Size and Shape Constraints of (486958) Arrokoth from Stellar Occultations

3.1.1. SwRI–NH Systems, T01–T22

3.1.2. UVA Systems, T23–T25

All of the systems once again used the QHY cameras with embedded GPS receivers. SharpCap was again used for data collection after upgrading to version 3.1.5219.0. With this version, the error in recording the position was fixed. Most operations were the same as before but the gain control values were a factor of 10 higher in the new software. Thus, our previous "standard" gain value of 30 was now 300. Additionally, the GPS receiver status was now visible all the time on the main control screen to help monitor its state more closely.

3.2.1. SwRI–NH Systems, T01–T22

3.2.2. UVA Systems, T23–24

The prediction for this event was finalized very close to deployment. We should have had new astrometry from HST in 2017 March, but those observations were lost to an HST schedule interruption due to an unrelated technical anomaly. The earliest we were able to reschedule HST was 2017 May 1. Until we obtained the 2017 May 1 data, the most recent observation data were from 2016 October 24. The new data provided a substantial increase in the total arc length of the Arrokoth astrometry, from 2.3 yr to 2.9 yr with a corresponding decrease in the extrapolation to the time of the event from seven months down to just one month. Also on May 1, we obtained the HST observations of the three 2017 target stars. We used these target star observations for astrometry and to search for stellar duplicity. We did not find any stellar companions or duplicity in the HST images down to the resolution limit of the data (∼40 mas).

We were able to significantly improve the orbit estimate with this new astrometry; however, we still needed to resolve fundamental questions about the position of the occultation star and the associated uncertainty. We began working on the HST data to improve our constraints on the star positions. However, on 2017 May 6, we were provided access to preliminary data from the planned Gaia DR2 (Gaia Collaboration et al. 2016). Those data included the occultation stars among the stars in the region around Arrokoth back to 2014. We reprocessed all of the HST data with updated reference stars to improve the orbit estimate. Within a week, we had refined the event prediction enough so that we could determine where to deploy the observing teams and begin the process of shipping equipment and setting up travel logistics. We obtained one more epoch of data from HST on 2017 May 25, just a day before the first teams left. We completed the final prediction a couple of days before the June 3 event with a cross-track uncertainty of 44 km. The in-track (timing) error was 67 km (3.3 s). Unless otherwise stated, all uncertainties stated in this work are 1σ values.

We had 24 mobile stations available for deployment. The equipment was all sent via air freight to Argentina and South Africa due to the extremely tight schedule. Local movement of the systems was handled by individual vehicles carrying one team and system.

Even with this large number of stations, we could not cover all possible cases for the object, e.g., small versus big given the prediction uncertainty. To guide the deployment process, we used a Monte Carlo simulation. The simulation uses the cross-track positions for the observing locations relative to the prediction. The model employs a circular representation of the occulting body with an adjustable diameter. For a given size and set of observing locations, we draw a random location for the center line from a normal distribution consistent with the prediction and its uncertainty. For a given draw, we compute the chord length for each site (or note a miss) and record the number of chords seen. To be counted, we required a chord to be no shorter than half the diameter. This adjustment recognized that we might not see very short grazing chords given the anticipated noise in the data. The tool also provides additional provision for a small random component to the site location. We could always indicate a desired location to a team, but local constraints could force them to set up some distance away from the desired location. By using this extra random component, we were able to give guidance on how close each team needed to be to their assigned location. For this event, the teams needed to observe from within a 1 km region centered on the assigned location. After running 10,000 trials, we then generate a histogram as a function of the number of chords from which to evaluate a given scenario.

A baseline goal for this event was to observe or rule out the largest size based on a 4% albedo. The deployment strategy was guided by the desire to obtain a strong constraint using just one set of stations (either T01–T12 or T13–T25, but not both). A spacing of 15.5 km between sites was chosen so that we would have no more than a 3% chance of a null result (zero chords). This spacing covered a range of ±1.9σ or ±83 km and had a 93% chance of getting two or more chords. Given the 44 km cross-track uncertainty for this event, it would have taken a much larger number of mobile stations to address a smaller object scenario, and we had to accept a poorer constraint for that case. With a half-space shift between Argentina and South Africa, the net spacing if all sites participated in the optimum plan would have been 7.8 km. The same pattern would have had a 5% chance of a null result but an 84% chance of a single-chord outcome on a 20 km object. This tool was very effective in guiding the Mendoza, Argentina, area deployment where the teams had a great deal of flexibility without the need for detailed site selection scouting days before the event. We made adjustments up to the last hours before teams left for their sites. The teams in South Africa required more advance warning, due to more complex logistics for site access. We were able to use this same tool to assess the outcome for the actual site locations after the event.

