THE PAN-STARRS SOLAR SYSTEM SIMULATION

Larry Denneau, Jr. Pan-STARRS Team Pan-STARRS, Institute for Astronomy, University of Hawaii

ABSTRACT

The Institute for Astronomy at the University of Hawaii is developing a large optical astronomical surveying system–the Panoramic Survey Telescope and Rapid Response System (Pan-STARRS). The Moving Object Processing System (MOPS) client of the Pan-STARRS image processing pipeline is developing software to automatically discover and identify >90% of near-Earth objects (NEOs) 300m in diameter and >80% of other classes of asteroids and comets. In developing its software, MOPS has created a synthetic solar system model (SSM) with over 10 million objects whose distributions of orbital characteristics match those expected for objects that Pan- STARRS will observe. MOPS verifies its correct operation by simulating the survey and subsequent discovery of synthetically generated objects. MOPS also employs novel techniques in handling the computationally difficult problem of linking large numbers of unknown asteroids in a field of detections.

We will describe the creation and verification of the Pan-STARRS MOPS SSM, demonstrate synthetic detections and observations by MOPS, describe MOPS asteroid-linking techniques, describe accuracy and throughput of the entire MOPS system, and provide predictions regarding the numbers and kinds of objects, including as yet undiscovered "extreme objects", that MOPS expects to find over its 10-year lifetime.

INTRODUCTION

The Institute for Astronomy at the University of Hawaii is developing a large optical astronomical surveying system–the Panoramic Survey Telescope and Rapid Response System (Pan-STARRS). Pan-STARRS will provide state-of-the-art capability in several areas: four wide-field (7 deg 2) identical telescopes operating in parallel, a gigapixel orthogonal transfer array (OTA) detector for each telescope, 0.01 arcsecond astrometric precision, and a limiting magnitude of R=24. In a single night Pan-STARRS will observe approximately 6000 deg 2 of sky. All combined, this capability will allow Pan-STARRS to perform automated asteroid searching on an unprecedented scale. The Pan-STARRS single prototype telescope, called PS1, is expected to see first light in 2006, followed by the complete four-telescope system, PS4, in 2009.

MOVING OBJECT PROCESSING SYSTEM

The Moving Object Processing System (MOPS) client of the Pan-STARRS Image Processing Pipeline (IPP) is developing software to automatically discover and identify >90% of near-Earth objects (NEOs) 300m in diameter and >80% of other classes of asteroids and comets. The Pan-STARRS Solar System Simulation (SSS) exists so that the MOPS can be developed and verified and so that PS4 operating efficiencies can be monitored. MOPS will not have any live data until the Pan-STARRS prototype telescope and subsequent astrometric/photometric survey are completed in 2007. So MOPS must construct its own population of Solar System objects and simulate their observation. Once synthetic telescope fields are created, MOPS can develop and verify algorithms that perform automatic discovery of asteroids.

During the operation of PS4, Pan-STARRS and MOPS will require a way to measure how efficiently MOPS is processing its input data stream. MOPS will estimate its operating efficiency on real sky data by injecting its full synthetic model into the real data stream and then extract efficiency parameters from the synthetic stream after processing.

As MOPS discovers and verifies new objects, in particular near-Earth objects (NEOs) and potentially hazardous objects (PHOs), orbital parameters and observations will be reported to external sources for further evaluation of impact hazard.

MOPS SOLAR SYSTEM SIMULATION

Synthetic Asteroid Population

In order for MOPS survey strategies and software design to be tested, there must exist a source of fictitious asteroid- like bodies from which MOPS can synthesize observations. The MOPS team has synthesized over 10 million Solar System objects for its simulation, shown in Table 1.

Table 1. MOPS Synthetic Asteroid Population

NEOs 250,000 Main Belt 10,000,000 Trojans 420,000 Centaurs 60,000 Trans-Neptunian 72,000 Scattered Disc 20,000 Comets 20,000 Total 10,842,000

The NEO population is based on the Bottke et al. NEA population model [1], and the Main Belt population is based on current known orbital distributions of Main Belt asteroids, scaled to reproduce a sky-plane density of approximately 200 objects/deg 2 in the ecliptic [2]. Other populations were developed similarly, with some selection criteria for observability in the case of distant populations (Trans-Neptunian, Scattered Disc objects).

