The Population and Mass of the Oort Cloudlal.univ-lille1.fr/talks-oortws2011/LD.pdf · The...
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The Population and Mass of the Oort Cloud
Luke Dones Southwest Research Institute
Boulder, Colorado
Megan E. Schwamb Yale Center for Astronomy and Astrophysics
andDepartment of Physics
Yale UniversityNew Haven, Connecticut
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Population
Francis (2005)
perihelion distanceabsolute magnitude
inverse semi-major axis
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Long-Period Comet Sample of Francis (2005)
• 51 comets that passed perihelion in 2000, 2001, or 2002 and
• Were discovered (or could have been discovered) by LINEAR
• Broad range of perihelion distances: 0.3 - 9.7 AU
• Broad range of absolute magnitudes: 3.1 - 16.6
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0
0.05
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0.15
0.2
0 2 4 6 8 10
Frac
tion
of C
omet
s/AU
Perihelion Distance (AU)
raw data from Francis 2005
Perihelion Distance Distribution
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0
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0.1
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0.14
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4 6 8 10 12 14 16
Frac
tion
of C
omet
s with
Abs
olut
e M
agni
tude
H
Absolute Magnitude H
Absolute Magnitude Distribution
raw data from Francis 2005Thursday, October 20, 11
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Definition of Absolute Magnitude (H)
• Hdis: magnitude of comet at discovery
• r: distance of comet from Sun (AU)
• Δ: distance of comet from Earth (AU)
• H: absolute magnitude of comet - an estimate of the comet’s brightness at r = Δ = 1 AU. H is supposed to be an intrinsic property of the comet.
Flux from comet ∝Δ-2r-n
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What is the value of n (“activity index” or “photometric index”)?
Flux from comet ∝Δ-2r-n
• n = 4 (Vsekhsvyatskii): Catalog includes “just over a thousand apparitions of various comets from -466 to 1975”
• n ~ 2 to 6 (Francis): 51 long-period comets
• “... the value of n has ranged between 2 and 8 for various comets” (Meech and Svoreň 2004)
Francis, P. (2005). The Demographics of Long-Period Comets, Astrophys. J. 635, 1348-1361.
Vsekhsvyatskii, S. K., A.C. Raugh and M. A'Hearn (1998). Physical Characteristics of Comets, EAR-C-5-DDR-PCC-V1.0, NASA Planetary Data System. http://starbrite.jpl.nasa.gov/pds/viewProfile.jsp?dsid=EAR-C-5-DDR-PCC-V1.0
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Problems with Activity Index (n)
(Meech and Svoreň 2004)
• n should be 2 at very large r (bare nucleus) and very small r (all solar energy going into gas production); larger at intermediate r
• Gas production depends more strongly on r than dust → n is smaller for dusty comets
• Scattering phase function of coma and nucleus need to be taken into account.
Marsden, Sekanina, and Yeomans 1973
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Specifically, Francis assumes ...
based on Whipple (1978)
Dynamically new comets:
• Before perihelion passage: n = 2.44 ± 0.3
• After perihelion passage: n = 3.35 ± 0.27
Other comets:
• Before perihelion passage: n = 5.0 ± 0.8
• After perihelion passage: n = 3.5 ± 0.5
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These assumptions are necessary because LINEAR did not publish photometry of the comets and asteroids they discovered, so absolute magnitude is calculated from the discovery observation alone:
H = Hdis − 5 log10 Δ − 2.5n log10 r
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http://aerith.net/comet/catalog/2000A1/2000A1.html
Seiichi Yoshida: H = 3.8
JPL: 4.4 ± 0.7
Paul Francis: H = 8.13
Difference due to assumed values of n.