Twelve stations in each continent successfully deployed and all collected useful data. Table 2 provides a summary of the mobile stations. All Earth-based positions for this deployment are provided on the WGS84 datum. Every station in Argentina had clear conditions but some had to deal with preventing the formation of dew on the telescope optics. The teams near Clanwilliam, South Africa, had variable amounts of clouds, but the teams that headed east had clear skies. Because the Moon had set in South Africa, the teams in South Africa experienced systematically lower background levels. They also had better seeing than the teams in Argentina. The Argentina teams observed with a 66% illuminated Moon and higher contributions from light pollution, which resulted in generally higher background noise levels. The background information for T23 is not provided, due to it being a very different system and the intercomparison with other stations is not particularly useful. All stations used a 0.5 s exposure time. The shadow speed of 20 km s⁻¹ meant a central chord on a D = 40 km body would be four frames. We ran all observations for 45 minutes centered on the local predicted event midtime. We designed this range of time to cover the stable region of the estimated Hill sphere for Arrokoth. We did not see any lightcurve signatures related to Arrokoth in any of the data sets—fixed or mobile. Figures 2 and 3 show the data from the mobile stations. These figures only show data within 30 s of the predicted event midtime. The lightcurves are sorted north to south across the predicted track. There is a lot of variability in data quality as can be seen in the plots. Most of the apparent dropouts in these data are due to high winds and severe image smearing. In these cases, we visually examined the data to confirm that the target star was, in fact, still visible and the dropout was not an occultation.

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The mobile station effort was augmented by fixed-station observations. Those stations participating are listed in Table 3. Key data sets from these are summarized in the remainder of this section.

4.4.1. Gemini

4.4.2. South African Astronomical Observatory (SAAO)

We also took observations on the 74 inch telescope at the SAAO using one of the Sutherland High-speed Optical Cameras (Coppejans et al. 2011). This instrument is optimized for stellar occultation observations utilizing a frame-transfer CCD which can trigger each image from a GPS. The conditions on the night of the event were good, with scattered, light clouds and seeing of roughly 14. For these observations, we took 27,000 frames starting at 02:47:00.0 UT with a cadence of 0.1 s and a 6.7 ms deadtime. We set the instrument to −70 °C in 3 MHz conventional mode with the 5.2× amplifier, binned 8 × 8 (for a plate scale of 0608 pixel^–1), and no filter.

We reduced the data using biases taken on the night of the event and flat fields taken the previous night, which was cloudless. We performed photometry on the target star and the one nearby brighter comparison. We carefully selected a background region to avoid other stars in the field. The optimal aperture was 6 binned pixels or 365. Figure 4 shows the resulting differential lightcurve, normalized to one, with an S/N (mean over standard deviation) of 21. These data are the closest to the shadow center line and have significantly higher S/N and time resolution compared to the mobile stations. We saw no evidence for any solid-body event. The data have a cadence of roughly 2 km per sample and grazing events as short as 200 m can be ruled out. In the subsequent analysis, we simply treat this as a nondetection and do not consider potential grazing chord constraints. We will return to the constraints provided by these data when discussing the data from all occultation events together (see Section 7.7).

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Based on the final prediction prior to the June 3 event and the actual site locations, the chance of getting zero chords for D = 40 km was 3%. For a D = 40 km object, a single chord would be based on multiple frames with the star occulted and could be recognized with high confidence. For D = 20 km, the chance of a null result was only 14%. In this case, either zero or one chord would likely be a null result because the chord would be so short. It was very unlikely that we would have seen even smaller objects because the chance of getting a single chord at all was so small. Even if we got a chord, there was a large chance it would be too short to be recognizable. We also did not observe a solid-body event from any fixed site; however, most fixed sites were too far away from the mobile chords to provide much constraint.

Under the assumption that all of our error sources (random and systematic) are known and well characterized, these results indicated that the large and dark case for Arrokoth was unlikely. We chose to then optimize for the small object case for subsequent occultations.

The nondetection of any occultation in the Gemini data provided upper limits on the presence of dust particles within the Gemini beam. The interexposure deadtime was the limiting factor in the size of detectable particles in the Arrokoth environment. The minimum detectable size was a particle perfectly centered on the occulted star, which would have cast a shadow on the detector that would be mostly contained in the deadtime, but with just enough on-exposure shadow to cause a detectable dip in flux. We consider a 5σ dip such that we would not have expected any one of the ∼16,000 exposures to vary by this amount by chance. Thus, in this limiting case, a shadow of duration $t=\tfrac{5}{{\rm{S}}/{\rm{N}}}\,{t}_{e}+{t}_{d}$, where t_e = 0.1 s was the exposure time and t_d = 0.107 s was the deadtime, could have produced a detectable dip in flux. With a ground-track shadow velocity of 20 km s⁻¹, the minimum detectable particle size (or narrow and opaque ring) was 2.3 km.

SOFIA approved this flight opportunity because the likelihood of a positive outcome was deemed sufficient. Of the three 2017 events, it was the only one with a track accessible using a single flight from the summer deployment base of Christchurch, NZ. The primary goal of the flight was to probe the system for material potentially hazardous to New Horizons. A secondary goal was to observe a solid-body event; however, it was very challenging to target the aircraft on the occultation track. The support requirements for the SOFIA flight set the timing of the prediction work for this event.