Survey Strategy

Considerable study has already been dedicated to optimal observing strategies for the detection of asteroids and in particular NEOs by Pan-STARRS [3]. During its nightly 1000-field scan, the preliminary Pan-STARRS asteroid survey will include two 2,200-deg 2 opposition regions (~660 fields each) flanked by two 550-deg 2 —sweet-spot“ regions (~160 fields each). The sweet-spots represent locations on the sky more likely to contain PHOs of highest impact risk, so the greatest impact reduction can be achieved by searching for asteroids in these regions. These regions of sky coverage will move along the ecliptic at approximately one degree per day to remain opposite the Sun; after one year the sky coverage pattern returns to its original location and the survey is repeated. Fig. 1 shows Pan-STARRS sky coverage at four different times during a single year of the MOPS simulated survey.

Fig. 1. MOPS simulated survey sky coverage during one year

In addition to appropriate sky coverage, Pan-STARRS must consider the optimal numbers of visits per night and number of days between visits for a particular location on the sky. MOPS has developed several survey simulations using various intra-night and inter-night intervals, and for its testing and development has selected a survey that generates 30-minute intervals between visits to the same location per night, and on average 3-4 days between visits, for a 10-12 day observational arc. Previous Pan-STARRS studies have shown that 10-12 day arcs provide sufficient orbital definition to find objects the following month [4], at which point their orbits can be more precisely calculated.

MOPS has programmed its survey scheduler to simulate random coarse weather losses. Currently MOPS can only simulate entire nights lost to weather, but future MOPS survey simulations may be able to simulate finer-grained losses.

Synthetic Telescope

After creating a population of synthetic asteroids and suitable surveys, MOPS simulates the observation of its synthetic Solar System essentially by calculating the position and magnitude on the sky for all objects and selecting the objects that appear within a single field. The naïve or brute-force approach to this problem is computationally prohibitive, and MOPS employs multiple-hypothesis testing and spatial indexing routines among other optimizations to substantially reduce computation required for this process.

After calculating exact position and magnitude within a field, MOPS —fuzzes“ the observation by applying astrometric (position) and photometric (magnitude) errors consistent with expected total astrometric and photometric error for the PS4 system. The astrometric error can be modeled as a Gaussian distribution that is a function of photometric signal-to-noise, and for bright objects the expected Pan-STARRS astrometric precision will be about 0.01 arcsec. False detections are also added to the detection stream, at a rate of about 200 false detections per deg 2 at a 5 σ confidence level.

Fig. 2 shows a complete synthetic Pan-STARRS field, as seen by MOPS.

Fig 2. Simulated Pan-STARRS field

MOPS Software

Upon generation of synthetic telescope fields of moving objects, MOPS can get to the business of finding asteroids. Algorithms for automatic discovery of asteroids by wide-field surveys is a complicated and rapidly changing area of research [5], and while MOPS has its own methods for finding asteroids, one consideration in the MOPS design is to allow other algorithms to be —plugged into“ the MOPS pipeline. Fig. 3 shows the general flow of data through the MOPS pipeline.

Generally, MOPS asteroid discovery (—linking“) consists of the identification of candidate detection pairs (using the current survey strategy; triplets are under consideration) of moving objects within a single night, called tracklets . Conceptually, all detections consistent with quasi-linear motion within an acceptable velocity range become candidate tracklets. After three nights of observations have been performed at a given region on the sky, tracklets from these three nights are assembled into proposed tracks , or linkages, of detections. In the MOPS design, many of these tracks are unlikely to represent correct linkages of detections–that is, they may contain mixed detections from two or more different objects. These mixed tracks are not discarded until orbit computation is performed on the track. Computed orbits that satisfy a maximum-residual requirement are accepted as provisional discovered objects and are preserved in the MOPS system.

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Fig 3. MOPS software pipeline

MOPS does not introduce physics into its linking process due to computational cost. Instead the linking software assumes an approximately quadratic motion on the sky over the time interval under question. Only once proposed linkages are obtained are orbital parameters calculated. Fast-moving objects, in particular NEOs, can have highly non-quadratic motion on the sky and thus pose difficulty. However by adjusting thresholds in its search algorithms MOPS can effectively loosen up the search enough so that even these fast-moving NEOs can be recovered.

RESULTS

The full 10-million object MOPS requires years of processing to simulate 10 years of observations. Since this is impractical, MOPS has created several different lighter-weight models to evaluate various aspects of its system design.

