An Optical Search for Small
Comets
R. L. Mutel & J.D. Fix
University of Iowa
Small Comet Detection Papers
DE-1 (April 1986)
Polar (May 1997)
Small Comet Scenario
(From L. Frank Website)
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 H20
Number density: (3 ± 1) · 10-11 km-3
Flux at Earth:
1 every 3 seconds (107 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
Tests of the Small Comet Hypothesis
Observations of Atmospheric Dark Spots
DE-1 (1986)
Polar (1997)
Frank et al.(1986); Frank & Sigwarth (1997)
Meteroid Plumes?
(rate 10,000x too low)
Boslough & Gladstone (1997)
Atmospheric Effects
Lunar Effects
No Seismic Evidence
David (1986)
Nakamura et al. (1986)
No Impact Craters
Grier & McEwen (197)
'Small Comets'
20-40 ton, water ice
Dark mantle
Frank et al. (1986)
Noble Gas Inventory
Density of Xe, Ar, etc
30,000x too low
Swindle & Kring (1997)
Deuterium Abundance
HDO comets >> Earth
Blake et al. (1999)
Instrumental Artifact
Parks et al. (1997;1998)
McFadden et al. (1998)
Mozer et al. (1998)
Radar Search
No detection (n<10^-4)
Knowles et al. (1999)
Oxygen Trails
Frank & sigwarth (1997)
Polar Images 130 nm
5-10 per day
OH Trails
Frank & Sigwarth (1997)
Polar images 308 nm
required mass ~ SC
Optical Searches
Trajectory Study
Wrong am/pm asymmetry
Harris (2000)
Spacewatch
140,000 km
171 images, 36 detections
Yeates (1989)
Spacewatch
140,000 km
48 image prs., 6 detections
Fran & Sigwarth (1990)
Naked Eye Test
1000-3000 km
0 detections
Rizk & Dessler (1997)
Iowa Robotic Obsevatory
55,000 km
0 detections
Mutel & Fix (2000)
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.
Search Geometry
Iowa Robotic Observatory
Star Visual Magnitude Calibration
Faint Galaxy
V=14.9
Visual Magnitude Calibration using Standard Stars:
ADU counts vs. V, FWHM
 t 
Apk (V , t , )  108.70.4V  2 
 
ADU count vers us V (Days 47,51)
4
2.512 10 1 10
5
16.7
FWHM = 2.8"
1 10
4
ADU1 i
ADU2 i
Amod1 ( x)
15.6
Amod2 ( x)
1 10
3
FWHM = 4.2"
17.1
301.995
100
12
12
12.5
13
13.5
14
V1i  V2i  x
14.5
15
15.5
16
16
Visual Magnitude Detection vs. Trail
Length
(20 April 1999, 60 s: fixed & 30 pixel
 t
 t  trailed A (V , t , , L)  10
Apk (V , t , )  10
8.7 0.4V
8.7 0.4V
 2
 
pk
16.7
17.1
15.6
17.1
16.7



 L 
Example of Trails Caused by Cosmic Rays,
Geostationary Satellite
Cosmic Ray
Visual Detection Calibration Using Synthetic Trails
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 .
V = 16.4
39 pixels
Sample Synthetic Comet Calibration Images
V=
16.4
39
pixels
V=
15.1
417
pixels
V=
16.6
103
pixels
Synthetic Comet Trail
Nearing Limiting
Magnitude (V=17.0)
V = 17.0
124 pixels
Calculation of Sampled Volume
1. Sampled volume as function of trail length L, field of view  :
2
Vol ( L)  
r  dr 
  r ( L)3  r ( L)3 

r ( L )
3
r ( L )
2
Observer
r
2. Use faintest visual magnitude vs. trail length from
synthetic comet test (60 s,  = 17 ADU  = 3.5"):
mmin  L   21.7  2.5  log  L 
3. Detection volume as a function of visual magnitude
(mv), speed (vobj ):
Vol (mV , vobj )  1015.50.4mV
 vobj 
 10 