A large observing campaign with HST on Arrokoth, timed to be completed just prior to the SOFIA flight, significantly improved the prediction. HST GO-14627 (PI: Benecchi) provided 24 orbits that returned 119 images and resulted in 118 new astrometric measurements during the interval from 2017 June 25 to 2017 July 4 (Benecchi et al. 2019). The goals of the lightcurve investigation dictated the time span and spacing of the observations, while we set the end time of those observations to allow all of these data to be included in the SOFIA prediction, with the smallest temporal gap between the end of data and the time of the occultation opportunity. The new data set doubled the number of astrometric measurements between this and the previous occultation. We once again reduced all images against the prerelease version of the Gaia DR2 catalog (Gaia Collaboration et al. 2018). The vastly improved prediction uncertainty for the cross-track position was 14 km. The in-track error (timing) was 21 km (0.86 s).

Assuming no error in delivering SOFIA to the target point, the odds of getting one chord on a D = 40 km object were 76% based on the final prediction. As the object size decreases, the odds of getting a chord decrease. Even at D = 20 km, the chance of getting a chord was 44%. The targeting window for the flight was to place the aircraft within 1 km and 1 s of the aim point along the track (due north of New Zealand). We chose a target point on the shadow center line of 2017 July 10 07:49:11 UTC at latitude −16403333 and east longitude of 184960000 for a nominal flight altitude of 30,000 ft.

5.3.1. SOFIA

SOFIA contains a Focal Plane Imager (FPI+) based the Andor iXon DU-888 commercial CCD camera (Pfūller et al. 2018). The FPI+ usually serves as the guide camera for SOFIA, receiving visible wavelengths via the telescope's dichroic tertiary mirror. Many of the FPI+ characteristics that are advantageous for a guide camera (fast readout rates, zero deadtime between frames, high quantum efficiency, and low read noise) are also critical for an occultation camera, where the desired cadence often produces scenarios with low source counts (Pfūller et al. 2016). In this case, given the relative velocity between Arrokoth and the occultation star of 24 km s⁻¹, we planned for a sampling rate of 20 Hz. That rate was intended to detect rings with equivalent widths of ∼1 km.

Our S/N estimator predicted that each 0.05 s exposure would have an S/N of 13, assuming an open filter, an occultation star G mag of 15.57 and 4 × 4 pixel binning (for an effective plate scale of 204 per spatial element). Our S/N estimate was comparable to the published FPI+ sensitivities (SOFIA Observers Handbook, Figure 5.1), where an S/N of ∼50 is expected in a 1 s exposure of a 15.6 V-mag star. Unfortunately, the full Moon was fewer than 10° away from Arrokoth during the event, and the highly variable background counts became the dominant noise source. In practice, we found that the S/N per time step was between 3.5 and 5. Nevertheless, the SOFIA/FPI+ lightcurve produced the first occultation detection of Arrokoth—a very short grazing chord, though this was not clear until much later.

Based on the final aircraft telemetry, we were 550 m from the target point in latitude and longitude at the target time. The minimum distance from the target point was 1.8 s later at a distance of 330 m. This degree of success in getting to our aim point took considerable skill and effort on the part of the flight crew and demonstrates what SOFIA can achieve despite the lack of tools for this specific purpose. The most difficult requirement levied on the flight was getting to the aim point at the right time. We attempted to get within 1 s and got very close. In the end, the limiting aspect of our deployment was our ability to predict the right place.

We saw no obvious signs of an occultation during the flight on the real-time monitors. The data required very careful photometric extraction because individual images had rather low apparent S/N on the target star. Figure 6 shows one of the five independent lightcurve reductions. In these data, there is one singularly deep dip in the lightcurve at about 45 km prior to minimum separation. This particular analysis is the result of 2× image binning prior to photometry. We did not apply any spatial shifts to the images and combined the images prior to processing. Because of how the images are indexed, there were two possible binned outcomes. Here we show the outcome that returns the strongest dip. The other option shows a weaker two-point dip. Looking at the original frames prior to combining, the star is missing on the frame at the center of the dip while its flux is reduced somewhat on the frame before and the frame after the center. At our sampling rate, this dip corresponds to a solid-body chord length of ∼1 km. We did not immediately identify this dip, but independent processing of the data confirmed the short dropout. Because on-chip reference stars do not show this dip, we believe this to be a real signature associated with Arrokoth. However, we did not complete this analysis until after the third deployment. As far as we knew at the time of the July 17 event, we had come away empty-handed from the first two attempts.

