Lecture 20: Planet formation II. Clues from Exoplanets

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1 Lecture 20: Planet formation II. Clues from Exoplanets 1 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.

2 Definition of Planet Although controversial, we adopt the definition that planets are not sufficiently massive for fusion to ever consume a majority of their deuterium ( 13 M J ). Brown dwarfs (13 M J < M < 75 M J ) are large enough for deuterium fusion but not massive enough to sustain fusion of hydrogen. Gravitational contraction is a major source of the energy radiated by giant planets and brown dwarfs. These objects shrink and cool as they age, so there is not a unique relationship between luminosity and mass. Stars log L/L! log age (yr) } } } Brown dwarfs Planets Burrows et al. 1997, ApJ, 491, 856 Kulkarni 1997, Science, 276, Observed properties of exoplanets The first planet known to orbit a main sequence star other than the Sun is the M sin i = 0.47 M J, P orb =4.23 days companion discovered to orbit the star 51 Pegasi by Mayor & Queloz (1995): Since then, we learned that gas giant planets are common and that the planetary formation process may produce a surprising variety of configurations: masses considerably larger than Jupiter Planets moving on highly eccentric orbits Planets orbiting closer than 10R * Planets in resonant multi-planet systems Planets orbiting components of stellar binaries Udry, Fischer, Queloz 2007, PPV Radial velocity measurements of the star 51 Pegasi (points) as a function of phase of the orbital fit (solid line): P=4.230 days, K=55.3 m/s, e=0.01.

3 Detecting extrasolar planets: radial velocity measurements At the telescope, the change in the wavelength of light coming from a star over the course of days, months, and years is measured. This changing wavelength is the Doppler shift of the light, resulting from the star orbiting a common center of mass with a companion planet. For example, Jupiter's gravitational pull causes the Sun to wobble around in a circle with a velocity of 12 meters per second. Detecting extrasolar planets: radial velocity measurements

4 Radial Velocity Detection Bias Observed properties of exoplanets Separation-eccentricity diagram for extra-solar planets as discovered by The size of the dots is proportional to the minimum mass of the planet candidate: M p sin i 18 M J. Udry et al. 2007, PPV The numerous giant planets orbiting very close to their parent stars (P < 10 days), i.e. hot Jupiters were unexpected before the first exoplanet discoveries. In fact, the standard model (Pollack et al. 1996) suggests that giant planets form first from ice grains in the outer region of the system where the temperature of the nebula is cool enough " migration? Disk-instability in-situ-formation?

5 Observed properties of exoplanets Armitage (2010) Distribution of exoplanets (~2010) Armitage (2010)

6 exoplanets.org 12/9/ Planet Mass [Jupiter Mass] V E Separation [Astronomical Units (AU)] J S U N Radial velocity Transit Micro-lensing Imaging Kepler Summary of Exoplanet Search Methods Radial velocity Transit Micro-lensing Direct Imaging Astrometry

7 Observed properties of exoplanets Even considering selection effects (which prevent detection of low mass planets and those planets with long orbital periods) the extrasolar planet distribution is strikingly different from what might be expected based on the Solar System: 1. Hot Jupiters: population of massive planets detected at radii a < 0.1 AU. Their frequency around main sequence Sun-like stars is ~ 1%. They have almost circular orbits (tidal circularization?). T ~ 1500 K. 2. With improving survey sensitivity: the mass distribution of close-in planets extends to masses below that of the giants in the Solar System. These planets are often dubbed super Earths : i.e. from ~1 to 10 Earth masses. Observed properties of exoplanets 3. At larger orbital radii, extrasolar giant planets do not have nearly circular orbits! The eccentricity distribution is broad, and both Jovian planets (planets at a few AU with close to circular orbits) and very eccentric planets with almost cometary orbits e > 0.9 are detected. 4. Within the currently detectable region of parameter space, the planet mass function declines toward large masses, while the number of planets per logarithmic interval of orbital radius, dn p /d log(a), increases toward large a up to the radius where selection effects cut in.

8 Observed properties of exoplanets 5. Multiple planet systems are found to be common: of the 797 stars with planets, 174 are multi-planet systems (see With candidates, 4544 exoplanets. H8799 Example of direct imaging Observed properties of exoplanets Planet Metallicity Correlation P planet ~ ( N Fe / N H ) 2 Abundance Analysis of 1000 stars on planet search Fischer & Valenti 2005

9 Comparison of Solar System with exoplanets ; & ~100AU orbit planets seen. Main formation scenarios Gravitational instability in disk 1. Direct formation of gas giant planets 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

10 Gravitational Instability Self-gravity is an important potential mechanism for planetesimal formation. Within a disk, the self-gravity of the disk gas always has a tendency to form denser clumps. Pressure forces and shear tend to oppose clump formation. To approximately estimate the conditions under which self-gravity wins over these stabilizing effects, we require that the time scale for collapse be shorter than the time scales on which sound waves can cross a clump, or share destroy it. Remember that: P = nk B T = c s 2 ρ, with c s = k B T µm H the sound speed. Gravitational Instability Consider a forming clump of scale Δr and mass Such clump would collapse on the free-fall time scale: t ff = 3π 32Gµm H n ~ Δr3 Gm ~ Δr πgσ. Stabilizing influences that may prevent collapse are pressure and shear. The time scale for a sound wave to cross the clump is: t p ~ Δr c s.

11 Gravitational Instability The shear time scale (the time scale required for a clump to be sheared azimuthally by an amount Δr) is: t shear = 1 # % r $ dω dr & ( ' 1 ~ Ω 1. The disk will be marginally unstable to clump formation if the free-fall time scale on the scale where shear and pressure support match is shorter than either t p or t shear. Setting all three time scales equal via tff 2 =tshear tp, we obtain a condition for instability in the form: πgσ c s Ω. At a given radius (i.e. at fixed Ω) the disk will be unstable if it is massive (large Σ) and/or cool (small c s ). Gravitational Instability A more formal analysis (Toomre 1964) gives the same result. The stability of a disk of either gas or stars is controlled by the Toomre Q parameter: c s sound speed κ epicyclic (radial) frequency at which a fluid element oscillates when perturbed from circular motion (in a nearly Keplerian disk, κ ~ Ω, the rotational angular speed). Σ surface mass density of the disk Q T = c sκ πgσ < 1 For axisymmetric disturbances, disks are stable when Q T > 1.

12 Gravitational Instability Density contours for a 0.09 M! disk around a 1 M! star. A multi-jupiter mass clump forms by 374 yr. Boley & Durisen (2008) 0.17 M! Boss 2000, ApJ See also Durisen et al. 2007, PPV and references therein How and when does GI arise in real disks? Possiblities include: #The formation of a massive disk from protostellar core collapse #Clumpy infall onto a disk #Cooling of a disk from stable to unstable state #Slow accretion of mass #Perturbation by a binary companion #Close encounters with other star/disk systems #Accumulation of mass in a magnetically dead zone

13 How and when does GI arise in real disks? A disk evolving primarily due to Magneto-Rotational Instabilities (MRIs; Balbus & Hawley 1998) may produce rings of cool gas in the disk midplane where the ionization fraction drops and quell MRI s " onset of GI. How and when does GI arise in real disks? BUT hard to explain the enhanced abundance of heavy species in giant planets disks may need to be too massive (?) hard to account for small bodies problems with differentiation in planet composition

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