Solar System Science with the One Metre Initiative

Frank Roy, frank.roy@onemetreinitative.com

 

Abstract

The proposed One Metre Initiative, a high efficiency wide-field imaging platform, is shown to be an extremely good instrument at detecting small solar system bodies such as asteroids, comets, Main-Belt asteroids, Near-Earth-Objects etc. The geographic position at 45 degrees north latitude is also excellent for detecting objects located over Earth’s North Pole.

 

Introduction

The OMI is designed to provide a highly corrected monolithic 5 degrees2 field-of-view with superb camera performance. Small Main-Belt solar system bodies, typically moving at 1 arcsec/minute, are difficult to detect even with larger instruments because of this rapid motion against the background stars. The key components in enabling the detection of fast moving bodies are:

 

  1. A large WA
  2. Widest possible FOV
  3. Efficient camera system, i.e. fast download times
  4. Low cycles times
  5. Largest possible spectral bandwidth
  6. Good balance between pixel size and seeing

 

The integration time is limited by the motion of the object across a pixel. The OMI has a pixel pitch of 1.52”/pixel (2x2 binning with 0.76”/pixel) and expected seeing of 1.25” this would imply maximum exposure time of 90s for an object moving at 1”/min. This case is only true if the seeing is equal or smaller than the pixel. If the seeing disc is larger than the pixel than the seeing disc would determine the maximum exposure time, for example the CHFT has mean seeing of 0.85”/pixel and a pixel pitch of 0.187”pixel yielding a maximum exposure of 40s.

 

Detecting rapidly moving Bodies

 

The OMI is an efficient tool at detecting the faint (small) rapidly moving solar system bodies. Its key performance characteristics are as follows (all tables and data provided are derived from these numbers):

 

  1. Omega-Area                              à 6.0
  2. Camera download time      à 2s
  3. FOV                                à 5 degrees2
  4. Spatial sampling               à 0.76/1.52 arcsec/pixel, single/2x2 binning
  5. Spectral bandwidth           à 400nm
  6. QE                                  à 92%
  7. Read noise                       à 12e-
  8. Seeing                                       à 1.25 arcsec (expected)
  9. Sky Brightness                  à 21.80 mag/arcsec2 (v) measured
  10.  Telescope move               à 2s to move to the next field
  11.  Total cycle time               à Exposure + 4 seconds, typically 94s
  12.  Guiding and acquisition    à Not required because of the short exposures
  13.  Angle relative to zenith     à 0 degrees
  14.  Altitude                          à 400m

 

The longest exposure time would be limited by the motion of the object across the pixel grid. The OMI has a raw spatial sampling of 0.76 arcsec/pixel and an expected seeing of 1.25 arcsec; a 2x2 binning (1.52”/pixel) taking about 90s to cross a pixel at 1”/min.

 

Figure 1 – OMI curves of object motion (arcsec) vs. disc size (arcsec) this is in effect the trailing caused by the motion of the object across the pixel grid, and severally limits the maximum integration time thus the smallest detectable object. The curves represent motions from 0.25”/min to 10”/min. The curves are calculated by taking the seeing disc (1.25”) and adding the motion of the object. For example for an object moving at 1”/min with an 90 second exposure the total apparent trail would be an 1.25” disc stretched by 1.5” yielding 2.75 arcsec

 

Three key factors determine the optimum exposure time: the seeing disk, the pixel size and the motion of the object. Typically for best s/n you would want the entire seeing disk (1.25” expected for the OMI) to be smaller than the pixel pitch. Thus some spatial information is sacrificed in order to maximize the signal-to-noise ratio. Another very important reason for keeping the pixel pitch bigger than the seeing is to ‘track’ the object as long as possible. In this case a large pixel size compared to the object disc has a higher probability of keeping the flux on the same pixel for a longer time before it drifts over to the next pixel. Fig. 2 shows the time it would take an object to cross a pixel. The measurement is calculated from the 50% entry (50% of the object is in the pixel) to the 50% exit point. The larger the pixels relative to the object image the longer the possible integration time.

 

Figure 2 – OMI object cross rate for a motion of 1”/min for different seeing discs. Curves for seeing discs from 0.75” to 2” are shown.

 

For a given pixel size, and as the seeing disc gets larger, it covers more and more adjacent pixels and thus will in effect stay on any given pixel that much longer. As a consequence the larger disc seeing has a degraded s/n and thus reduced limiting magnitude. The OMI is expecting a seeing disc in the vicinity of 1.25”, with 2x2 binning (1.52”/pixel) the cross rate is 90 seconds, which means in 90 seconds most of the flux will on any given pixel. Fig. 3 clearly shows that larger pixels (relative to the seeing disc) will be able to integrate longer and achieve a deeper limiting magnitude, at the cost of spatial sampling (i.e. confusion limited).  