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With respect to timekeeping during the flight, we emphasized with both the observing team and flight crew the importance of unambiguous timing information for all images during the occultation sequence. We carried out numerous tests during the outbound flight leg prior to the occultation. We identified and compared four different time sources during the flight: (1) navigation clock used on the flight deck, (2) clock at the science flight control station, (3) GPS-slaved time source used by FPI+ recorded with the science images, and (4) GPS time from an application running on a cell phone with GPS receiver. There was no way to electronically measure the differences between these time sources, and we had to rely on verbal callouts of the clocks to investigate offsets. Past experience with this type of test shows that one can, with care and practice, detect shifts down to about 0.1 s. Clock #4 proved to be unreliable with variable shifts compared to the other three, and we discounted this time source. None of the other three clocks were identical. Clock #1 was 1 s ahead of Clock #2, and Clock #2 was 1 s ahead of Clock #3. After careful analysis of the various systems, we concluded that Clock #3 was the one that had been most heavily tested and best understood and were confident that the time tags on the images were correct to within the usual precision limits of a GPS-based system. The targeting of the aim point in time may have been affected by these clock offsets though there was no meaningful degradation of the experiment as a result. A reasonable explanation for the offsets is that Clocks #1 and #2 had (different) out-of-date leap-second almanac information that had never before been recognized because they are not normally tested or relied upon to this level. We had a hard time testing this potential timing concern with the occultation prediction uncertainties at the time. The final postevent reconstructions show that our chosen time reference decision is clearly the most reasonable, giving us additional confidence that the FPI+ timing is correct as expected.

5.3.2. Gemini-south

5.3.3. SOAR

5.3.4. Infrared Telescope Facility (IRTF)

We based the final ground track prediction on the same ephemeris used for the July 10 event. Our uncertainty estimates gave a 1σ cross-track error of 14.2 km (0.46 mas) and a timing error of 0.88 s (0.70 mas). These uncertainties were higher than for July 10, due to a larger uncertainty in the star position from Gaia DR2 (Gaia Collaboration et al. 2018). Even so, this prediction was three times better than that for June 3, permitting us to deploy ground stations with smaller spacing. As a precaution against a miss as on June 3, instead of deploying to an extremely tight spacing between stations, the deployment plan covered just over 4σ in cross-track spacing relative to the prediction, with a mean spacing between sites of 4 km. Unlike the June event, this coverage and spacing was sufficient for all plausible albedos.

We chose Comodoro Rivadavia to be the central base for the deployment based on local resources, commercial air carrier access, proximity to a major road for transporting the equipment, and proximity to the predicted ground track. At the time this choice was made, the ground track was still uncertain by 200–300 km. The equipment that was used in South Africa was sent via air freight directly to Buenos Aires where it was recombined with the equipment used in Mendoza in June. Everything was then trucked down to Comodoro Rivadavia and distributed to the teams and their vehicles.

We built our deployment pattern around a four-day schedule of events similar to the June 3 deployment. The first night all the teams gathered at the same location in town to test the equipment. The first night provided all teams with an opportunity to practice with the system with other teams nearby. This was particularly useful to troubleshoot difficulties, especially for those new to the telescopes. We split the large group into four subgroups for the second night and sent them to different nearby locations to practice a deployment with less help available. We treated the third night as a dress rehearsal, choosing site locations as if they were actual locations. This strategy provided us with an opportunity to test both the site choices and the teams as if it were the actual event night. The fourth night was the event night. Incredibly, all four nights were workable, which allowed us every opportunity for practice and event-night observations.

This deployment was not without challenges. We had very few roads to work with and our mobility was highly constrained. This forced most teams to work rather close to National Route 3 (RN3), the major north–south highway along the coast. Stray light from passing vehicle headlights caused significant time-variable glare on the images during data collection. Also, this region of Argentina is well known for its generally windy conditions. Indeed, one of the nicknames for Comodoro Rivadavia is the "Capital of the Wind." The conditions started out very calm on the first night but the wind gradually grew in strength with each passing night. The consensus among the teams after the third night was that stray light and telescope shaking from the wind would create serious problems for the event night. The National University of Patagonia, Comodoro Rivadavia campus (Prof. Marquez), and the mayor's office offered an amazing amount of help with our difficulties. We received help from Prof. Marquez in designing and building windbreaks to shield the telescopes from the winds. The mayor also offered to provide large trucks as windbreaks. We tested all of these on the dress rehearsal night and found these made significant improvements in the data quality. The mayor and the University suggested shutting down RN3 during the time of our observations to address the stray-light problem. Local authorities enforced a two-hour cessation of all traffic movement through the area where we had deployed telescopes. This level of help was absolutely essential to the success of our efforts on event night.

Table 4 provides the final deployment locations. We recorded all of the positions from cell phone-based GPS applications and later confirmed these measurements with Google Earth. We experienced some variation in sky background signal among teams but variation in image motion due to wind dwarfed the variation in sky background signal. Despite the wind mitigation efforts, the wind affected all sites, though it affected some much more strongly than others. Those sites with high levels of wind shake had strongly varying image quality. In the end, this wind shake made the data reductions more difficult but not impossible. Note that the seeing values tabulated are really just an indication of the image quality for normal quality images and the occasional large smearing from wind is not particularly evident from the mean seeing tabulated.

