* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Lecture 21: Planet formation III. Planet
Aquarius (constellation) wikipedia , lookup
Discovery of Neptune wikipedia , lookup
Astrobiology wikipedia , lookup
Rare Earth hypothesis wikipedia , lookup
Planetary system wikipedia , lookup
Planets in astrology wikipedia , lookup
Formation and evolution of the Solar System wikipedia , lookup
Planet Nine wikipedia , lookup
Late Heavy Bombardment wikipedia , lookup
Extraterrestrial life wikipedia , lookup
History of Solar System formation and evolution hypotheses wikipedia , lookup
Star formation wikipedia , lookup
Satellite system (astronomy) wikipedia , lookup
Planets beyond Neptune wikipedia , lookup
IAU definition of planet wikipedia , lookup
Exoplanetology wikipedia , lookup
Definition of planet wikipedia , lookup
Timeline of astronomy wikipedia , lookup
Lecture 21: Planet formation III. Planet-disk interactions Outline • Definition of a planet • Properties of exoplanets • Formation models for exoplanets • gravitational instability model • core accretion scenario • migration Armitage 2010, “Astrophysics of Planet Formation” & arXiv notes Udry, Fischer and Queloz 2007, PPV PPVI: Chapters by Raymond, Baruteau, Benz, Fischer etc. Main formation scenarios • Core accretion scenario 1. Coalescence of solid particles. Growth from dust to rocky planets. 2. Big rocky planets (>= 10 M⊕) accrete gas and form gas planets Core Accretion Scenario The core accretion model for gas giant formation rests on one assumption: a seed of a planet or core forms rapidly enough that it can exceed a certain critical mass prior to the dissipation of the gas disk. If this condition is satisfied, it can be shown (e.g. Perri & Cameron 1974) that the core triggers a hydro-dynamical instability that results in the onset of rapid gas accretion on to the core. Since the critical core mass is typically of the order of 10 Mearth, the end result is a largely gaseous but heavy element enriched planet that at least qualitatively resembles Jupiter or Saturn. The main phases in the formation of giant planets via core accretion are: Core formation Hydrostatic growth Runaway growth Termination of accretion Core Accretion Scenario Armitage 2010 Core Accretion Scenario Core formation: A solid protoplanet (“core”) grows via a succession of twobody collisions until it becomes massive enough to retain a significant gaseous atmosphere or envelope (similar to terrestrial planet formation). Hydrostatic growth: Initially the envelope surrounding the solid core is in hydrostatic equilibrium. Over time, both the core and the envelope grow until the core exceeds a critical mass. Runaway growth: Once the critical mass is exceeded a runaway phase of gas accretion ensues. The rate of growth is “supply-limited” and defined by the hydrodynamic interaction between the growing planet and the disk. Termination of accretion: Eventually the supply of gas is exhausted, either as a consequence of the dissipation of the entire protoplanetary disk or, more probably, as a consequence of the planet opening up a local gap in the disk. Accretion tails off and the planet commences a long phase of cooling and quasi-hydrostatic contraction. Core Accretion Scenario The first fully consistent time-dependent models of giant-planet growth were published by Pollack et al. (1996): Truncated by gap formation Σ 1. Embryo formation (runaway) 2. Embryo isolation 3. Rapid gas accretion Pan Planetary Migration The presence of a planet in a protoplanetary disk (PPD) modifies the distribution of gas in the planet vicinity. Gravitational interaction between the planet and the non-uniform arrangement of gas generates torques that alter the planet’s orbit. This causes a planet to migrate toward or away from the star and also dumps or excites the orbital eccentricity and inclination. The direction and rate of migration vary depending on the mass of the planet and the local properties of the gas disk. Planetary Migration (Chambers 2009) Type I migration The perturbation the planet causes is small enough that it does not alter the background structure of the gas disk. It affects Earth-mass planets, which induce a linear perturbation in the surrounding disk. The