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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Thursday, October 20, 11

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

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Frac

tion

of C

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s/AU

Perihelion Distance (AU)

raw data from Francis 2005

Perihelion Distance Distribution

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0

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4 6 8 10 12 14 16

Frac

tion

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omet

s with

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olut

e M

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tude

H

Absolute Magnitude H

Absolute Magnitude Distribution

raw data from Francis 2005Thursday, October 20, 11

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

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

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tion

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olut

e M

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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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14.5

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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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