an optical search for small comets r. l. mutel & j.d. fix university of iowa
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An Optical Search An Optical Search for Small Cometsfor Small Comets
R. L. Mutel & J.D. Fix R. L. Mutel & J.D. Fix
University of IowaUniversity of Iowa
An Optical Search An Optical Search for Small Cometsfor Small Comets
R. L. Mutel & J.D. Fix R. L. Mutel & J.D. Fix
University of IowaUniversity of Iowa
Small Comet Detection Small Comet Detection PapersPapers
DE-1 (April 1986)
Polar (May 1997)
Small Comet ScenarioSmall Comet Scenario(From L. Frank Website)
Small Comet ParametersSmall 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
Small Comet ParametersSmall 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 HypothesisTests of the Small Comet Hypothesis
M eteroid Plum es?(rate 10,000x too low )
Boslough & G ladstone (1997)
No Seism ic EvidenceDavid (1986)
Nakam ura et al. (1986)
No Im pact CratersGrier & M cEw en (197)
Lunar Effects
Noble Gas InventoryDensity of Xe, Ar, etc
30,000x too lowSw indle & Kring (1997)
Deuterium AbundanceHDO com ets >> Earth
Blake et al. (1999)
Oxygen T railsFrank & sigw arth (1997)
Polar Im ages 130 nm5-10 per day
OH TrailsFrank & Sigw arth (1997)
Polar im ages 308 nmrequired m ass ~ SC
Atm ospheric Effects Radar SearchNo detection (n<10^-4)Know les et a l. (1999)
Spacew atch140,000 km
171 im ages, 36 detectionsYeates (1989)
Spacew atch140,000 km
48 im age prs., 6 detectionsFran & Sigw arth (1990)
Naked Eye Test1000-3000 km0 detections
Rizk & Dessler (1997)
Iowa Robotic Obsevatory55,000 km
0 detectionsMutel & Fix (2000)
Optical Searches Trajectory StudyW rong am /pm asym m etry
Harris (2000)
'Sm all Com ets'20-40 ton, w ater ice
Dark m antleFrank et al. (1986)
Instrum ental ArtifactParks et al. (1997;1998)M cFadden et al. (1998)
M ozer et al. (1998)
Observations of Atm ospheric Dark SpotsDE-1 (1986)Polar (1997)
Frank et al.(1986); Frank & Sigw arth (1997)
ObservationsObservations
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.
ObservationsObservations
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 GeometrySearch Geometry
Iowa Robotic ObservatoryIowa Robotic Observatory
V=14.9V=14.9
Faint Galaxy
Faint Galaxy
Star Visual Magnitude CalibrationStar Visual Magnitude Calibration
Visual Magnitude Calibration using Standard Stars:Visual Magnitude Calibration using Standard Stars:ADU counts vs. V, FWHMADU counts vs. V, FWHM
12 12.5 13 13.5 14 14.5 15 15.5 16100
1 103
1 104
1 105ADU count versus V (Days 47,51)
2.512 104
301.995
ADU1i
ADU2i
Amod1 x( )
Amod2 x( )
1612 V1i V2i x
12 12.5 13 13.5 14 14.5 15 15.5 16100
1 103
1 104
1 105ADU count versus V (Days 47,51)
2.512 104
301.995
ADU1i
ADU2i
Amod1 x( )
Amod2 x( )
1612 V1i V2i x
FWHM = 2.8"FWHM = 2.8"
FWHM = 4.2"FWHM = 4.2"
8.7 0.42
( , , ) 10 Vpk
tA V t
16.7
15.6
17.1
Visual Magnitude Detection vs. Visual Magnitude Detection vs. Trail LengthTrail Length
(20 April 1999, 60 s: fixed & 30 (20 April 1999, 60 s: fixed & 30 pixel trailedpixel trailed8.7 0.4
2( , , ) 10 V
pk
tA V t
8.7 0.4( , , , ) 10 V
pk
tA V t L
L
16.7
17.1
15.6
17.1
16.7
Example of Trails Caused by Cosmic Rays, Example of Trails Caused by Cosmic Rays, Geostationary SatelliteGeostationary Satellite
Cosmic Ray
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 TrailsVisual Detection Calibration Using Synthetic Trails
V = 16.4
39 pixels
V = 16.6
103 pixels
V = 16.4
39 pixels
V = 15.1
417 pixels
Sample Synthetic Comet Calibration ImagesSample Synthetic Comet Calibration Images
Synthetic Comet Trail Synthetic Comet Trail Nearing Limiting Nearing Limiting
Magnitude (V=17.0)Magnitude (V=17.0)
V = 17.0
124 pixels
Calculation of Sampled VolumeCalculation of Sampled Volume
2( ) 2 3 3
( )( ) ( ) ( )
3
r L
r LVol L r dr r L r L
Observer 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"):
min 21.7 2.5 logm L L
