2. An Optical Search for Small Comets R. L. Mutel & J.D. Fix University of Iowa An Optical Search for Small Comets R. L. Mutel & J.D. Fix University of Iowa

3. Small Comet Detection Papers DE-1 (April 1986)Polar (May 1997)

4. Small Comet Scenario Small Comet Scenario (From L. Frank Website)

5. Small Comet Parameters (from Frank and Sigwarth 1993, Small comet Web site) Mass:20,000 – 40,000 kg Size: 4 – 10 m Density:~ 0.1 x H 2 0 Number density:(3 ± 1) · 10 -11 km -3 Flux at Earth:1 every 3 seconds (10 7 per yr.) Composition: Water ice with very dark mantle (albedo 0.01-0.02) Orbit:Confined to ecliptic, prograde Speed:~10 km-sec -1 at 1 a.u. Origin:Hypothesized comet belt beyond Neptune Small Comet Parameters (from Frank and Sigwarth 1993, Small comet Web site) Mass:20,000 – 40,000 kg Size: 4 – 10 m Density:~ 0.1 x H 2 0 Number density:(3 ± 1) · 10 -11 km -3 Flux at Earth:1 every 3 seconds (10 7 per yr.) Composition: Water ice with very dark mantle (albedo 0.01-0.02) Orbit:Confined to ecliptic, prograde Speed:~10 km-sec -1 at 1 a.u. Origin:Hypothesized comet belt beyond Neptune

6. Tests of the Small Comet Hypothesis

7. Observations  The observations were made using the 0.5 m f/8 reflector of the Iowa Robotic Observatory between 24 September 1998 and 11 June 1999.  Observations were scheduled every month within one week of new moon. A total of 6,148 images were obtained, of which 2,718 were classified as category A (visual detection magnitude 16.5 or brighter in a 100 pixel trail).  Seeing conditions varied from 2 - 5 arcsec (see histogram). For quality A images, seeing was < 3.5 arcsec.  All images were has thermal and bias corrections applied.  Images were recorded on CDROM and sent to the University of Iowa for analysis.  All images are available for independent analysis via anonymous ftp at node atf.physics.uiowa.edu.Observations  The observations were made using the 0.5 m f/8 reflector of the Iowa Robotic Observatory between 24 September 1998 and 11 June 1999.  Observations were scheduled every month within one week of new moon. A total of 6,148 images were obtained, of which 2,718 were classified as category A (visual detection magnitude 16.5 or brighter in a 100 pixel trail).  Seeing conditions varied from 2 - 5 arcsec (see histogram). For quality A images, seeing was < 3.5 arcsec.  All images were has thermal and bias corrections applied.  Images were recorded on CDROM and sent to the University of Iowa for analysis.  All images are available for independent analysis via anonymous ftp at node atf.physics.uiowa.edu.

8. Search Geometry

9. Iowa Robotic Observatory

12. V=14.9 Faint Galaxy Star Visual Magnitude Calibration

13. Visual Magnitude Calibration using Standard Stars: ADU counts vs. V, FWHM FWHM = 2.8" FWHM = 4.2" 16.7 15.6 17.1

14. Visual Magnitude Detection vs. Trail Length (20 April 1999, 60 s: fixed & 30 pixel trailed 16.717.115.617.116.7

15. Example of Trails Caused by Cosmic Rays, Geostationary Satellite Cosmic Ray

16.  Synthetic comet trails were added to 520 search images with randomly chosen magnitudes and trail lengths.  Three observers independently inspected all images  Result: Visual detection threshold is ~0.9  per pixel, with a suggestion that longer trails can be detected slightly fainter, perhaps 0.7 - 0.8 .  Synthetic comet trails were added to 520 search images with randomly chosen magnitudes and trail lengths.  Three observers independently inspected all images  Result: Visual detection threshold is ~0.9  per pixel, with a suggestion that longer trails can be detected slightly fainter, perhaps 0.7 - 0.8 . Visual Detection Calibration Using Synthetic Trails V = 16.4 39 pixels

17. V = 16.6 103 pixels V = 16.4 39 pixels V = 15.1 417 pixels Sample Synthetic Comet Calibration Images

18. Synthetic Comet Trail Nearing Limiting Magnitude (V=17.0) V = 17.0 124 pixels

20. Calculation of Sampled Volume Observer r-r- r+r+  1. Sampled volume as function of trail length L, field of view  : 2. Use faintest visual magnitude vs. trail length from synthetic comet test (60 s,  = 17 ADU  = 3.5"): 3. Detection volume as a function of visual magnitude (mv), speed (v obj ):

21. Trail Length versus Range

22. Detection Probability Per Image Detection Probability Per Image (assumes n sc = 3x10 -11 km -3 )

23. Upper Limit to Small Comet Number Density () Upper Limit to Small Comet Number Density (99% confidence level) Rejected density region Allowed density region 0.05 n 0