Twenty-two of the twenty-four stations were successful in collecting useful data on the target star around the time of minimum separation. Table 4 provides a summary of the data quality and notes for the mobile stations. The Moon was 46% illuminated and 105° away. All stations used a 0.2 s exposure time. We ran all observations for 45 minutes centered on the local predicted event midtime. As with the other 2017 events, we designed this range of time to cover the stable region of the estimated Hill sphere for Arrokoth. The T14 entry shows no sky value, and the data were also not processed due to the target star drifting off the detector prior to the occultation and due to nonstandard data collection settings. The T23 entry again shows no sky value due to it being a very different setup and comparison of sky values has no meaning. The T24 system suffered fatal damage to its internal wiring and could not be repaired in time for the event.

We processed all the standard systems (T01–T22) data together, similar to the June 3 data. The lightcurves from all stations are shown in Figures 8 and 9. We copied images within ±1 minute of the predicted midtime out of the full data set for processing. There was no measurable need for bias, dark, or flat-field calibration steps, and therefore, we did not apply these types of corrections. However, the raw images contained a low-level horizontal striping pattern. This striping is a feature of the bias pattern inherent in the detector readout and varied from frame to frame. We easily removed the pattern by computing a robust mean for each row and then subtracting that mean. Each image had a large number of stars (∼100) from which we generated a frame-by-frame numerical point-spread function (PSF). We then fit the PSF to all the stars by adjusting the position and flux. However, we excluded the target star from fitting at this step. From the fit positions, we derived an astrometric solution for each image based on the Gaia DR2 star catalog positions (Gaia Collaboration et al. 2016), corrected for proper motion to the epoch of the images. We then used the astrometric solution to compute a pixel location for the target star. At this point, we computed a PSF fit to the target star where the only free parameter was the star flux. We then computed the midtime for each observation from the GPS time and exposure time recorded in the header of each image.

This data processing methodology was quite valuable, particularly for the images with significant image smear due to wind. In these cases, the PSF is arbitrarily complicated—not just a simple linear smear. As long as the PSF fit accurately replicated the smear, it was possible for us to extract a useful target star flux. Taking full advantage of the PSF method required significant manual effort to guide the PSF building and fitting process. We only applied this extra effort as needed to critical images in and around the time of the actual event. Without this extra corrective step, the target star may appear to drop out for a frame or two. We inspected these cases visually and saw a tortuous wind-driven PSF; however, the target star is still visible. For noncritical images, we noted that the star is still visible and a given dropout is not interesting.

6.5.1. SOAR

For this event, we obtained five positive occultation detections roughly in the center of the deployed stations. Table 5 lists the measured timings of these events. Figure 10 shows a plot of the combined geometry between the stations and the occultation timings. These observations clearly showed that Arrokoth was more complicated than a simple ellipsoidal object. Our first interpretation of these data was that Arrokoth was a contact binary shape. In the months following the initial data reduction, we began tracking two additional scenarios to explain the outline from this occultation. One extra option was that the occultation happened during a mutual event between two closely orbiting bodies and just look like a contact binary due to projection effects. This scenario received a lot of attention due to its implication for the New Horizons flyby: the spacecraft pointing was effectively set to look at the center of mass. With a binary, that point would be in between the two objects and the New Horizons spacecraft might see nothing. The last option was simply a very irregular shape. This option had no special implications for the New Horizons encounter and received no special attention. Still, the kink in the shape inferred from the T13 and T16 chords would require a degree of nonsphericity not seen in any other objects in this size class and was thus considered to be unlikely all along.

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The prediction for this event was potentially better than for any of the 2017 occultations. The observational arc was extended by additional HST data; further, the successful occultation itself added a new astrometric constraint that was more than an order of magnitude more constraining than any single HST observation. The formal uncertainty for the occultation prediction was 13 km cross-track and 1.8 s (36 km) down track. This uncertainty was a useful guide, provided our assumption of a single body was true. The size shown by the 2017 data was roughly 30 × 14 km. We had no basis to predict what the projected shape would be in 2018 or what the orientation would be. The prior result could only then suggest the minimum (14 km) or maximum (30 km) cross-track extent. In the case of the binary scenario, the chance of observing during a mutual event a second time was low, and we had to be concerned with the implications of there being two separated bodies to cover. With two bodies, we expected diameters between 14 and 20 km requiring tighter coverage. However, there could also be a significant offset between the two bodies relative to the barycenter by tens of kilometers or more. Thus, even though we had an excellent prediction of the center of mass relative to the target star, that knowledge was insufficient to decide on the deployment strategy. Instead, our decisions were driven by what we did not know about Arrokoth, a new regime for stellar occultation predictions and deployments.

