26.9 |  | 14PN70 | 2014 09 02.08204 | 18 40 21.443 | -20 40 27.05 | 26.7
486958 | 2014 10 22.38282 | 18 41 02.533 | -21 01 49.94 | 27.0 |  | 14PN70 | 2014 09 02.08819 | 18 40 21.424 | -20 40 27.08 | 26.6
486958 | 2014 10 22.38897 | 18 41 02.545 | -21 01 49.95 | 27.2 |  | 14PN70 | 2014 09 02.12996 | 18 40 21.369 | -20 40 27.11 | 26.3
486958 | 2015 05 04.69178 | 18 54 04.856 | -20 45 17.13 | 28.3 |  | 14PN70 | 2014 09 02.13611 | 18 40 21.354 | -20 40 27.24 | 26.7
486958 | 2015 05 04.69791 | 18 54 04.834 | -20 45 17.09 | 27.0 |  | 14PN70 | 2014 09 02.14225 | 18 40 21.335 | -20 40 27.35 | 26.5
486958 | 2015 05 04.70403 | 18 54 04.815 | -20 45 17.03 | 27.1 |  | 14PN70 | 2014 09 02.14840 | 18 40 21.315 | -20 40 27.42 | 26.2
486958 | 2015 05 04.71015 | 18 54 04.796 | -20 45 16.99 | 26.7 |  | 14PN70 | 2014 09 02.15454 | 18 40 21.299 | -20 40 27.47 | 25.5
486958 | 2015 07 04.60444 | 18 50 04.474 | -20 49 11.58 | 27.0 |  | 14PN70 | 2014 10 15.27217 | 18 40 25.447 | -20 43 14.81 | 26.4
486958 | 2015 07 04.61057 | 18 50 04.437 | -20 49 11.60 | 26.8 |  | 14PN70 | 2014 10 22.90739 | 18 40 44.701 | -20 43 25.60 | 26.1
486958 | 2015 07 04.61670 | 18 50 04.399 | -20 49 11.61 | 27.4 |  | 14PN70 | 2014 10 22.91968 | 18 40 44.723 | -20 43 25.68 | 24.5
486958 | 2015 07 04.62284 | 18 50 04.360 | -20 49 11.62 | 26.8 |  | 14PN70 | 2015 05 04.75190 | 18 53 27.895 | -20 28 23.23 | 26.7
486958 | 2015 07 04.62897 | 18 50 04.324 | -20 49 11.64 | 26.8 |  | 14PN70 | 2015 05 04.75802 | 18 53 27.878 | -20 28 23.21 | 26.4
486958 | 2016 03 15.00829 | 18 59 12.343 | -20 42 13.66 | 27.0 |  | 14PN70 | 2015 05 04.76414 | 18 53 27.858 | -20 28 23.16 | 26.3
486958 | 2016 03 15.01440 | 18 59 12.355 | -20 42 13.66 | 27.1 |  | 14PN70 | 2015 05 04.77027 | 18 53 27.836 | -20 28 23.11 | 26.7
486958 | 2016 03 15.02051 | 18 59 12.363 | -20 42 13.62 | 27.3 |  | 14PN70 | 2015 05 04.77639 | 18 53 27.821 | -20 28 23.06 | 26.3
486958 | 2016 03 15.02662 | 18 59 12.373 | -20 42 13.52 | 26.7 |  | 14MT69 | 2014 06 24.44453 | 18 44 46.035 | -20 52 50.73 | 26.9
486958 | 2016 03 15.03273 | 18 59 12.386 | -20 42 13.41 | 27.1 |  | 14MT69 | 2014 06 24.45068 | 18 44 45.998 | -20 52 50.81 | 27.8
486958 | 2016 05 15.09107 | 18 59 07.565 | -20 39 50.46 | 26.6 |  | 14MT69 | 2014 06 24.46297 | 18 44 45.919 | -20 52 50.92 | 29.0
486958 | 2016 05 15.09718 | 18 59 07.541 | -20 39 50.50 | 26.5 |  | 14MT69 | 2014 06 24.59571 | 18 44 45.266 | -20 52 51.65 | 26.8
486958 | 2016 05 15.10329 | 18 59 07.518 | -20 39 50.47 | 26.6 |  | 14MT69 | 2014 08 02.61786 | 18 41 40.228 | -20 56 50.25 | 27.5
486958 | 2016 05 15.10940 | 18 59 07.491 | -20 39 50.45 | 27.0 |  | 14MT69 | 2014 08 02.63016 | 18 41 40.162 | -20 56 50.20 | 27.1
486958 | 2016 05 15.11551 | 18 59 07.468 | -20 39 50.38 | 26.8 |  | 14MT69 | 2014 08 03.80002 | 18 41 35.393 | -20 56 57.75 | 27.1
486958 | 2016 07 03.57750 | 18 55 39.511 | -20 43 53.11 | 27.5 |  | 14MT69 | 2014 08 03.80616 | 18 41 35.362 | -20 56 57.74 | 27.5
486958 | 2016 07 03.58339 | 18 55 39.474 | -20 43 53.17 | 26.6 |  | 14MT69 | 2014 08 03.81231 | 18 41 35.328 | -20 56 57.75 | 28.1
486958 | 2016 07 03.59587 | 18 55 39.400 | -20 43 53.14 | 28.8 |  | 14MT69 | 2014 08 03.81845 | 18 41 35.297 | -20 56 57.72 | 27.0
486958 | 2016 07 03.60205 | 18 55 39.361 | -20 43 53.07 | 28.0 |  | 14MT69 | 2014 08 03.82460 | 18 41 35.266 | -20 56 57.72 | 27.0

