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Astronomy 340 Fall 2005

Astronomy 340 Fall 2005. 6 December 2005 Class #27. Review. What are the orbital differences between classical and resonant KBOs? How does the distribution of particle size differ between that found in the rings of Saturn and the population of KBOs? Generating a global magnetic field.

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Astronomy 340 Fall 2005

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  1. Astronomy 340Fall 2005 6 December 2005 Class #27

  2. Review • What are the orbital differences between classical and resonant KBOs? • How does the distribution of particle size differ between that found in the rings of Saturn and the population of KBOs? • Generating a global magnetic field

  3. Review • What are the orbital differences between classical and resonant KBOs? • How does the distribution of particle size differ between that found in the rings of Saturn and the population of KBOs? • Generating a global magnetic field • Rotation • Fluid, conducting region • covection

  4. Planetary Magnetic Field • Flavors of global magnetic field

  5. Planetary Magnetic Field • Flavors of global magnetic field • Remnant  solidified rocks (e.g. magnetite) • Dynamo • Induced by solar wind • Terrestrial Planets

  6. Planetary Magnetic Field • Flavors of global magnetic field • Remnant  solidified rocks (e.g. magnetite) • Dynamo • Induced by solar wind • Terrestrial Planets • Moon’s B-field  associated with crater basins (youngest material) • Mars  residual  did it once have a dynamo? • Venus  lacks current B-field  slow rotation?

  7. Earth’s Dynamo • Differentiation • Solid inner core, liquid outer ccore • Viscosity – need liqud H2O for liquid Fe at those conditions • Convective velocity ~10 km s-1 • Cooling of the Core • Convection  still partially driven by chemical convection • conduction

  8. Earth’s Dynamo • B-field amplified via twisting (convection + rotation) at core-mantle boundary • B ~ (2ρΩ/σ)1/2 • Other planets? Probably similar • Note alignment  what’s up with Uranus? • Jupiter • Rotation  yes • Convection  yes • Conducting medium  yes  metallic H

  9. Jupiter’s Magnetic Field • Planck Function & Tb • B = 2kT/λ2 • Tb = c2Bν/2kν2 • Jupiter’s emission • T = 130 K  10-35 W m-2 Hz-1 • Real emission is 10-19 W m-2 Hz-1  1018K!!!

  10. Jupiter’s Magnetic Field • Planck Function & Tb • B = 2kT/λ2 • Tb = c2Bν/2kν2 • Jupiter’s emission • T = 130 K  10-35 W m-2 Hz-1 • Real emission is 10-19 W m-2 Hz-1  1018K!!! • Non-thermal emission • Relativistic particles + B-field  synchrotron emission at radio frequencies  accounts for most of the radio emissoin

  11. Jupiter’s Magnetic Field • Shielding from solar wind  magnetic pressure B2/8π = nemv2/ 2RJ2 V = 400 km/s, n = 10 cm-3 V = velocity of solar wind, n = density of solar wind RJ = distance to Jupiter from Sun Pressures balance at 33 Jupiter radii

  12. Jupiter’s Magnetic Field

  13. Extrasolar Planets • Detection Methods

  14. Extrasolar Planets • Detection Methods • Radial velocity variation • Astrometry • Direct imaging • transients

  15. Imaging • Detection of “point source” image  reflected stellar light • Lp/L* = p(λ,α)(Rp/a)2 • α  angle between star and observer as seen from planet • p  geometric albedo • Ratio ~ 10-9 for Jupiter • Difficulties • Planets are overwhelmed by starlight • Separations are tiny  need space interferometry, adaptive optics

  16. Dynamical Perturbation • Motion of planet causes reflex circular motion in star about the center of mass of star/planet system • Observables:

  17. Dynamical Perturbation • Motion of planet causes reflex circular motion in star about the center of mass of star/planet system • Observables: • Radial velocity variations • Variations in position (astrometry) • Variation in the time of arrival of some reference signal (generally used for pulsars)

  18. Radial Velocity Variations • Just use Newton and Kepler….we’ll do this on the board…

  19. Radial Velocity Variations • Just use Newton and Kepler….we’ll do this on the board… • For Jupiter-Sun system  K = 12.5 m s-1 with a period of 11.9 years • For Earth-Sun system  K = 0.1 m s-1 • Only measure Mpsin i, not Mp • All extrasolar planets were initially detected using radial velocity variations • Resolution of 15 m s-1 are possible  but keep in mind the orbit times! • Might get down to 1 m s-1

  20. Astrometric Position • Star moves a bit as it orbits about the center of mass • Angular semi-major axis: • α = (Mp/M*) (a/d) • Units: a (AU), d (pc) • Jupiter-Sun system viewed from 10 pc away  500μas • Earth-Sun  0.3μas Need space interferometry  impossible from the ground

  21. Timing • 1st “planet” detected was around a pulsar  hard to believe! • Planet causes a tiny wobble which would affect timing of pular • Τp = 1.2 (Mpulsar/Mplanet)(P/1 year)2/3 ms • Discovery of few Earth mass sized objects around pulsar PSR 1257+12 • Where did they come from? • Survived the SNe? • Captured • Formed after the formation of the neutron star

  22. Transits/Reflections • How does planetary motion affect the apparent brightness of the star? • In suitable geometry, planet blocks out part of the star  2% for a Sun-Jupiter system • ΔL/L ~ (Rp/R*)2 • Tiny fractions for terrestrial planets  10-5 • Timing – transits are short! • Τ = (P/π)(R*cosδ + Rp)/a = 13(M*)-1/2(a)1/2(R*) h • In units of solar masses, solar radii, and AU • 25 hours for jupiter • 13 hours for Earth Maybe a large survey of large numbers of possible stars?

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