24. Probability of Non-detection vs. Number Density Probability of Non-detection vs. Number Density (N=2,713, no detections, n 0 = 3  10 -11 km -3 ) n = 0.05  n0 n = 0.25  n0

25. Small Comet Optical Search Comparison ParameterYeates (1989)Frank & Sigwarth (1990) Mutel & Fix (2000) TelescopeSpacewatch Iowa Robotic Observatory Diameter (m)0.9 0.5 Field of View (arcmin)9x15 21x21 Co-rotation range (km)140,000 55,000 Images analyzed17148 prs2,713 Solar phase angle20º 4º - 9º Single image sample volume (10 9 km 3 ) 991.1 Total sampled volume (10 11 km 3 ) 15.18.631.0 Limiting magnitude (120 pixel trail) ~19 16.5 Number detections3360 Inferred number density (10 -11 km -3 ) 23 ± 1< 0.05 (99% confidence)

26. Comparison with Previous Searches: Detection magnitude comparison 2a. Visual magnitude m as function of solar phase angle , scattering parameter Q, phase function  (  ) [Lumme & Bowell 1981]: 2b. Best fit phase function for solar system objects is: 2c. For Q ~ 0, magnitude difference between previous searches (fixed phase angle 20  ) and present search (4  <  < 9  ) is: 1. Visual magnitude m correction for distance (55,000 km vs. 137,000 km) is 2.0 magnitudes.

27. Multiple Scattering Factor Q versus Albedo for Solar System Objects (from Lumme & Bowell AJ 86, 1705) Asteroids Planets, Satellites Small comet albedo range

28. Phase angle versus local time for IRO search 6 am/pm Midnight 8  average solar phase angle

29. Q = 0.0 Q = 0.3 Magnitude difference between IRO search and previous searches at fixed  = 20  Q = 0.6 8°8° 0.54

30. Implications for Physical Characteristics of Small Comets The magnitude limit can be converted to limits on the physical properties of small comets. Assuming a single scattering function Q = 0 and and a mean solar phase angle of 8°, the allowed range of geometrical albedo and density for a mass of 20,000 kg (Frank et al. 1990) is shown below. Implications for Physical Characteristics of Small Comets The magnitude limit can be converted to limits on the physical properties of small comets. Assuming a single scattering function Q = 0 and and a mean solar phase angle of 8°, the allowed range of geometrical albedo and density for a mass of 20,000 kg (Frank et al. 1990) is shown below. V=16.0 V=16.5 Darkest solar system objects (Iapetus) Permitted Region Forbidden Region Darkest part of Halley nucleus

31. Physical Conditions of Small Comets Alternatively, assuming a mass density of 0.1 gm-cm -3 (e.g. Frank and Sigwarth 1993), the mass-albedo allowed range is shown below. Physical Conditions of Small Comets Alternatively, assuming a mass density of 0.1 gm-cm -3 (e.g. Frank and Sigwarth 1993), the mass-albedo allowed range is shown below. Density 0.1 x H 2 O V = 16.5 V = 17.0 Frank et al. (1990) estimated mass range

32. Summary  We have conducted an extensive optical search for small comets proposed by Frank et al. (1986; Frank & Sigwarth 1997,1999).  After careful visual inspection of more than 2,700 images, we found no objects consistent with small comets. The detection limit depends on magnitude and trail length: e.g. for V = 16.5, trail lengths up to 120 pixels are robustly detected.  These results strongly disagree with previous optical searches of Yeates (1989) and Frank et al. (1990). Extrapolation of their detections to our search predicts more than 60 detections brighter than V = 16.5.  The null detections place an upper limit to the number density n < 0.05 (99% confidence) of the value claimed by Frank and Sigwarth (1990).  Any object with mass M = 20,000 kg and fainter than the magnitude-trail length limit must have either:  An implausibly low geometric albedo (p<0.01) or  Density greater than ice (  > 1 gm/cm 3 ).Summary  We have conducted an extensive optical search for small comets proposed by Frank et al. (1986; Frank & Sigwarth 1997,1999).  After careful visual inspection of more than 2,700 images, we found no objects consistent with small comets. The detection limit depends on magnitude and trail length: e.g. for V = 16.5, trail lengths up to 120 pixels are robustly detected.  These results strongly disagree with previous optical searches of Yeates (1989) and Frank et al. (1990). Extrapolation of their detections to our search predicts more than 60 detections brighter than V = 16.5.  The null detections place an upper limit to the number density n < 0.05 (99% confidence) of the value claimed by Frank and Sigwarth (1990).  Any object with mass M = 20,000 kg and fainter than the magnitude-trail length limit must have either:  An implausibly low geometric albedo (p<0.01) or  Density greater than ice (  > 1 gm/cm 3 ).