3. Detection volume as a function of visual magnitude (mv), speed (vobj ):
3
15.5 0.4 3( , ) 10 km10
V objmV obj
vVol m v
Trail Length versus RangeTrail Length versus Range
2.5objs
vL t
r
Detection Probability Per ImageDetection Probability Per Image(assumes nsc = 3x10-11 km-3)
3
0.4 (16.5 )( , ) (0.024 0.008) 1010
V objmV obj
vp m v
Upper Limit to Small Comet Number Density Upper Limit to Small Comet Number Density ((99% confidence level))
Rejected density regionRejected density region
Allowed density regionAllowed density region
0.05 n0
Probability of Non-detection vs. Number DensityProbability of Non-detection vs. Number Density (N=2,713, no detections, n0 = 310-11 km-3)
15 15.5 16 16.5 1710
8
6
4
2
0
Prob. of non-detection vs. magnitude1
10
P 0.05n o V 9km
sec
P 0.05n o V 10km
sec
P 0.05n o V 11km
sec
P 0.25n o V 9km
sec
P 0.25n o V 10km
sec
P 0.25n o V 11km
sec
1715 V
15 15.5 16 16.5 1710
8
6
4
2
0
Prob. of non-detection vs. magnitude1
10
P 0.05n o V 9km
sec
P 0.05n o V 10km
sec
P 0.05n o V 11km
sec
P 0.25n o V 9km
sec
P 0.25n o V 10km
sec
P 0.25n o V 11km
sec
1715 V
0
( ; , ) 1!
jN pk
j
kP k N p e
j
n = 0.05 n0n = 0.05 n0
n = 0.25 n0n = 0.25 n0
Small Comet Optical Search ComparisonSmall 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:Comparison with Previous Searches:Detection magnitude comparison Detection magnitude comparison
2a. Visual magnitude m as function of solar phase angle , scattering parameter Q, phase function () [Lumme & Bowell 1981]:
( (0 ) 2.5 log 1 sin cosQ
m a m Q
2b. Best fit phase function for solar system objects is:
0.632
exp 3.343 tan2
2c. For Q ~ 0, magnitude difference between previous searches (fixed phase angle 20) and present search (4< < 9 ) is:
( ) 2.5 log 1.21m
1. Visual magnitude m correction for distance (55,000 km vs. 137,000 km) is 2.0 magnitudes.
Multiple Scattering Factor Q versus Albedo Multiple Scattering Factor Q versus Albedo for Solar System Objectsfor Solar System Objects
(from Lumme & Bowell AJ 86, 1705)(from Lumme & Bowell AJ 86, 1705)
Asteroids Planets,
Satellites
Small comet albedo range
Small comet albedo range
Phase angle versus local time for IRO searchPhase angle versus local time for IRO search
01234562
3
4
5
6
7
8
9
109.083
2.658
h( )
deg
06 h
deg 15
01234562
3
4
5
6
7
8
9
109.083
2.658
h( )
deg
06 h
deg 15
6 am/pm6 am/pm
MidnightMidnight
8 average solar phase angle
0 5 10 15 201
0.8
0.6
0.4
0.2
0
V 0
V 0.3
V 0.6
V 1
deg
0 5 10 15 201
0.8
0.6
0.4
0.2
0
V 0
V 0.3
V 0.6
V 1
deg
Q = 0.0Q = 0.0
Q = 0.3Q = 0.3
Magnitude difference between IRO search and previous Magnitude difference between IRO search and previous searches at fixed searches at fixed = 20 = 20
Q = 0.6Q = 0.6
8°
0.54
Implications for Physical Characteristics of Implications for Physical Characteristics of Small CometsSmall 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 Implications for Physical Characteristics of Small CometsSmall 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.
0.00 0.01 0.02 0.03
Geometric Albedo
0.1
0.3
0.5
0.7
0.9
De
nsi
ty (
gm
/cm
3)
Limits on Albedo and Density
Solar elongation 8 degSingle scattering function Q = 0
0.00 0.01 0.02 0.03
Geometric Albedo
0.1
0.3
0.5
0.7
0.9
De
nsi
ty (
gm
/cm
3)
Limits on Albedo and Density
Solar elongation 8 degSingle scattering function Q = 0
V=16.0
V=16.5
Darkest solar system objects (Iapetus)
Permitted Region
Forbidden Region
Darkest part of Halley nucleus
Physical Conditions of Small CometsPhysical Conditions of Small CometsAlternatively, 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 CometsPhysical Conditions of Small CometsAlternatively, 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 H2ODensity 0.1 x H2O
V = 16.5
V = 17.0
Frank et al. (1990) estimated mass range
Summary 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).
Summary 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).
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