Cometary Orbit Dynamics & Physical Structure and Evolution Kuliah AS3141 Benda Kecil dalam Tata Surya Budi Dermawan Prodi Astronomi 2006/2007

Cometary Orbits Enormous range of periods Correlation between periods and inclinations Classifications by means of period and Tisserand parameter

Orbital parameters Orbital energy z = 1/a Period P = a 3/2 Perihelion distance q = a(1-e) Inclination i Tisserand parameter

Orbital Classification By means of period P short-period comets: P<200 yr long-period comets: P>200 yr By means of Tisserand parameter T (for short-period comets) Jupiter Family: 2<T<3 Halley Types: T<2 Short-period comets

Periods and Inclinations Long-period comets have a fairly uniform distribution of cos i from -1 to +1 Comets with 20 0) Comets with P<20 yr (≈Jupiter Family) only have low inclinations

Original and future orbits Due to planetary perturbations, z (and therefore P) is quite unstable for long-period comets Original orbits = orbits before entry into the planetary system Future orbits = orbits after exit from the planetary system

The Oort Cloud (1) Future orbits are often hyperbolic: Ejection of comets into interstellar space Original orbits show an extreme pile-up at yr) This is the “Oort peak”, and the comets are newcomers from the Oort Cloud

The Oort Cloud (2) Number of comets in the cloud : Observed rate of perihelion passages within 1 AU ~ 1/yr Average orbital period for a  AU ~ 4·10 6 yr  the number of comets with q<1 AU ~ 4·10 6 The distribution of q is rather flat  the number of comets with q<25000 AU ~ 1  10 11

Orbital transfer scenario Observed orbits Injection mechanisms Low perihelion from the Oort cloud distances Loss mechanisms But this is a false or incomplete picture!

Cometary orbital evolution The comets were formed in quasi-circular orbits in the region of the giant planets

Cometary orbital evolution After the formation of the giant planets, a transneptunian disk acted as a source to replenish both external and internal regions with comets

Cometary orbital evolution Now the transneptunian disk is depleted but continues to provide comets along with the Oort cloud, whose external regions have a nearly isotropic orbital distribution

Cometary Dynamics Sources of perturbations : Planetary perturbations Stellar encounters with the solar system Encounters with GMCs (Giant Molecular Clouds) Galactic tidal perturbations Nongravitational effects

Planetary perturbations Close encounters, especially with Jupiter: Gravitational scattering Indirect perturbations (long-period) Mean motion resonance (short-period) Secular oscillations of perihelion distance and inclination (Kozai cycles) Secular resonances

Encounter frequencies On a time scale of 10 9 yr, a GMC encounter may upset the whole Oort Cloud On a time scale of 10 8 yr, a stellar encounter within 10 4 AU may upset the inner core of the Oort Cloud and cause a cometary shower On a time scale of 10 6 yr, stars pass through the outer parts of the Oort Cloud

Galactic tides The disk tide Grav. force toward the Galactic midplane Causes oscillations of perih. distance and Galactic inclination The radial tide Grav. Force toward the Galactic centre Causes both oscillations of (q,i) and changes of semimajor axis

Capture of the Jupiter Family Low-inclination routes with T p ≈ 3 Handing down process: Neptune-Uranus-Saturn- Jupiter Most efficient source: the Scattered Disk

Capture of Halley Types Subsequent perihelion passages give uncorrelated perturbations ∆z Random walk along the z axis with absorbing wall at z=0 A small fraction will reach short-period orbits

Physical Structure Main components : Nucleus (typical size ~1-10 km) Coma (visual coma ~10 5 km) Tail(s) (length sometimes ~10 8 km)

Cometary nuclei Determination of sizes : Close-up imaging by spacecraft Separation of nucleus from inner coma by high- resolution remote imaging Photometry of the quasi-nucleus of inactive comets Resolution of the albedo ambiguity by simultaneous thermal IR radiometry

Recent spacecraft imaging NASA DS-1 imaged the nucleus of 19P/Borrelly NASA Stardust imaged the nucleus of 81P/Wild 2

Recent spacecraft imaging Pictures of the nucleus of comet 9P/Tempel 1 taken by the NASA Deep Impact spacecraft on 4 July, 2005 Upper image: the impact event Lower image: “geological” structure of the nucleus with features similar to impact craters and landslides