Table 6 summarizes the final deployment locations. The goal for all teams was to observe from a location along an assigned line at a fixed distance from the center line and within 500 m of that line. We spaced these tracks at 4 km intervals centered symmetrically around the predicted center line. This spacing would insure two chords on a 10 km body and the number of stations covered almost 120 km in the cross-track direction to better cover the close binary case. The case of the contact binary would thus be covered by more than 4σ relative to the prediction.

7.2.1. Sénégal

7.2.2. Colombia

On the night of the event in Sénégal, a storm developed and moved northward in the hours just before the observations. The southern sites of the deployment were either rained out or totally clouded out. The weather to the north had local clouds that affected telescope setup and caused strong variability in transparency. We took all data with 0.25 s integration times. Only two sites were unaffected by clouds at the appulse midtime: T08 and T14. The data from T08 show no obvious occultation signal. The data from T14 show a clear dropout of the target star for four consecutive frames.

In Colombia, the dress rehearsal night was successful for setting up and taking practice data. Had the event been this night, these teams would have observed the event. On the actual night of the event, a large storm rolled over the deployment area, preventing any data collection.

We reduced the data for these observations in essentially the same way as the 2017 data (see Section 6.4). Figure 12 shows the data from teams whose data could be processed. T08 and T14 provided the two best data sets, and both were straightforward to process, requiring no special treatment.

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The T18 data were very challenging. All of the data suffered from extinction due to clouds at roughly 30% of the signal level found at the other two sites. Also, one of the frames during the middle of the occultation happened to be at an instant of a guiding correction or tracking glitch, and the PSF looks like a dumbbell shape. For this case, the automatic tools treated each end of the PSF as a separate source and the resulting stacked PSF was a very poor representation of the image. This problem required a manual edit of the source list to remove the second copy of each source, giving a much better representation of the image PSF. This new PSF was fit to the sources and then a new PSF stack was generated from the improved positions. This second-generation PSF was then fit to the stars and the target as usual.

The extinction suffered by the challenging data sets was nontrivial. For instance, the signal from the target star was usually not even visible in the images. Normal photometric extraction tools that depend on measuring a position and a flux could not retrieve the occultation signal. However, we can compute an accurate location for the star with our astrometric knowledge of the image and the image positions of catalog stars. This computed position enables us to retrieve the flux with a constrained fit that treats the location as a given. The T18 data have a distinctive set of consecutive images where the fitted flux was consistent with zero, indicating an event. The temporal coincidence between T14 and T18 gives us high confidence that the measurements from T18 do, in fact, represent measurements of the limb of the object. The constraints provided by the data from T01, T07, T16, and T17 are minimal, but also not likely to be important given the miss recorded by T08.

We obtained two positive occultation detections and one unambiguous miss for this event. Figure 12 shows the useful data from the campaign. Table 7 lists the measured timings of the two chords. From this we see that the cross-track offset is comparable to the size of the object and is consistent with the uncertainty of the prediction (13 km). The miss was useful to rule out a second object at the location probed by T08, 14 km north of the predicted center line. However, this constraint was weaker than the implication of getting the successful occultation observations so close to the predicted position. Additionally, both chord lengths are longer than the minimum dimension seen in 2017. These data had to have hit the larger lobe or body. With the continued improvements in the orbit estimate of Arrokoth, the contact binary scenario was really considered to be a formal, but not likely, possibility. For the binary case, the cross-track offset would imply that the position angle of the system was along the track and yet we did not see a second object. In the end, explaining both the 2017 and 2018 data with a binary system required many special and unlikely circumstances and thus the contact binary option was recognized as the more likely explanation. A more quantitative analysis of the data would have been interesting but there was no time to do so before New Horizons arrived at the target and definitively showed the object to be a contact binary (Stern et al. 2019).

A very powerful result of any successful occultation is in constraining the position of the object relative to the occulted star. This constraint is in physical (i.e., kilometer) scale units and can easily be as good as 1 km or better. Because the scale (km arcsec⁻¹) increases linearly with distance, these positional constraints are especially tight in angular quantities. For instance, at the time of the July 17 event, 1 km was equivalent to 32 μas. Before the release of the Gaia DR2 catalog, this information was of little use as the positions of the stars were not very well known. We can see from the values given in Table 1 that the position of the July 17 star was good to about 5–6 km. Even with Gaia DR2, astrometry that is derived from a measured occultation position at this distance is limited by the catalog.

Given that our occultation-derived astrometry was limited by the catalog, we did not put special effort into extracting an optimized position for Arrokoth. Prior to the New Horizons encounter, we took our reference position from the center of the observed chords that were the closest to the center of the body.

For the July 17 observation, we used the center of the longest chord from station T13 and the coordinate of the occultation star (given in Table 1) from the topocentric location for site T13 (given in Table 4) at the midtime between disappearance and reappearance (Table 5). This derived time is thus 2017 July 17 03:50:06.238 UT. The result for the August 4 event is not quite as good because we only have two chords, but even here the uncertainty in the star position dominates. As before, we used the position of the star to define the location of the object as seen from the T14 site (longest chord) at the midtime of the event, 2018 August 4 01:21:30.650 UT (see Table 7 for disappearance and reappearance times).

