Lecture 19: Planet Formation I. Clues from the Solar System 1 Outline The Solar System:! Terrestrial planets! Jovian planets! Asteroid belt, Kuiper belt, Oort cloud Condensation and growth of solid bodies The minimum mass solar nebula
The Solar System Planets and most of the other bodies of the solar system do orbit the Sun in about the same plane, called the ecliptic plane. Not to scale! The Solar System: content e 4
The Solar System: the terrestrial planets Mercury, Venus, Earth, and Mars share many similar features. Small compared with the huge planets beyond them, these inner planets also have rocky surfaces surrounded by relatively thin and transparent atmospheres. Together, we call these four the terrestrial planets (from the Latin terra, meaning earth). Earth R=6378 km M E =6.0 10 24 kg Mars R=3397 km M=0.11 M E Mercury R=2440 km M=0.06 M E Venus R=6052 km M=0.82 M E 5 The Solar System: the Jovian planets Jupiter, Saturn, Uranus, and Neptune are giant planets; they are also called the jovian planets. They are much bigger, more massive, and less dense than the inner, terrestrial planets. Their internal structure is entirely different from that of the four inner planets. D = 5.2 AU R = 71,492 km = 11.2 R earth M = 317.8 M earth 6 T = 165 K (cloudtops)
The Solar System: the Jovian planets The Solar System
The Solar System: Other constituents 9 http://www.telegraph.co.uk/science/space/ 8052528/Water-carried-on-asteroids-are-common.html 10
11 http://www.sciencedaily.com/releases/2010/10/101007114114.htm Herschel makes a splash and fuels the controversy of the origin of Earth's water. H 2O HDO Hartogh et al. 2011, Nature,12 478, 218
HDO/H2O in Jupiter family comet = HDO/H2O in oceans! The Solar System: Other constituents
The Solar System: Other constituents The Solar System: 16
The Formation of the solar system: Condensation and growth of solid bodies The mechanical and chemical processes related to grain agglomeration are poorly understood. Loosely packed fractal structures which are held together by Van der Waals forces may be formed. IDP Interplanetary Dust Particle Dominik et al. 2006, PPV The Formation of the solar system: Condensation and growth of solid bodies The motions of small grains in a protoplanetary disk are strongly coupled to the gas. For solid particles smaller than 1 cm, the dust-gas coupling is well described by Epstein s drag law: FD = A ρ g vc s A projected surface area of the body ρg gas density v velocity of the body with respect to the gas cs mean thermal velocity of the gas
The Formation of the solar system: Condensation and growth of solid bodies When grains condense, the vertical component of the star s gravity causes the dust to sediment out towards the midplane of the disk. Current models (appropriate for the solar nebula) suggest that the bulk of solid material was able to agglomerate into bodies of macroscopic size within 10 4 yr at 1 AU. Most of the bodies confined to a thin region. The Formation of the solar system: Condensation and growth of solid bodies Growth from cm-size particles to km-sized planetesimals depends on the relative motions between the various bodies. The motions of (sub-)cm-sized material are coupled with the gas. The gas is partially supported against stellar gravity by a pressure gradient in the radial direction " gas circles the star slightly less rapidly than the keplerian rate. The effective gravity felt by the gas is: g eff = GM * r 2 + 1 ρ g dp dr acceleration due to pressure gradient For circular orbits, the effective gravity must be balanced by centrifugal acceleration. Considering that the pressure is much smaller than gravity, one finds that the gas rotates ~0.5% slower than the keplerian speed. 20 In the next slides we will demonstrate this.
The Formation of the solar system: Condensation and growth of solid bodies Let P be the gas pressure, ρ its density and r the distance from the nebular axis. The central gravity g and the circular Keplerian orbital velocity V K are related by g = GM! r 2 = V 2 K r. In a reference frame rotating with the gas, the residual gravity is Δg = 1 ρ g dp dr, which is the condition for hydrostatic equilibrium. [see Weidenschilling (1977, MNRAS)] The Formation of the solar system: Condensation and growth of solid bodies If V g is the rotational velocity of the gas, g eff = V 2 g r = V 2 K r + Δg. Therefore, the deviation of the gas velocity from the circular orbital velocity is: ΔV = V K V g, V g = V K 2 + rδg with = V 2 K + Δg V 2 K g = V K 1+ Δg g
The Formation of the solar system: Condensation and growth of solid bodies If Δg/g << 1: and 1+ Δg g ~ 1+ 1 Δg 2 g, $ ΔV = V K V g ~ V K V K 1+ Δg ' $ Δg' & ) = V K & ). % 2g( % 2g( Over some range of r, the pressure can always be approximated by a powerlaw: P = P 0 (r / r 0 ) -a. Therefore, for an ideal gas: Δg = 1 dp ρ g dr = a nk T B ρ g r = ak B T µm H r The Formation of the solar system: Condensation and growth of solid bodies Example: assuming M = 1 M!, a = 2, T = 300 K and r = 5 AU: Δg 2g = 5.8 10 3 Therefore, the gas rotates ~0.5% slower than the keplerian speed.
The Formation of the solar system: Condensation and growth of solid bodies Large particles thus encounter a headwind which removes angular momentum and causes them to spiral inward toward the star. Small grains drift less. A meter-sized body at 1 AU would approach the Sun in ~ 100 yr! As a consequence of the difference in velocities, small (sub-)cm sized grains can be swept up by the larger bodies, while gas drag on the meter-sized planetesimals induces considerable radial motions. The material that survives to form planets must complete the transition from cm- to km- size rather quickly!! unless the material is confined to a thin dust-dominated subdisk in which the gas is dragged along at the same Keplerian velocity. Two alternative hypotheses describe the growth through this size range: The Formation of the solar system: Condensation and growth of solid bodies 1. If the nebula is quiescent, the dust and small particles settle into a layer thin enough to be gravitationally unstable to clumping, and planetesimals are formed. The planetesimals produced have sizes of the order ~ 1 km. 2. In a turbulent nebula, growth continues via simple two-body collisions. The growth of solid bodies from mm to km size must occur very quickly, but the related physics is poorly understood. Molecular forces can lead to ~1 km-sized planetesimals by coagulation (van der Waals binding energies [~10 3 erg g -1 ] ~ gravitational binding energy of a 1 km body). Then, when size 1 km, gravity takes over and mutual gravitational perturbations become important.
The Solar System: -Material within the disk condenses into several large chunks of material called planetesimals. -These collide with other planetesimals and coalesce into larger bodies, eventually forming planets. -Since the Sun and planets all form from the same cloud all rotate in the same direction as initial cloud. -Planets rotate counter-clockwise around the Sun. -Also planets and Sun rotate counterclockwise about their axes, -with the exception of Venus which rotates clockwise (retrograde motion) The Solar System: 28
The Solar System: 29 The Solar System: The snowline r snow 30
The Solar System: 31 The Solar System: T C material, further away both lecture 9 32
The Solar System: [1 Pa = 1 N/m 2 = 10 5 bar = 9.8692 10 6 atm] 33 The Solar System: 34
The Solar System: 35 The Solar System: 36
The Solar System: 37 The Solar System:
Summary The Solar System: Terrestrial planets, Jovian planets, Asteroid belt, Kuiper belt, Oort cloud. Problems with the condensation and growth of solid bodies from cm- to kmsize (headwind on large particles) Minimum Mass Solar Nebula 39