Sizes, albedos, active fractions CometRadius (km) Visual albedo Active fraction Tempel 1 Borrelly Neujmin 1 Arend-Rigaux Wild 2 Halley

Jupiter Family size distribution “Complete” sample only for small perih. distances The cumulative size distribution is a power law with index -2.8 Nuclei smaller than ~0.5 km radius seem to be strikingly underabundant

The active fraction (1) Thermal model gives outgassing flux Z (mol. m -2 s -1 ) around a sphere at a given distance from the Sun The water production rate for an active nucleus with radius R is Q a = 4πR 2 If the observed water production rate at the same distance is Q o, the active fraction f a = Q o / Q a

The active fraction (2) Interpretations of f a < 1:  The outgassing is limited to active spots covering a fraction f a of the area  The thermal model overestimates Z Interpretation of f a > 1:  The thermal model is inappropriate

Quenching of the outgassing Formation of large “dust grains”: the gas drag does not overcome the nuclear gravity and/or cohesion These grains accumulate until they form a coherent “dust mantle” Gradual enrichment of the refractory component in the surface layer due to subsurface ice sublimation The vapor has to flow through pores in this layer before it escapes into the coma

Evolution of cometary nuclei Erosion mechanisms : -Sublimation of ice with entailment of the dust component -Splitting into major fragments -Surface layer fragmentation Deactivation mechanism : Quenching of the outgassing

Structure of cometary nuclei Density = Mass / Volume Volume determinations: Spacecraft flybys 1P/Halley V=500 km 3 (Giotto, Vega) 19P/Borrelly V=60 km 3 (DS 1) 9P/Tempel 1 V=130 km 3 (Deep Impact) Visual+thermal photometry (few cases)

Nongravitational effects Timing of perihelion passage ∆P (relatively easy to measure) Turning of the orbit in space ∆  (difficult to measure)

Mass/Density determination Force = Mass x Acceleration Nongravitational effect = Integral of acceleration Model the momentum flow of outgassing: Force Results: ∆P M (kg)  (g/cm 3 ) 1P/Halley 4.1 d 2  P/Borrelly d 1.5  P/Tempel d 6 

Density and porosity Ice density: 1 g/cm 3 Dust density: 2 g/cm 3 Hence, compact density of 50/50 ice/dust mixture: 1.5 g/cm 3 Observed densities of g/cm 3 imply porosities of %

Activity profile (1) Consider a spherical, isothermal nucleus made of H 2 O ice. Assume it to be a black body. Place it at different distances r from the Sun. Global energy balance: Insolation = Irradiation + Latent heat of sublimation π R 2 S/r 2 = 4π R 2 [  T 4 + L Z(T)] for H 2 O:

Activity profile (2) Near the Sun, sublimation dominates the heat loss. Far away, irradiation dominates. The transition between the two regimes occurs at r ≈ 2.5 AU, for H 2 O ice.

Cometary comae Gas particles (molecules, radicals, atoms, ions, electrons) Solid grains (dust)

Coma gases Primary source: Outflow from the nucleus Parent molecules: H 2 O, CO 2, CO, CH 3 OH, HCOOH, etc. Secondary source: Release of molecules from coma grains

Cometary production rates Observed molecular production rates in comets, relative to H 2 O The grey part indicates the range of variation from comet to comet The number of comets observed for each molecule is given to the right Crovisier (2006)

The collisional region Knudsen layer: A gas in thermal equilibrium is established Thickness: about 10 mean free paths Hydrodynamic regime: The gas expands radially outward, and cools adiabatically, until it gets too rarefied Thickness: out to exospheric limit

The free-flow region Molecular zone: until the molecules get photodissociated or otherwise destroyed Radical zone: until the radicals get photodissociated or otherwise destroyed Atomic halo

Observed spectral features (1) OH 18 cm Hyperfine splitting of the ground state CO J(2-1) 2.6 mm Rotational transition Silicates µm Organics 3.4 µm C-H stretching

Observed spectral features (2) [OI] 630 nm Prompt emission after H 2 O photodissociation C 2 Swan bands 500 nm, CN 390 nm, OH 308 nm Sunlight fluorescence

The ion tail

The dust tail The dust tail forms a curved pattern outward from the Sun with a distribution of grains that reflects the ejection history and mass spectrum The largest grains leave the comet at very low speeds and form a dust trail along the cometary orbit