 

 

Figure 3 – An object takes about 90s to cross the 1.52” pixel; this is in effect the longest possible integration time and thus limits how small an object could be detected. In this particular case the seeing disc is 64% by area (80% by linear diameter) the size of the pixel (1.25” seeing and 1.52”/pixel). The large blue circle indicates the CFHT seeing (0.85”) to its pixel area (0.187”/pixel) for comparison. As the seeing disc becomes larger than the pixel, the cross rate actually takes longer because the entire seeing disc must cross the pixel. For example in the case of the CFHT with its 0.85” seeing disc it takes about 40s to cross a pixel at 1”/min motion.

 

Positional Information

 

Most of the time the seeing disc will be on 4 pixels (1.52”/pixel) thus yielding a positional accuracy of 0.1 pixel or about 0.15 arcsec, Fig. 6 demonstrates the concept.

 

Figure 4 – The majority of the time the object would most likely be in the ‘offset’ situation where the flux is distributed in 4 pixels for a dim object. Bright objects (mag~17) will always occupy more than 4 pixels. A single pixel situation (#4) is expected only a very small percentage of the time. In a worst case situation the positional accuracy can be determined to better than 0.5” and in most cases to 0.15” (1/10th of a pixel).

 

Limiting Magnitude

 

The limiting magnitude is determined by the length of time the flux remains on a single pixel, as shown in figure 5.

 

Figure 5 - The limiting magnitude with a mean seeing of 1.25” and a pixel pitch of 1.52”/pixel (2x2 binning).

 

Sky Coverage

 

The Sky coverage depends on the total cycle time; exposure + (download + telescope move) in seconds and of course the FOV. The OMI sweet spot in terms of limiting magnitude and field coverage is with a 90s exposure, whereas the OMI could cover some 650 degrees2 in 10 hours with 3 passes.

 

Exposure

Area

Size

Size

Limiting mag

Coverage

2-P Coverage

3-P Coverage

4-P Coverage

Notes

 

arcsec²

x

y

magnitude

per hour

per 10 hrs

per 10 hrs

per 10 hrs

 

Seconds

 

arcsec

arcsec

s/n =10

degrees²

degrees²

degrees²

degrees²

 

10

1.77

1.42

1.25

21.31

1,268

6339

4226

3169

10% overlap

20

1.98

1.58

1.25

21.76

740

3698

2465

1849

 

30

2.19

1.75

1.25

22.01

522

2610

1740

1305

 

40

2.40

1.92

1.25

22.19

403

2017

1345

1008

 

50

2.60

2.08

1.25

22.32

329

1643

1096

822

 

60

2.81

2.25

1.25

22.43

277

1387

924

693

 

70

3.02

2.42

1.25

22.52

240

1199

799

600

 

80

3.23

2.58

1.25

22.6

211

1056

704

528

 

90

3.44

2.75

1.25

22.66

189

944

629

472

 

100

3.65

2.92

1.25

22.72

171

853

569

427

 

Table 1 – Parameters used in graphs with 1 arcsec/minute motion. The cycle time includes 4s to move the telescope to the next position, 5 degrees away and settle. During the telescope move the camera is downloaded which takes about 2s. These short exposures do not require guiding thus improving the cycle time.

 

 

Figure 6 – Sky coverage vs. limiting magnitude with varying passes.

 

Search Pattern

 

With a 94 second cycle time, three passes separated by 16 and 32 minute interval as in Fig. 7 will yield about 625 degrees2 per 10 hour period reaching magnitude 22.5 with a s/n of 10. This will produce block coverage of about 50 degree2 and 100 degrees2. The pattern is optimized for minimum telescope slew distance.

 

 

Figure 7 – OMI 5x2 and 5x4 search patterns. As suggested this will yield about 625 deg2 in a 10 hour period with a 94s cycle times and reaching magnitude 22.5. The interval is 16 and 32 minutes between the passes.

 

Conclusion

 

Discovering rapidly moving objects is only one of the many capabilities of the OMI. Due to its ability to detect very faint objects over a very large coverage area the OMI can make valuable contributions to discovering NEO’s and other fast moving objects.

 

 

Acknowledgement

 

The author wishes to thank Paul Wiegert, the University of Western Ontario, to have taken the time to provide valuable comments and suggestions.