The Population and Mass of the Oort Cloud

Transcription

1 The Population and Mass of the Oort Cloud Luke Dones Southwest Research Institute Boulder, Colorado Megan E. Schwamb Yale Center for Astronomy and Astrophysics and Department of Physics Yale University New Haven, Connecticut

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3 Population perihelion distance absolute magnitude inverse semi-major axis Francis (2005)

4 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: AU Broad range of absolute magnitudes:

5 Perihelion Distance Distribution 0.2 Fraction of Comets/AU Perihelion Distance (AU) raw data from Francis 2005

6 0.18 Absolute Magnitude Distribution Fraction of Comets with Absolute Magnitude H Absolute Magnitude H raw data from Francis 2005

7 Definition of Absolute Magnitude (H) Flux from comet Δ -2 r -n H dis: 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.

8 What is the value of n ( activity index or photometric index )? Flux from comet Δ -2 r -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, 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.

9 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

10 Specifically, Francis assumes... 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 based on Whipple (1978)

11 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 = H dis 5log 10 Δ 2.5nlog 10 r

12 Comet with Largest Perihelion Distance (q = 9.74 AU) Seiichi Yoshida: H = 3.8 JPL: 4.4 ± 0.7 Paul Francis: H = 8.13 Difference due to assumed values of n.

13 Comet with Smallest Perihelion Distance (q = 0.32 AU) Seiichi Yoshida: H = 13 JPL: 12.6 ± 1 Paul Francis: H =

14 The Most Famous Comet in Francis s Sample, C/1999 S4 (LINEAR) (q = 0.77 AU) Seiichi Yoshida: H = 8.3 JPL: 9.4 ± 0.8 Paul Francis: H =

15 C/1999 S4 (LINEAR)

16 Perihelion Distance Distribution 0.2 Fraction of Comets/AU Perihelion Distance (AU) Francis 2005 Fit for True Distribution

17 0.18 Absolute Magnitude Distribution Fraction of Comets with Absolute Magnitude H bright Absolute Magnitude H Francis 2005 Fit for True Distribution Hb= 6 or 6.5 b undetermined (Hughes: 2.29; Everhart 3.65) f = 1.03 ± 0.09 faint

18 H > 6.5 H < 6.5 Hughes (2001) Comets since < q < 0.74 AU Normalization: 0.53 comets/year with H < 6.5, q < 1 AU Hale-Bopp: 400-year event Size distribution must steepen for very large nuclei

19 Complete List of Comets with Rigorous Dynamical Mass Determinations

20 Intrinsically Brightest Comets (Kidger, based on Vsekhsvyatskii and Kronk) r q H d C/1729 P1 (Sarabat) C/1577 V1 (Tycho) C/1995 O1 (Hale-Bopp) C/1746 P1 (de Chéseaux) C/1811 F1 (Flaugergues) C/1743 X1 (de Chéseaux) C/1882 R1 (Cruls) C/1913 Y1 (Delavan) C/1433 R C/1961 R1 (Humason) Actual diameter 60 ± 20 km r = heliocentric distance at discovery (AU); q = perihelion distance (AU); H = absolute magnitude; d = diameter (km), assuming log m = *H and density = 0.6 g/cm 3

21 Next best way to calculate mass: measured volume + density (assumed or estimated from nongravitational forces)

22 Note: Weissman s relation is equivalent to flux proportional to mass, not surface area. 18 Fit to 5 comets: log 10 (mass, g) = H Weissman s relation: log 10 (mass, g) = H Density = 0.6 g/cm 3 assumed for all comets 17.5 Halley log 10 (Nucleus Mass, g) Borrelly Wild 2 Tempel Hartley Cometary Magnitude H

23 Densities of 5 Comets Visited by Spacecraft Comet Type a (AU) q (AU) H d (km) (g/cm 3 ) M (g) 1P/Halley HTC ± ± ± 0.3 (3.2 ± 1.2) P/Tempel 1 JFC ± ± ± 0.1 (2.3 ± 1.6) P/Borrelly JFC ± ± ± 0.04 (2.7 ± 2.1) P/Wild 2 JFC ±1 3.8 ± (+0.5, -0.3) 8.1 (+17, -8) P/Hartley 2 JFC ± ± (+0.66, -0.04) 1.8 (+5.4, -0.3) Masses and densities from Sosa and Fernández (2009), except for 103P/Hartley 2

24 Saturn s coorbital satellites SL9 Hale-Bopp ρ = 0.6 g/cm 3

25 Assume comets with H < 6.5 (d > 9.3 km) log(m) = H (Weissman); density = 0.6 g/cm 3 Mass in Outer Oort Cloud (Earth Masses) 100 Hughes Everhart Diameter Cutoff (km)