With the then assumption and now knowledge of a single body, these occultation-based positions provided an exceptionally strong constraint on the mean motion of Arrokoth, or equivalently, the semimajor axis of its orbit. This result gave us the most important piece of information needed for a successful spacecraft encounter and that is the heliocentric distance. This constraint also helped to better separate out bad astrometry from the HST data set. The consequences of this improvement are discussed in the next section as well as final astrometry that takes advantage of the post-encounter shape model for Arrokoth.

A key component of this effort was to provide an orbit estimate for the navigation of New Horizons in preparation for its encounter with Arrokoth on 2019 January 1 (Stern et al. 2019). The preoccultation predictions and the postobservation reconstructed ground tracks demonstrate the evolution of this preparation. The first four rows of Table 8 provide a summary that shows the final pre-event prediction uncertainties for each occultation campaign. In this case, the improvement is due to each updated orbit estimate. We experienced the largest improvement between the 2017 June and July events because the HST lightcurve campaign added a substantial amount of astrometry just prior to the events. Starting in July 2017, each of our successful occultation observations, with their much higher precision positional measurements, also improved the orbit estimate. The final four rows of Table 8 show the formal uncertainties of the reconstructed postdictions using all of the HST and occultation data as well as the orbit estimate delivered to the New Horizons project.

The orbit ID "may25a" refers to the orbit based on all HST data up through and including data taken on 2017 May 25. This was the final orbit solution prior to the first observing campaign. "May25a" was based on 83 good observations providing a total astrometric arc of almost three years. This was our first orbit reduced against the Gaia DR2 catalog (first prerelease version). The orbit with ID "lc1" was the first to include all of the HST lightcurve campaign data and was used to target SOFIA for its flight. This version was based on 187 HST data points. Subsequent work in the next couple of days led to improved bad-point filtering largely driven by the requirement that the photometry associated with the astrometry must all be consistent rather than filtering based on astrometric residuals alone. This led to the orbit denoted "lc1gr" based on 197 data points which was used to target the third occultation campaign. The marked reduction in the prediction errors was crucial to the success of the July 17 effort. The orbit with ID "ey3jul1" included numerous improvements in data reduction and new observations. This orbit was based on 230 observations from HST up through 2018 July 1 and included the 2017 July 17 occultation measurement. The final Gaia DR2 release (Gaia Collaboration et al. 2018) further improved the orbit along with a new pipeline image product from STScI that eliminated trails in the images that can strongly affect measurements of all sources, especially those on the faint end of the detectable range. We discovered these "flc" image products as an unanticipated bonus during a data processing detour working on astrometric measurements of 1I/'Oumuamua (Micheli et al. 2018). The 'Oumuamua observations exhibited faint S/N levels comparable to those seen with Arrokoth but with very different geometric circumstances. This overlapping effort lead to a few more improvements in astrometric processing of the HST data. The "ey3jul1" orbit has the smallest range uncertainty of those shown in Table 8.

The final orbit ID "ey7" was the last orbit provided to New Horizons for navigation support that did not include any New Horizons data. This orbit was based on 195 HST observations and two occultations, MU20170717 and MU20180804. The overall improvement for postdictions for all events is evident. Timing and cross-track uncertainties are significantly smaller in all cases. Although the range uncertainty is larger than was computed for the MU20180804 prediction, we consider it more reliable due to the two high-precision occultation constraints separated by slightly more than a year.

Data from four occultation campaigns provided very powerful constraints for both the nature of Arrokoth and its orbit—both clearly of concern for the New Horizons encounter. The simplest and most likely explanation for the occultation data throughout most data analysis efforts was a contact binary. However, mission constraints pushed the analysis even further to quantify those scenarios that could not be firmly ruled out. This led to a parallel track of interpretations: Arrokoth could have been either a pair of objects orbiting a mutual center of gravity or a single object with a strange shape. Without a mutual orbit for a putative pair, we needed to pursue heliocentric orbit estimates without constraints from the occultations. Doing so made the HST-only orbit estimates robust against the interpretation of the nature of the object but at a significant increase in the uncertainty of the resultant fit. Had the signal level of the Arrokoth images from HST been a little higher, it is unlikely these issues would have surfaced. However, the low signal level meant the orbit fit was uncomfortably dependent on the bad-point editing and weighting applied during the orbit fitting process. If Arrokoth were double, we expected to see strong signatures of barycentric offsets in the occultation-derived positions. We could not completely rule out a binary with just the MU20170717 event. The MU20180804 event indicated that the binary case was far less likely because that event happened at the right cross-track position for a single-object scenario. The larger than anticipated time shift for the MU20180804 event is entirely consistent with a scenario where the second occultation provides a much better determination of the semimajor axis, especially as the interpretation of the other two events, MU20170603 (miss) and MU20170710 (graze), were also still completely consistent with the conclusions. By leaving out the occultation constraints, the four occultation data sets (detections and nondetection) were much harder to explain. In the end, the inclusion of two occultation points led to the removal of some data that were having a systematic erroneous effect on the orbit solution.