migration rate is proportional to the mass of the planet and the surface density of the disk. Time scale of inward Type I migration (1 solar mass star): ~105 yr. Planetary Migration (Chambers 2009) Type II migration As planets become more massive, the Type I torque that they exert on the disk increases and eventually starts to modify the disk structure in the neighborhood of the planet. Since the interaction adds angular momentum to the disk exterior to the planet and removes it from the interior gas, the overall effect is that a strong torque repels gas from the vicinity of the planet orbit, creating a gap. It affects Jupiter-mass planets. The planet’s motion becomes tied to the viscous evolution of the disk. 9 Viscous torques Since all molecules revolve around the protostar in ~Keplerian orbits, those closer to the center move faster than those farther away. Collisions speed up the outer molecules, driving them outwards and slow down the inner molecules, which falls towards the center. The net effect is that most of the matter diffuses inwards, angular momentum is transferred outwards and the disk as a whole spreads. Viscous torques The disk evolves on a diffusion timescale (Armitage II, C, 4): t diff 2 rdisk = νv rdisk is the disk radius and νv is the molecular viscosity. Considering thermal motions: € ν v = l fp c s l fp ≡ mean free path of the molecule = 1 nσ mol c s ≡ sound speed € Molecular viscosity is far too small to produce significant viscous evolution over the lifetime of a PPD. € Viscous torques If turbulence is present, turbulent fluid motions will result in the macroscopic mixing of fluid elements at neighboring radii, which can act as an “effective” or “turbulence” viscosity. The magnitude of this turbulent viscosity can be estimated from dimensional arguments: • If the turbulence is approximately isotropic, the outer scale of the turbulent flow is limited to be no larger than the smallest scale in the disk (the disk scale-height, Hz). • The velocity of the turbulent motions can be limited to be no larger than the sound speed cs, since supersonic motions result in shocks and rapid dissipation. Viscous torques We therefore write the turbulent viscosity in the form: ν v = α v c sH z αv is a dimentionless quantity, known as the Shakura-Sunyaev α parameter, that measures the efficiency of angular momentum transport due to turbulence (typically between 10-2 and 10-4; Shakura & Sunyaev € 1973). With the above equation, it is possible to specify the viscosity in terms of local disk quantities and then compute the local disk structure. Limitations: α may vary with temperature, density and composition of the disk gas, but it is assumed constant to proceed with the calculation! Planetary Migration 15 Disk-Planet Interactions Disk-Planet Interactions Model Comparison Outstanding Questions Lissauer & Stevenson 2007, PPV: !How rapid do solid cores accrete in the giant planet formation region? !How does a (growing or formed) giant planet interact with the surrounding protoplanetary disk ? (predicted migration rates are too rapid for the survival of all the giant planets known - are disks significantly more massive??). (Chambers 2009) 20 Some Recent Exoplanet Results: 2011: the Earth-like exoplanet! http://upload.wikimedia.org/wikipedia/commons/0/07/Kepler-22b_System_Diagram.jpg Potentially Habitable Worlds http://phl.upr.edu/projects/habitable-exoplanets-catalog Kepler 62 Kepler 62e 1.61 Earth Radii 1.2 times solar flux Kepler 62f 1.41 Earth Radii 0.41 times solar flux NASA/Ames/JPL-Caltech Gliesse 667C 4 – 8 Earth masses 2 – 4 Earth masses 3 – 5 Earth masses Recent Exoplanet Results: 2012: http://www.huffingtonpost.com/2012/07/18/alien-planet-ucf-101-nasa-telescope-lava_n_1683793.html 28 Alpha Centauri B has an Exoplanet Dumusque et al. (2012) Frequency of Planets - One in 6 stars has an Earth or Super-Earth sized planet with a period of less than 50 days (Petigura et al. 2013) - 50% of all Sun like stars have a planet, of any size, with a period less than 85 days – roughly the period of Mercury (Fressin et al. 2013) - Twice as many planets in the galaxy as there are stars (Cassan et al. 2012) - 94% chance of an Earth like planet within 10 light years (Kopparapu 2013)