###  4.8 Targetability Assessment

Table 9: HST List of Potential Targets Name | Mag | Est. Diameter | Target | First | Arc | Encounter |  $\Delta$V | Enc. Helio | Notes
---|---|---|---|---|---|---|---|---|---
|  | Range (km) | Prob | Seen | (days) |  | (m/sec) | Distance |
PT1, 1110113Y (2014MU69) | 26.8 | 28-53 | 1.00 | 6/26/14 | 118 | Dec 2018 | 59 | 43.4 |  100% targetable with multiple models and assumptions, selected for flyby
PT2, E31007AI (2014OS393) | 26.3 | 34-66 | 0.25-0.55 | 7/30/14 | 83 | Feb 2019 | 181 | 43.3 |  Observed as a DKBO
PT3, G12000JZ (2014PN70) | 26.4 | 34-66 | 0.04-0.90 | 8/6/14 | 76 | Apr 2019 | 118 | 44.1 |  Observed as a DKBO
PT4, 0720090F (2014MT69) |  | 27.4 |  | 0.05 | 6/24/14 | 40 | n/a |  |  Unlikely to be targetable based on first follow-up - no further follow-up requested
PT5, 4510067S |  | 26.9 |  | 0.00 | 7/8/14 | $<1$ | n/a |  |  Inaccessible based on discovery images- no follow-up requested

Our HST discoveries are listed in Table 9. The measurements in Table 8 were
used as time progressed to produce orbit fits and to evaluate the likely
$\Delta$V needed to re-target New Horizons for a close encounter. On this
basis alone, the candidate object 4510067S (PT5) was immediately discarded as
out of reach due to its relatively high-inclination and no further followup
observations were attempted. For the remaining candidates, we obtained
additional observations to improve the orbit estimates (GO-13663, GO-13311).
Objects 0720090F (PT4, 2014 MT69) and E31007AI (PT2, 2014 OS393) were
eventually revealed to also be beyond reach, the later became a distant
encounter object. The objects G12000JZ (PT3, 2014 PN70) and 1110113Y (PT1,
2014 MU69) survived as potential candidates into 2015. Of the two objects
2014PN70 was slightly brighter, implying a larger object, but the required
$\Delta$V was at the very limit if the remaining resources and would leave
very limited margins. In the end, our choice was (486958) Arrokoth (formerly
2014 MU69) which required the smallest trajectory maneuver and left ample fuel
reserves for other contingencies. Table 10 summarizes the final orbital
elements for the three objects that were carried forward from this search
based on all data collected through the end of 2016 with estimates of their
uncertainties.