Comet with Largest Perihelion Distance(q = 9.74 AU)
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http://aerith.net/comet/catalog/2000W1/2000W1.html
Seiichi Yoshida: H = 13
JPL: 12.6 ± 1
Paul Francis: H = 10.44
Comet with Smallest Perihelion Distance(q = 0.32 AU)
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Seiichi Yoshida: H = 8.3
JPL: 9.4 ± 0.8
Paul Francis: H = 7.84
The Most Famous Comet in Francis’s Sample, C/1999 S4 (LINEAR)
(q = 0.77 AU)
http://aerith.net/comet/catalog/1999S4/1999S4.htmlThursday, October 20, 11
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C/1999 S4 (LINEAR)
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0
0.05
0.1
0.15
0.2
0 2 4 6 8 10
Frac
tion
of C
omet
s/AU
Perihelion Distance (AU)
Francis 2005
Perihelion Distance Distribution
Fit for True Distribution
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0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
4 6 8 10 12 14 16
Frac
tion
of C
omet
s with
Abs
olut
e M
agni
tude
H
Absolute Magnitude H
Absolute Magnitude Distribution
Francis 2005
Hb= 6 or 6.5b undetermined (Hughes: 2.29; Everhart 3.65)
f = 1.03 ± 0.09
bright
faintFit for True Distribution
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Hughes (2001)Comets since 18400.53 < q < 0.74 AU
Normalization: 0.53 comets/year with H < 6.5, q < 1 AU
H < 6.5
H > 6.5
Size distribution must steepen for very large nuclei
Hale-Bopp: 400-year event
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Complete List of Comets with RigorousDynamical Mass Determinations
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r q H dC/1729 P1 (Sarabat) 4.07 4.05 -3 170C/1577 V1 (Tycho) 0.28 0.18 -1.8 120C/1995 O1 (Hale-Bopp) 7.14 0.91 -1.3 100C/1746 P1 (de Chéseaux) 3.15 2.20 -0.5 80C/1811 F1 (Flaugergues) 2.72 1.04 0.0 70C/1743 X1 (de Chéseaux) 2.07 0.22 0.5 60C/1882 R1 (Cruls) 0.02 0.01 0.8 50C/1913 Y1 (Delavan) 4.24 1.10 1.1 50C/1433 R1 1.26 0.49 1.2 50C/1961 R1 (Humason) 5.25 2.13 1.5 40
r = heliocentric distance at discovery (AU); q = perihelion distance (AU); H = absolute magnitude; d = diameter (km), assuming log m = 20 - 0.4*H and density = 0.6 g/cm3
Actual diameter 60 ± 20
km
Intrinsically Brightest Comets (Kidger, based on Vsekhsvyatskii and Kronk)
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http://planetary.org/blog/article/00002780/
Next best way to calculate mass: measured volume + density (assumed or estimated fromnongravitational forces)
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14
14.5
15
15.5
16
16.5
17
17.5
18
6 8 10 12 14 16
log 1
0(N
ucle
us M
ass,
g)
Cometary Magnitude H
Halley
Wild 2
BorrellyTempel 1
Hartley 2
Density = 0.6 g/cm3 assumed for all comets
Fit to 5 comets: log10(mass, g) = 19.80 - 0.344 HWeissman’s relation: log10(mass, g) = 20 - 0.4 H
Note: Weissman’s relation is equivalent to flux proportional to mass, not surface area.
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Comet Typea
(AU)q
(AU) H d (km) ⍴(g/cm3) M (g)
1P/Halley HTC 17.8 0.6 5.5 ± 0.4 10.4 ± 2.0 0.5 ± 0.3 (3.2 ± 1.2) × 1017
9P/Tempel 1 JFC 3.1 1.5 13.1 ±1.1 6.0 ± 0.2 0.2 ± 0.1 (2.3 ± 1.6) × 1016
19P/Borrelly JFC 3.6 1.4 8.9 ± 2 4.8 ± 0.4 0.05 ± 0.04 (2.7 ± 2.1) × 1015
81P/Wild 2 JFC 3.5 1.6 8.6 ±1 3.8 ± 0.1 0.3 (+0.5, -0.3) 8.1 (+17, -8) × 1015
103P/Hartley 2 JFC 3.5 1.1 14.6 ±1 1.16 ± 0.04 0.22 (+0.66, -0.04) 1.8 (+5.4, -0.3) × 1014
Masses and densities from Sosa and Fernández (2009), except for 103P/Hartley 2
Densities of 5 Comets Visited by Spacecraft
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Hale-BoppSL9 ρ = 0.6 g/cm3
Saturn’s coorbital satellites
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10
100
100 1000
Mas
s in
Out
er O
ort C
loud
(Ear
th M
asse
s)
Diameter Cutoff (km)
Hughes
Everhart
log(m) = 20 - 0.4H (Weissman); density = 0.6 g/cm3
Assume 1011 comets with H < 6.5 (d > 9.3 km)
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