This analysis also helped us understand the reference systems used for astrometry and orbit analysis. We were concerned about unrecognized systematics between "ground-based" data and spacecraft navigation (radio tracking and optical navigation). This concern often leads to significant underweighting of ground-based priors and places higher demands on the spacecraft navigation data, leading to more conservative uncertainty estimates for spacecraft encounters. For New Horizons, we had very little time to observe Arrokoth with spacecraft instruments prior to encounter, and consequently, these priors became unusually important. In particular, the constraint on the heliocentric distance of Arrokoth was dominated by the orbit estimate based on HST and occultation data and could not be independently derived from optical navigation until it was too late to use the information. One element of the cross-comparison centered on whether the ICRF was the same for the astrometric support catalog used for ground-based measurements as the ICRF used for spacecraft navigation. The Gaia mission team's attention to this issue (Lindegren et al. 2018) was very important to how the New Horizons mission used our orbit fitting results. Even so, we used very conservative estimates of the time-of-flight uncertainties for the encounter planning. However, this process indicates that for future missions, the Gaia ICRF is close enough to that used for radio tracking to allow treating them as indistinguishable. While this does not lessen the need for care with the measurements themselves, the concern for this particular systematic error has been eliminated through the use of a common reference system.

The four occultation observations also provide important constraints on the spin state of Arrokoth. While we have not completed the shape-model analysis, we can use the preliminary analysis to demonstrate how the encounter observations can be linked to the occultation results. The New Horizons imaging data alone are sufficient to fit a shape model with a spin state (pole and rotation period). The current best estimate is a J2000 pole direction of (311°, −42°) and a spin period of 15.92 ± 0.02 hr (Stern et al. 2019). We can use this model and any period consistent with the estimate to render Arrokoth on the plane of the sky as seen from Earth at the time of each occultation. The occultation data from July 17 provide an unambiguous orientation of Arrokoth at that time. Within ±0.06 hr of the nominal period, there are seven discrete periods that match the orientation on July 17 equally well, differing by a single full rotation between the occultation and encounter for adjacent period options. The nominal period implies 803.3 rotations over this time; thus, periods that match within ±3 rotations of this case are all possible. For these seven possibilities, we can then look to the orientation at the time of the other events. The June 3 event mostly rules out any option where the major axis of Arrokoth is perpendicular to the shadow track, but this is a weak constraint. Similarly, the July 10 SOFIA data can be used to rank the likelihood of each option, but again, the constraint is weak. The last event from 2018 with the two chords gives the strongest constraint. For this example case, the only period that provides a plausible match for the two chords from 2018 is a period of 15.9380 hr. Assuming the rotation is located to within 10° by the July 17 data, the period would then be good to roughly 0.0005 hr, an improvement of a factor of 100. The full analysis is left for future work that will fully integrate the encounter imaging with the occultation profiles.

Figure 13 shows an example of how the current shape model matches the occultation data using this updated period. In this figure are shown views of Arrokoth based on the shape model from Stern et al. (2019) and projected to the time and location of the occultation observation. The dates for each view are indicated in each subpanel. The projected scale is given for a sky-plane view of the object in the J2000 coordinate system. The field of view of each rendered view is about 2 mas. Relevant observations for each event are shown by the colored lines. Nondetections do not intersect the body and are shown in red. The other lines (green and yellow) are for sites recording an occultation. The green lines are a special marker to indicate the reference chord that was used for astrometry (described in Section 7.6). In the case of the 2017 July 10 data, there are two options to match the detection with the body and shown with dashed and solid lines. The solid line is the most likely based on the current orbit of Arrokoth and the Gaia DR2 position of the star. Note that the star position uncertainties are all about 4 km in the frame of reference shown in this figure.

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We used the shape model as shown in Figure 13 to derive final astrometry from all occultations except for the first where the object was not detected. In the case of the SOFIA event, we provide astrometry for both options shown in the figure for completeness but the option where we clip the southern projected end of the body is preferred. The preference is driven by the better match to the shape model. The southern end of the model (plane-of-the-sky coordinates) comes almost to a point, making it easier to get the short chord duration seen by SOFIA. On the northern end, there is a flat facet at that location that appears to preclude getting such a short chord. A more detailed shape analysis combining spacecraft imaging data with the occultation constraints may be able to reveal the correct interpretation.

These rendered images were converted to silhouettes, preserving the orientation as shown in Figure 13. We do not know the mass distribution within Arrokoth but we derived an approximate location of the center of mass by finding the area-weighted center of the silhouettes. Any error made with this approximation is significantly smaller than the uncertainty in the star positions. The position of the center is noted with respect to the center of the closest positive chord. The inferred astrometric positions are given in Table 9 along with the topocentric location for each of the measurements.