Table 10: Orbital Elements for HST Discoveries  Object | a (au) | e | i (deg) | Hr Mag.
---|---|---|---|---
486958 | 44.085$\pm$0.0001 | 0.0355$\pm$0.0001 | 2.4513$\pm$0.0001 | 11.01
2014OS393 | 44.013$\pm$0.1956 | 0.060$\pm$0.051 | 3.818$\pm$0.007 | 10.07
2014PN70 | 44.071$\pm$0.006 | 0.058$\pm$0.003 | 4.119$\pm$0.004 | 10.12
2014MT69 | 47$\pm$10 | 0.15$\pm$1.04 | 3.10$\pm$0.33 | 11.46

##  5 Discussion/Lessons Learned

In summary, our combined ground-based efforts from Subaru and Magellan
resulted in the discovery of 80 new KBOs. An additional 5 KBOs came out of our
HST search including the fly-by target (486958) Arrokoth. Eleven of these
objects (excluding Arrokoth) became New Horizons long-range observation
targets which received measurements at phase angles far greater than can ever
be observed from earth-orbit locations. These observations are allowing us to
map surface scattering properties of small KBOs for the first time (Verbiscer
et al. (2019),Verbiscer et al. (2022)). The tools we developed using the
excellent Gaia astrometric catalog have also allowed us to make occultation
predictions for many of these objects at high precision (Porter et al.
(2022)). The successful Arrokoth occultations were an excellent validation of
this approach (Buie et al., 2020).

We also gained significant insight into searching for KBOs in general, but in
the galactic plane specifically. When we started we expected that a target
search would be a relatively straight forward process resulting in multiple
potential mission objects to select from or prioritize among. Many on the
search team had previously been part of dedicated KBO search projects from the
time of the Kuiper Belt’s observational discovery and we thought we had a
pretty good handle on what the Kuiper Belt population density and
distribution.

Our initial 2004-2005 survey didn’t find a target, but it served a critical
role in learning just how challenging it was to work in extremely crowded
galactic plane fields. It also provided sample datasets for developing tools
and techniques to deal with identifying faint objects in high density star
fields and was thus very successful in moving us forward in the search. These
lessons learned were carried forward into the second 2011-2014 survey epoch
and helped us to optimize both data collection and level of effort or image
analysis. In particular we learned that image quality, both observing
conditions and seeing stability, was critical. Observations at high ($>$1.6
airmass) or under non-photometric conditions were insufficient to meet the
search goals. We also quickly learned the importance of having an astrometic
star catalog that went deeper than the standard databases of the time (USNO
B1.0). Our solution was to use MegaCam on the CFHT from 2012-2018 to build a
deeper (fainter magnitude) high precision astrometric star sub-catalog
specific to our search fields. Stephen Gwyn built these catalogues from a
variety of references, building off various Gaia (DR2) and 2.MASS references
sets for the global frame and then internally building up to measure high
precision relative positions. When the official Gaia DR2 version became
available we re-calibrated the final catalogue. This took a tremendous amount
of effort, but using this secondary reference sub-net made a huge difference
in the earlier efforts and was essential for the second and third epoch
searches.

Our search effort was also fairly early in the timeline of large data volumes
among astronomical projects. Due to the volume of information, we quickly
learned the critical importance of having effective pipelines that could
process the data inclusive of data quality metrics on image characteristics,
performance etc. so that one could quickly identify if quality data were being
collected and also how prioritize data analysis. These lessons have directly
informed searches for additional objects following New Horizons’ fly-by of
Arrokoth. The new search epoch, 2019 and following (Fraser et al. 2024,
submitted), as a result, are far better designed and characterized. Likewise,
it became clear by the end of 2013 that the likelihood of the data we were
collecting at the time for identifying a fly-by object was minimal at best and
a new strategy needed to be employed, hence a search with HST.

