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).