Low-Density Simulation (1/250)

The 1/250 model consists of 10 years of simulated Pan-STARRS fields, but the source asteroid population is 1/250 the size of the full MOPS model. Fig. 4 shows the cumulative discovery rate of NEOs and Main Belt objects in the model over 10 years. It is seen that MOPS easily achieves the 80% recovery rate for Main Belt objects and is near the 90% target for 300-meter NEOs. Due to the small number of 300-meter NEOs in the 1/250 model (31) this may simply be an artifact of small-number statistics; in any case it shows that the MOPS approach is satisfactory but should be investigated further using a higher density model.

Cumulative Fraction of SSM Objects Visible >= 3 Nights

1.00

0.90

0.80

0.70

0.60 ALL 26352 0.50 NEO 31 MB 24094 0.40

0.30

0.20

0.10

0.00 0.00 0.33 0.67 1.00 1.33 1.67 2.00 2.33 2.67 3.00 3.33 3.67 4.00 4.33 4.67 5.00 5.33 5.67 6.00 6.33 6.67 7.00 7.33 7.67 8.00 8.33 8.67 9.00 9.33 9.67 10.00 Years

Fig 4. 1/250 model cumulative discovery rates for 300-meter NEOs and Main Belt objects

Medium Density Simulation (1/100)

In this simulation the Main Belt is sampled at 1/100, and all other populations are fully represented, for a total of about 2 million objects. Due to time and storage considerations MOPS uses this model to test linking efficiency for an entire lunation (month) of simulated observations and to test the quality of computed orbits by attempting to locate discovered objects in the following lunation where possible.

Fig 5. Shows the prediction error on the sky of MOPS computed NEO orbits from a single lunation of observations (typically six observations) to the following lunation. A large distribution of errors here would indicate that MOPS might have difficulty —finding“ an object in the future.

< 0.2 arcmin 2

Fig 5. NEO one-month prediction error, MOPS 1/100 model

Spacewatch Incidental Astrometry (IA), October 2004

MOPS has tested its asteroid discovery pipeline using Spacewatch (Tucson, Arizona) Incidental Astrometry (IA) data from October of 2004. Spacewatch employs three visits per night instead of two, so it provides a useful test of the generality of MOPS processing in addition to being the first significant body of real-world observations pushed through the pipeline.

Fig 6. Shows two scatter plots of orbital semi-major axis a vs. eccentricity e for the Spacewatch IA data and the MOPS 1/100 simulation. The MOPS model contains full populations of NEOs and other non-Main Belt objects, resulting in higher density of objects at low a and high e. The Main Belt areas between a > 2AU and a < 3.5AU exhibit Kirkwood resonance gaps, and the Main Belt Hilda population is clearly visible at 4AU.

Fig 6. Semi-major axis a vs. eccentricity e for Spacewatch IA data and MOPS 1/100 model

SUMMARY

The MOPS Solar System Model with its 10 million asteroid population, sophisticated survey simulation and astrometric and photometric error model is currently one of the most advanced Solar System simulations of its kind. It has proven effective in helping MOPS design and assess observing strategies and software development. With the recent successful injection of real-world Spacewatch data into a MOPS test model, the overall MOPS design has been proven sound and should achieve its goal of discovering 90% of recoverable hazardous asteroids and reducing by 90% overall global impact risk [6].

REFERENCES

1. Bottke, W. F., Jedicke, R., Morbidelli, A., Petit, J. & Gladman, B. Understanding the Distribution of Near-Earth Asteroids. Science , 288:2190œ2194, 2000. 2. Jedicke, R. Pan-STARRS Moving Object Pipeline Requirements, Institute for Astronomy, University of Hawaii, 2003. 3. Kaiser, N., Pan-STARRS Project Team. Asteroid Collision Hazard Reduction Requirements, Institute for Astronomy, University of Hawaii, 2004. 4. Chesley, S., Heasley, J., Jedicke, R. & Spahr, T. MOPS: NEO Preliminary Orbit Calculation Studies, Institute for Astronomy, University of Hawaii, 2004. 5. Petit, J.-M., Holman, M., Scholl, H., Kavelaars, J. & Gladman, B. An automated moving object detection package. Mon. Not. R. Astron. Soc. 347, 471œ480, 2004. 6. Jedicke, R. ACM 2005 Plenary Oral Presentation, 2005.