Design of the HST search was itself a critical point in the discovery process
as it required a full review of the state of knowledge of the Kuiper Belt at
the time, in 2014. A 10-year improvement was made in our understanding of the
absolute density and extent of the region in addition to search technique and
analysis gains. We also accurately estimated what we would be able to find
using HST. Finding 2 objects that we could consider targeting out of the
sample of 5 detected was in fact an expected outcome rather than an under or
overestimate. It is safe to say that by the time the survey was completed we
knew the types of targets we were looking for, and had a good handle on the
systematics, characteristcs and processes required for success.

Looking to the future, searching for additional KBOs, this work has led us to
push our techniques even further into building deeper images stacks, applying
machine learning, and considering additional (non-classical) KBO populations.
These details are left to a future publication. However, it can’t be
overstated that the work presented here was a critical step along the pathway
for identifying a fly-by object for New Horizons and in designing,
characterizing and executing these sorts of search surveys.

This work is dedicated to the memory of Peter Collins (1949-2017),
instrumental to much of the software for the 2004 search that began this
entire project. Based on observations made with the NASA/ESA Hubble Space
Telescope, obtained at the Space Telescope Science Institute, which is
operated by the Association of Universities for Research in Astronomy, Inc.,
under NASA contract NAS5-26555. These observations are associated with
programs 13633, 14053, 14092, 14485, and 14629. We are greatly indebted to
Mike Ryschkewitsch (John’s Hopkins Applied Physics Lab), Jim Green (Director
of NASA’s Solar System Exploration Division) and Ken Sembach (Space Telescope
Science Institute) for their efforts in helping us to acquire the time for
these observations. This paper includes data gathered with the 6.5 meter
Magellan Telescopes located at Las Campanas Observatory, Chile. It is also
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 at National Astronomical Observatory of Japan. Access to the Subaru
telescope was supported through NOAO Keck-Subaru exchange time, NASA HQ
support and direct support from Taiwan through the Academia Sinica Institute
of Astronomy and Astrophysics. The Subaru Telescope is operated by the
National Astronomical Observatory of Japan. Likewise, the authors wish to
recognize and acknowledge the very significant cultural role and reverence
that the summit of Maunakea has always had within the indigenous Hawaiian
community. We are most fortunate to have the opportunity to conduct
observations from this mountain. This research used the Canadian Astronomy
Data Centre facilities operated by the National Research Council of Canada
with the support of the Canadian Space Agency. This work also made use of the
Gemini Observatory Archive, NASA’s Astrophysics Data System Bibliographic
Services, and the JPL HORIZONS web interface
(https://ssd.jpl.nasa.gov/horizons.cgi). Some of the follow-up astrometry to
refine orbits of newly discovered objects to access object targetability by
New Horizons were obtained at the international Gemini Observatory, a program
of NSF’s NOIRLab, which is managed by the Association of Universities for
Research in Astronomy (AURA) under a cooperative agreement with the National
Science Foundation on behalf of the Gemini Observatory partnership: the
National Science Foundation (United States), National Research Council
(Canada), Agencia Nacional de Investigación y Desarrollo (Chile), Ministerio
de Ciencia, Tecnología e Innovación (Argentina), Ministério da Ciência,
Tecnologia, Inovações e Comunicações (Brazil), and Korea Astronomy and Space
Science Institute (Republic of Korea). The Zooniverse.org platform,
development of which is funded by generous support, including a Global Impact
Award from Google, and by a grant from the Alfred P. Sloan Foundation, hosted
and promoted the “Ice Hunters” project with all of the data handling and
analysis being prepared by the authors of this paper. This work was also
supported by a Harvey Mudd College Clinic Program team in 2009, consisting of
faculty member Patrick Little, and team members Austin Lee, Claire Robinson,
Florian Scheulen, Steven Berry, Chris Sauro, and Cullen McMahon. We also thank
James Miles of Boulder, Colorado for his volunteer work in support of software
development, observing support, and data processing.