3
km3
r+
Trail Length versus Range
L 
vobj
r
 2.5   s  t
Detection Probability Per Image
(assumes nsc = 3x10-11 km-3)
p(mV , vobj )  (0.024  0.008)  10
0.4(16.5 mV )
 vobj 
 10 


3
Upper Limit to Small Comet Number Density
(99% confidence level)
Rejected density region
0.05 n0
Allowed density region
Probability of Non-detection vs. Number Density
(N=2,713, no detections, n0 = 310-11 km-3)
Prob. of non-detection vs. magnitude
1
P 0.05 n o  V 9

sec

P 0.05 n o  V 11




2
n = 0.05  n0
km 
sec


km 
sec


4
km 
sec
P 0.25 n o  V 10

P 0.25 n o  V 11

k
km 
P 0.05 n o  V 10
P 0.25 n o  V 9
Np
kj
P( k ; N , p )  1  e  
j 0 j !
0


km 
sec


6
n = 0.25  n0
km 

sec 
8
 10
10
15
15
15.5
16
V
16.5
17
17
Small Comet Optical Search Comparison
Parameter
Yeates (1989)
Frank &
Sigwarth
(1990)
Mutel & Fix (2000)
Telescope
Spacewatch
Spacewatch
Iowa Robotic
Observatory
Diameter (m)
0.9
0.9
0.5
Field of View (arcmin)
9x15
9x15
21x21
Co-rotation range (km)
140,000
140,000
55,000
Images analyzed
171
48 prs
2,713
Solar phase angle
20º
20º
4º - 9º
Single image sample
volume (109 km3)
9
9
1.1
Total sampled volume
(1011 km3)
15.1
8.6
31.0
Limiting magnitude
(120 pixel trail)
~19
~19
16.5
Number detections
33
6
0
Inferred number density
(10-11 km-3)
2
3±1
< 0.05
(99% confidence)
Comparison with Previous Searches:
Detection magnitude comparison
1. Visual magnitude m correction for distance (55,000 km vs. 137,000 km) is 2.0 magnitudes.
2a. Visual magnitude m as function of solar phase angle , scattering parameter Q, phase
function () [Lumme & Bowell 1981]:
Q


m(a   m(0 )  2.5  log 1  Q        sin       cos   



2b. Best fit phase function for solar system objects is:
0.632

 

    exp  3.343  tan  
2  


2c. For Q ~ 0, magnitude difference between previous searches (fixed phase angle 20) and
present search (4<  < 9 ) is:
m( )  2.5  log     1.21
Multiple Scattering Factor Q versus Albedo
for Solar System Objects
(from Lumme & Bowell AJ 86, 1705)
Asteroids
Small comet
albedo range
Planets,
Satellites
Phase angle versus local time for IRO search
9.083
10
9
8 average
solar phase
angle
8
7
 ( h)
deg
Midnight
6
5
4
6 am/pm
3
2.658
2
6
6
5
4
3
h
deg  15
2
1
0
0
Magnitude difference between IRO search and previous
searches at fixed  = 20
0
0.2
V 0   
Q = 0.6
0.4
V 0.3  
V 0.6  
V 1   
Q = 0.0
0.54
0.6
Q = 0.3
0.8
8°
1
0
5
10

deg
15
20
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.
Limits on Albedo and Density
V=16.5
Density (gm/cm3)
0.9
0.7
V=16.0
Permitted
Region
Forbidden
Region
0.5
0.3
Solar elongation 8 deg
Single scattering function Q = 0
0.1
0.00
Darkest solar system
objects (Iapetus)
0.01
0.02
Geometric Albedo
0.03
Darkest part of Halley nucleus
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 H2O
Frank et al. (1990) estimated mass range
V = 16.5
V = 17.0
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/cm3).