##  Appendix A Astrometric description of an image

The astrometric tools for this project pre-dated any development of a FITS
standard for the astrometric coordinate description of an image that required
a non-linear transformation. The current standard system is described in
Greisen & Calabretta (2002) and Calabretta & Greisen (2002). As a result, Buie
developed a system for this purpose. This appendix describes the system and
how it is encoded into a FITS header. As the FITS standard was developed, the
system described here was adjusted to be complementary to any existing system
by using a set of non-overlapping keywords so that both can co-exist in the
same header. This alternate system was designed to be used with software that
can modify an existing FITS header and place these keywords in the header (an
operation that is now very commonplace).

The task at hand is to describe a transformation from raw coordinates internal
to some image or digital detector to coordinates on the celestial sphere, that
is, right ascension and declination. This process involves the four coordinate
systems indicated below,

$(x,y)\Leftrightarrow(x_{m},y_{m})\Leftrightarrow(\xi,\eta)\Leftrightarrow(\alpha,\delta)$
(A1)

where $(x,y)$ denote the native coordinate system implied by the image array
or detector pixels, $(x_{m},y_{m})$ are the monolith coordinates, $(\xi,\eta)$
are the tangent plane coordinates, and $(\alpha,\beta)$ are the right
ascension and declination on the sky. For this problem one needs to be able to
convert between any coordinate system as indicated. Note that these are
considered to be linked in the order shown. Thus, to compute tangent plane
coordinates from raw pixel positions you first convert to monolith coordinates
and then to the tangent plane. In the case of a single detector focal plane,
the monolith and native coordinate systems are one and the same. A monolith
coordinate system is a virtual pixel scale that mimics the native coordinate
system of a chip but this single system extends to include the area of all of
the detectors. Typically, detector coordinates are never negative and the
implementation of this system uses (0,0) for the coordinates of the first
pixel in the image and the coefficients and IDL software reflect this design
choice.

###  A.1 Tangent plane and celestial sphere

The transformation between the tangent plane $(\xi,\eta)$ and celestial sphere
$(\alpha,\delta)$ can be found on p. 283 from Smart & Green (1977) and is
reproduced below:

$\displaystyle\eta$ $\displaystyle=$
$\displaystyle{{\tan\delta-\tan\delta_{0}\cos(\alpha-\alpha_{0})}\over{\cos(\alpha-\alpha_{0})}+\tan\delta\tan\delta_{0}}\hskip
10.0pt{\rm and}$ (A2) $\displaystyle\xi$ $\displaystyle=$
$\displaystyle{{\sin(\alpha-\alpha_{0})}\over{\cos\delta(\cos(\alpha-\alpha_{0})+\tan\delta\tan\delta_{0})}},$
(A3)

where $\alpha_{0}$ and $\delta_{0}$ are the coordinates of the tangent point.
These expressions have been re-written from those found in Smart to minimize
the impact of mathematical singularities in the equations and to speed their
execution on a computer. Despite the re-write, take note that equation A3
still contains a singularity at the celestial poles ($\pm\pi/2$). The inverse
transformation is written,

$\displaystyle\tan(\alpha-\alpha_{0})$ $\displaystyle=$
$\displaystyle{{\xi}\over{\cos\delta_{0}-\eta\sin\delta_{0}}},~{}{\rm and}$
(A4) $\displaystyle\tan\delta$ $\displaystyle=$
$\displaystyle{{\cos(\alpha-\alpha_{0})(\eta+\tan\delta_{0})}\over{1-\eta\tan\delta_{0}}}~{}.$
(A5)

Note that care must be taken when evaluating equation A4 so that all 4
quadrants of the arctangent are preserved. Equations A2 and A3 are evaluated
by the IDL procedure astrd2sn.pro. Equations A4 and A5 are evaluated by IDL
procedure astsn2rd.pro. Both transformations are included in astcvt.pro. By
virtue of these transformations, one can treat tangent plane and sky
coordinates as completely interchangeable and the discussion below will often
make little distinction between the two. Tangent plane coordinates are also
referred to as “standard coordinates.” The natural units of calculating the
tangent plane coordinates would be radians. However, it is usually more
convenient to work in units of arcseconds instead.

###  A.2 Image and tangent plane

A plane tangent to a sphere at a given point is also known as the tangent
plane. This plane is very similar to the physical mapping that takes place
when a camera takes a picture of the sky. For small enough angular range
images the mapping is linear. Departures from non-linearity are usually a
consequence of optical distortions in the camera optics but also inevitable
with a large field-of-view. The mapping from detector (image) pixels to the
tangent plane is thus an approximate process that needs to be adjusted to
match the characteristics of the image so that a sufficiently accurate mapping
is achieved.

Digital image data collected with a single device is a common type of data and
represent a simple initial case for consideration. The mapping between these
two coordinate systems can be accomplished by any set of basis functions
capable of reaching the desired accuracy. A common and sufficient basis set is
an $n$-degree polynomial in x and y. In its simplest, linear form the
transformation would look like this:

$\displaystyle\xi$ $\displaystyle=$ $\displaystyle a_{0}+a_{1}x+a_{2}y$ (A6)
$\displaystyle\eta$ $\displaystyle=$ $\displaystyle b_{0}+b_{1}x+b_{2}y$ (A7)

where the $a_{n}$ and $b_{n}$ coefficients determine the transformation.
Typically, the coefficients are determined from some least-squares fit between
the image and a stellar catalog. For the sake of this discussion the method of
determination is not important. Other terms are possible such as $xy$,
$x^{2}$, $y^{2}$, $r=\sqrt{x^{2}+y^{2}}$, $x^{2}y$, $xy^{2}$, $x^{3}$,
$y^{3}$, and so on. Some approaches often used the $r$ term instead of the
more appropriate xy term but this is a bad choice. The use of $xy$ is
preferred over $r$ if at all possible. Other basis sets are possible, such as
Chebyshev and Legendre polynomials. Thus, to specify this transformation it is
necessary to indicate which basis set is to be used and then which terms are
provided along with the coefficients. The IDL routine astcvt.pro supports all
three of these basis sets. Note that this methodology does not require or
enforce orthogonality between the $\xi$ and $\eta$ coordinates.

If the transformation is non-linear it becomes important to specify the
location of the optical axis. This point is special in that it will represent
a point of symmetry in the mapping. If the device is well fit by a linear
transformation it is common to use the center of the device as the optical
center. In this case the center $(x_{c},y_{c})$ is defined to be
$(n_{x}/2,n_{y}/2)$ where $n_{x}$ and $n_{y}$ are the $x$ and $y$ size of the
image, in pixels. In non-linear cases it works best to use the optical axis
position, wherever that might be. While it is important to know the optical
axis position, the determination of this via a least-squares fit often leads
to a poorly constrained answer. Knowledge of this position will usually give a
better answer than relying on a fit but a precise determination is not needed.

It is often necessary to rescale x and y prior to solving for coefficients.
For a linear polynomial fit this rescaling is optional. For non-linear
polynomials, the rescaling also helps make the solutions more robust even for
a simple polynomial basis set. For Chebyshev and Legendre polynomials, the
rescaling is required since the input range of values must be between -1 and
1. Normally this is done by dividing by a renormalization factor, $d$, such
that $x^{\prime}=x/d$ and $y^{\prime}=y/d$. Renormalization is usually done by
using the size of the image array or detector. One form of normalization is
$d=\sqrt{n_{x}^{2}+n_{y}^{2}}$. However, this can lead to an incomplete
filling of the allowed range of $x^{\prime}$ and $y^{\prime}$ between $\pm 1$.
A better choice is $d=\rm{max}(n_{x}/2,n_{y}/2)$ if the center is used for the
optical axis position. Otherwise, use the maximum of the absolute value of the
corners of the array after subtracting the optical axis position. In the IDL
software, the renormalization is carried only in the monolith coordinates.

###  A.3 Image mosaic conversions

A closely related problem to a single image is dealing with a mosaic of images
from an array of detectors within a single camera. They are also related
though a presumed constant physical bond between detectors. Processing and
fitting individual images from a mosaic can, in principle, be handled as if
they were each independent images subject to the treatment in the previous